invest(igations)

Alphanomics: The Study of Security Mispricing

I just finished reading Alphanomics by Charles M. C. Lee and Eric So, published by a small academic press in 2015. The subtitle is The Informational Underpinnings of Market Efficiency, but that doesn’t really give a sense of the book, which essentially summarizes the last five decades of academic research into market pricing mechanisms. I’d like to give readers a summary of what the book accomplishes.

I: Is the Market Efficient?

There are a lot of arguments against the efficient market hypothesis (the belief that the price of a stock reflects all available information and therefore approximates the intrinsic value of a company), and Lee and So seem to marshal practically every one of them. But my favorite is their surfing analogy.

Market efficiency, or so argue its proponents, is “an inevitable outcome of continuous arbitrage,” where arbitrage is defined as “trading aimed at profiting from imperfections in the current price.” Because so much arbitrage is going on, prices rapidly adjust to reflect the information available.

Lee and So point out that this belief “is akin to believing that the ocean is flat, simply because we have observed the forces of gravity at work on a glass of water. No one questions the effect of gravity, or the fact that water is always seeking its own level. But it is a stretch to infer from this observation that oceans should look like millponds on a still summer night. . . . If we are in the business of training surfers, does it make sense to begin by assuming that waves, in theory, do not exist? A more measured, and more descriptive, statement is that the ocean is constantly trying to become flat.”

Because price discovery is an ongoing process, there is always going to be a lot of adjustment as the market searches for some sort of equilibrium, and this adjustment involves lots of mispricing and correction of that mispricing even as new information and signals come in. “In fact,” Lee and So write, “it strikes us as self-evident that arbitrage cannot exist without some amount of mispricing. Therefore, either both mispricing and arbitrage exist in equilibrium, or neither will.” (What Lee and So mean by “mispricing” is essentially the divergence between the market price and the net present value of a security.)

Lee and So then take on the idea that abnormal returns (pricing anomalies) are a compensation for risk factors. This doesn’t fit with empirical observations. There is a great deal of evidence that “healthier and safer firms, as measured by various measures of risk or fundamentals, often earn higher subsequent returns. Firms with lower beta, lower volatility, lower distress risk, lower leverage, and superior measures of profitability and growth, all earn higher returns.” In other words, these companies all appear to be less risky than comparable companies.

Let’s take the opposite assumption (please note that Lee and So don’t go here) for a moment. Let’s hypothesize that the market is fundamentally inefficient and that while arbitrage makes it slightly more efficient, it doesn’t even begin to make it fully efficient. Let’s hypothesize that mispricing is ever-present in part because information is always imperfect. Let’s hypothesize that arbitrage—a industry that costs, in management fees, $600 billion per year, as Lee and So estimate—succeeds only occasionally and is mostly making stabs in the dark. Under this model, investing in less risky assets is more likely to succeed than investing in highly risky assets, and there’s no need to worry about “compensation for risk factors.”

II: Who Are “Noise Traders”?

In 1984, Robert J. Shiller came up with the idea that you can classify investors into two types, smart-money investors and ordinary investors. Fischer Black quickly characterized these ordinary investors as “noise traders.” These are basically people who do not trade on the basis of information about fundamentals; they ignore arbitrage methods and instead trade on the basis of other beliefs, fads, or impulses. If noise traders are more predominant than smart-money investors, you end up with a model that can explain asset pricing very well. It can explain why the price of most stocks is far more volatile than the stock’s intrinsic value could possibly be, why closed-end funds veer so far from their net asset values, why the same stock can trade in two different markets with wide differences in price, and why investor inflows and outflows are inversely correlated with subsequent returns. (The efficient market hypothesis can explain none of these “anomalies.”) With the burgeoning field of behavioral economics, we can understand better the various psychological forces that influence stock pricing, and we can recognize that successful arbitrage can be based not just on the disparity between a stock’s price and its intrinsic value, but on the patterns of (mis)behavior that shape that disparity. However, as Lee and So conclude, “In a noisy market, we are all noise traders.”

III: Why Does Value Investing Still Work?

Lee and So ask the big question: why hasn’t the value effect been arbitraged away? Why has it persisted for so long?

The answer isn’t that value stocks are riskier. If you incorporate quality (or growth potential, which is really the same thing) into your definition of value, as Benjamin Graham did and Lee and So do, value stocks are actually less risky than expensive/growth stocks.

The answer is behavioral. Ordinary investors prefer glamor stocks, stocks with exciting stories; value stocks are pretty boring. Ordinary investors look at recent price performance of a stock and think it will persist; value stocks are usually low-priced. Ordinary investors overweight far-future earnings and underweight present earnings due to overconfidence when information is highly uncertain; wise value investors concentrate on known/present revenue, earnings, and cash flow when judging a stock’s worth.

IV: The Practical Limits of Arbitrage

“Information complexity matters,” write Lee and So. Financial markets have a hard time quickly processing information about stocks, and when subtle signals arise (for example, between the lines of quarterly earnings reports or among “boring” or low-volume stocks that are not subject to much attention), they tend to be ignored for a while, resulting in persistent mispricing.

Another limitation is due to whether the information is right or not. Let’s say you identify a large discrepancy between the market price of an asset and its estimated value. As Lee and So write, “there are two possibilities. The first is that the market price is wrong and the discrepancy represents a trading opportunity. The second is that the theoretical value is wrong and the discrepancy is due to a mistake in the valuation method. How can an active investor tell the difference?” Arbitrage is limited by this kind of doubt.

In addition, capital constraints come in many forms. One is high transaction costs, which tend to minimize trading, which in turn tends to diminish arbitrage. Another is that near market tops, when money can be put to little good use, come the heaviest cash inflows. But around market bottoms, outflows tend to congregate and funding constraints are severe, and that is precisely when money can be put to best use.

With all these limits to effective arbitrage, it’s no wonder that securities are so often mispriced. As Lee and So sum it up, “smart money seeking to conduct rational informational arbitrage faces many costs and challenges. These challenges can dramatically limit the deployment of arbitrage capital in financial markets, leading to significant price dislocations. Such effects are pervasive across asset groups.”

V: How Can We Tell If Excess Returns Are a Result of Increased Risk-Taking or Market Mispricing?

If you’re a smart investor, you’d want to capitalize on market mispricing and avoid risk-taking as much as possible. But academics and professional investors have come to opposite conclusions about the source of excess returns. Warren Buffett and his myriad followers talk about “margins of safety” and espouse value investing as far safer than any other kind. At the same time, a number of Nobel Prize–winning economists say that the excess returns from value investing, like those from momentum investing and other factor-based investing (including even low-volatility investing!), is based on compensation for additional risk-taking. One couldn’t come up with more opposed conclusions.

The orthodox position among academics has been that an asset’s expected returns are determined by its sensitivity to a given “risk factor,” as measured by a linear asset-pricing model. But as Lee and So point out, referring to a large number of more recent academic studies, these models fail to distinguish between mispricing and risk; many of the “risk factors” do not conform to any common-sense ideas of what is actually risky; the models can’t explain post-earnings announcement drift or the fact that firms with strong accounting fundamentals outperform firms with weak ones; looking at the returns of the various “risk factors” on their own predicts future returns better than their factor-loading (sensitivity) on the factor portfolio; and the regression-based model is based on the assumption that the returns of a given firm are uncorrelated over time (independently and identically distributed), a violation of which leads to an over-rejection of the null hypothesis. In other words, there’s no good reason to use the complicated linear multi-factor asset-pricing model that so many use these days.

What Lee and So do not challenge is the idea that there is a linear relationship between risk and reward. As I have shown, the relationship is by no means linear; past a certain point, the riskier the asset, the lower the reward, and the relationship is therefore best characterized by a curve whose shape looks something like this:

VI: Conclusion

It’s hard not to come away from this book with mixed feelings about academic research on investing. On the one hand, highly questionable conclusions have become orthodoxy, and the basic models taught to students have very little, if any, empirical foundations. On the other hand, academics are challenging these models, and their research has been excellent and very useful.

The book, I think, should be an essential read for anyone who wants to understand how current asset-pricing models work (or don’t). But I think the authors don’t go quite far enough.

My own conclusion after reading Alphanomics is that markets are fundamentally inefficient, that arbitrage is mostly ineffective, and that mispricing is seldom risk-related. There are plenty of very good behavioral reasons for investors to be more attracted to risky investments than to safe ones, thus presenting plenty of opportunities for investors who take advantage of the consequent mispricing of safer securities.

And, practically speaking, how do you do that?

The first step is to find mispriced safe securities. Take all the factors that academics have shown work—in Lee and So’s words, quoted above, “lower beta, lower volatility, lower distress risk, lower leverage, and superior measures of profitability and growth”—and combine them with value factors, which, as Buffett and other value investors have shown, create a margin of safety. Use a powerful screen or, better yet, a ranking system such as those available from www.portfolio123.com (design your own, or rely on the seven pre-built “core” ranking systems).

Here are eight stocks that I think are “safe” by almost any measure. In alphabetical order, they are: Barrett Business Services (BBSI), Mix Telematics (MIXT), National General Holdings (NGHC), Points International (PCOM), Perion Network (PERI), Pilgrim’s Pride (PPC), TTEC Holdings (TTEC), and WNS (WNS). But that’s my list. Make your own!

The next step is to wisely invest in safe securities and sell them when and only when they begin to seem unsafe. (Or, conversely, short those securities that are the riskiest.)

The great investors have long recognized that you can get superior returns at the same time as minimizing your risk. An inefficient market is ripe for successful arbitrage, and it’s up to smart investors to take advantage of that.

CAGR since 1/1/16: 33%.

My top ten holdings right now: MIXT, RMNI, PCTI, SPNS, PALDFF, MGIC, QMCO, PRPL, CO, TTEC.

How to Be a Great Investor, Part Four: Compare Effectively

This article is the third in a ten-part series loosely based on Michael J. Mauboussin’s white paper “Thirty Years: Reflections on the Ten Attributes of Great Investors.” See Part 1: Be Numerate, Part 2: Understand Value, and Part 3: Properly Assess Strategy for previous installments. And please keep in mind that although I quote Mauboussin a great deal, I am departing from his ideas on occasion.

Part I: Fundamentals Versus Expectations

Mauboussin begins:

Investors compare all day: stocks versus bonds, active versus passive, value versus growth, stock A versus stock B, and now versus later. Humans are quick to compare but not very good at it. Perhaps the most important comparison an investor must make, and one that distinguishes average from great investors, is between fundamentals and expectations. Fundamentals capture a sense of a company’s future financial performance. . . . Expectations reflect the financial performance implied by the stock price. Making money in markets requires having a point of view that is different than what the current price suggests. Michael Steinhardt called this a “variant perception.” Most investors fail to distinguish between fundamentals and expectations. . . . But great investors always distinguish between the two.

Let’s pretend that you had to choose between investing in Intel (INTC) and Advanced Micro Devices (AMD).

Intel’s ROE is 27% and its margins are massive. It has low debt, plenty of cash, pays a nice and growing dividend, and has solid growth in both sales and EPS.

AMD, on the other hand, has an ROE of 14% and its margins are pretty poor. Its sales and EPS growth have been in a steep decline lately. Its debt-to-EBITDA ratio is close to 3, which is pretty high; it doesn’t look like it’ll be paying any dividends in the foreseeable future.

Let's look a little deeper. Both Intel and AMD are spending plenty of money on R&D, which is good. AMD has huge projected EPS growth for the next quarter while Intel is projected to have negative growth. AMD has significantly better asset turnover, another point in its favor; on the other hand, it has the highest share turnover of any company in the S&P 500, which is a point against it. AMD’s cash conversion cycle is growing too fast for my liking; on the other hand, their net operating assets are only 40% of their total assets, which is a good thing. Lastly, AMD’s cash-flow accruals are appallingly high, while Intel’s are quite low.

What are the market’s expectations for these two firms? As of market close on 9/4, Intel is selling at an 18% discount to its 52-week high, while AMD is only 13% from its high. AMD’s price has risen 10% in the last year; Intel’s has risen 2%. Intel’s enterprise value is $239 billion, which matches my estimate of its intrinsic value based on its free cash flow and EBITDA, $246 billion. AMD’s enterprise value is $35 billion, which is more than five times higher than my estimate of its intrinsic value, $5.8 billion. Institutions are, overall, selling shares in Intel and buying shares in AMD. Clearly the market has significantly higher expectations for AMD than for Intel.

The reason is clear. With its 80% to 90% market share, Intel seems like a dinosaur, with nowhere to go but down, while AMD is on the cutting edge, producing brilliant CPUs that outperform Intel’s. They’ve just inked several valuable partnership deals, while Intel has been labeled a “chronic underperformer.”

The average investor will look at these signs and put their money into AMD. The great investor will see that there’s a huge divergence between fundamentals and expectations, and will keep their money out of AMD and in solid, safe, boring, inexpensive firms like Intel.

Why? AMD certainly seems to have better prospects than Intel. Cutting-edge technology stocks can really pay off. If this were a race, AMD seems to have much better odds.

Mauboussin continues:

One vivid analogy is pari-mutuel betting. Horse racing is a good example. The amount bet on a horse gets reflected in the horse’s odds, or probability, of winning the race. The goal is not to figure out which horse will win but rather which horse has odds that are mispriced relative to how it will likely run the race.

(I’ve written about this gambling analogy here.) AMD may have better odds, but they’re mispriced. Even if AMD performs spectacularly well over the next few years, its risk of failing to meet expectations is far higher than that of Intel.

Basically, the expectations, based on their market price, for these two companies are that one will remain roughly the size it currently is and that the other will grow to be five or six times its current size. Now which, I ask you, is a safer bet?

Part II: Instinctive Versus Reasonable Comparisons

Mauboussin writes,

Humans tend to think by analogy, which can create some cognitive trouble. One issue is that a single analogy, or even a handful of analogies, may fail to reflect a full reference class of relevant cases. For example, rather than asking whether this turnaround is similar to a prior turnaround, it is useful to ask for the base rate of success for all turnarounds. Psychologists have shown that properly integrating the outcomes from an appropriate reference class improves the quality of forecasts.

The price of Apple, after adjusting for dividends and splits, has gone up by over 8,000% in the last twenty years. And how many times have you heard someone say of a company, “This could be the next Apple!” That is a simple analogy, easy to grasp.

What people don’t say is that twenty years ago there were stocks quite similar to Apple. The proper response when someone says “This could be the next Apple!” is “Yes! And this could be the next Gateway!” or “Yes! And this could be the next Lexmark!” or “Yes! And this could be the next ATI Technologies!” Stretch it a little and this could also be the next Comverse, or Altera, or Unisys, or BMC Software, or Teradyne! All of these companies showed some strong similarities to Apple in 1999.

As Mauboussin writes, “What you are looking for is what you see.” Choosing companies to compare a potential investment with is a daunting task. If you do so on a purely intuitive level, you’re bound to choose companies you’re familiar with rather than companies that sank without a trace. If you try to use a more data-driven approach, using screens to narrow down your options, you’ll come up with a better class of comparisons, but only barely. Every company is truly unique.

Moreover, this method can lead to another trap. Mauboussin writes,

A final challenge is considering causality from the point of view of attributes versus circumstances. Attributes are features that allow for categorization. For instance, animals with wings and feathers can fly. Circumstances capture causal mechanisms. Since the physics of lift causes flight, animals or objects that can create lift will fly, including most birds and airplanes, and those that can’t create lift won’t fly. To learn from history, you need to understand causality. We commonly limit our comparisons to attributes and hence miss essential insights.

What caused Apple’s price to rise over 8,000%? Clearly it was not the fact that its market cap in 1999 was $10 billion or that its P/E was 18 or that it was in the technology sector. Was it the fact that it had a visionary at its helm? In that case, let's take a quick look at people who were called “visionary” in 1999 and see where they and their companies ended up.

• Marc Collins-Rector was the visionary founder of Digital Entertainment Network, one of the first Internet media content delivery companies, a precursor of Netflix. The company was valued at $58.5 billion in 1999, and was slated for a $75 billion IPO. Collins-Rector and his cofounders were accused of sexual assault and the company went bankrupt in 2000.
• Noboyuki Idei was the visionary CEO of Sony; if you had bought shares in Sony in 1999, they would now be worth 2% more than what you paid for them.
• Mark Weiser was the visionary chief technology officer of Xerox, and the father of “ubiquitous computing.” But then he died at the age of 46. If you had bought shares in Xerox in 1999, you would have lost 68% of your money by now.
• Robert B. Shapiro was the visionary CEO of Monsanto. In 2000, Monsanto was merged with Pharmacia and Upjohn, and Shapiro stepped down in 2001. If you had invested in Monsanto once it was spun off in 2002, you would have made a boatload of money, but by that time Shapiro was no longer working for them.

Clearly, following visionary CEOs won’t make you rich.

What kinds of comparisons will, then? Data-driven ones, perhaps.

The main thing is not to get lost in analogies. Rather than looking for what made Apple’s price rise 8,000%, one might better ask what factors will at least somewhat consistently induce a future rise in a stock’s price. And there is data that will answer that question.

To stick with comparisons, let’s say you’re faced with the choice of investing in two companies, one with low accruals and the other with high accruals, but they’re otherwise pretty similar. If you look at the data, companies in the Russell 3000 with the lowest accruals have gained, on average, 7.04% in any given six-month period over the last twenty years (I ascertained this fact using a screen on Portfolio123 that chose companies that ranked among the lowest 25% on two very different and largely uncorrelated methods of measuring accruals); companies with the highest accruals have gained, on average, 3.09% (which is lower than the average six-month gain of the S&P 500). Now are low accruals simply an attribute of a stock or a cause of the price gain? There are some very good arguments to be made for the latter position.

And that’s how factor-based investing works. We look for factors that seem to result in price increases. We then compare thousands of companies and choose those that rank the best on each factor or on all of them combined. We should not only compare each company to all others, but perform industry-specific comparisons too. We can focus on causal factors and let attributional factors take a back seat.

This goes back to Mauboussin’s initial point in this part: “rather than asking whether this turnaround is similar to a prior turnaround, it is useful to ask for the base rate of success for all turnarounds.” I just did that for low accruals, and if I had a data-driven definition of a turnaround, I could get such a base rate.

Using data, backtesting it, discovering properties and relationships, looking for causal factors—that is the best way to compare effectively.

My CAGR since 1/1/16: 33%.

My top ten holdings right now: RMNI, MIXT, PERI, PALDF, SPNS, PCTI, VISI, TTEC, QMCO, GTS.

How to Be a Great Investor, Part Three: Properly Assess Strategy

This article is the third in a ten-part series loosely based on Michael J. Mauboussin’s white paper “Thirty Years: Reflections on the Ten Attributes of Great Investors.” See How To Be A Great Investor, Part 1: Be Numerate and How To Be A Great Investor, Part 2: Understand Value. Please note: in this article, I’m departing from Mauboussin’s ideas at a number of junctures.

Part I: Assessing a Business Strategy

Every business has a strategy, a plan for beating its competitors. It’s a good idea for an investor to assess that strategy before investing in the company. But doing so is complicated.

One obvious way to do so is to look at its numbers. Mauboussin primarily looks at the difference between a company’s CFROI, or cash flow return on investment (free cash flow divided by net operating assets), and its cost of capital, and compares that to other companies in its industry.

Arriving at CFROI and cost of capital is not an easy job. I covered some of the pitfalls in cash flow and cost of capital measures in How To Be A Great Investor, Part 2: Understand Value, and also discussed how to get around them. (Also see my article on net operating assets: My Favorite Balance Sheet Ratio.) In addition, it’s probably best to use the cost of capital for the industry or industry group rather than for the firm in question.

So, for example, let’s look at two chemical companies. Celanese (CE) has about $1.5 billion in annual free cash flow and $6.7 billion in net operating assets, giving it a CFROI of 22%. Albemarle (ALB) has under $200 million in annual free cash flow and $5.6 billion in net operating assets, so its CFROI is 3%. Assuming the cost of capital for both companies is around 8.5%, Albemarle is what Mauboussin calls a “value destroyer” while Celanese is a “value creator.”

If you look only at this measure, the best “value creators” in the S&P 500 (excluding the financial and real estate sectors and excluding firms that are less than five years old) are Verisign (VRSN), Qualcomm (QCOM), Fortinet (FTNT), Starbucks (SBUX), and Boeing (BA), while the worst “value destroyers” are Netflix (NFLX), GM (GM), Carmax (KMX), Alliant Energy (LNT), and Advanced Micro Devices (AMD).

And value creators do tend to outperform value destroyers: over the past ten years, the top decile (value creators) in the S&P 500 have beat the bottom decile (value destroyers) by 4.2% in annualized returns (if rebalancing monthly with no transaction costs), and in the past twenty years that spread has been 7.0%. (I use Portfolio123 to get these numbers.) That’s quite a remarkable spread for a quality factor—the stock’s market price and its growth rate don’t come into the calculation.

But obviously, a business can change its strategy, and one number can’t tell you that much about a strategy’s future viability. Assessing strategy is a complicated and rich subject, and I can’t possibly give you better pointers than Mauboussin can. His papers on the subject are well worth reading, and can be found here and here. At the end of each of those papers is a checklist you can use to assess each company you investigate. There are close to a hundred useful questions in those checklists, and you can learn a lot about a company while trying to answer them.

Part II: Assessing an Investment Strategy

Mauboussin does not cover assessing your own investment strategy in his “Ten Attributes of Great Investors,” but I think it’s just as important as assessing the strategy of the companies you invest in—if not more so.

Before you can properly assess your strategy, you need to properly articulate it. You can begin doing so by asking yourself a number of questions. There are no right or wrong answers here: this is just a way to get to know what kind of strategy is right for you.

1. Are you interested in beating the market over the short term, investing wisely for long-term portfolio growth, or both?
2. Are you interested in maximizing your returns, minimizing your risk, or both?
3. Are you interested in finding a single strategy that suits you or developing a number of different strategies for portions of your portfolio?
4. Are you interested in making money primarily from stock price appreciation, dividend income, or both?
5. Are you interested in stocks, ETFs, options, or all three?
6. Do you consider yourself a gambler, a trader, an investor, a speculator, or some combination of those?
7. Would you rather use a fully automated strategy or get stock ideas which you’d then accept or reject on a discretionary basis?
8. Do you believe that backtesting will guide you to better strategy development or do you believe that backtesting offers illusory results and that it’s best to limit its use?
9. Do you consider yourself financially skilled enough to come up with new, untried methods of beating the market, or do you think you’d do better to follow established paths?
10. What is most important to you when considering a stock purchase: the company’s quality, price, growth potential, or category (size, industry, etc.)?
11. Are you most comfortable with approaches to investing based on the ideas of professional investors such as Warren Buffett, Peter Lynch, James O’Shaughnessy, and Joel Stern, or do you prefer to take a scholastic approach, using sophisticated statistical analysis and keeping up with the latest academic research?
12. Do you place your faith primarily in fundamental analysis, technical analysis, or sentiment indicators?

(I myself would choose the first option in all these questions.)

Once you’ve articulated your strategy, try to think of what chance it has to succeed. Everybody overestimates their chances. It’s very rare to encounter someone who estimates her chances of success at a particular endeavor as below average.

To avoid this pitfall, the first thing to consider is your base rate. In other words, try to assess not your own skill at achieving your strategy goal but the average skill. Pretend you come across another investor with exactly the same strategy, and you have no idea whether she’s good or not. You know nothing about her except her articulated plan. What chance would you give her of success? That’s your base rate.

So, for example, my own strategy is to use an automated system based on fundamentals (primarily quality, secondarily value and growth) to choose stocks, trading frequently, concentrating primarily on microcaps, doing a lot of backtesting, placing big bets, and trying to beat the market every year. If I were to meet someone else implementing this strategy, knowing nothing about her particular skill set, I would give her a 40% chance of beating the market. That’s my base rate, and I need to acknowledge that my own chances aren’t a whole lot better, even if my performance so far has been quite good.

Speaking of performance, the standard way to assess an investor’s past strategy is to look at her alpha. Some would prefer to look at her Sharpe ratio, or use another risk-adjusted return measure, but in my opinion, of all the conventional measures of strategy performance, alpha is the best. Here’s why:

1. It shows the relationship of an investor’s performance to the performance of the market as a whole; CAGR and certain other performance measures are market neutral.
2. The Sharpe ratio, Sortino ratio, and information ratio divide average performance/outperformance by the standard deviation of the returns. But standard deviation is a flawed measure of volatility that has little persistence and—in the final analysis—makes little difference in terms of out-of-sample performance.
3. High alpha correlates with low beta, and a low-beta strategy is less subject to market-induced volatility than a high-beta strategy.

Estimating the future alpha of a strategy is a very tricky business. Even measuring past alpha is tricky. The first thing to do is to choose the right benchmark. If you have access to good research tools, you can construct your own benchmark made up of the type of stocks that you’re likely to invest in (look at size, industry, minimum price, and, if you have other requirements, such as limiting yourself to stocks listed on the major exchanges, include those). But there are also a wide variety of ETFs available that may be suitable benchmarks.

The conventional way of measuring alpha is extraordinarily susceptible to outliers. There are lots of ways around this—you could Winsorize your returns, for example. I calculate beta by using the Theil-Sen estimation (this is the median slope of all pairs of points) and then calculate the median difference between my returns and the product of that beta and the benchmark returns. (I subtract the risk-free rate from both my returns and those of the benchmark before calculating any of this.) By this measure, and using the microcap ETF IWC as my benchmark, my strategy has gotten an annualized alpha of 26% since its inception in November 2015, which is 3% lower than if I’d used the conventional calculation.

Once you have past alpha—or even if you don’t—estimating future alpha has certain pitfalls you should be aware of. First, if your strategy is successful and you don’t make regular withdrawals, your assets will grow, and the more assets you have, the harder it will be to maintain a good alpha, because either the market impact of your trades will be greater or you’ll be investing in more stocks and thus underweighting your best ideas compared to what you used to do. Second, if you use backtests to optimize your strategy, reduce your backtested returns by at least a third in order to compensate for the fact that out-of-sample returns are almost never as good as optimized backtested returns.

If your strategy has certain inherent advantages over other folks’ strategies and you’re getting high alpha, you’re likely doing a good job. If, however, your strategy is just one out of many, with few or no inherent advantages over that of others, then a high performance may indicate a low performance in the future simply due to the axiom of regression to the mean (uncorrelated performance has, by definition, a high probability of relative reversal; if that weren't the case, the performance would be correlated).

Even if your base rate is high, your skill set is strong, and your performance is exemplary, ask yourself some additional questions about your strategy.

1. Are you willing to stick with your strategy, making only minor tweaks, even if you underperform for an extended period? If so, give yourself a point.
2. Are you liable to change your strategy radically during a market downturn? If not, give yourself a point.
3. Are you juggling several different equal but uncorrelated strategies, and are you choosing those that have performed the best in the recent past? If not, give yourself a point; if so, regression to the mean will doom you.
4. Pretend your strategy has utterly failed and you have lost not only a good portion of your savings but all faith in your strategy. What will you do then? If you have a good answer, give yourself a point; if you have no idea, try to come up with one.
5. How much research is involved in your strategy? If a lot, give yourself a point. Doing your homework should be an essential part of your investment strategy.

This last point is perhaps the most important part of assessing your strategy. A strategy that involves little to no research is doomed to eventually fail. And that brings us back to the first part of this article. Assessment is at the very core of successful investment: assessing the investments themselves, and assessing your ability to take advantage of them. Without spending the time and effort to assess, your investment success will be no better than that of a dart-throwing monkey.

CAGR since 1/1/16: 34%.

My top ten holdings right now: RMNI, MIXT, PERI, PALDF, SPNS, VISI, PCTI, TTEC, GTS, GSL.

Thirteen Rules for Winning the Investing Game

For me, the key to successful investing is to approach it like you would a game—a deadly serious game, but still a game. In order to win, you have to:

1. Think in terms of probabilities, not in terms of gut instincts. Every choice you make should maximize the probability of an excellent outcome.
2. Keep in reserve what you need to get you through your month-to-month expenses and treat your funds for investing as “play money.” If you think of it as real money, you may be unable to justify putting a large percentage of your savings into a single security.
3. View setbacks and temporary defeats as part of the game, not part of your real life. This is tough for investors. This year I lost about 30% of my yearly salary in one day; a few months later I gained the same amount in one day. Expect long periods of underperformance and occasional major losses, and don’t panic.
4. Keep a poker face and don’t tell others why you’re doing what you’re doing or how you’re getting the results you’re getting. (This is a rule I break all the time. I should know better.) And when you win, don’t brag about it. (This is a rule I break all the time too. I should know better.)
5. Make big bets confidently. I often put more than ten percent of my portfolio in a single stock. Don’t let diversification become di-worse-ification.
6. Nobody has ever won a game by employing three different strategies at once. Figure out your best strategy and stick with it.
7. Never switch strategies, especially not in the middle of a game. Tweak your strategy instead, improving it constantly.
8. Constantly question what you’re doing and why you’re doing it, but don’t take action on the answers you come up with until you’re absolutely sure. And even then, sleep on it first.
9. Research, research, research. Constantly investigate securities, accounting rules, exceptions to your beliefs, process, and all sorts of stuff you’ve never thought of.
10. Play other, related games. For example, design a strategy for a group of securities you’ll never invest in. Enter stock-picking contests. Make small side bets. You’ll learn a lot from these challenges.
11. Enjoy every moment. If it’s no longer fun, just buy an index fund.
12. Be determined to win, but be even more determined to play, in every sense of that word.
13. And remember, money can’t buy you happiness or love or friendship or family. Those things come first.

Now if your aim isn’t to win but simply to do reasonably well while minimizing your risk, don’t follow these rules—I’m sure you can come up with ones that better apply to your situation. But if your aim is to win—whether that means consistently beating the market, wowing your friends, or gaining a seat in the pantheon of great investors—you need to approach the game as a dedicated and fearless player.

CAGR since 1/1/16: 35%.

My top ten holdings right now: MIXT, SPNS, RMNI, VISI, PERI, PALDF, HALL, TTEC, GTS, CPIX.

How to Be a Great Investor, Part Two: Understand Value

This article is the second in a ten-part series loosely based on Michael J. Mauboussin’s white paper “Thirty Years: Reflections on the Ten Attributes of Great Investors.” For the first part, see How To Be A Great Investor, Part 1: Be Numerate. Please note: in this article, I’m departing from Mauboussin’s ideas at a number of junctures.

The Intrinsic Value of an Object

Obviously, an orange has some intrinsic value. It is nutritious and tasty and can be used in a variety of ways. It has value on its own and has value as an ingredient. But what is that value? Fifty cents? Three dollars?

When we go to a grocery store and buy oranges, we can imagine saying to ourselves, wow, oranges are cheap today, or oranges are expensive here! We have some notion of how much an orange should cost. How do we get that notion? From experience and from comparison. We’ve bought oranges before; or, if we haven’t, we’ve bought apples and plums and lemons and bananas.

What I’m getting at is this: intrinsic value can only very rarely be stated in terms of dollars and cents. It’s instead a range, and it’s arrived at through comparison and experience.

The Intrinsic Value of an Investment

When we determine a fair price to pay for a bond, we consider the following variables: the coupon payments, the market rate, the number of periods per year, the number of years to maturity, and the face value of the bond.

Generally speaking, these same factors—income, payment schedule, market rate, duration, and value upon maturity or sale—are the factors in play for every investable asset, from real estate to collectibles to stocks (although for many investments, such as collectibles, there may be no income or payment schedule, and for others, such as life annuities, there’s no value upon maturity). To understand value, the questions are simple (I’m quoting Mauboussin here):

1. What will the cash flows be?
2. When will I receive them?
3. How risky are they?

But with stocks, we have no idea what the coupon payments, the market rate, the face value, or the number of years to maturity are. It’s much harder to determine a stock’s fair value than it is to determine a bond’s.

Applying this model to stocks is the basis for the dividend discount model. The fair value of a stock is the sum of its dividends over the length of holding it and its final value, discounted by a certain rate. The problem with this idea is that a lot of stocks that are worth investing in do not pay dividends, so this covers only a fraction of possible stocks to buy; in addition, this model favors stocks with unsustainably high dividend yields.

Many investors therefore treat stocks as if they are collectibles. They’ll think, for example, that a certain company is probably going to grow to ten times its present worth due to some quirky trait or an expectation of consumer demand. Others think of stock investments as safe places to park their money for the long run, disregarding value and simply buying stocks in the largest companies, trusting that because they’ve been so successful in the past, they’ll continue to be successful in the future. Yet others believe in the efficient market hypothesis (in which intrinsic and market value are equal) and/or the capital asset pricing model and/or the Fama-French five-factor model and/or some other version of econometrics.

These may be fine ideas and strategies, but they’re really not about value.

The Intrinsic Value of a Company

If you’re acquiring an entire company, there are basically eight different ways to determine the price you’re willing to pay. In alphabetical order:

1. You could do a comparison analysis (or precedent transaction analysis) by looking at recent acquisitions of similar companies and comparing those to this one.
2. You could use the discounted cash flow method, which is derived from investment valuation as outlined above, and about which I’ll write more below.
3. If it’s a public company, you could simply value it at its current enterprise value (though you’d want to adjust that upwards a little, considering the effect of a takeover offer on the stock’s price). This is basically the sum of the market value of the company and its debt, minus any cash it has on hand. In this case, the current price of the stock is an important factor in determining a value for the company.
4. You could do a leveraged buyout (LBO) analysis. The factors here are the required return for the financial sponsor and the appropriate debt-to-equity ratio.
5. You could ascertain its liquidation value. (This is not the same as the company’s book value, as it is the sum of the market value of its assets.)
6. You could do multiples analysis, in which you look at the P/E, P/S, and so on of comparable companies to determine a reasonable valuation.
7. You could try to calculate its replication value by estimating the amount of cash you’d need to build the company from the ground up.
8. And then there’s the strategy-based valuation: what difference will acquiring this company make to your business strategy? How much do you want to pay for it in order to transform your business? If it’s a competitor, you might be willing to pay a lot for it in order to decrease competition.

Ideally, most acquirers will combine more than one of these methods. But all acquirers of public companies are also going to take into consideration the market value of the company’s equity, or else they’ll never get the deal approved by the shareholders.

Can a Company’s Intrinsic Value Be Negative?

Let’s say you’re shopping for a used car. You find one that you fall in love with and buy it. But it needs work. Over the next two months, you spend $4,000 fixing it up. But then, over the following two months, the carburetor, the engine, and the clutch all suffer fatal failures. You decide to sell the car, but the best price you can get for it is $1,000. How much was the car worth originally? Considering you lost $3,000 on top of the purchase price, you shouldn’t have bought the car at all and, in fact, you should have been paid $3,000 for owning it.

The same is true for a business. Many businesses cannot run only on internally generated capital. They require investment. Whenever a new owner buys an existing business, there’s a chance she will lose more than she paid for it if the business fails. The net present value of the business, in that case, was a negative one at the time of purchase.

The Intrinsic Value of a Stock

Once you have figured out the intrinsic value of a company, you subtract its debt, preferred stock, and non-controlling interest, add its cash, and then divide that by the number of fully diluted shares. It’s really that simple. But figuring out the intrinsic value of the company isn’t.

Discounted Cash Flow Analysis

(The next two sections are quite technical. If you have no interest in DCF analysis, please feel free to skip them. There’s more to read later.)

Let’s look closely at discounted cash flow analysis for a moment, because Mauboussin has written a great deal about it. If the intrinsic value of a company is determined by the sum of its free cash flows and its final value, all discounted by the market rate, then one should be able to find companies whose intrinsic value differs substantially from their market value and, by investing in those that are comparatively cheap, make money.

The basic idea behind DCF analysis is as follows. We start with a basic equation called Gordon’s Growth Model, P = D / (r – g), where P is price, D is dividend, r is the required rate of return, and g is the growth of dividends over time. There’s a very elegant proof of this equation, which you can read about here.

Because most stocks don’t pay dividends, however, investors have substituted free cash flow for D, and because cash flow and growth rates change over time, and because the “required rate of return” is so amorphous, they’ve expanded the model into a multi-year, hugely complicated mess. (But nobody ever said valuation should be easy.)

There are a number of major problems with DCF analysis.

1. Determining cash flows. There is no clear method for determining future cash flows. I must have come across at least a dozen of them. (Mauboussin’s is explained in a book he co-wrote with Alfred Rappaport called Expectations Investing.) Most of them involve inputting a lot of guesses. There isn’t even a standard way to measure present free cash flows. Many analysts use different formulae from those provided by the CFA Institute. A big question is how to calculate maintenance capital expenditures (as distinguished from those that contribute to growth); if one deducts all capital expenditures from operating cash flow, then certain industries, such as utilities, have overall negative cash flows. And then there’s the problem exemplified by Hertz (HTZ), in which a company with a market cap of $1.25 billion has maintenance capital expenditures of $10 to $12 billion a year (the amount it spends on new cars), resulting in massively negative free cash flows.
2. Variability of free cash flow. Free cash flow is probably the most variable of all value measures. I measured this on Portfolio123 using a pretty wide universe of over 4,000 stocks: the median absolute percentage deviation of EPS over the last five years is 58%, while the same of free cash flow is 73%.
3. Applying growth rates to negative numbers. If one takes a negative number and multiplies it by one plus a growth rate, one comes up with an even more negative number. And a large number of companies have negative free cash flows.
4. Determining the cost of capital. There’s no standard way to calculate the cost of capital, which determines the discount rate (the required rate of return), a huge factor in DCF analysis.
5. Determining the terminal value. There seems to be no agreement on which of two very different methods an investor should use: the perpetuity growth model or the EV/EBIDTA multiple model. Most academics insist on the former; most investors use the latter. There are problems with both. The perpetuity growth model is based on the sixth or eleventh year’s free cash flow, which is a wild guess to begin with, and is then divided by the difference between the cost of capital and the terminal growth rate, both of which are more wild guesses. The multiples model has all the problems of conventional valuations like P/E and P/S, and the way it’s often applied means that the terminal value ends up making up about 80% or 90% of the eventual valuation, which negates the whole idea behind DCF analysis.
6. Discrepancies in cost of capital. Most people assign different costs of capital to companies in different industries. So let’s take two companies with exactly the same free cash flow, growth rates, and debt to equity ratios. If the first company is a utility and the second is a technology firm, the first’s cost of capital is about 4.5% and the second’s is about 10%. Let’s assume that the initial growth rate for both companies is 10% and it decreases every year until in year 6 it’s 3%, and that after the tenth year we calculate the final value of the firm based on that final growth rate of 3% and a discount rate equal to the cost of capital. The intrinsic value of the utility will be 4.5 times the intrinsic value of the technology firm. (The discrepancy will be even higher if you stop after five years or if your growth rate for the first five years remains constant.) Does that really make sense? It does if you’re taking into account the risk of investing in each company—clearly the utility is far less risky. But it makes no sense if you’re trying to find bargains. In the latter case, you want to invest in the cheapest companies, and the two companies should have the same intrinsic value. Or does the technology company really need to produce four times the amount of cash flow than the utility to make up for its greater cost of capital?
7. Close-to-zero denominators. In the perpetual growth method of calculating the “terminal value” of the firm, one divides the final projected free cash flow by the difference between the weighted average cost of capital (WACC) and the terminal growth rate of the firm. The terminal growth rate is usually pegged to inflation and GDP growth, while the cost of debt is usually pegged to the interest rate on BBB-rated bonds. Currently, the interest rate on these bonds, after deducting for taxes, is lower than the twenty-year average of GDP growth. Thus the final projected free cash flow of a very heavily indebted company is going to be divided by a fraction of 1%, or multiplied by more than a hundred. This problem extends to other companies with low costs of capital; often the difference is between one and three percent, thus providing a multiplier between thirty-three and a hundred. Just a fraction of a percentage change in the terminal growth rate or the WACC will result in a huge change in terminal value.
8. Market neutrality is unrealistic. Discounted free cash flow analysis usually pretends to be market neutral. In many methods, there’s not a single factor in the process that reflects the value that the market has currently assigned to the company. Mauboussin defends this stance ardently. But if you look at the price that acquirers actually pay for public companies, there’s a very strong correlation with market price. (I must issue a warning here. There are some major financial firms out there who only pretend to assign a “fair price” to securities based on discounted cash flow analysis. Anytime you see a fair price analysis that, over time, hews very closely to the market price, you can be sure it’s not strictly based on DCF analysis, which will usually give you results that veer very far from the market price.)
9. Unrealistic future projections. DCF analysis relies too much on the future and not enough on the past and present. Take, for example, the company that Mauboussin and Rappaport used as their prime example when they wrote their book: Gateway, Inc. After analyzing this company in great detail and projecting future free cash flows, their spreadsheet, dated April 2000, predicted that over the next seven years the company’s cash flow would continue to increase. But Gateway’s cash flow plunged into negative numbers in 2001 and never recovered, and the stock’s price plunged from $52 to $2.20 over those years. In most examples of discounted cash flow analysis, free cash flow follows a smooth curve, based on sales growth expectations that are unsustainable. In real life, that rarely happens. Below is a chart of ten companies whose free cash flow in 2000 was about the same as Gateway’s. I’ve contrasted Gateway’s projected free cash flow, according to Mauboussin and Rappaport’s analysis, with the actual free cash flow (in millions) of these other ten companies. The difference is clear. Free cash flow varies hugely from year to year, and never conforms to a simple exponential curve.

Solutions to DCF problems

For my own DCF analysis, I’ve tried to come up with solutions to each of these problems. How well I’ve succeeded will be up to you to judge.

1. Determining future free cash flows. I start with the following formula. Unlevered free cash flow (or free cash flow to the firm) is operating cash flow minus capital expenditures plus after-tax interest expense. But because one should only subtract maintenance capex, I add back a very rough estimate of growth capex, using Bruce Greenwald’s suggestion, which is the average ratio of gross plant to sales times the annual increase in sales. In many cases (Hertz being a good example), capital expenditures need to be offset by other cash flows from investing activities—Hertz’s capital expenditures consist of vehicle purchases, and its other cash flows partially offset that with vehicle sales. As for future free cash flows, there’s a weak but real correlation between future free cash flow growth and historical asset turnover, so I use a complicated formula based on the latter measure to estimate an initial growth rate.
2. Variability of free cash flow. I use a weighted average of unlevered free cash flow, giving more weight to recent figures than those from the distant past. Using only trailing twelve-month numbers won’t get you much consistency, and using five-year averages ignores recent changes in cash flow generation.
3. Applying growth rates to negative numbers. I add to the previous period’s free cash flow the greater of two numbers: the growth rate times the previous period’s free cash flow, and the growth rate times a small percentage of the company’s sales. This way a company with negative free cash flow but a positive growth rate will have a higher free cash flow number each year.
4. Determining the cost of capital. The cost of capital (or WACC) is the weighted average of the cost of debt and the cost of equity, weighted according to the market value of the company’s debt and equity. I have estimated the cost of debt by looking at bond ratings for the industry group to which the company belongs, which are often significantly worse than BBB. The cost of equity is notoriously difficult to estimate. The basic formula is to take a risk-free rate based on the payment of ten-year treasury bonds, add an equity risk premium, and multiply the premium by the stock’s beta. Determining the equity risk premium is a wild guessing game, and stocks have crazily variable betas if measured by conventional means. I determine the equity risk premium by using the following formula: ERP = D*(1 + G) / P + G – Rf, where D is levered free cash flow (unlevered free cash flow minus interest expense plus debt increase), G is the terminal growth rate (the average of the projected inflation rate and long-term GDP growth), P is the market value of equity, and Rf is the risk-free rate (ten-year treasury bonds). So by looking at the sum of all companies’ levered free cash flow and the total value of the market, one can arrive at a reasonable premium (by my calculation, it’s 7.22%). I then multiply that by the twenty-year beta of the industry group the stock is in, measured according to weekly returns, which is a far more stable and reasonable number than the monthly beta of an individual stock over the last five years.
5. Determining the terminal value. I have chosen to use the EV/EBITDA multiples method. It has some problems, but I’ve taken measures to reduce those by making extensive modifications to the method. Considering that the discount rates I use average around eight or nine percent and the terminal value is not applied until the eleventh year, the balance between the contributions of free cash flow and EBITDA to the intrinsic value is about even.
6. Discrepancies in cost of capital. The average cost of capital of a utility company is 4.75% and the average cost of capital of a semiconductor manufacturer is 12%, which remains a very large discrepancy. But my emphasis on EV/EBITDA multiples in my method reduces this discrepancy to a large degree, especially since the multiple for utilities averages about 10 and the multiple for semiconductors averages about 13.
7. Close-to-zero denominators. Since I don’t use the perpetual growth terminal value, which is where this problem really asserts itself, this isn’t a problem for me. But if you do use that, I recommend using the WACC for the entire industry group rather than for the particular stock. In addition, for the cost of debt I typically use the B bond rate rather than the BBB rate (except for certain very safe industries), so this would really only be a problem for utilities, as they have by far the lowest cost of capital.
8. Market neutrality is unrealistic. I use an EV/EBITDA multiple in my terminal value estimate. This multiple I base on the current multiple of all stocks, the current multiple of the stocks in the particular industry group (but only those that are over ten years old), and the historical multiple of the particular stock. Thus my intrinsic value estimate is not market neutral.
9. Unrealistic future projections. The key to solving this problem is to apply strict maximums and minimums to one’s initial growth projection and then to weight the average of that projection after the first year with the terminal growth number (3%) until, after five years or so, you’re simply using the latter.

Ben Graham on Intrinsic Value

Benjamin Graham and David L. Dodd dealt with many of the problems of value analysis forthrightly in their masterpiece, Security Analysis, a book which should be in every great investor’s library. It’s worth quoting them at length:

We must recognize . . . that intrinsic value is an elusive concept. In general terms it is understood to be that value which is justified by the facts, e.g., the assets, earnings, dividends, definite prospects, as distinct, let us say, from market quotations established by artificial manipulation or distorted by psychological excesses. But it is a great mistake to imagine that intrinsic value is as definite and as determinable as is the market price. . . .

[The] concept of intrinsic value, as . . . definite and ascertainable, cannot be safely accepted as a general premise of security analysis. . . .

The essential point is that security analysis does not seek to determine exactly what is the intrinsic value of a given security. It needs only to establish either that the value is adequate—e.g., to protect a bond or to justify a stock purchase—or else that the value is considerably higher or considerably lower than the market price. . . .

To express the uncertainty of the picture, we might say that it was difficult to determine in 1933 whether the intrinsic value of Case common was nearer $30 or $130. Yet if the stock had been selling at as low as $10, the analyst would undoubtedly have been justified in declaring that it was worth more than the market price. . . .

It would follow that even a very indefinite idea of the intrinsic value may still justify a conclusion if the current price falls far outside either the maximum or minimum appraisal.

Expected Net Present Value

Net present value is the present value of future cash flows and is at the heart of discounted cash flow analysis. It is widely used throughout the financial industry, by appraisers, accountants, bankers, analysts, and many others. But a variation of it is widely used as well, and it is variously labeled “expected net present value” and “risk-adjusted net present value.” Basically, this method takes the best- and worst-case scenarios and provides a range of net present values. One can weight these probabilistically to come up with one net present value, or one can accept the entire range as possibilities. The latter is the approach Graham and Dodd were clearly in favor of. As long as a security is within that range, it can be said to be fairly priced.

Fairly Priced, Overvalued, and Undervalued Stocks

As noted, I’ve developed complicated formulae for calculating the intrinsic value of stocks. I think, though I’m not entirely sure, that the formulae perform better, on the whole, than using comparative measures like price-to-sales or price-to-forward-earnings. At any rate, it’s gratifying to see what numbers they spit out.

If you use those formulae to get the intrinsic value of S&P 500 stocks and set outer bounds at 50% and 200% of that value, close to 400 of those 500 stocks can be classified as “fairly priced.” The most overvalued stocks of the S&P 500 right now, excluding financial and real estate firms, are, according to my formulae, Netflix (NFLX), Advanced Micro Devices (AMD), Autodesk (ADSK), Fiserv (FISV), Adobe (ADBE), Mastercard (MA), Fidelity National Information Services (FIS), salesforce.com (CRM), Twitter (TWTR), and Visa (V); the most undervalued are Cardinal Health (CAH), AmerisourceBergen (ABC), McKesson (MCK), Kroger (KR), Gilead Sciences (GILD), Newell Brands (NWL), Centene (CNC), H&R Block (HRB), Micron Technology (MU), and NRG Energy (NRG). I won’t claim, however, that the undervalued stocks are especially likely to increase in price or that the overvalued stocks are especially likely to decrease. A lot of other factors go into that.

Expectations and Value

While understanding value may be essential for great investors of Mauboussin’s stripe, there have been other great investors—including T. Rowe Price and Ed Thorp—who paid very little attention to (intrinsic) value. One can actually invest quite profitably without even looking at a company’s price at all.

In an article called “A Universal Theory of Stock Market Investing,” I wrote that a stock has no intrinsic value; its value is simply what the market says it is at any moment, and one can use various measures to predict which stocks will increase and which will decrease in value. I was wrong. The problem with this view is that it utterly fails to explain why when we buy an orange, we’re not going to pay $20 for it. Nothing is without intrinsic value, and that value can’t be entirely unmoored from market value.

But its intrinsic value should never be the only reason to buy or sell a stock. It’s better to focus on the probability that a stock will rise in price due to changes in investor expectations. And Mauboussin insists that this is the real key to valuation: “At the end of the day, we can prove very little about valuation. The reason is simple: stock prices (and the inputs that derive them) reflect investor expectations. Changes in investor expectations, in turn, largely dictate total shareholder returns.”

Value Drivers

Many dozens of factors drive changes in investor expectations. These are often called value drivers.

If you look at what could change a company’s intrinsic value, the most obvious thing is free cash flow. Anything conducive to increasing operating cash flow or reducing maintenance capital expenditures over the very long haul is therefore a value driver.

Reducing a company’s cost of capital will also drive value, and the easiest way for a company to do this is through share buybacks. (Increasing debt will also drive value if you look purely at intrinsic value, since it also decreases the cost of capital. But at the same time it significantly increases the company’s current enterprise value, thereby reducing its discount to intrinsic value.)

Obviously, increasing revenue will drive value, and most companies are focused on that as their primary goal. But revenue allocation involves a host of strategic decisions, many of which will end up destroying rather than driving value.

And that will be the subject of my next article in this series.

CAGR since 1/1/16: 35%.

My top ten holdings right now: VISI, KMDA, PERI, RMNI, IDT, NATR, LMB, SPNS, TPRFF, CPIX, HALL.

How to Measure and Assess Company Growth

Let’s talk about the Container Store Group (TCS) for a moment. If you look at the current quarter’s estimate and compare it to the “actual” analysts’ figure for its EPS four quarters ago, its EPS growth rate is –25%. If you look at the latest reported quarter (GAAP EPS) over the same quarter last year, its growth rate is 3,400%. If you look at the latest annual figure compared to the previous year, its growth rate is –41%. If you look at the trailing twelve months’ EPS and compare those to the previous twelve months, its growth rate is –36%. The Container Store’s three-year EPS growth rate is –5% but its five-year EPS growth rate is 15%. How crazy is that?

This problem is hardly unique to the Container Store. Most companies have widely varying EPS growth rates depending on what periods you look at. The discrepancies are mind-boggling. And that’s not even considering other growth numbers, such as sales, book value, free cash flow, and operating income.

So how do we best measure a company’s growth?

Well, let’s first look at why you’d want to measure growth. I can think of three reasons.

• One is momentum-related: you want to ride the wave. It’s well-known that a company that posts strong growth numbers in its latest quarterly statement is likely to increase in price, and that price increase doesn’t only take place in the first day or two but tends to last a few weeks. High growth numbers make investors optimistic, and following investor sentiment can lead to short-term profits.
• A second reason is more forward looking: you want to be able to anticipate growth and invest in stocks that are going to post strong numbers in the future. Here analyst estimates can be valuable, and past growth rates, if used correctly, can help. This article won’t be discussing these measures, which were the subject of an earlier article, “Predicting EPS Growth.”
• A third reason is value-related, and is almost the reverse of the first two. For a long-term investment, you want to choose stocks whose growth is going to exceed expectations. In other words, you want to choose companies whose current growth is either a) discounted or ignored by the market, b) signifies little compared to other signs of future growth, or c) is weak but shows strong signs of improvement, signs that may be hidden to other investors.

As you can see, not only can growth be measured in all sorts of different ways, but those numbers can have a variety of different interpretations depending on what you’re looking for in your investments.

Earnings Growth and the Negative-Number Problem

The standard way to measure the growth of anything is to divide the present figure by the past figure and subtract one. This is equivalent to taking the present figure, subtracting the past figure, and then dividing by the latter.

Measuring earnings growth, however, is quite unlike measuring the growth of other things. If you’re measuring the growth of a tree, a person, a supernova, or the population of cells in a petri dish, you’re not going to start with a negative number. But with earnings (as with book value, free cash flow, operating income, and a number of other financial measures), the starting point could easily be negative. In fact, almost all young companies occasionally report negative earnings, and some companies can report them for years.

If past earnings are negative, using division and subtracting one will give you a growth rate below -100%, which is not just impossible, but wrong. A company that has turned a corner and is now earning healthy returns should display a positive growth rate. To solve this problem, we take the present figure, subtract the past figure, and divide by the absolute value of the latter.

This, of course, leads to some weird growth rates. A company that has gone from earning –$0.01 per share to $0.02 per share will show a growth rate of 300%, while a company that has gone from earning –$0.03 per share to $0.02 per share will show a much lower growth rate of 166%. To ameliorate this, and to measure earnings growth when past earnings are $0.00 per share, I recommend using a minimum of $0.05 per share in the denominator. So if present EPS is E₁ and past EPS is E₀, the final formula would be (E₁ – E₀) / max (0.05, |E₀|). Using this rule, the first company would show a growth rate of 60% and the second a growth rate of 100%.

Some people argue that growth figures based on negative numbers in the denominator are meaningless. But nobody, as far as I know, has come up with a satisfactory solution to the problem. One needs to scale growth: if two companies increase their earnings by $0.30 a share and the first was earning $4.00 per share while the second was earning $0.50 a share, they have equal growth but not equal growth rates. So the same is true if one is comparing companies earning –$4.00 a share and –$0.50 a share. In both cases, the first company increased its EPS by 7.5% and the second by 60%.

Adjusting Earnings

GAAP earnings should be adjusted before use. The numbers available either include or exclude “extraordinary items”; but even excluding these, a number of “special items” (non-recurring pre-tax items such as moving expenses, severance payments, write-offs, write-downs, and reserves for litigation) remain, and should be taken into account. My rule of thumb is to deduct from (or add to, as the case may be) net income 80% of these. So to get an EPS measure, you take net income, deduct 80% of special items, and divide by the fully diluted share count.

Another option is to use analysts’ numbers, which reflect their judgment of special items and other one-time costs or income. These sometimes differ significantly from the EPS you get with the above approach; it’s probably best to take both numbers into account.

Fifteen Growth Measures

Now that we’ve done our homework, we can make a little better sense of the Container Store’s growth. I’m going to look at fifteen factors, explain how I calculate each one, and what I do with them. This is by no means an exhaustive list, and others might find different numbers useful, but I think this gives a pretty good picture.

• Book value growth. Warren Buffett famously relied on this measure for many years, though he has now abandoned that practice. Book value growth of zero to fifteen percent seems pretty healthy to me. A lot more or less than that could be a warning sign of upcoming instability. The Container Store’s book value growth over the past twelve months is 6.4%, which is nice.
• Dividend growth. The Container Store doesn’t pay dividends, so this is inapplicable, but it’s a good thing to look at. Companies that are increasing their dividends are often healthier than companies that are decreasing them.
• Projected annual EPS growth. If you compare the analyst estimate for the current fiscal year to the analyst actual figure for last fiscal year, you end up with a modest 9.5% growth for the Container Store. But if you compare it to the GAAP EPS adjusted for special items, that drops down to –28%.
• Actual annual EPS growth. If you factor in special items, the Container Store’s trailing twelve-month EPS growth (that is, compared with the previous twelve months) is –14%.
• Projected quarter-to-quarter EPS growth, current quarter. The Container Store is projected to earn –$0.10 this quarter, which is lower than the “actual” EPS of the same quarter last year (–$0.08). So that’s a 25% decrease. If you compare it to GAAP EPS of that quarter, adjusted for special items, the number becomes worse: a decrease of 67%.
• Actual quarter-to-quarter EPS growth, most recent quarter. Here we have our first piece of good news: the Container Store’s quarter-to-quarter EPS growth (the most recent quarter's compared to the same quarter last year), after adjusting for special items, is 651%. But since this is such an outlier, it’s not necessarily such good news.
• Employee growth. The staff at the Container Store, using annual employee numbers, has shrunk by 3%.
• Free cash flow growth. While the Container Store has had positive free cash flow, that has shrunk by 36% between the trailing twelve months and the twelve previous months.
• Operating income growth, most recent quarter. Here the Container Store shows a very healthy 32% growth, from $21 million to $28 million.
• Operating income growth, last four quarters. This is the average of the last four quarters’ growth over the same quarter the previous year. The Container Store’s growth averages 40%, which is truly excellent. In my view, these last two numbers are more significant than any of the previous numbers, and portend quite well for the company’s future.
• Operating margin growth. I look at the difference in one year’s operating margin from the previous year’s, every quarter over the past three years, and take the median. Here I’m looking for stability. The Container Store’s growth here is about 1%, which is pretty ideal. You really want to be wary of companies that post huge growths in operating margin, because that means that either their operating earnings are increasing a lot faster than their sales or they’re manipulating the numbers.
• Sales growth, three-year. The Container Store’s number here, 3.11%, is a little below average for the sector. But we’re not looking for very high numbers here—huge sales growth is not ideal.
• Sales growth, one-year. Here we’re very average: 4.4% annual sales growth.
• Sales acceleration. The way to measure this is to take the sales growth of the most recent quarter over the same quarter the previous year, then subtract the annual sales growth, and lastly divide by the absolute value of the latter. Since the most recent quarter’s sales increase is 8.8% and the annual sales increase is only 4.4%, the Container Store is showing strong acceleration of sales.
• Sales stability. Here the Container Store fares worse than average. The way I measure this is to take the absolute value of the difference in sales between one quarter and the previous quarter over the last four quarters and divide that by the total sales over the year. The closer that number is to zero, the better. The Container Store’s stability is 11%, which is a little too high, in my opinion.

From these numbers, you might think the Container Store is overall in a middling position. Its EPS growth is weak to terrible, but that appears to be compensated by especially strong operating income growth and a nice acceleration in sales.

But in my judgment, the Container Store is in quite a strong position. Operating income growth and sales acceleration are better signs that a stock will beat expectations, in my experience, than EPS growth. In addition, there are a few other signs of healthy growth here. If I had to rate the Container Store’s growth on a scale of 1 to 10, I’d give it an 8.

Of course, growth isn’t the only thing I look at when I assess a company’s prospects. Overall, the Container Store’s stock appears to me to be pretty fairly priced, maybe slightly low. My Seeking Alpha marketplace service, The Stock Evaluator, gives it a score of 75 out of 100.

Growth Factor Bucket Charts

Below are the results of backtests of some of these growth measures as single factors, which I’ve run on Portfolio123. Single-factor backtests are problematic, in my opinion, because every factor interacts with other factors; a single-factor backtest of, say, accrual ratios will show some rather unpromising results even though accruals must be one of the main backbones of any evaluation system, simply because accruals interact with other important factors like earnings growth, earnings yield, profit margins, and return on equity. But single-factor backtests can display some interesting tendencies. My method here is to take Portfolio123’s approximation of the Russell 3000, set a minimum price of $3.00 per share, rebalance every four weeks, and measure the decile results for each factor over the last ten and the last twenty years. The results might be quite different if I were running these tests on cheap small caps, or expensive large caps, or including foreign companies and microcaps, but these charts still give you some valuable clues as to how growth metrics affect price.

First up is EPS growth, measured by comparing the current estimate with the adjusted EPS for the previous quarter/year. The only way I can explain the dip in the ninth decile, which is present in all four decile charts, is to surmise that EPS growth works like most growth factors—a general bell-shaped curve, with the highest values in the middle—except that companies with exceptionally high EPS growth (the tenth decile) benefit from a short-term surge in price after the earnings announcement.

The next chart shows operating income growth, measured by comparing the most recent quarter with the same quarter last year and also by doing the same for the last four quarters. Here the bell curve is quite lopsided: when it comes to operating income, companies with negative growth fare a lot more poorly than companies with very high growth.

Here is three-year sales growth and sales acceleration, which give you very different curves. Notice that with sales growth (the blue and red bars), extremely high is almost as bad as extremely low. That’s definitely not the case with sales acceleration.

And lastly, here is book value growth and employee growth. Notice how low the top decile is: you really don’t want to be among the fastest growing companies by these measures.

Conclusion

Growth is complicated. It’s not easy to measure, and the measurements have to be interpreted wisely. With some measures you might want to look for high growth and with others you might want to look for average growth. It’s best to look at companies from all angles, and that means a lot of different growth angles in particular. And don’t shy from companies with negative earnings, either in the past or in the present. Every company worth investing in has room to grow.

My top ten holdings right now: GSB, LMB, RMNI, CLCT, NATR, SPNS, NXGN, HALL, PERI, NODK.

My CAGR since 1/1/2016: 36%.

How to Be a Great Investor, Part One: Be Numerate

In 2016, the analyst, teacher, writer, and researcher Michael J. Mauboussin published a white paper called “Thirty Years: Reflections on the Ten Attributes of Great Investors.” In it, he outlines “the top ten attributes” that he believes “great fundamental investors share.”

When I read it, I had to take a step back. Although I’d never read much of Mauboussin’s work before (much to my shame), my thoughts had been traveling very much along the same lines as his. I now see that I’m not exactly the first investor to compare stock market investing to parimutuel betting on horses, to take just one example out of many. Mauboussin has much more experience than I have, so the fact that we agree on so much makes me feel less alone in the investing world.

I am writing a series of ten articles on the ten attributes he singles out. This is the first.

Be Numerate (And Understand Accounting).

When we invest in a company, we can consider a lot of things: how smart the CEO is, how well the company seems to manage its employees, what news sources are telling us about the stock, an evaluation of the product. But the most solid evidence for a company’s prospects lies in its financial statements.

The trick to meaningful analysis is to figure out which numbers to combine with others to arrive at a consequential assessment. I use a computerized ranking system on Portfolio123 to analyze companies, and in doing so I look at about 35 different line items—and not just the latest figures, but figures from the last eight or twelve quarterly statements. Using various combinations of these numbers, I can assess to some degree how well a company is doing and how likely it is to beat expectations.

It’s vital to properly understand these numbers and ratios. If you have no idea how a company’s book value can be negative, or if you don’t understand the distinction between R&D expenses and capital expenditures, or if you don’t know why you’re supposed to use market cap when considering net income but enterprise value when considering operating income, or if you think that a company’s cost of debt can exceed its cost of equity, your assessment of a company’s potential is likely to be flawed.

And it’s equally vital not to ignore any major aspect of a company’s financial statements. There are simply too many red flags. Is the company’s short-term debt, accruals, or net operating assets too large? Is its free cash flow consistently negative? Is its growth unsustainable? Some of these may not be warning signs, depending on what industry that company is in (financial and utility companies, for example, can thrive with negative free cash flow).

Other numbers are also essential, and the most essential are the stock’s price and the volume traded. You may also benefit from taking into account the bid-ask spread, some historical prices and volume levels, how long it has been since the last earnings announcement, analyst estimates and recommendations and how they’ve changed, short interest, and so on.

But numeracy doesn’t mean only dealing with the facts and figures about individual investments. It also means using mathematical skills to design a strategy that has the best chances of beating the market, and being mathematically savvy enough to realize when researchers are misusing mathematics.

Take, for example, a recent presentation published by Marcos López de Prado (a principal at AQR) entitled “The 7 Reasons Most Econometric Investments Fail.” In it, López de Prado convincingly shows that econometric models (most of them based on regression analysis) “rely on strong assumptions that are not satisfied by financial phenomena.”

Almost all econometrics is based on linear regression. In his book Advances in Financial Machine Learning, López de Prado compares this to pre-Kepler astronomy, which was based on circular orbits. Financial functions are, to put it plainly, not linear. The risk-reward relationship, for example, is far better described by a fourth-order polynomial than a straight line. To analyze non-linear functions using multiple linear regression models will result in terribly flawed investment tools.

Imagine throwing out the entire canon of econometrics, including the efficient market hypothesis, the capital asset pricing model, the ideas of alpha and beta, the Sharpe ratio, risk factor analysis, and so on. (I could write a very long article pointing out the numerous errors, mostly mathematical in nature, that the creators of all those ideas made; if you’re curious, these two articles are a good start.) After all, of the great investors of the past and present, very few of them have had any use for these metrics or have subscribed to these theories.

Are there better mathematical tools for analyzing the performance of a strategy, or for helping us to decide what strategy to follow?

I believe that there are. You can use correlations, for example, without using ordinary least squares methods—Kendall’s tau is a great tool for analysis—and you can take into account that data can be strongly codependent without being correlated if the relationship is nonlinear. You can examine the entirety of a returns distribution without ever using regression by looking at omega ratios, and arrive at risk measures that are unaffected by flawed analysis methods. You can look at probabilities, one of the most useful of all mathematical tools. You can rank investments without using any econometrics. You can even find and assess factors without impractical long-short strategies and significantly flawed p-tests.

Numeracy enables you to question established orthodoxy, whether that’s the price that the market assigns to a stock or a theory whose reasoning is flawed. And that is perhaps its most valuable function.

My top ten holdings right now: TGA, GSB, FSTR, NATR, LMB, SPNS, CLCT, PERI, HNRG, PCOM.

CAGR since 1/1/16: 38%.

Why Refinancing Your Mortgage at a Lower Rate May Be a Bad Idea

Let’s say you got a ten-year mortgage at 4% on a balance of $250,000 after down payments and costs. Now it’s two years later and you want to refinance at 3.5%. Your balance is $207,652 and you’ve paid $18,399 in interest. If you don’t refinance, you’ll have to pay an additional $35,336 in interest over the next eight years. If you do refinance at 3.5% on that $207,652, however, you’ll have to pay $38,754 in interest over the next ten years, an increase of $3,418. And then there are all the refinancing costs. By getting a significantly lower rate, you’ll be significantly out of pocket.

Now let’s say you have a thirty-year mortgage at 3.5% and after ten years you’re offered a refinance at 2.625%, also for thirty years. That’s a reduction of 0.875%, or 25% of your initial rate. How can you refuse?

Well, let’s say the initial mortgage was for $300,000. Your balance is now $231,611 and you’ve paid $94,612 in interest. If you keep your mortgage, you’ll pay an additional $90,360 in interest. If you refinance your current balance at that significantly lower rate, however, you’ll pay $103,289 in interest over the next thirty years, an increase of $12,929, plus all the refinancing costs. (And those refinancing costs are typically added to your principal, meaning you have to pay interest on them too.) Your monthly payments will go down some, but you’ll be paying them for an additional ten years. The math is decidedly not in your favor.

How is it possible to pay more interest on a lower rate?

Well, there are two reasons for the increase.

The first is that when you refinance, all your interest payments up to now are ignored. They’re gone—zip!—as if you’d never paid a cent. You’ve lost every penny that you’ve paid between the initial mortgage payment and now, except for the amount you’ve paid on the principal.

The second lies in how amortization works, and it’s significantly more complicated than the first.

You start by figuring out your monthly payment, which is determined by the amount of the loan divided by the discount factor, and the discount factor is determined by the interest rate and the number of periodic payments. If i is the interest rate per month (the annual interest rate divided by 12) and n is the number of payments (for a thirty-year loan, it’s 360), the formula for the discount rate is

What does this formula do? Well, for a thirty-year mortgage, it effectively takes the annual interest rate and multiplies it by 0.69. In other words, if you’re getting an interest rate of 5%, you’re actually paying only an annual rate of 3.11% if you apply it to the entirety of the loan. (This is a rough approximation reached by dividing 1 by the discount rate, subtracting 1/360 for principal, and multiplying that by 12.) This is because the stated loan rate is applied only to the remaining principal, and as that principal gets reduced, the actual interest paid goes down.

Because you’re paying a fixed amount each month, the ratio of interest to principal in each payment will steadily diminish throughout the life of the loan. So at the beginning of the mortgage, you’ll be paying a lot more interest than halfway through the mortgage, and near the end of the mortgage almost all of your monthly payments will consist of the principal.

The precise formula isn’t terribly complicated. For the first month, apply your monthly interest rate to the entire amount of the loan, and that’s the amount of your monthly payment devoted to interest. The rest of the payment is devoted to principal. For the second month, apply your monthly interest rate to the lowered principal amount (lowered by the amount you paid in the first month), and then subtract that from your monthly payment to figure out the amount of principal you’re paying. And so on.

When you’re ten years into the loan process (assuming you have a thirty-year loan), the amount of your monthly payment devoted to interest is going to be a lot lower than when you started. Here’s a chart showing how the amount of interest per payment decreases over the life of the loan (assuming you start by paying about $500 per month in interest).

But when you refinance, the whole process begins over again. Each time you refinance, you’ll be front-loading your interest payments anew.

The idea behind refinancing with a lower rate is to reduce your interest payments. That’s what a lower rate implies, and that’s how the mortgage companies package their offers. But that’s not what actually happens.

Now sometimes it is a good idea to refinance. Sometimes the total interest you’re going to pay plus the refinancing costs are less than the amount of interest you have left to pay on your original loan. This can happen if the interest rate you’re being offered is significantly lower and/or if the period of the new loan is significantly shorter; it helps if you haven’t paid much interest yet because your existing loan is quite recent. But the mortgage companies may not tell you that, and it might be up to you to do the math. And the farther along you get into your mortgage, the harder it’ll be to find a refinancing rate that will make it cheaper to make the switch.

There’s a very easy online way to find out if refinancing your mortgage is going to save you money, and that’s to visit the Mortgage Refinance Calculator. It’s a terrific free service provided by NerdWallet, and it takes into account just about everything you want to take into account. You can adjust it according to your estimated closing costs and you can add cash out. But just remember: a lower rate doesn’t necessarily mean a better deal.

I must add, however, that if your monthly payments go down and you put every penny you save on those monthly payments into a wise stock-market investment strategy, or if you get a cash-out refinance that you can invest profitably, paying the extra interest may well be a very good idea. But look into the alternatives first. You may well be better off with a second mortgage or a HELOC than a cash-out refi. And, as I’ve explained in a previous post, using personal debt for investing is a bad idea compared to investing the money you have in companies that use debt wisely.

My top ten holdings right now: TGA, GSB, ARC, DLHC, PCOM, KMDA, NATR, LMB, CLCT, PERI.

CAGR since 1/1/16: 39%.

Minimize Your Slippage

Transaction costs for most stock investors and traders can be broken down into two categories: commissions and slippage. Commissions are fees that brokers charge to implement trades; slippage is the difference between the price as listed and the price you actually pay. Slippage, in turn, can be broken down into three categories: spread costs, market impact costs, and volatility costs. In this article I’ll skip over commissions (which I will deal with in another article) and advise you how to quantify and minimize your slippage.

Spread Costs

At any moment during a trading day, there will be two prices listed for a stock: a low price, the “bid,” which is the highest price a market maker will pay for the stock, and a slightly higher price, the “ask,” which is the lowest price a market maker will accept for the stock. If you place a market order to buy the stock, it will be filled at the current ask price, assuming there are sufficient shares to fill it at that price; if you place a market order to sell the stock, it will be filled at the current bid price, assuming there is sufficient demand at that price. (If there aren’t enough shares or demand available, some of your order will probably get filled at a worse price.) For stocks priced $1.00 or higher, the minimum bid-ask spread is $0.01; for stocks priced less than $1.00, the minimum bid-ask spread is $0.0001.

There is a very simple way to avoid the bid-ask spread altogether, and that is to use limit orders. A limit order tells the market maker that you won’t pay more than a certain amount for a stock, or that you won’t sell a stock for less than a certain amount. You’re effectively setting your own bid or ask; if you place a limit order between the bid and the ask, you’ll immediately see that the bid has risen or the ask has fallen to take your order into account. You’ve become a market maker yourself. But the drawback to using limit orders is that they might not get filled, or may only get partially filled (sometimes incurring a full commission on a sale of only one share), and the wider the bid-ask spread is, the less likely that a limit order placed far from the market order fill price (the ask if you’re buying, the bid if you’re selling) will be filled. A market order, though it pays the spread, is guaranteed to be executed unless there simply isn’t enough availability or demand to fill it at any price.

While limit orders will effectively eliminate the bid-ask spread, the actual price at which a limit order is executed will be much more in your favor with a low spread than with a high one. Let’s say you want to buy two stocks, both of which have closing prices of $5.00 a share. Stock A has an average closing spread of $0.02 and stock B has an average closing spread of $0.20. Now let’s say you place pre-open limit buy orders for both stocks at $4.98. The chance that Stock A will get filled at that price at some point during the day is probably about 50%; the chance of a fill at that price for Stock B is far lower.

How much of the bid-ask spread are you actually paying? One could say that a fair price for a stock is halfway between the bid and the ask. Given that assumption, you’re paying at least half of the bid-ask spread with a market order.

Spread costs vary widely during any given trading period, and are usually significantly higher for low-liquidity stocks. I estimate that if you use only limit orders and use them wisely, adjusting them in order to get a fill, you’ll end up effectively paying about one-quarter of the bid-ask spread per transaction. Some of your limit orders will get filled at a much better price and others will run away from you and you’ll end up paying more than you would have if you’d placed a market order. If you never adjust your limit orders, you’ll avoid paying the bid-ask spread altogether, but you also won’t get a lot of fills. If, on the other hand, you use only market orders, you’ll occasionally pay more than half the bid-ask spread if you get some partial fills at the bid or ask and then go beyond that for a complete fill, and you’ll never pay less than half the spread. Some brokers, particularly Interactive Brokers, offer other types of orders that may decrease what you’re paying or will be more aggressive about getting a quick execution. I personally have found them less effective than placing limit orders and adjusting them through the day, but that’s based on a very small sample of trades.

It’s important when trading to have an idea of the average bid-ask spread as a percentage of the stock’s price. There aren’t many sources for this information. You can easily find the current, up-to-the-minute bid-ask spread on Yahoo Finance or from most brokers. You can very roughly estimate the average bid-ask spread using information about open, close, high, and low prices; price volatility; and volume. But only Portfolio123 and my Seeking Alpha Marketplace subscription service will give you the average or median closing bid-ask spread of a stock over the past month. Getting the average spread over the past few weeks may influence your decision as to whether or not to buy the stock. If the average bid-ask spread is, say, 4% of the stock’s price, that means that you’re likely to give up 1% of the stock’s price when buying it and another 1% when selling it if you use limit orders; and if you use market orders, the cost will be at least double that. Because of this cost, you might want to eliminate from consideration stocks with high average or median bid-ask spreads, even if the current spread is very small.

Market Impact Costs

Placing a relatively large order will almost inevitably move the price away from you. This is called market impact. There are dozens of complicated mathematical formulas, all empirically tested and published in academic papers, for estimating market impact. The one I like best is a simple one: take the square root of the ratio of the amount you buy to the median daily dollar volume, and that’s the market impact in terms of the percentage of your transaction. So if you’re buying 25% of the median daily dollar volume, you take the square root of 25% and get 50%, so your market impact will cost you about 50 basis points; if you’re buying 4% of the median daily dollar volume, the square root of 4% is 20%, so your market impact will be about 20 basis points. This is, of course, only a very rough estimate; some people multiply this cost by the relative volatility of the stock, but I fail to be convinced that price volatility correlates with market impact.

Some people spread out their orders over several days to avoid market impact, but as this formula makes plain, that’s not a wise move. Buying 4% of the daily dollar volume per day over six consecutive trading days will cost you 20 basis points per day, which is more than twice as much as buying 24% of the daily dollar volume in one day, which will cost you 49 basis points. I’ve seen this play out in real time. Placing moderate sell orders every day for a week is going to drive the stock price farther down than placing one very large sell order on one day.

If you place an order greater than the median daily dollar volume of a stock, it probably won’t get completely filled, and you’ll end up paying about 1%, according to the above formula. You’ll then have to fill it the next day, and pay an additional market impact cost.

Volatility Costs

This is not a cost that most people take into consideration as it’s very difficult to estimate. Essentially, it’s the cost incurred by the stock’s price movement between the time you place the order and the time it’s executed. If you place orders before the market opens, this cost can be very high, but it can also work in your favor. For example, let’s say a stock closes at $4.60 and you place a limit order to buy it at $4.57 the next day. If you don’t get the order filled and the price goes up to $4.65, you’re incurring a $0.05 volatility cost. On the other hand, if the market open ask price is $4.55, you’ve saved a nickel per share.

It’s very important to realize that you cannot take advantage of a stock’s volatility by using wisely placed limit orders. You might think that you could come up with an algorithm that will get a better fill, on average, than you would have gotten if you’d just been filled at some random point in the day. Indeed, that’s what I myself have thought for years.

Here’s the flaw in the logic. Let’s say you invent an algorithm that, on average, gets better fills than a fill at some random point during the day. It shouldn’t be too hard, you reason.

The next step, then, would be to pair trade. You’d have two different accounts. One would buy a particular stock (one with a very low bid-ask spread) on one day and sell it on the next, and the other would sell the stock on one day and buy it the next. Because your fills will be better, on average, than random, you’ll be able to buy low and sell high almost every day. If you get a sell fill at price s and a buy fill at price b, every day you’ll be making, on average, √(s/b) - 1. If you average just 10 basis points a day, you’ll walk away with 28.6% a year, and if you make 50 basis points a day, you’ll make 251% a year.

It seems almost crazily easy. Of course your algorithm will, on average, get higher fills for sells than it will for buys. Why wouldn’t it?

Because of history. In the entire history of the stock market, nobody has actually been able to do this. And it’s highly unlikely that nobody has actually tried it.

An unfilled buy order just sits there until you adjust it. And you may have to keep adjusting it upward and upward until it gets filled. An unfilled sell order just sits there until you adjust it. And you may have to keep adjusting it downward and downward until it gets filled. If a buy order gets filled close to market open, the stock may keep plunging downward for hours. If a sell order gets filled close to market open, the stock may continue to increase in price for hours.

Even if your algorithm works 70% of the time—even if 70% of the time your sell fill is higher than your buy fill—you’re not going to be able to predict the day’s high and low prices, and the money you lose on the other 30% will always be approximately equal to the money you make on your 70%.

Volatility costs may be significant, and may be either positive or negative (costs or benefits). But they’re going to always average out, in the long run, to zero, simply because of the unpredictability of price movements.

Estimating Slippage Costs

Here are the formulae I use. Let’s take the bid-ask spread divided by the closing price every day over the last six weeks. Let’s call b the median of those percentage spreads. Let’s call d the median daily dollar volume of the stock over the last six weeks. And let’s call a the amount of money you’re going to buy or sell in the stock.

For limit orders, your slippage cost will be approximately b/4 + 0.01 * √(a/d). For market orders, it will be approximately b/2 + 0.01 * √(a/d). For the round-trip cost of buying and selling the stock, double that.

If your order is larger than the median daily dollar volume, you’re going to have to execute it over several days, which will cost you much more in terms of market impact. In that case, you’d want to remove the square root sign from the above formulae, since the "a/d" in the formula will become approximately 1 on each day, and the number of days will be calculated by dividing a by d.

Here are the slippage costs calculated for twenty randomly chosen tickers (using data from Portfolio123).

How to Minimize Slippage Costs

The easiest way to avoid paying the bid-ask spread is to use limit orders.

One extremely simple way to avoid slippage altogether is to set a limit order for a stock at the price you’re willing to pay for it (or the price you’re willing to sell it for), make it good until cancelled, and simply walk away. Sometimes you’ll get filled, sometimes you won’t.

If I’ve decided to buy or sell a stock, I want to do so within a day or two. A good-until-cancelled limit order isn’t fast enough or enough of a sure thing for me. So I place limit orders before the open and adjust them over the course of the day in order to get a fill. If the price moves away from me too much, I might abandon the order or wait until the next day.

Many traders use technical analysis to find a point at which to buy or sell. They might watch a stock’s chart and decide on the right time, or they might use an algorithm to adjust order placement based on a stock’s price movement. In any case, wise traders will use limit orders rather than market orders for this purpose.

But using limit orders isn’t the only way to minimize slippage costs. The other way is to avoid placing large orders of stocks with high spreads and low volume. By factoring your slippage costs into your strategy, you can save yourself a lot of money.

Here’s how I go about doing this. When I design a system for buying and selling stocks, I calculate the average transaction slippage. I then use Portfolio123 to simulate that system, backtesting it, and input that average slippage into that simulation. If I modify the strategy, sometimes the average slippage cost will go down, and sometimes the number of transactions involved will go down. I can see, through backtesting, the impact of the modification, and can proceed accordingly.

I also limit the universe of stocks that I buy to those whose transaction costs are under a certain limit. And then when I actually buy a stock, I’ll adjust the amount I buy according to its slippage cost, investing less of my money in stocks with high slippage.

Don’t ignore slippage

Beginning investors often pay no attention to slippage costs, using market orders for quick fills, buying low-volume stocks without paying attention to spread and market impact costs, trading more frequently than necessary, and/or believing that they can outsmart the market by getting better fills with technical analysis or clever algorithms. I have fallen into all these traps myself, and still do on occasion. Slippage costs will dramatically affect your overall rate of return if you’re not careful. It pays to consider them in every step of your investing process.

CAGR since 1/1/2016: 39%.

My top ten holdings right now: PCOM, TGA, ARC, GSB, DLHC, NATR, AVID, KMDA, PCMI, PERI.

My Investment Strategy Statement

Seeking Alpha, a website I write for, asked me a number of questions so that I could make the answers into an "investment strategy statement." I published it there a few days ago; I thought I'd publish it on my blog here as well.

My Investment Focus

I am a disciplined investor who believes that applying strict mathematical logic, sound financial principles, and thoroughly backtested strategies in a systematic and non-discretionary process will enable me to beat the market. I invest mostly in US microcaps that exhibit strong growth potential, have high-quality financials, and are underpriced.

The Securities I Choose From

The universe of stocks that I choose from is defined as broadly as possible, and includes over 4,000 stocks. Conceivably, I could choose some mid-cap and large-cap stocks, but those very rarely come out on top in the stock-picking system I’ve designed.

My Investment Process

I use a research platform called Portfolio123. There I have developed a ranking system based on over forty factors. Several times a week, I look at the top-ranked stocks and compare them to my holdings. I then increase and decrease my positions based on their ranks, and buy additional highly ranked stocks as need be. I also take into account liquidity and bid-ask spreads, putting less of my money into stocks with heavy transaction costs.

A lot of thought and experimentation goes into choosing the factors I rely on. I use some standard metrics, and a great variety of them; but I’ve also devised quite a few valuable metrics of my own. And I’m constantly tweaking my system as I develop new ideas for improvement or discover potential flaws.

I only use limit orders when buying and selling stocks. I place them before market open and if they don’t get filled, I adjust them through the course of the day.

Ideal Long Ideas

There are dozens of things that I look for in a long idea. But here are the ten most important ones:

1. strong operating income growth;
2. the industry the stock is in (I’ve classified them into groups and favor those most sensitive to the metrics I use, but I also take into account industry momentum);
3. steady sales growth—not too high, but accelerating;
4. low market cap;
5. low but increasing volume;
6. good sentiment indicators (estimate revisions, recommendation changes, earnings surprises);
7. low share turnover;
8. strong EPS growth (both estimated and GAAP);
9. high forward earnings yield; and
10. low price to sales (both estimated and actual).

My Approach to Valuation

When looking at the price of a stock, I think it’s important to compare it to other companies in the same industry. I do so with a variety of ratios: price to expected earnings and sales, price to actual sales, price to free cash flow, price to R&D expenses, price to tangible book value, and so on. But I also look at the stock’s enterprise value (unless it’s a financial or real estate company), and in those cases I compare it to other stocks in general. I use enterprise-value based ratios with unlevered free cash flow, gross profit, and long-term debt.

My Approach to Portfolio Risk

I use a performance measure called the omega ratio to measure risk-adjusted performance, and by designing my portfolios using that measure, I lower my risk. Omega basically takes the sum of a portfolio’s positive excess returns and divides them by the sum of its negative returns, so any time a portfolio’s return is worse than the median market return, it drastically lowers omega. Using omega as a performance measure thus ensures that your portfolio has as few periods as possible with low or negative returns. In addition, I favor stocks with low share turnover, which lowers my beta a lot. Although I invest in microcaps, the beta and standard deviation of my portfolio has been consistently far lower than that of IWC, the microcap ETF, while my returns have been far higher, with fewer and shorter drawdowns.

My Portfolio Return Objectives

I really only have two: to beat the market, and to make as much money as possible. I’ve been very successful at this so far, maintaining a CAGR of over 40% for over three years. My return in 2016 was 45%, my return in 2017 was 58%, my return in 2018 was 14%, and my return in 2019 so far is 15%. My objective is to keep this up despite the fact that I have a lot more money to manage than I ever have before.

The Investors I've Learned From

James P. O’Shaughnessy, Joel Stern, and T. Rowe Price. O’Shaughnessy’s approach not only has always made instinctive sense to me, but he has provided innumerable practical examples of how to carry out a thorough investment analysis. Basically, O’Shaughnessy posited that one could find out what factors have worked in the past and could then use that knowledge as a basis for a systematic analysis of stocks. This is precisely my approach as well. Joel Stern, on the other hand, came up with two of the best financial metrics I’ve ever seen, free cash flow and economic value added. He started with rigorous accounting analysis, and really understood what drove company profits and growth. His insights into cash flow and the cost of capital are priceless. Lastly, T. Rowe Price recognized that one could invest successfully in growing companies without ever considering what they cost. Price has been overemphasized in investing, whether you’re looking at fundamentals or using technical analysis. The inspiration of T. Rowe Price has allowed me to think of price as a secondary consideration. For me, a company’s quality comes first.

Liquidity Constraints

For me to invest in a stock, it has to have a moderate bid-ask spread and a minimum median daily dollar volume of $30,000; it also has to cost more than $0.50 a share. I buy and sell stocks three or four days a week.

Investment Time Horizon

Some stocks I keep for months, others I sell within a month. My median holding period is about two months.

Asset Allocation

100% in equities. I usually have one or two stocks in which I invest 8% to 12% of my portfolio; my other positions are smaller.

My Hardest Investment Lesson

It took me close to two years losing a huge amount of money while the stock market was rising before I realized that buying and selling ETFs based on technical analysis was a surefire way to go broke. At that point, everything changed for me.

How My Investment Process Has Changed Over the Last Few Years

Since I had the epiphany, late in 2015, that the best way to invest is

• a) to examine every single purchase from as many angles as possible
• b) to do so systematically rather than by discretionary means, and
• c) to do so using a ranking system rather than screens,

my basic investment process hasn’t changed much. The biggest changes have been

• a) the realization that reliable backtesting should always be done on a much larger portfolio than the one you plan to invest in;
• b) using variable portfolio weighting rather than putting the same amount of money into each stock;
• c) selling only when I need money to buy a better stock;
• d) using divided universes and time periods in backtesting;
• e) using good risk-adjusted performance measures like the omega ratio;
• f) employing innovative value and quality measures that are starkly different from what I used at first; and
• g) allowing projected transaction costs to influence portfolio weights (i.e. I put less money in stocks with big bid-ask spreads than I do in stocks with more modest spreads).

My CAGR since 1/1/2016 is 39%.

My top ten holdings right now: PCOM, CVGI, ARC, PCMI, NATR, RLGT, VLGEA, GSB, KMDA, CTEK.

Shouldn't Price-Fixing Be Legal?

When I lived in Bolivia a few years ago I noticed some market behavior that I’d never seen before. In the central market, all the vendors got together and set their prices, which they posted for the public to see. There were two bus companies in Sucre, and they charged the same amount and drove the same routes. Much of the local economy seemed to be based on price-fixing.

When I thought about it, it made sense. If you have thirty people all selling the same products—vegetables, say, or potatoes, or cow snouts (yes, there’s a whole row of cow-snout vendors in the central market)—does it make sense to have each one compete with the rest by lowering prices? Wouldn’t that cause every vendor to starve? Vendors in the Sucre market competed with each other to see how nice they could be to their customers, often offering a yapa—a little something extra­­—with each purchase. They hawked wares based on quality, appearance, and taste. Price was not—could not be—a basis for competition, because it would be ruinous.

This was an eye-opening revelation. Price-fixing is illegal in practically all of North America and Europe. Yet it was common practice in Bolivia. And it seemed to work.

So it occurred to me that, contrary to our conventional understanding that the most natural mode of economic behavior is the kind of ultra-competitive “free” market where price-fixing is not allowed, perhaps an economy that includes price-fixing is more natural.

Indeed, Adam Smith, the founder of modern economics, recognized this. In The Wealth of Nations, he wrote, “People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in . . . some contrivance to raise prices. It is impossible indeed to prevent such meetings, by any law which could be executed, or would be consistent with liberty and justice.”

In other words, Smith did not foresee a world in which price-fixing was illegal. Such legislation seemed impossible to him—not to mention contrary to “liberty and justice.” The maximization of profit and price-fixing go hand in hand.

But now it is almost equally impossible to imagine a world in which price-fixing is legal. Except if you’ve spent time in Bolivia.

So let’s imagine it: the entire Western world does away with its laws against price fixing, perhaps with certain exceptions (for example, for price-rigging in government contracts, or price-fixing that effectively creates an industry monopoly). What would happen?

Well, there has been plenty of tacit price-fixing in the Western world, and it seems to have worked quite well.

For thirty years I worked for publishers, and I am 100% certain that we never met with other publishers to discuss the pricing of our books. Yet there currently is an implicit understanding that a hardcover under three hundred pages will almost always be priced at $26.99, and twenty years ago a paperback of a certain length would always be priced at $14.99. When pricing a book, we didn’t try to undercut the price of other publishers—we always tried to price it the same as everyone else did. There was no price-fixing per se, but the result was exactly the same. Competition in the book industry is almost completely unrelated to price, and is based almost solely on quality and appeal.

The airline industry used to operate in a similar manner. A flight from Los Angeles to Atlanta might be offered by four different airlines, and the price was the same. Instead of competing on price, the airlines competed by advertising the quality, comfort, promptness, and friendliness of their flights.

In a competitive market, the legalization of price-fixing would encourage innovation, quality, and diversity.

But there’s something else going on in the developed world, the world where price-fixing is illegal. And it’s actually more insidious than price-fixing itself.

In Bolivia, when all the vendors in the market fix prices, or when the competing bus companies decide to serve the same customers and charge the same price, they get together and form a syndicate (also known as a cartel).

In the United States and Europe, by contrast, that kind of activity is highly illegal. The technical term for it is a “horizontal price-fixing conspiracy.”

But there’s actually a very easy way around it. Here in the developed world, all the vendors in the market can also agree to fix prices. They simply get together and form a . . . firm.

Now I’m not talking about monopolies here. If you didn’t like the prices in the mercado central in Sucre, you could always go to the mercado campesino, which was a lot cheaper, though also a lot more chaotic. In the US, horizontal price-fixing agreements are illegal even if they don’t work, even if other competitors are going to be around. Similarly, if vendors get together and form a firm, there very well may be other firms that will compete with it.

So what are the essential differences between a price-fixing syndicate and a firm?

In a syndicate, each vendor owns her own operation. In a firm, each vendor is either a part owner or an employee. She can no longer make a little extra money by giving away yapas or having her goods be of better quality than those of the other vendors. A firm’s products rarely compete with each other, while those of a syndicate are perfectly free to. A firm aims to be efficient; a syndicate has no such need. A firm has a strong interest in standardizing all the goods it produces, while a syndicate has a strong interest in individualizing them. When firms innovate, they replace their old products with new ones; when syndicate members innovate, their new products are sold right alongside the old ones.

In a syndicate, the vendors all earn more or less the same amount. A firm, on the other hand, is run by executives, who earn huge sums of money, while the employees who actually make and sell the products earn relative pittances.

It has been commonly believed for a very long time that regulations against price-fixing are essential to a free market. But in fact, the result is a less free market. By outlawing syndicates and promoting the formation of firms in their place, the government is effectively shutting down small businesses and encouraging the proliferation of corporate monsters.

If you don’t believe me, try reading a recent paper by Sanjukta Paul called “Antitrust as an Allocator of Coordination Rights.” The abstract reads, “It is conventionally understood that the purpose of antitrust law is to promote competition. . . . [But] our current antitrust framework authorizes large, powerful firms as the primary mechanisms of economic and market coordination. . . . The pro-competition norm has served to undermine other coordination mechanisms—such as workers’ organizations, ‘cartels,’ and the public coordination of markets.” (I’m grateful to Matt Levine of Bloomberg, who alerted me to this paper in a recent very smart column.)

Paul basically argues that the right of business entities to coordinate with one another is allocated by current antitrust law to the firm and to the firm only. This is not a natural or foretold outcome but rather a product of the influence of the Chicago School and especially the famous judge Robert Bork (author of the vastly influential book The Antitrust Paradox), which redefined competition to exclude collaboration and coordination, both natural features of competitive markets worldwide. Antitrust legislation originally didn’t make exemptions for firms—“trusts,” which were the original focus of antitrust legislation, were firms, since they were business entities under common ownership and control, and lawmakers treated trusts and corporations interchangeably. The language of the Sherman Antitrust act made no distinction between inter-firm and intra-firm coordination, but that distinction is central to antitrust actions today.

Basically, Western governments favor firms over business consortia, unions, so-called cartels, syndicates, and other forms of business associations, all of which are suspect, and all of which are enjoined from setting prices. In doing so, these governments are acting not in support of competition, but against it.

Paul gives a couple of terrific examples.

Let’s say there are five trucking companies, with twenty drivers each. Each trucking company sets the prices its drivers charge. This is not considered price-fixing, and is perfectly legal. Now let’s say one of those companies goes belly-up and the twenty drivers employed by it decide to form a bargaining unit for the purpose of negotiating their contracts with customers, agreeing on rates. The situation, for all intents and purposes, is the same as when there were five trucking companies, rather than four, but the independent drivers are now engaged in a “price-fixing conspiracy,” simply because they own their own labor rather than being employed by a firm.

Let’s say a number of organists who play for special events get together to fix prices. This actually happened, and the organists were prosecuted by the Federal Trade Commission. Now let’s say a bunch of investors create a corporation that contracts with those same organists and charges a set price for organists who play at special events, skimming a bit off the top. This is perfectly legal under current US practice. The net effect is almost the same. The organists get a little less money; the investors get a little more. But more perniciously, an organizer of a special event now has less control over which organist to hire—that’s largely up to the corporation; and the organists themselves will get much less advantage out of giving superb performances.

And then there’s Uber. What exactly is Uber but a price-fixing syndicate made up of independent drivers? Well, it’s a firm, and a very big one too, so it’s perfectly legal. But if all of Uber’s drivers suddenly quit and decided to drive independently but agreed to use a price algorithm similar to the one that Uber developed, the FTC would hound them, stop them, and levy huge fines on them. Why should this be the case?

In the United States and Europe, large businesses have numerous advantages over small ones, many of them due to government regulations. Large businesses require tremendous government support in order to survive. And one of those supports is the current interpretation of antitrust laws.

An unfettered free market can present terrible problems. But in the case of price-fixing, I think a little more freedom and less regulation might prove a valuable corrective to the over-corporatization of the American economy.

My top ten stocks right now: ARC, PCMI, GSB, KMDA, PCOM, CTEK, PERI, SCX, CLCT, PFSW.

CAGR since 1/1/16: 40.5%

 

How to Sell Your Stocks

Just after New Year, an amazing paper was posted on SSRN called “Selling Fast and Buying Slow: Heuristics and Trading Performance of Institutional Investors.” A few days later, Matt Levine, who writes daily for Bloomberg and whom I read almost religiously, published a terrific column about it called “Investors Have to Sell Stocks Too.” They’re both worth reading in full. But I’ll tell you about this new research in case you don’t feel inclined to navigate away from this page.

Basically, the paper found that professional investors—portfolio managers—put a lot of thought and effort into what stocks to buy, and they’re very good at choosing them. The stocks they buy tend to perform much better than if these managers had simply picked stocks at random. However, when it comes to selling these stocks, portfolio managers basically have no idea what they’re doing. If they had just trained monkeys to throw darts at their portfolios, they’d perform considerably better. How much better? By over 1% per year. And that really adds up. Training monkeys to throw darts is considerably cheaper.

Portfolio managers tend to sell stocks based on astrology. Just kidding. Actually, they base their decisions on price performance, which is almost as bad. The study shows that stocks that have performed extremely well or extremely badly are those most likely to be sold (actually, 50% more likely!). This is the exact opposite of what these managers do when they choose stocks to buy. When buying stocks, portfolio managers look at the fundamentals, not at price performance. But when choosing which stocks to sell, fundamentals go out the window. Instead these managers seem to rely on silly heuristics like “sell your losers and let your winners run” or “sell if you double your money” or “sell your most volatile holdings.” It doesn’t take a lot of savvy to realize that these “rules,” if strictly followed, would rather quickly bankrupt almost any investor.

Value investing has always focused on finding bargains to buy, not on choosing holdings to sell. There are many good psychological reasons for this emphasis. For one thing, buying things is always more fun than selling them. Think of all the things you’ve bought in your life that you probably should sell but haven’t. Buying is an act of optimism—you’re meeting a new friend, looking forward to future gains. Selling is an act of pessimism—you’re saying goodbye to an old friend, abandoning a once-promising prospect. As a result, most investors base their decision to sell on gossip, a hunch, or a drastic move in price.

But your overall performance as an investor is going to be based not only on knowing what stocks to buy and when, but also knowing when to sell them. It’s essential to develop a reasonable and successful strategy for doing so.

I have only two rules for selling stocks, and they’re both rather simple. By sticking to these rules, I’ve kept my CAGR at 40% or higher for more than three years now.

Rule #1: never sell a stock unless you need the cash for another investment. Even if it has failed to live up to your expectations or has posted a terrible earnings report, if you have nothing to replace it with, hold it.

Rule #2: rank all your holdings before you sell. Either sell the ones with the lowest rank, or diminish the number of shares you own of the stocks whose weight is out of proportion to their rank.

To implement this second rule, think of all the factors that motivate you to buy a stock. Make a list of them, even if it’s a long one. It could be its P/E ratio or its EV/EBITDA. It could be a recent price and volume move, or a terrific earnings report. Maybe it’s an innovative CEO or even a tip from a trusted friend.

Now rank all your stocks according to each of these factors, and add up the ranks. Some of your holdings should rank quite a bit higher than others.

At this point, you have two options. You can simply sell the lowest-ranked stock. Or you can build an upside-down ideal holding pyramid, in which the highest-ranked stocks have the greatest portfolio weight. You can then adjust your holdings by buying and selling to better conform to that ideal.

There are subscription services that can help you accomplish this. I’ve been using Portfolio123 for years to rank my holdings, and as a result I no longer agonize over what stocks to sell. I have my own subscription service that will rank stocks for you.

But you can do this with pencil and paper if you’d like, or talk it out with fellow investors. Just disregard price movements.

Sometimes I sell stocks that have gone way up, sometimes I sell stocks that have gone way down, and sometimes I sell stocks that haven’t moved much at all. But I don’t look at what they’ve done price-wise: I look at how likely they are to do well down the road. And after I sell them, I don’t look to see how they’re performing, and I don’t try to second-guess my choice. Saying goodbye to an old holding now gives me just as much pleasure as saying hello to a new investment. After all, if the fundamentals are good, I may buy that old holding back one of these days.

My top ten holdings right now: ARC, PCMI, RLGT, GSB, LNTH, KMDA, CTEK, PERI, SCX, CLCT.

CAGR since 1/1/16: 41%.

What If Sector Classification Is All Wrong?

The Global Industry Classification Standards (GICS) classify industries into eleven different sectors, and do so on a purely intuitive rather than a data-driven basis. But once you look past that intuitive level, the sectors make no sense. What do Cigna and Amgen have in common, really? Yes, they’re both in the business of “health care.” But as businesses go, they couldn’t be more dissimilar. What does a semiconductor manufacturer have in common with an IT consulting service? They’re both in “technology,” but I can’t think of anything else. What does an airline, a defense contractor, a manufacturer of electrical equipment, and a human resources firm have in common? They’re all “industrials.” But they operate in completely different ways, and the market knows that very well.

So I started wondering if there were a better way to classify industries than by using GICS sectors. There are several ideas out there.

One is to use “themes.” Portfolio123 classifies all industries into five themes: macro economic (most industrials, transport, discretionary, most materials), population growth (staples, some health care, communications, utilities), special (energy, precious metals, airlines), financial (banks, insurance, real estate), and innovative (biotech, pharma, tech). This makes intuitive sense, but almost all of the GICS sector classifications (with the exceptions of materials, industrials, and health care) remain intact, so it’s more like a grouping of sectors than an attempt to rethink them altogether.

Some folks at Open Matters, a machine learning company, suggest that we classify companies according to whether they’re asset builders (make and sell physical things), service providers (use people to offer services), technology creators (generate and deliver intellectual property), or network orchestrators (facilitate transactions and interactions). I like this idea, but I haven’t seen anyone follow up with it and actually classify companies in this way. A similar idea, suggested to me by an RIA on a Portfolio123 forum, is to classify industries in five groups: input resources, business-to-business, business-to-consumer, infrastructure and government, and facilitators.

Another way to approach this problem is to look at industry factors such as gross margin, growth rate, regulatory barriers, and so on, and classify industries accordingly. This would be a massive project, and completely dependent on which factors were chosen.

So I’ve come to the conclusion that the least biased method of dividing industries into groups is to simply let the market do it for me. As one friend told me, “The market is the ultimate crowdsource.” One can gather the returns for each industry and then group them by how those returns are correlated.

So that’s what I did. I used the GICS to classify all stocks into one of sixty different industries. I then generated an equity curve for each industry from January 1999 to January 2019, based on equal weight per company (excluding stocks with extremely low liquidity) and rebalancing annually. I then created a correlation matrix (using Kendall’s tau as my measure of correlation). If two industries had market returns that were very similar, their correlation was close to 1; if their returns were extremely dissimilar, their correlation was below 0.

Once that was done, the problem was how to group the industries based on their correlations. After a lot of research and experimentation, I ended up relying on the k-means++ algorithm, which is a bit complicated to explain. However, let me try via an analogy.

Imagine a swarm of flies hovering various distances from a central object. That central object is the return of the market, and all the flies are the returns of the various industries. The returns of some industries—metals, for instance, or oil and gas companies—are going to be very far from the middle, because their correlation to the market is low. The returns of others—health care providers, insurance, machinery—are going to be quite close to the middle, because their correlation to the market is high.

What a good clustering algorithm will do with a swarm like this is to take the fly that is farthest from the middle and see what flies are closest to it, within reason. Those flies then get placed within a cluster. We then see what fly is next farthest from both the middle and that first cluster, and form a cluster around that fly. In the end, with a lot of iterations and difficult choices, you can create coherent clusters.

Now these algorithms tend to create clusters that are somewhat larger or smaller than I wanted. I wanted clusters that represented between 2.5% and 25% of the market as a whole when looked at historically. I had to continually adjust my parameters in order to get clusters of that size. I also had to take some of the outer clusters and remove them from my data in order to get any sort of differentiation for the inner clusters.

Here are the industry clusters I found, in rough order from least differentiated (closest to the market as a whole) to most (on the edge of the swarm). (I excluded REITs, MLPs, royalty trusts, and BDCs from consideration here, because those operate on such different principles than other stocks.) Please keep in mind that I clustered these industries based solely on their historical returns, not on any preconceived idea of how well they fit into distinct categories; in fact, I clustered them more or less blindfolded, without paying attention to what industries they were, just so that I could be objective. Also please keep in mind that industry clustering is never going to be very precise.

• PRIMARY. Staples, insurance, electricity, gas, water, road & rail, health care providers and technology, packaging. These are core stocks, commonly known as “defensive” stocks. They’re the products that you simply can’t do without, no matter how bad the economy is.
• SECONDARY. Chemicals, aerospace and defense, machinery, conglomerates, trading companies, professional services, health care equipment & tools, internet retail. These are complicated businesses that mostly depend on other businesses. Few of them are direct-to-consumer operations.
• BASIC. Paper, wood, clothes, stores, drugs, infrastructure, auto parts. This category is very similar to the “Primary” category above: these are also defensive stocks.
• COMPLEX. IT services, software, wireless, non-traditional utilities, construction. These are complicated goods that fall in between the “Secondary” category above and the “Edge” category below.
• SERVICE. Commercial and consumer services, finance, air freight, building and construction supplies, leisure. This is similar to the “Secondary” category except that it includes more direct-to-consumer businesses and, with an exception or two, is centered around the idea of providing services rather than goods.
• EDGE. Biotech, semiconductors, computers, electronics, media. These are cutting-edge businesses that depend upon innovation and creativity.
• CREDIT. Banks, real estate, distributors, cars, furniture. These are businesses that respond sharply to the credit cycle.
• SPEED. Internet, social media, telecom, communications equipment, airlines. These are businesses that depend upon and benefit from long-distance communication.
• EARTH. Energy, metals, electrical equipment, marine shipping. Stuff you get out of the earth, along with the means of getting it from one place to another.

(These clusters—their names and the industries included—are the expression of my idea about sectors and clusters, and are therefore protected by US copyright.)

Here’s how the clusters performed over the last twenty years:

Here are some possible uses for this new classification.

1. Cluster rotation. Keep track of the returns of each cluster and buy the ones with the strongest momentum or the most undervalued ones.
2. Cluster concentration. Invest in the clusters with the least volatile returns, or the clusters with the lowest beta, or the clusters with the highest alpha. (The least volatile clusters are, in order, secondary, basic, and primary, and the most volatile are earth, credit, and service. The clusters with the lowest beta are primary, credit, and secondary, and with the highest beta are edge, speed, and earth. The clusters with the highest alpha are primary, secondary, and complex, and the lowest are speed, earth, and credit.)
3. Recognize the differences between clusters in terms of investment strategy. The primary, basic, and credit clusters will respond best to a value strategy, while the secondary, edge, and service clusters will respond best to a growth strategy. Sentiment indicators are very important for the service and speed clusters and relatively unimportant for the credit cluster. You really want to favor tiny companies in the secondary cluster, while in the primary, basic, and credit clusters, size doesn’t matter as much.

So I propose that we replace the eleven GICS sectors with these nine clusters. I think they more accurately reflect the real differences between different industries.

My top ten holdings right now: ARC, PCMI, GSB, RLGT, CTEK, PERI, PFSW, NTWK, CLCT, PDEX.

CAGR since 1/1/16: 41%.

How to Avoid Value Traps

A value trap is a relatively cheap stock whose price simply doesn’t rise no matter how long you hold it. I’ve done a research study of factors that might characterize value traps, and here are the ones that I think provide the best warning signs. After going through these factors, I’ll tell you how I performed the study, describe some systems that incorporate these factors, give their performance, and recommend some value stocks that I think are not value traps.

1. Avoid companies who file late. The SEC has set deadlines for company filings; most companies must file a 10-Q within 40 days of the end of their fiscal quarter, though companies with a market cap of less than $75 million can take up to 45 days. After that, companies need to file a form NT (for “Non-Timely”), which will give them a five-day grace period. If a company doesn’t file a form NT or takes more than the five days given, it may face deregistration, delisting, and an inability to raise capital. In general, companies who are late with a quarterly or annual filing tend to do poorly over the next few months, lagging the S&P 500 by an average of more than 2% annually.
2. Avoid companies with negative or very low unlevered free cash flow. Unlevered free cash flow is cash flow from operating activities plus after-tax interest expenditures minus capital expenditures. If a company’s unlevered free cash flow is less than 2% of its enterprise value (the sum of its market cap, non-controlling interest, preferred equity, and debt minus its cash on hand), it’s going to be hard for it to grow enough to escape value-trap status.
3. Avoid any company whose negative cash flow from investing activities is a lot bigger than its cash flow from operating activities, or whose cash flow from operating activities is negative to begin with. A company may look like a good value, but if its cash flow from investing activities (which includes capital expenditures, acquisitions and divestitures, sales and purchases of investments and plants, and other investing activities) is negative $100 million while its cash flow from operations is only $50 million, it’s going to face a pretty tough year. To rank companies on this measure, I take the cash flow from operations, add it to the cash flow from investing (which is usually a negative number), and divide the total by the sales for the year.
4. Avoid companies with high balance-sheet accruals. Balance sheet accruals are the increase in the most recent year’s net operating assets (NOA) over the previous year’s, divided by the last two years’ average total assets. Anything over 5% is pretty dangerous, and represents a serious threat to future financing. If your NOA is growing, your proportion of cash and non-debt liabilities to total assets is shrinking, leaving you little breathing room to exceed investor expectations.
5. Avoid industries with poor unlevered free cash flow to enterprise value ratios. Right now the industries with the worst ratio of unlevered free cash flow to enterprise value are hospitality, construction, aerospace and defense, mining, food, construction materials, utilities, car manufacturers, air freight companies, communications equipment, trains and trucks, airlines, tobacco, and energy equipment. This list may change, of course, and certainly some of these industries have had better days in the past. But at the moment, they’re not the best industries to invest in.
6. Avoid companies whose price is extremely low compared to recent highs. Look at the company’s ten-month high one month ago, and compare that to its current price. If the latter is only a small fraction of the former (say, 60% or less), it’s going to take a good long time for the company to regain its former glory.
7. Avoid industries with strong negative momentum. Industries whose companies have, on the aggregate, fallen most sharply in price over the last year are probably best to avoid. As of early February, those industries are diversified telecom, mining, direct marketing retail, diversified financial services, consumer durables, distributors, car manufacturers, auto parts, pharma, biotech, energy equipment, and transportation infrastructure.
8. Avoid companies with low volume-weighted momentum. Divide the company’s VMA(15) by its VMA(200). If the result is below 0.8, that stock may well be in deep trouble.
9. Avoid companies with low projected EPS growth. In a previous post, I talked about five predictive signals for EPS growth: low profit margin or ROA, high EPS estimates, low accruals, strong momentum, and strong operating earnings growth. If those signals are mostly negative—i.e., if the company is showing high profit margin or ROA, low EPS estimates, high accruals, low momentum, and shrinking operating earnings—that’s a strong warning that the company is going to have a very hard time growing its earnings.
10. Avoid companies with a low ratio of gross profit to enterprise value. If using TTM numbers, I’d set my threshold around 0.15. Anything lower than that and the company is probably overvalued rather than undervalued.
11. Avoid companies that are issuing a lot more shares. Equity financing is far more expensive than debt financing, and a company that is issuing more shares rather than buying them back may be desperate for cash, leveraged to the hilt, or simply not fiscally foresighted.
12. Avoid companies whose trailing twelve months sales are either a lot higher or a lot lower than their sales the previous year. When looking at value companies, you want to see somewhat steady sales—ideally, sales growth should be close to the average for all companies. Companies with huge increases in sales are likely to disappoint investors in the near future; companies with huge decreases in sales are unlikely to easily make up for them. As a rule of thumb, avoid companies in the top or bottom decile in terms of sales growth (the most recent twelve months over the prior twelve months).

Here’s how I came up with these factors.

First, I created a universe of value stocks as follows. After establishing some minimum liquidity rules, I isolated those stocks that were in the top 50% of their industry in terms of book value to fully diluted market cap, sales to fully diluted market cap, and trailing-twelve-month net income to fully diluted market cap (in other words, the lowest 50% in terms of price to book value, price to sales, and P/E). They also had to be in the highest 50% of the entire universe in terms of EBITDA/EV, using a formula that adjusts extremely low or negative EV up to $5 million. That universe of value stocks included an average of 574 stocks during the 1999 to 2019 period, and today numbers 570 stocks.

I then ran a rolling backtest on Portfolio123, testing the six-month returns of these stocks if bought every week from 1999 to 2018. The average six-month return of one of these value stocks was pretty decent—7.22% compared to 3.49% for the S&P 500. I then tested about a hundred different factors by buying only the lowest quintile and measuring the six-month performance. The dozen factors above had the worst performance for that low quintile.

So now I’m going to limit this universe of 570 value stocks by excluding those that fail on one or more of the tests I’ve outlined above. I’m also going to exclude financial and real estate stocks because free cash flow and enterprise value are not great measures for those companies. That narrows our buying choices down to only 86 stocks.

The six-month performance of stocks that pass this rather complicated and strict set of screens is somewhat higher than the plain value stocks, averaging 7.93%, an improvement of 1.5% per year. If you include only companies with a market cap between $50 million and $1 billion and use the screen, your six-month return climbs to 8.42%.

I’ve always held that ranking is better than screening. A company might fail just one of these twelve screens but have excellent metrics on the others, making it a better buy than another company that has poor but passing metrics on all twelve. Screening is like simply requiring a student not to get F’s and judging her performance accordingly; ranking is like judging her on her grade point average. So if, instead of using the screen, you create a ranking system based on these twelve factors and just choose the top ten stocks, your six-month return climbs to 12.46%, for an annualized return of 26.47%.

But you can do even better than that. Instead of the strictly circumscribed value universe I’ve outlined, you can combine two ranking systems. The first will be the twelve-factor system I’ve just outlined, equally weighted; the second will equally weight the four value factors, except that I’ll be using forward earnings (the mean analyst estimates for the current fiscal year) rather than TTM earnings (which tend to be less reflective of a company’s potential). In total, that makes sixteen factors: the four conventional value factors weighted at 12.5% each, and the twelve value-trap-avoidance factors weighted at 4.17% each. My top-ten ranked stocks now earn 16.58% every six months, for an annual return of 35.91%. (Of course, one should take transaction costs into account; if one assumes that each transaction costs 75 basis points, the return falls to 15.08% every six months, for an average annual return of 32.43%. Also keep in mind that average annual returns are always significantly higher than compounded annual returns.) For comparison’s sake, if you had created a simpler ranking system with none of the value-trap factors and only the four value factors and chosen the top ten stocks, your six-month return would have been only 7.66% because you’d be buying a huge number of value traps.

Now it’s not very practical to check this every week and hold the top ten stocks for exactly six months. For one thing, when prices are very volatile, you’ll have a very large number of stocks and no cash to deploy, while when prices are not volatile at all, you’ll be holding the same stocks for a long time with lots of cash on hand. For another, a six-month sell point is completely arbitrary. Why put in so much effort into choosing which stocks to buy and use an arbitrary measure to choose which stocks to sell?

So here’s a system. Each week, buy the top ten stocks by rank, assuming you don’t already own them, apportioning 5% of your portfolio to each one. Only sell them after you’ve held them for three months and if they’re no longer in the top twenty-five.

Assuming transaction costs of 75 basis points, your compound annual growth rate over the last twenty years would be 32.07% and your average annual return would be 37.73%, while you would be leaving an average of 12% of your portfolio in cash. You would beat the S&P 500 in fourteen out of those twenty years. You would hold your stocks for an average of four months, and your average annual turnover would be 2.5X. Your maximum drawdown would be 50% (compared to 55% for the S&P 500), and your alpha would be 27.25%.

So what are these ten value-but-no-value-trap stocks right now? Resolute Forest Products (RFP), Fujitsu (FJTSY), L.S. Starrett (SCX), Tech Data (TECD), Perion Network (PERI), GameStop (GME), NetSol Technologies (NTWK), RWE (RWEOY), Corus Entertainment (CJREF), and Veon (VEON). I somewhat foolhardily predict that only one or two of these stocks will go down more than 20% in the next six months, and that their total returns will beat those of the market as a whole. We’ll see if I’m right in six months’ time . . .

My ten largest holdings right now: ARC, GSB, PCMI, CTEK, PERI, PFSW, OSIR, PDEX, HALL, CLCT. I also own a fair amount of SCX and NTWK.

My CAGR since 1/1/16: 40%.

Market Timing, Tactical Asset Allocation, and Trading: A Dialogue

Here’s a dialogue between two sides of myself: Moses, who’s a proponent of market timing and tactical asset allocation (TAA), and Celeste, who thinks it’s bunk.

Moses: What is the difference between trading, tactical asset allocation, and market timing? In all three cases you’re buying and selling assets that are designed to be held for far longer than the amount of time you’re holding them.

I’m a stock picker. I very rarely hold stocks longer than nine months. I place buy and sell orders every week, sometimes every day. I’ve been able to consistently beat the market, with a CAGR of over 40% for more than three years, by using a ranking system on Portfolio123 to invest in microcaps.

Now if I were to do exactly the same thing with a limited number of ETFs, buying and selling them at different times, I would be doing TAA instead of trading. And if I were to limit myself to just two ETFs, SPY (which tracks the S&P 500) and ICSH (which tracks short-term government bonds), I’d be doing market timing.

So my gut tells me that all those pundits who say that buy-and-hold always beats market timing are the same pundits who say that index funds always beat stock-picking. And if they’re wrong about the latter, why shouldn’t they be wrong about the former?

Celeste: People have been trying to do market timing for over a hundred years and nobody yet has gotten it right. If someone were to get it right, beautifully timing her entrances and exits so as to altogether miss every correction and every bear market but capture entirely every major upswing, she would basically rule the world. Why? Because enough people would follow her lead that she’d be able to effectively manipulate the entire stock market and make more money than anyone in history.

Let’s say she times the market impeccably for twenty-five years, becoming famous in the process. Let’s say that 75% of the investment world doesn’t believe her predictions despite her amazing success, but 25% does.

Now let’s say that she predicts that the stock market will take a downturn sometime in the next few weeks. 25% of investors will sell all their stocks, resulting in a massive downturn. Several months later, she predicts that the downturn is over, and that stocks will shortly stage a massive recovery. 25% of investors will promptly buy stocks, sending the market soaring again.

In other words, the more successful a market timer is, the more impact she will have on actual stock prices, making her prophecies self-fulfilling.

This conclusion won’t have escaped her. She will very quickly realize that she can sell her own personal holdings, then predict a stock market downturn. Stock prices will tumble. She can then buy up huge quantities of stock and predict an upturn. Stock prices will soar, and she’ll make a tidy profit. The more often she makes her predictions, the richer she will get.

What would happen then? The entire stock market would collapse. Nobody wants to buy into a rigged system.

This logically leads to the following conclusion, as a kind of axiom. The appeal of the stock market rests on its unpredictability. If the stock market were predictable, someone could game it, and every other participant in it would feel like they were being taken for a ride. Nobody wants to invest in something that someone else can game.

Moses: That’s not true at all. It’s pretty clear to everyone that the lottery is gamed in favor of the ticket-sellers, sports betting is gamed in favor of the bookie, slot machines are gamed in favor of the casino, and there’s always a house take in a poker game. Similarly, the stock market is gamed in favor of the market makers, who profit from the bid-ask spread. So there is room for a successful market timer in the mix. Good market timers don’t get everything perfectly right. But they can beat buy-and-hold investors, with less risk, and they typically keep their methods to themselves.

Celeste: The Nobel Prize–winning economist William Sharpe calculated that a market timer would have to be correct 74% of the time to beat a buy-and-hold investor. That’s a pretty tall order, especially when most pundits are right less than half the time.

There are plenty of investors who were devoted to market timing at one point and then realized the error of their ways. Take Paul Merriman, founder of Merriman Wealth Management, for example. His first book, published in 1985, two years after he’d launched the company, was called Market Timing with No-Load Mutual Funds: Low-Risk High-Return Investing with No Commissions. He has changed his tune completely. In 2013, he wrote, in an article entitled "Why Market Timing Doesn't Work," “Nearly half a century of working with investors has taught me this: Many people who try buy and hold succeed, while most of those who try timing (particularly those who do it themselves) fail.” He maintains that it’s impossible to beat the market with market timing, though it’s still useful for limiting losses. In essence, for Merriman, market timing is a way to smooth out his returns.

Moses: Merriman’s timing systems are all based on trend-following. There are many other ways to do market timing. The website Philosophical Economics has outlined some great strategies ("Growth and Trend: A Simple, Powerful Technique for Timing the Stock Market" and "In Search of the Perfect Recession Indicator") that combine trend-following with economic signals. One smart subscription-based website that offers a wide range of timing strategies is imarketsignals.com. Using some of those strategies may well help you smooth out your returns and reduce your drawdowns.

Celeste: Will they actually beat the returns of a buy-and-hold strategy? I think that’s doubtful.

Index Fund Advisors has published an extraordinarily forceful warning against market timing. You’ll read there that CXO Advisory Group tracked market-timing gurus over the 2000–2012 period, and not a single one beat Sharpe’s 74% threshold. Another study tracked 15,000 predictions made by 237 market-timing newsletters from 1980 to 1992. By the end of the period, 94.5% of the newsletters had gone out of business. John Bogle said that over a 55-year period he had never met anyone who knew how to “get out of stocks at the high and jump back in at the low,” and had never even met anyone who knew someone else who could do that.

Moses: Index Fund Advisors also makes an extraordinarily forceful warning that you can’t beat an index fund by wisely choosing stocks. And you and I both know that that’s wrong.

Market timing is just a simplified version of a much better strategy: tactical asset allocation. AllocateSmartly is a terrific subscription-based website that offers a large number of different strategies, all based on academic research and thoroughly backtested, to switch into and out of different index-based ETFs. One of the things I like best about this service is the way they’ve extended ETF data back fifty years to the days long before ETFs. I have little doubt that adopting some of these strategies will provide a smoother ride than a simple index fund.

Celeste: It’s hard for me to have much faith in any of these strategies as a long-term proposition. Charlotte Moore, a British business writer, has written a wide-ranging article that outlines the challenges that TAA strategies face. Her critique of TAA can be broken down into three main flaws:

• First, assessing where we are in the business cycle in real time can be challenging, to say the least, mainly because economic data is always lagging real-time developments and because different sets of economic data usually contradict each other or are inconclusive when looked at as a whole.
• Second, markets move much more rapidly than economic data. As Alfred Kassam, the head of equity applied research at MSCI, observes, “It is very hard to predict fast-moving financial markets using slow-moving economic data.”
• Third, the purpose of investing in alternative indexes is to beat the market over the long run, and switching in and out of them defeats that purpose altogether. If you’re buying value stocks because of the value premium, you deny yourself that premium if you switch in and out of that strategy.

Moses: This brings us back to the question that this article started with. In trading microcap stocks, I’m also buying and selling assets that were designed to be held onto for years, and doing so has made me a pile of money. If I were to practice TAA, I’d be doing the same thing; and if I were to limit my TAA to two ETFs, I’d be engaging in market timing. What’s the big difference?

Celeste: The difference, I believe, is in the nature of the assets themselves.

To successfully and consistently beat the market, you have to game the system, and in order to game the system, you can’t trade what everyone else is trading. You have to find rare opportunities—“mispriced” assets—and capitalize on them quickly. When you’re dealing with microcaps, such opportunities are legion; when you’re dealing with established indexes, those opportunities are far rarer.

Moses: Well, in most of my accounts, I can find those rare opportunities and capitalize on them. But in my family’s 401K accounts, I have very limited options and can’t invest in individual stocks. In those accounts, wouldn’t it be better for me to exit the market before a downturn and go back in when the recession is over? After all, the folks at iMarketSignals and Allocate Smartly have invested years of research into their particular strengths, and Philosophical Economics makes a very convincing case for using his/her market timer.

Celeste: Using market timing and TAA wisely may smooth your returns; you might, if you work hard enough and/or get lucky, even have a slight edge over buy-and-hold. But you might utterly fail. Go look at the real-time track records of some market timers on collective2.com, which tracks investors’ strategy results. They’re abysmal.

If your aim is to beat the market, I’m pretty certain that neither TAA nor market timing will do it. For that, you need to aim at much smaller targets than broad-based indices.

 

My top ten holdings right now: ARC, OSIR, CTEK, HALL, GSB, PFSW, PERI, INTT, NTWK, KTCC.

CAGR since 1/1/16: 40%.

Factor-Based Ranking Systems

I spend a lot of time creating and refining ranking systems for stocks. My entire system of investing/trading is based on systems that take a universe of stocks and rank them from lowest to highest based on various factors. Using these systems to buy and sell microcaps, I've been able to grow my own personal portfolio by leaps and bounds, making profits of 45% in 2016, 58% in 2017, and 14% in 2018. To do this, I use Portfolio123, a versatile subscription-based service that allows me to backtest ranking systems and measure their performance.

One way of measuring ranking system performance is to separate the stocks at each rebalancing point into ten or twenty groups based on their rank and seeing how those groups would have performed. So, for example, here is a performance chart of the ranking system I use for my own personal stock buys, with a wide universe of close to 4,000 stocks and rebalancing every four weeks between January 1999 and January 2019. It’s important to note that a lot of the stocks I buy are not very liquid and that the performance chart doesn’t reflect slippage/transaction costs.

Looking at this performance chart, it’s easy to realize that this kind of ranking system is very efficient at choosing outperforming stocks, but doesn’t differentiate very well between stocks in middling percentile groups (for instance, between the 35th and 70th percentiles). In order to evaluate a stock’s chances of success, a different approach is needed. Rather than optimizing a ranking system for the top quantile or the top 50 or 100 or 500 stocks, it would be better to optimize for the slope of the performance chart. A ranking system that maximized slope would be truly evaluative (as long as one assumes that past performance is somewhat predictive of future performance).

So I developed the Stock Evaluator, a ranking system that evaluates the chances that a stock will outperform. It’s quite different in many ways from the system I use to buy and sell stocks. Here’s the performance chart, this time on a wider universe of stocks, with a quarterly rebalance, over the same time period.

One huge difference between these ranking systems is that the long-only ranking system favors small caps, microcaps, and nanocaps, and the evaluative system doesn’t take size into account. Why?

Size works as an augmentative factor. The smaller the stock, the more it’s going to be affected by other quantifiable factors. Small-caps that are overvalued, for example, will do far worse than overvalued large-caps.

To illustrate this, here’s the performance of the Stock Evaluator in two different universes of stocks: the top image is its performance in the Russell 1000 (large stocks) and the bottom is in the Russell 2000 (small stocks). You’ll note that the spread between high-ranking and low-rankings stocks is a lot wider for small stocks than for large ones. This is true of almost all ranking systems I’ve seen.

Let’s take my evaluative system and add a size factor (market cap) equal to 17% weight. You’ll see the difference in the performance below. It’s become much more like my long-only ranking system, and much less evaluative.

One can also create a ranking system for going short, whose performance chart would look something like this:

This ranking system consists of only ten equally weighted factors, rebalanced monthly. No doubt I could create an even more extreme one using more factors and different weights.

In order to perform an experiment, after creating this system I created another system of ten equally weighted factors (almost all of them different from the short-only system), rebalanced monthly on the same relatively liquid universe, designed for going long. The performance chart looks like this.

Now here is the performance of the two ranking systems combined, so that each of the twenty factors gets a weight of 5%.

The top ventile (5%) here isn’t quite as high as the top ventile of the second system, and the bottom ventile isn’t as low as the bottom ventile of the first system, so possibly this “compromise” system wouldn’t be quite as useful for choosing stocks to buy or short. However, as a “stock evaluator,” it’s far better than either of the first two systems. What this ranking system is really useful for is looking up the percentile rank of a particular stock, which will give you a good estimation of its chances of success over the next rebalancing period (in this case, four weeks).

To sum up, there are three different uses for a ranking system, and these three systems are good examples. One use is to choose stocks to buy; another is to choose stocks to go short; and a third is to evaluate stocks. For the first, you want to have the top-ranked stocks do really well; for the second, you want to have the bottom-ranked stocks do really poorly; and for the third, you want both. For the first and second, you want to use size factors wisely, emphasizing small caps; for the third, the size factors cancel each other out, and you end up with a size-neutral system.

I'd like to explain this last point in detail. One good short-only system, just for example, might look for stocks with high accruals, low asset turnover, low margins, high share turnover, high volatility, negative momentum, high value ratios, and small size; a good long-only system might look for stocks with strong growth in EPS and sales, low accruals, increasing volume, exceptionally low value ratios, and small size. So if the evaluative system would combine the two, you’d rank stocks as follows: accruals (the lower, the better), asset turnover (the higher, the better), margins (the higher, the better), share turnover (the lower, the better), volatility (the lower, the better), momentum (the higher, the better), EPS and sales growth (the higher, the better), recent volume change (the higher, the better), and, most importantly, value ratios (the lower, the better). All these factors work oppositely for long and short systems. But since both the long and short ranking systems include a size factor that’s exactly the same instead of the exact opposite, a combination of the two would cancel the size factor out.

There has been a long tradition of looking at factors based on rank performance. The usual study takes the top-ranked stocks long and the bottom-ranked stocks short. A good example of a fund that works in this way is AGFiQ's US Market Neutral Value Fund (CHEP). This fund goes long equities with low valuations and shorts equities with high valuations. Its performance has been absolutely abysmal. A much more profitable strategy would be to choose different sets of factors for the long and the short holdings. And if overlap is a problem, you can combine the best-performing factors for each.

I hope I’ve provided some fodder for thought in how to use factors to rank stocks. There’s no one-size-fits-all way to do so, and thinking about factors and ranks in simplistic terms may be counterproductive. Buying the top-ranked stocks in a long-only ranking system may give you higher returns than buying the top-ranked stocks in an evaluative ranking system, but it’ll also give you a rockier ride. Some stocks may rank in the 99th percentile in the first, making them appear to be terrific bets, but only the 55th in the second, making them appear to be no better than average, because you’re using different factors with different weights.

In addition, you have to keep in mind that these systems have been optimized to some degree over very specific time periods with very specific sets of stocks, and out-of-sample performance over future time periods with different stocks may turn out to be very different. For example, small-cap stocks that ranked very highly using conventional value ratios performed extremely well between 1999 and 2006, and rather poorly since.

Despite the complexity of looking at factor performance through ranking, though, I believe that it offers a more comprehensive look at stock market opportunities than any other approach. The sophistication of ranking systems is far beyond the capabilities of ordinary screeners or, for that matter, of conventional discounted-cash-flow analysis. Factor-based ranking systems are truly the most versatile and comprehensive way to analyze stocks, and offer many extraordinary opportunities to beat the market.

CAGR since 1/1/2016: 40%.

My ten biggest holdings right now: ARC, OSIR, HALL, CTEK, GSB, PFSW, NTWK, SIGA, KTCC, PERI.

A Universal Theory of Stock Market Investing

This piece attempts to encapsulate my conclusions after several years of investigating stock-market conundrums. It is, in essence, a grand unified theory of stock market investing. It is in ten succinct points. After laying out each point, I will offer some further thoughts and elucidations, and link to my previous articles on the subject in question.

Tenet 1: The price of a stock is completely determined by investor expectations.

Because a stock’s price is determined entirely by the willingness of investors to buy or sell it, it reflects the aggregate of investors’ confidence that the price will rise or fall in the future, the expectations of dividends to be received, and the price of a potential acquisition. This investor confidence can be influenced by any number of things, from a Twitter recommendation to a careful discounted-cash-flow analysis; these things are called “factors,” and they are almost infinite in number. Some of them are based on rigorous accounting principles, some are based on investor beliefs (many of them incorrect), and a few seem to have no basis whatsoever.

Because the price of a stock is completely a function of investor behavior, stocks cannot be said to be “mispriced,” and there is no such thing as “luck” or “randomness” in the stock market. Many stock-market theorists try to separate the price of a stock into two components: value and noise. Others hold to the Efficient Market Hypothesis, that the price of a stock fully reflects all available information about it. But, as George Soros puts it, “The prevailing wisdom is that markets are always right. I take the opposite position. I assume that markets are always wrong.” Or, as I wrote here, “The stock market is a badly oiled contraption, stuck together with cellophane tape and staples, and full of rust spots and leaks and broken parts. Its pricing mechanism is terrible and inefficient, and it runs a crazy, circuitous, and illogical course. Why? Because many of the price movements in stocks are based on the quirks of human behavior rather than on sound financial sense.”

Tenet 2: Stock prices have only a very tenuous relationship to a company’s intrinsic value (if such a thing even exists).

Because a stock’s price is determined by millions of different investors’ confidence levels, most of which are the result of an almost infinite number of different factors, the complexity of the system that sets stock prices is beyond rational calculation. It is therefore impossible to rationally assign a “value” or a “target price” to a stock. When people talk about the “intrinsic value” of a stock, they are looking at the “intrinsic value” of the company of which the stock is technically a portion, and base that value on the company’s earnings, free cash flow, dividend payout, book value, enterprise value, and/or similar numbers. But while this may make some sense for a privately held company, once a company goes public, the equity portion of it becomes more or less unmoored from its intrinsic value and its value instead becomes whatever investors as an aggregate think it should be.

The very fact that the S&P 500 can include two technology stocks like Citrix Systems (CTXS), with a P/E of 123 and a price-to-book ratio of 21, and Hewlett Packard (HPE), with a P/E of 7 and a price-to-book ratio under 1 (these figures are as of 11/25/18), gives the lie to conventional measures of value. In addition, as I have shown, you can invest very successfully without ever looking at the price of the stocks you’re buying, which is further proof that “value” is an overrated factor.

Tenet 3: Successful investing requires thinking in terms of probabilities.

Successful investing lies not in accurately predicting the future value or prices of stocks but in holding the stocks that have the highest probability of delivering strong returns. In other words, think in terms of odds rather than targets.

Because stocks are so unmoored from so-called value and prices are set so capriciously, it makes more sense to focus on the odds that a stock’s price and dividend payments will go up or down than on how much the stock is “really worth.”

Tenet 4: These probabilities are determined by two interrelated things: the likelihood of a company’s future success and the likelihood that investor expectations are mistaken.

The stock market is quite a bit like parimutuel betting (betting where the odds are determined by aggregate bet size rather than by the house). Just like at the race track, the payout is determined by two things: whether a company succeeds and how much investors have bet upon that company (the stock’s market cap). When we buy a stock, we are essentially making a bet that its price (or market cap) will increase and/or that its dividends will pay off and/or that it will be acquired at a premium. And our odds are dependent on other people’s bets.

In parimutuel betting, we must take into account not only the factors that will make a horse more likely to win but the factors that will make other bettors less likely to bet on it. An example of the first kind of factor might be the horse’s pedigree or its time in previous races; an example of the second might be if you think the jockey or trainer is underestimated.

In the stock market, the first kind of factor is the kind that directly drives investor interest and thus increases prices, such as an excellent earnings report or an upgrade in analyst estimates. The second is the kind that signifies that a company is likely to exceed investor expectations, such as a high ratio of unlevered free cash flow to enterprise value (a value measure that few people use).

The ideal factor, then, is one which reverses conventional wisdom. For example, conventional wisdom says that a strong company has a high return on assets, exceptional revenue growth, a low debt ratio, a healthy ratio of net operating assets to total assets, a high beta, a high dividend yield, and a low price-to-book ratio. But a low return on assets is a strong predictor of future earnings growth, low but sustainable revenue growth is less likely to lead to investor disappointment, a high debt ratio enables a company to more efficiently use its capital resources, a low ratio of net operating assets to total assets signifies low accruals and a high proportion of cash on hand, low-beta stocks are more likely to have high alpha, a stock with a low dividend yield is less likely to have an unsustainable payout ratio, and stocks with very low or negative book values have an edge over those with high book values because equity financing is so much more expensive than debt financing.

An investor’s edge may lie in her ability to find advantageous factors like these and to leverage them efficiently.

Tenet 5: Low-volume stocks present the most opportunities.

The more people investing in a stock, the more complex the system of factors that sets its price; the fewer people investing in it, the more likely one can find some reason and rhyme to the stock’s price, and the easier it is to estimate the odds of its success or failure.

I use the word easier in a purely relative way: estimating the odds on a stock, no matter its size, is almost infinitely complex. But low-volume stocks, while expensive and difficult to buy and sell, are less complicated to evaluate. Jim O’Shaughnessy wrote a terrific article on this, which I recommend.

Tenet 6: In the stock market, risk and reward are related but not correlated.

Whether risk is measured as price variability, the likelihood of bankruptcy, or the likelihood of a steep loss in value, the relationship of risk and reward follows a curve that looks a bit like this.
In other words, the highest reward is achieved by taking some risk, but not too much, and the worst losses result from taking too much risk.

How does this relate to investor expectations, probabilities, and factors? Well, according to the conventional idea that the higher the risk, the greater the reward, a factor that lowers risk shouldn’t work. However many of the best factors are precisely those that lower risk. For example, investing in stocks with low share turnover lowers risk while increasing returns precisely because it goes contrary to investor expectations about the market as a whole. Looking at a company’s quality by measuring its accrual ratios, the stability of its cash conversion cycle, the stability of its quarterly sales figures, and so on are wise things to do not only because one lowers risk but also because most investors don’t bother to look at these important indicators of a company’s potential.

Tenet 7: Consider as many factors as possible (within reason) when examining a stock.

This is advantageous for a number of reasons:

• you’re lowering your risk by “checking under the hood,” looking at everything that could go wrong;
• you’re maximizing the chance of using both types of factors: those that drive investor interest and those that confound expectations;
• while you may be introducing type 1 errors (relying on a factor that doesn’t really work), you’ll be avoiding type 2 errors (ignoring a factor that does work), which tend to have greater consequences;
• you’re mirroring, to some degree, the complexity of how stock prices are actually set.

Tenet 8: Mechanical judgments are more likely to succeed than discretionary ones.

In order to consider all these factors, the investor can either use her own discretion or can employ computer-based tools. Discretionary judgments are more fallible than those made by an objective calculation, and are more likely to conform to the judgments of the majority of investors, thus denying the investor an edge. For example, in evaluating the management of a company, the investor would be better off relying on a deep, intelligent, careful, and original analysis of the company’s earnings statements and analyst estimates than on employee assessments or Internet scuttlebutt, since the latter are more likely to be already reflected in the stock’s price.

Tenet 9: It’s better to rank than to screen.

When employing computer-based tools to pick stocks to invest in, ranking systems offer more flexibility than screening systems. A screening system excludes a wide range of stocks that fail on a single measure, while a ranking system keeps more possibilities in play.

Tenet 10: Factors are best chosen by backtests.

Backtesting is a useful tool to test a stock-picking strategy, but it must be robust. A backtested strategy that is too closely aligned with historical data may have little predictive power. Moreover, every factor used in a backtest must have a logical explanation. Backtesting can too easily become data-mining, which is useless for out-of-sample success. But simply using a factor without backtesting it can lead to unintended results, and backtesting is an invaluable tool for looking at how a factor has worked in the past, and for refining factors to best reflect the disparities between investor confidence levels and likely future company performance. And finding those disparities is the key to successful stock picking.

CAGR since 1/1/2016: 41%.

My top ten holdings right now: ZIXI, ARC, GSB, CTEK, KTCC, PERI, HALL, OSIR, CRNT, NTWK.

The Stock Picker's Dilemma

Not many of us have an overarching theory that guides us in our approach to picking winning stocks. But I think one could classify most stock pickers into one of three types. In this article, I’m going to present these types by creating a conversation between three imaginary investors whose last names are Buzz, Carr, and Chance.

(I’m assuming from the start that you believe that stock-picking can be profitable. If you’d rather invest in index funds, you can probably stop reading now.)

Buzz: Buying a stock is like buying a business. Well, it’s not just like buying a business, it is buying a business—a part of a business, to be sure, but still a business. Now what do we do when we buy a business? We look carefully at the books and estimate the present value of the sum of all the future income and the terminal value of the business if we were to sell it down the road. It’s not a simple process, but it’s an essential one. It’s really the only way to invest wisely.

Carr: I find that a rather idealistic way of looking at stocks. I mean, “terminal value”? What’s the “terminal value” of a company? It’s a pretty random guess. So is, for that matter, the company’s earnings five years from now. No, buying a stock is more like buying a used car. You don’t calculate the earnings or the terminal value. You look at what similar cars cost and measure their advantages and disadvantages. You look under the hood to make sure all the parts still work and are in good shape. And then you bargain with the salesperson. There are other considerations too. Is this going to be your only vehicle (i.e. are you putting 100% of your savings into this stock)? Then you need to be able to use it to go to work and go to the store (in other words, it should be an all-weather kind of stock, not a speculative one). But if you already have a dozen cars and are just going to keep it in your hangar and drive it to occasional car shows, you can make a much more speculative bargain.

Chance: That’s a very wishy-washy way of looking at investing, in my opinion. Investing is like gambling: you calculate the expected return and then place your bets accordingly. What is the expected return? It’s the probability-weighted average of all possibilities. Look at it like buying lottery tickets. If there’s a million-dollar payout and there are only 900,000 tickets for a dollar each, your expected return on each ticket is $0.11, and that stays constant no matter how many tickets you buy. You can do similar calculations with stocks. By looking at historical returns of similar stocks, you can calculate the expected return on your investment. In other words, you do the math.

Buzz: But how do you define a “similar stock”? Each stock has hundreds of different characteristics. You can get into “risk premia” and “smart beta” and all that junk, but where does that get you? All the math in the world won’t allow you to estimate a stock’s “expected returns” with any degree of certainty. Let’s check these analogies out for a moment. Let’s say you had a million dollars and you could invest it in stocks, used cars, or lottery tickets. How much would you put into each one? Lottery tickets don’t pay you any dividends, and the terminal value of a lottery ticket is almost always nil. And used cars can only increase in value if their price goes up because they’re collectible. Stocks, on the other hand, are pieces of businesses that actually make money. Not only do they have a present and a future value, but they generate cash. They’re money-making machines. You have to look at stocks as businesses first and foremost.

Carr: Some stocks are actually money-losing machines. And not just some stocks: more than half the stocks on the market at any one time are going to go down in price, some of them catastrophically. The way to solve the million-dollar investment problem is to look carefully at the risk of each asset. A classic car is not going to suddenly plummet in value like an overpriced stock will. If you choose the right cars to buy, they are far safer bets than either stocks or lottery tickets.

Chance: There’s actually a good, mathematical way to calculate this. The historical returns on lottery tickets are terrible. The historical return on the stock market has been about 9.3% per year over the last twenty-five years, while the historical return on classic car investing has been about 6.8% per year over the same period. Depending on how you think the historical returns should be adjusted to come up with expected returns, you’ll either allocate your entire $1 million to stocks or put some in classic cars and some in stocks.

Buzz: Fine. But how do we go about choosing the best stocks to invest in? My discounted-cash-flow method does an excellent job. As long as you get your formulae right, you can depend on it to make you money. It can’t necessarily be fully automated, and you sometimes have to dig pretty deep into the financial statements. But logically, it can’t be beat.

Carr: But what about the massive drawdowns that come with value investing, Buzz? I mean, they’re truly massive. Pick the hundred cheapest stocks by any criteria or a lot of different criteria put together, invest in them, and you’ll get drawdowns of seventy percent at times. There are reasons why the stocks you buy are priced so low. Many of them are seriously defective. Take my advice: the real way to pick stocks is to choose the most reliable, safest bets. Check out all your stock purchases from every possible angle before you decide what to buy.

Chance: You’re not making mathematical sense, folks. Investing is gambling, and you have to maximize your expected returns if you want to make a profit. Look. I can design a system that has been robustly backtested using rolling returns that will get you a far higher yearly return than either of you will ever get. As long as you trust history and use criteria that make good, sound, financial sense, as long as you use robust backtesting methods to avoid too much curve-fitting, you can consistently beat the market through stock-picking by trusting the numbers.

I myself combine all three approaches. From Chance, I take the idea of backtesting historical returns to come up with an algorithm that selects stocks with similar characteristics to those that have performed well in the past. From Carr, I take the idea of evaluating all my stocks as carefully as possible and eliminating or diminishing my investment in the most risky of the lot. And from Buzz, I take the ratio of unlevered free cash flow to enterprise value as one of the mainstays of my investment system, and I only buy stocks that I judge to be selling below their real value.

Is there one single correct way to pick stocks? I don’t think so. But if you’re going to maximize your returns, you want to consider the underlying assumptions behind why you’re buying what you’re buying, and how those assumptions will play out if challenged by opposing assumptions. That’s what I’ve tried to do with this dialogue.

CAGR since 1/1/16: 41%.

My top ten holdings right now: ZIXI, KTCC, ORRF, PERI, ARC, CRNT, OSIR, PDEX, CHMG, HSII.

Is It Better to Rebalance Your Portfolio Periodically or Leave It Alone?

Whether you hold only stocks or a wide variety of assets, a question you’ll be forced to face sooner or later is whether you should rebalance to a specific preset weight periodically or just let some positions get bigger and others smaller. This article aims to help you make that choice wisely.

Part I: The Math

In 1996, A. J. Wise published an article in the British Actuarial Journal called “The Investment Return from a Portfolio with a Dynamic Rebalancing Policy.” It is far and away the most comprehensive and mathematically sound analysis ever written on the probabilities that periodic rebalancing will outperform leaving your portfolio alone (buy and hold), and by how much. Unfortunately, it wasn’t widely read. Twenty years later, Michael Edesess published an article in Advisor Perspectives called “The Academic Failure to Understand Rebalancing,” which provided a valuable overview of the academic literature on the subject and brought Wise’s article back to the forefront. Without a thorough knowledge of higher mathematics, Wise’s article is difficult to follow, but Edesess’s article is straightforward and compelling reading. I highly recommend the first to anyone who wants a thorough grounding in the mathematics behind rebalancing, and the second to anyone with an interest in the subject. The purpose of my article is to summarize their conclusions and make a few observations of my own.

First, here’s the basic math behind rebalancing and not rebalancing. Let’s express an asset’s return over a set period as its price at the end of the period (adjusted for dividends and splits) divided by its price at the beginning. (Usually we express returns by doing this division and then subtracting one; I want to skip that last part for the sake of this illustration.) Let’s say we have a finite number of these period returns for a finite number of assets. Then the total buy-and-hold return would be the average of the products of each asset’s returns. And the total rebalanced return would be the product of the average of each asset’s returns in each period.

To illustrate, let’s say we were holding four stocks equally with the following returns:

So the basic mathematical problem is: when is the product of averages greater than the average of products? This is a very thorny problem indeed, without any easy solution. But we can make some very basic conclusions.

First, however, I must introduce a very fundamental concept. The expected return of an asset or portfolio is the probability-weighted average of all possible outcomes. This is based on unannualized total returns. If you annualize the returns, you end up with very different—and very flawed—results. Averaging annualized returns makes no sense—you’re combining a geometric mean (annualization) with an arithmetic one. (In a cogent 2014 article, “Does Rebalancing Really Pay Off?,” Michael Edesess points out this and other fundamental flaws in William Bernstein’s 1996 article “The Rebalancing Bonus,” an article which has had a significant and unfortunate impact on financial advisors’ advice. Basically, advisors have been using Bernstein’s and others’ academic articles to advocate rebalancing portfolios of all types without regard to the serious flaws in those articles; some of these advisors have a vested interest in giving this advice, since rebalancing costs are not negligible, and brokers make significant profits by implementing the practice.)

Second, all these conclusions assume that there is an ideal world of uncorrelated assets with equal expected returns. I would argue that such conditions cannot actually exist. So take these conclusions with a grain of salt.

Without further ado, here are the mathematical conclusions:

1. The expected return of a continually rebalanced portfolio is equal to the weighted geometric mean of the expected returns of the individual assets, while the actual return of a buy-and-hold portfolio is by definition the weighted arithmetic mean of the expected returns. Since the arithmetic mean will always be greater than or equal to the geometric mean, the expected return of a buy-and-hold portfolio will always exceed or be equal to the expected return of a continually rebalanced portfolio, but the differences between them will not be large.
2. If the expected return of the various assets is more or less the same, the median result of a rebalanced portfolio will usually exceed the median result of a buy-and-hold portfolio.

Taking these two points together, the median return of a rebalanced portfolio with equal expected returns is higher but the expected return is lower. The reason for the difference is that in the relatively few cases that the buy-and-hold portfolio beats the rebalanced portfolio, it can crush it, thereby making its expected return over all cases somewhat higher.

3. If the expected return of the various assets is quite different, a buy-and-hold portfolio will usually beat a rebalanced portfolio no matter what measure you use.
4. For relatively short time periods and with similar expected returns, it is quite likely that a rebalanced portfolio will beat a buy-and-hold portfolio. With two assets, the probability is about two-thirds, and decreases as you add more assets, but remains above one-half. (Once again, in the cases that the buy-and-hold portfolio beats the rebalanced portfolio, it is likely to beat it by a large margin.)
5. Ex-post (after the fact), rebalancing always beats buy-and-hold if the total returns of the constituent assets are exactly the same. In other words, if you have five assets that all end up with a 25% total return over four years but have very different sequences of returns, it’s always going to be better to rebalance them than to simply buy and hold. Ex-ante (before the fact), however, buy-and-hold can beat rebalancing (sometimes) even if the expected returns are exactly the same.
6. As the time period stretches toward infinity, if the difference between the expected returns of the assets is small (less than half of their standard deviation), the likelihood that rebalancing will beat buy and hold approaches a certainty; and if the difference between the expected returns of the assets is larger than that, the likelihood that buy and hold will win approaches a certainty. In other words, if you’re going to hold two or more assets for a very, very long time and you have no idea which will perform better, it may be better to rebalance; if, however, you are reasonably certain that one has better or worse expected returns, it’s better to just buy them and not do anything further. (The first part of this point clearly contradicts point 1 above, and I do not know how A. J. Wise would resolve this contradiction.)

None of these conclusions, which are purely mathematical, take into account transaction costs, which do not pertain to a buy-and-hold portfolio, but may be significant in a rebalanced portfolio. None of them take into account risk either, which, if you consider variability a good measure, is significantly greater with a buy-and-hold portfolio. And none of them take into account correlation of returns: rebalancing provides a significant diversification benefit by putting more money into uncorrelated assets.

Part II: The Reality

So let’s look at some real-life examples. I have chosen, at random, fifty stocks and fifty ETFs, and have put into a database their monthly returns over the last sixteen years. (For convenience, I am only using stocks and ETFs that have survived over the entire sixteen-year period with beginning and ending prices greater than $1.00 per share.) In the case of the stocks, I am starting with the assumption that the expected returns of the various stocks are more or less equal (in my own opinion, this is nonsense, but many investors think that stock picking can be done by monkeys); in the case of the ETFs, which include some bond and leveraged and short ETFs along with normal equity ETFs, most people would admit that the expected returns were quite unequal.

I am going to choose random portfolios of five stocks and five ETFs (four equity and one bond-based) and measure their performances over four four-year periods (2002 to 2006, 2006 to 2010, 2010 to 2014, 2014 to 2018), both with monthly rebalancing to equal weight and without. I will repeat this experiment two hundred times so that we have eight hundred pieces of data for each asset class. I think this should be sufficient for a general illustration of the advantages and disadvantages of both approaches.

Here are the results:

For the stocks, there’s a 52% chance that rebalancing will improve returns. The average rebalanced return is 4% better (unannualized, over a four-year period) than the average buy-and-hold return, and the median rebalanced return is 6% better. Rebalancing definitely seems to improve returns, as long as you can keep its cost under 1% per year. This differs from the results you would get by using a purely mathematical approach, and I believe that’s because rebalancing provides an additional benefit that the purely mathematical approach doesn’t take into account: when you rebalance, you automatically increase your allocation to the less correlated assets.

The portfolio of five ETFs is chosen as follows: four of the ETFs are chosen randomly from a set of forty stock ETFs, and one is chosen randomly from a set of ten bond ETFs. Because bonds have generally underperformed stocks throughout history, the bond ETFs have a lower expected return than the equity ETFs, and the results reflect that difference. With this portfolio, there’s only a 50% chance that rebalancing will improve returns. The average rebalanced portfolio has a lower return by 1.7% than the average buy-and-hold portfolio, and the median is 0.7% lower. Of course, if you add rebalancing costs, the results will favor the buy-and-hold approach even more strongly. The math shows, and the simulation confirms, that with different expected returns, it’s better not to rebalance if you want maximal returns.

Part III: Conclusions

Most investment advisers tell their clients to rebalance regularly. Those who work for brokerages have a vested interest in doing so. I take a more complex approach, rebalancing according to a ranking system. But, as Wise puts it, “Which strategy should be preferred by any particular investor will depend upon the utility attached to the various potential outcomes. Some will prefer a better-than-even chance of small performance gains over a long period. Others may prefer the return profile of the passive strategy.”

My recommendation is as follows. If you have no idea which assets are going to outperform, and if you are not going to hold them for very long, rebalance. (That is my own situation.) If the standard deviation of your returns is of great concern to you (for example, if you use leverage or are making regular withdrawals), rebalance. If you intend to hold your assets for a very long time and you’re reasonably confident that their total returns will be very similar, rebalance.

But if you expect some of your assets to outperform or underperform others, or if rebalancing incurs substantial transaction costs, don’t bother rebalancing. By rebalancing, you are likely to lower your expected return.

CAGR since 1/1/16: 43%.

My top ten holdings right now: NTWK, PCOM, ZIXI, PERI, KTCC, LFVN, CHMG, PDEX, ORRF, DRAD.

The Strange Relationship of Risk and Reward

It is commonly believed that you cannot have more reward without taking on more risk. I take a different view. You certainly can have more reward by taking on less risk, simply by switching from highly risky investments to more dependable ones. By evaluating every investment from as many angles as possible, you both reduce your risk and increase your reward.

I. The difficulty of quantifying risk

There is no general agreement on how to quantify risk. The capital asset pricing model (CAPM) defines risk as beta, the slope of the linear regression between the price of an asset and its benchmark. Another commonly used measure is the variability of returns, which is the basis for the Sharpe ratio. The most straightforward measure, and the most intuitive one from the man-on-the-street standpoint, is the probability of a permanent financial loss. Downside variability is another measurement of risk, and this basically combines the last two measures.

I mean to show that no matter which of these four measures you use, taking on less risk in your investments can increase your reward.

II. Risk as beta

It has been well known since the 1970s that, in any given asset class, alpha, or reward, is actually inversely correlated to beta, and that low-beta strategies outperform high-beta strategies. I have shown here, mathematically, that this has to be so because of the way the two terms are defined. By decreasing your beta, or systematic risk, you’re likely to increase your reward.

III. Risk as variability

This definition is historically based on the idea that risk is a failure to meet expectations, and standard deviation is a mathematical shorthand for the probability of this failure.

If you switch from an all-cash portfolio, which has no variability whatsoever, to an all-equity portfolio, you will be increasing your risk and also increasing your reward. But if you switch from an all-cryptocurrency portfolio, which suffers from extreme variability, to an all-equity portfolio, it’s quite probable that you’ll also increase your reward. In fact, there are all sorts of wildly unsafe investments whose returns sport enormous standard deviations. If you’re invested in one of these, you can certainly increase your reward while diminishing your risk.

IV. Risk as the probability of permanent loss of capital

Let’s look only at the stock market for a moment. The riskiest stocks in terms of a permanent loss of capital are the stocks most likely to go bankrupt. Edward Altman quantified this risk back in 1967 using what he called the Z-Score, a combination of five factors: working capital to total assets, retained earnings to total assets, earnings before interest and tax to total assets, sales to total assets, and market value of equity to total liabilities. If you had invested in all the stocks in the Russell 3000 with Z-Scores below 1.8 (the threshold for significant bankruptcy risk; there are about 600 of these stocks), rebalancing every quarter since 1999, with no slippage, you would have seriously underperformed the market (I tested this using Portfolio123). If you had excluded these stocks, thus lowering your risk, your return would have gone up significantly.

The same lesson can be applied to other types of investments. As I’ve shown in another article, if you have a fixed amount of money and you’re withdrawing some of it every month, you’re much more likely to go broke if you keep it in cash than if you invest it in equities. Cash, in this case, is far riskier (by this definition—the probability of a permanent loss) than equities. It’s no coincidence that cash’s return is negative. By putting your money to work, you’re both decreasing risk and increasing returns.

V. Risk as downside variability

This is basically a combination of the last two forms of risk, and is often measured by drawdown. If you’re looking at stock returns, portfolios with large drawdowns are usually high-beta portfolios, while portfolios with small drawdowns tend to be low-beta portfolios, and tend to outperform. If you’re comparing different types of investments, many of the same examples that I gave above will apply here too.

VI. The Risk Fallacy

If you were to assume that increasing your risk would mean increasing your return, you would wind up with a logical contradiction, because if a higher return were assured, it wouldn’t be risky. Nobody, of course, actually assumes that—every investor knows that some risks are worth taking and others definitely are not. Yet the prevalent belief remains: increased risk is somehow the price you pay for higher earnings. If you think about it, that’s a logically impossible proposition.

VII. The Paradox of Risk-Adjusted Returns

If we assume, as most people do, that higher risk is justified by the possibility of higher returns, we then want to adjust those higher returns to take risk into account. But this leads us to the paradox of risk-adjusted returns, which I discussed at length in this article. I’ll quote from it here:

We've seen that financial risk can be defined in two very different ways. If we define it as the failure to meet expectations, the essential component of risk is unpredictability. Logically, then, no measure of risk will exhibit any persistence, since persistence is the opposite of unpredictability. Therefore, a measurement of ex-post risk will have no correlation with ex-ante risk. On the other hand, if we define risk as the permanent loss of capital, then there's no logical way to adjust returns for risk, since positive returns are the sole guarantee against the permanent loss of capital, and negative returns are the sole guarantee of the permanent loss of capital. The concept of risk-adjusted returns is a chimera.

There’s a pretty strong relationship between the risk fallacy and the paradox of risk-adjusted returns. If we reject the idea that there’s a positive correlation between risk and reward, then risk-adjusted returns make no sense at all.

VIII. Why take on risk?

One of the prime justifications for the supposed correlation between risk and reward is a simple question: why would people invest in risky assets if there were no corresponding reward? There is a purely psychological answer: because risk-taking has its own psychological rewards, entirely apart from economic ones. Why else would anyone play Russian roulette, or go base jumping or free solo climbing? The entire Red Bull aesthetic is built around the psychological rewards of risk-taking. So, one could argue, is cryptocurrency trading.

IX. Alternative Ideas of Risk

Rejecting the risk-reward correlation leaves us with several possibilities. First, that there is simply no financial relationship between risk and reward. Second, that there is an inverse relationship between risk and reward—in other words, that the riskier the investment, the less reward there will be. Third, that risk is absolutely unquantifiable, that no definition of risk can really make sense, and that therefore the entire topic should be discarded since you can’t compare an unquantifiable thing to a quantifiable thing (reward).

None of these alternatives are very satisfactory for the simple reason that if any of them were true, very few people would invest in stocks, or anything else risky, for that matter. And lots of people do invest in stocks, taking all sorts of risks, and make money doing so.

But there is a fourth alternative.

X. The Risk-Reward Curve

I want to propose that risk and reward enjoy a non-linear correlation with the following characteristics. With no risk at all, there is no reward. As risk increases, reward increases, to a certain point. After that point is reached, as risk increases further, reward decreases.

I’ll illustrate this with a scatter-plot chart. I have looked up the percentage deviation of weekly returns of all of the ETFs in Portfolio123's database five years ago, along with their annualized returns over the past five years (this includes ETFs that have since been removed from the marketplace, so it does not suffer from survivorship bias).

On the x-axis is the standard deviation of weekly returns in the year prior to the ETF selection (the year prior to October 13, 2013). On the y-axis are the subsequent five-year returns of the ETF, annualized. The blue dots represent the actual ETFs. The red line is the closest-fit fourth-order polynomial trendline for the blue dots, and the green line is the fifty-period moving average (i.e. the average annualized return of the previous fifty ETFs arranged in order of standard deviation). As you can see, the reward is pretty minimal for the risk-free ETFs, those with almost no standard deviation. But as the standard deviation climbs toward 1.4%, the reward gets pretty close to 10% per year. As the standard deviation continues to climb, however, the reward gets lower and lower. For the sake of space, I cut the chart off at a standard deviation of six, but if you were to continue it, the average “reward” of the last fifty ETFs—the riskiest of the lot, most of them leveraged, short, or derivative, with standard deviations between 6.2% and 21%—is negative 21.5% per annum, or a total loss of 70%.

This makes intuitive sense. Divide the investment world into asset classes, from cash to cryptocurrencies, and you’ll see that up to a certain point (say, an index fund, or well-chosen stocks), increased short-term risk generally results in increased rewards over the long run, while after that point (options, leveraged ETFs, penny stocks), the rewards tend to be evanescent.

XI. Implications

Financial textbooks all picture the risk-reward continuum as a straight upward line. If we think of it as a curve instead, with a shape quite like that of the red line in the above chart, what does that imply in terms of financial practice?

For one thing, risk-adjusted rewards become far more complicated. Two investments with the same Sharpe ratio may have the same risk-adjusted reward if the risk-reward ratio is a straight line; but if the ratio is a curve, then you have to make some pretty radical adjustments to that ratio. This is a good thing, since both a municipal bond ETF and a 3X daily leveraged ETF can have higher Sharpe ratios than an index fund, and arguably that shouldn’t be the case.

For another, the recognition that at a certain point lowering risk can increase returns should make a big difference in how we look at investing. It helps justify low-beta approaches, low-volatility approaches, and increased carefulness in how thoroughly we examine our investment opportunities. The idea that higher risk will lead to higher returns has been used to justify a lot of very risky investments without due consideration of their merits.

XII. How to reduce risk while increasing reward

Let’s take this out of the financial markets for a moment, and apply this question to other things in life. If you’re buying a used car, for instance, how do you reduce the risk of engine failure while increasing the chance that you’ll be driving that car for a good while? You look under the hood. If you’re planning a vacation, for instance, how do you reduce the risk of stinky motels, bad meals, and missed flights while increasing the chance that you’ll have a great time? You spend a lot of time researching your options and plan every day carefully. (There are other ways to have a great vacation, but they’re a lot riskier.) If you’re hiring a new employee, how do you reduce the risk of getting a malcontent, an embezzler, or a bum while increasing the chance of hiring a productive worker who’ll come up with fresh ideas to improve your business? You interview your prospects carefully and check their references. These are all extremely standard practices.

The same is true for investing. Research every stock you buy, every investment you make. Don’t follow the hype, don’t trust talking heads, don’t rely on hunches or instinct, don’t follow one or two simple rules/factors and ignore everything else about your investments. Remember that risk and reward are on a curve, and reach for the top of that curve. That’s the way to win the investment game.

CAGR since 1/1/16: 45%.

My top ten holdings right now: NTWK, PCOM, OSIR, PDEX, PERI, RLGT, LFVN, FGBI, ELMD, DAVE.

How Much of Your Portfolio Should You Keep in Cash?

At some point, I am going to retire, so I wanted to calculate how much of my portfolio I should put into cash in order to protect myself against sequence-of-returns risk. If you’re withdrawing monthly from a portfolio that’s partially invested in equities and a bear market comes along, you’ll run out of money a lot sooner than if you’re in a bull market, and it only makes sense that putting part of your portfolio in cash would provide some protection. So I looked at various scenarios over the last 47 years, and I’ve come to a rather surprising conclusion.

Let’s assume you have $1,000,000 and you withdraw $5,000 a month. If you keep it all in cash, you run out of money after 200 months, or less than 17 years.

Now let’s assume that you put a portion of that money in an index fund (for the sake of convenience I’ve used the Wilshire 5000 index in this article, with dividends reinvested; you can read about it here). How much of it would you need to put in equities in order to eliminate the chance that you’d run out of money in less than 30 years? I’m assuming you keep the percentage constant and rebalance every month. In other words, if you decide to put 40% in the index fund, you’d look at your total balance at the end of every month and make sure that exactly 40% was invested in the index fund.

Well, let’s take starting points on January of every year from 1971 to 2003, giving us 33 different trajectories (after 2003 doesn’t give us enough years to evaluate). If you put all your money in cash, your chance of running out of money is 100%. If you put 40% of your money in an index fund and 60% in cash, you’d still run out of money at some point in four out of those 33 possibilities, and moreover, 12 of them have a less-than-30-year track record, so it’s possible that you’d run out of money in some of those scenarios too. So 40% simply isn’t enough to put into equities to provide protection.

However, if you put 50% of your money in an index fund and kept 50% in cash, you wouldn’t run out of money, ever, no matter what year you started investing. And the same is true if you put 100% of your money in an index fund. Or if you put any amount in between. So if you assume that returns in the future will match to a greater or lesser degree returns over the past 47 years, at the 50/50 equity/cash level and at an initial withdrawal rate of 0.5% per month, there is no sequence of returns risk at all.

Now what if your withdrawal rate is higher, say $10,000 per month, or an initial withdrawal rate of 1% (12% annually)? In all cash, you run out of money in 100 months, or a little over eight years. That’s bad.

We can now add five more starting points, extending our list of beginning years to 38, including the possibly dire scenario of beginning in 2007 or 2008. With a 50/50 allocation to equities, you run out of money in 143 months, on average, or close to 12 years (the range of possibilities is 99 to 199 months). There’s a 1 out of 38 chance that your money will run out sooner than if you had kept your money in cash, but that’s only one month sooner.

With a 75/25 allocation to equities/cash, you run out of money in 189 months, on average, or close to 16 years (the range of possibilities is 96 to 385 months). Now the chance of running out of money sooner than if you were in 100% cash is 2 out of 38, but again, “sooner” means a difference of less than six months. Clearly, a 75/25 allocation to equities is better than a 50/50 allocation, no matter what your withdrawal rate is.

And what if you put the whole sum into equities? Well, in a number of cases - 15 out of 38 - you never run out of money. You can just keep withdrawing $10,000 per month until today, which means between 16 and 44 years (remember we’re comparing to an eight-year period for the all-cash scenario). In 2 out of the 38 cases (if you’d started in 2000 or 2001), you’d have run out of money sooner than you would if you had been in all cash, but again, “sooner” means less than a year sooner (the range of possibilities is 91 months to forever).

In other words, I failed to find any historical instances over the last 47 years in which holding some money in cash gives you a distinct survival advantage over putting all your money into equities. I admit that I didn’t consider the possibility of an absurdly high withdrawal rate, but if you’re going to run out of money in less than eight years, you probably have more pressing things to worry about than sequence-of-returns risk.

A lot of RIAs advise keeping some portion of your funds in cash. There are certainly very good reasons to do so. It’s convenient to have cash if you want to pounce on an undervalued asset, take fast advantage of an opportunity, use as a liquidity reserve in case you’re unable to sell your holdings, or simply pay your bills. But to keep cash on hand because of sequence-of-returns risk simply makes no sense.

Is sequence-of-returns risk a myth? Absolutely not. Starting returns make a huge difference to the longevity of your retirement account. But is the solution to this risk to hold a portion of your portfolio in cash? Absolutely not. Cash is a terrible hedge. It offers no long-term advantages whatsoever over equity holdings.

Of course, even if cash has had no advantage in the past 47 years, it’s possible that we’ll see a bear market that is far worse - deeper and longer lasting - than any since 1971. There are certainly countries where this has happened. But not in the US. Compared to a domestic equity index fund, cash is truly trash.

CAGR since 1/1/16: 47%.

My top ten holdings right now: NTWK, PCOM, OSIR, PDEX, PERI, RLGT, LFVN, ELMD, BDL, AVNW.

The Characteristics of Five-Year Tenbaggers

A “tenbagger” is a stock in which you make ten times your initial investment. As Peter Lynch wrote in One Up on Wall Street, “a tenbagger is the fiscal equivalent of two home runs and a double.” Of course, it could take a long time to make back ten times your investment—if you take a long view, the S&P 500 is a tenbagger. So I’m going to focus in this article on five-year tenbaggers: stocks whose five-year return (including dividends and splits) is over 900%. Today, for example, if you have been holding any of these stocks for five years, you’ve made ten times your money: Abiomed, Codexis, Educational Development, EnviroStar, GTT Communications, GW Pharmaceuticals, Heska, Intricon, MGP Ingredients, Neurocrine Biosciences, Natural Health Trends, Nvidia, Siebert Financial, TAL Education Group, Texas Pacific Land Trust, and World Wrestling Entertainment. OK, you’ve probably only heard of a few of these amazing stocks. But a lot of the most famous companies of the last two decades were five-year tenbaggers at one point, including Tesla, Netflix, Domino’s Pizza, Avis Budget Group, DSW, Pilgrim’s Pride, Tenneco, Dana, Starz, Keurig Dr Pepper, Baidu, Questcor Pharmaceuticals, NutriSystem, Publix Supermarkets, Monster Beverage, ArcelorMittal, Apple, NetEase, BlackBerry, Urban Outfitters, Bally Technologies, and Chico’s FAS.

I was curious about what qualities tenbaggers generally had back before their price rose ten times. So I set up a little experiment. Using Portfolio123, I identified companies whose price (adjusted for dividends and splits) was ten times what it was five years ago so long as that price five years ago was greater than fifty cents, and did so repeatedly, going back from now to the 1999–2004 period. I then fed the list I generated into a ranking system with over 120 different factors on each inception date (five years prior to the stock achieving the ten-times price). I could now see what factors these stocks had in common.

The first thing I noticed was how few of these stocks had positive earnings: only 15% of them. The second thing I noticed was how strong their downward momentum had been. These are stocks whose median rank out of all stocks in terms of one-year total return is only 30. One momentum measure I like to look at is how well a stock compares to its 52-week high one month ago. By that measure, the median rank of these stocks is only 25. These stocks are not only losing money, but their price is cratering.

Because of their nonexistent earnings, most measures of these companies’ potential are worthless. Return on equity, profit margin, and earnings yield are all negative. And these companies aren’t evincing much hope either. If you look at those stocks that had analyst coverage, their average projected profit margin for the next year (projected EPS divided by projected sales per share) was in the 23rd percentile.

Warren Buffett likes to look at a company’s growth in terms of book value. By that standard, these companies are doing quite badly: the median book value growth is in the 41st percentile. In other words, these stocks are not only losing money, they’re either increasing their debt, decreasing their assets, or both. That’s the worst growth metric for these companies, but there aren’t really any good ones.

In terms of quality, there’s not much to say about these companies that I haven’t already said, except for one measure: income stability. This measure looks at the variability of annual operating income, with lower numbers being better. On that measure, these companies are pretty miserable—their income, negative as it is, is significantly less stable than that of the average company.

If earnings, quality, and growth are somewhat hopeless for these stocks, they do measure highly in terms of size (the smaller, the better) and value. The median price of a tenbagger is in the 28th percentile, and its size, in terms of market cap, is in the 32nd (and that’s out of all stocks, including penny and OTC stocks, that are on Compustat’s radar). These stocks are good buys if you use almost any value-based ratio (except for P/E)—price to book, price to sales, price to working capital, EV to EBITDA, EV to gross profit, EV to long-term debt, EV to sales, and a handful of other measures. Sales is the best indicator of value here: the median price-to-sales ratio of a future tenbagger is in the 76th percentile of that company’s industry.

Tenbaggers do tend to be concentrated in certain sectors. Health care, consumer discretionary, and technology stocks make up the largest percentage of tenbaggers, while the number of telecom, utility, and staples tenbaggers is pretty negligible. But then again, there have been a lot more companies overall in those first three sectors than in the last three.

Unfortunately, I have not found anything actionable when it comes to these stocks. Let’s say you used an algorithmic approach. You limit your universe to stocks with no earnings. You use a multifactor ranking system to rank these stocks in terms of all these factors: low book value growth, high income variability, low price performance, high value ratios, etc. What are the five-year results of buying stocks like these? Absolutely dismal. If you invested in the top 100 stocks according to such a system and held them for five years, starting every month from January 1999 to September 2013 (five years ago), your median annualized return for each five-year holding period would be four percentage points lower than if you’d invested in an index fund, with far worse drawdowns. And that’s with the benefit of hindsight, since there’s no way you would have known eighteen years ago the typical characteristics of a tenbagger over the last eighteen years (which are quite different from the stocks that Peter Lynch was looking for back in 1989, when he wrote One Up on Wall Street, probably the first book to glamorize tenbaggers).

I’m not a discretionary stock-picker. I leave that to others. No doubt some folks are very skilled at it. I never hold a stock for five years. Heck, I rarely hold a stock for one year. I have only two things in common with a tenbagger hunter: a passion for cheap microcaps, and a burning desire to beat the market.

But there is something I can take away from this study. The stocks with the most potential are usually found among the stocks with the least potential. If you want a diamond, you have to sift through a lot of dirt.

CAGR since 1/1/16: 50%.

My top ten holdings right now: LFVN, AUDC, PDEX, OSIR, PCOM, PERI, RLGT, NAII, GVP, AVNW.

The Two Types of Investing or Trading Errors

I

If you read enough about algorithms and backtesting, you come across story after story of false positives, or type I errors. A backtest shows that such-and-such a factor or strategy will produce outsize returns, and then, when people actually invest real money in it, the returns are dismal. People have become so scared of curve-fitting that they radically simplify their system to avoid it, or they completely discount the value of backtesting, or they won’t rely on any backtests at all.

But what they seem to be rarely scared of is the absence of a factor. In fact, that absence can do just as much harm, or more. It’s the opposite problem, a type II error, a false negative. Missing something that actually works can be more harmful than using something that doesn’t.

Let’s say you’re a doctor diagnosing a complaining patient. A false positive is when you tell the patient that he has pneumonia, but there’s nothing really wrong with him that a few days in bed won’t cure. A false negative is when you tell the patient that there’s nothing really wrong with him that a few days in bed won’t cure, but he really has pneumonia. Both are pretty bad, but only one will have potentially fatal consequences.

It’s the same in trading and investing. If you rely on a factor that doesn’t actually work very well, you may not beat the market. But if you ignore a factor that can have serious consequences, you might end up losing your shirt.

II

Type I and type II errors are statistical terms. A type I error is the mistake of accepting a hypothesis when it’s not true—when the results the hypothesis explains can be attributed to chance or explained by something else. This is exemplified in the contemporary period by the idea that stocks with a low ratio of price to book value will outperform. Or the idea that because a factor worked in the past it will definitely work in the future.

A type II error occurs when the “null hypothesis” is false and we fail to recognize that because of a lack of a better hypothesis. In the world of factors and algorithmic trading systems, the “null hypothesis” is the random-walk theory—that true, long-lasting proficiency in trading or stock-picking is impossible, and that so-called “factors” don’t exist.

One of the clearest explanations of investing errors—"Pascal's Wager and Type I and Type II Errors"—was written by Nick Ryder of Kathmere Capital Management, who is a proponent of investing in indexes, and who thinks that type I errors are much worse than type II errors. If you don’t accept my explanation or analogies, I suggest you read his article.

But a far more academic and evidence-based approach was taken in a recent paper—"What is the Optimal Significance Level for Investment Strategies?"—by Marcos López de Prado and Michael J. Lewis, who reach the opposite conclusion. They point out that “a particularly low false positive rate (Type I error) can only be achieved at the expense of missing a large proportion of the investment opportunities (Type II error).” In other words, by rejecting a lot of factors or tactics because you can’t prove that they work, you end up diminishing your returns.

III

There is no way to completely avoid type I and type II errors. We don’t have the knowledge or foresight to include every factor that might possibly exist, nor can we know with any degree of certainty that a factor that has worked in the past will work in the future. Our work, as traders and investors, is always going to be error-filled.

The best way to avoid type I errors is to use logic, mathematics, common sense, and robust backtesting techniques. If a factor or tactic looks promising, question it from all angles before adopting it. Make sure it works not just in general, but for the particular assets that you’re interested in buying—and not only for the particular assets you’re interested in buying, but in general. Make sure there’s not a better way of calculating things—for example, using fully diluted shares rather than current shares outstanding when calculating market cap, or comparing the value to other companies in the same industry rather than to all stocks or to an ideal. Make sure that it makes logical sense—some “technical” factors turn out to have fatal flaws because they’re unexplainable.

The best way to avoid type II errors is to work very hard to evaluate stocks and/or investing/trading tactics on as many solid factors as possible. Only leave a factor or tactic out if you conclude that it’s redundant, flawed, or doesn’t apply to you. For example, asset turnover (sales to assets) can be a powerful factor, but if you are already using factors that reward high sales (e.g. price to sales), you may not need to include it. But there are other factors that can have serious negative consequences if you ignore them. Companies can thrive even if their sales are steadily diminishing or if their short-term debt is a lot larger than their gross profit, but the chances are low. You don’t have to treat everything as a ranking factor—simply setting some logical limits through screening rules might be good enough. But type II errors are the ones that can really get you.

IV

I’m going to perform an experiment to illustrate this. I have 120 different factors. Some seem to have worked in the past, some certainly didn’t, some have worked sometimes and not other times. Some I use in my own systems, others I wouldn’t dream of using, and a few don’t really make much sense. In other words, there are plenty of opportunities for type I errors here.

I’m going to backtest 75 different ranking systems based on those factors, using Portfolio123. The first five will have one factor, then I’ll add another factor to each system for another five with two factors, and so on until I get to fifteen factors. All the factors in these systems will be chosen completely randomly out of my set of 120 factors, so that the final fifteen-factor systems will be quite different from each other.

I’ll use as my universe stocks with a minimum market cap of $100 million, a minimum median (over the last three months) daily dollar volume of $100,000, and a minimum price of $1.00, and I’ll exclude REITs. The portfolio will consist of the forty stocks ranked highest on the equally weighted factors used, and will be rebalanced to equal weight monthly, with transaction costs of 0.25%. I’ll show the results for four different five-year periods as graphs with annualized returns.

If type I errors are worse than type II errors, you should see pretty much the same (or worse) results no matter how many factors are introduced, for the introduction of a new factor will present more or as many problems as leaving a factor out. If type II errors are worse than type I errors, the results should improve as we add more factors, even if a lot of them don’t actually work.

Below are the results of my experiment.

As you can see, in all four five-year time periods, fourteen- or fifteen-factor ranking systems tended to work better than one- or two-factor ranking systems. If you read the charts from left to right, you can see how type I errors are often introduced when we put new factors in (and that what might be a type I error in one period may not be in another). And if you read the charts from right to left, you can see how type II errors are introduced as we reduce factors. If this experiment has validity, type II errors—false negatives—are quite a bit more dangerous than type I errors.

Single-factor investing takes type II errors to an extreme. Traders who put all their money into stocks with low ratios of “the acquirer’s multiple,” enterprise value to EBITDA, for example, without looking at anything else about the company, may well lose their shirts because of type II errors. Ditto for those who invest using Joel Greenblatt’s “Magic Formula,” in which the only factors they consider are that multiple and return on capital; or those who look for stocks selling below their net current asset values without looking at other aspects of those stocks. Ditto for those who invest in single-factor ETFs.

I don’t know how to design an experiment that would generalize this from stock-picking factors to investment/trading decisions in general. But I am 100% sure that the same principle applies. It’s better to overthink things than to underthink them. When it comes to investing, simplicity is your enemy.

V

When investing or trading, it’s best to use as much information as possible, and to look at your options from every angle. If you were playing poker, you would want to consider not only what cards you held, but what cards other players might be holding; you’d want to consider their “tells”—their body language, the way they hold their cards, how confidently they’re betting, the likelihood they’re bluffing; you’d want to consider how much is in the pot and how much you have left to bet; you’d want to consider the probability of each card left in the deck helping or hurting your hand and those of your opponents; you’d want to consider how likely a strong bet is going to force them to fold and how likely a weak bet will leave them in the game; you’d want to consider the cost of seeing the next card after all bets are placed. Even if you’re completely wrong about some of these factors (a type I error), it’s better to consider them all than to ignore one or more of them (a type II error). Don’t be swayed by all the “curve-fitting” arguments out there, or the studies that purport to show that actively managed portfolios underperform indexes (they fail to take into account the multiple disadvantages those portfolios face). Instead, decrease your risk and increase your returns by examining every trading or investment decision you make from as many angles as possible.

CAGR since 1/1/16: 52%.

My top ten holdings right now: AUDC, OSIR, PERI, PCOM, FNJN, LFVN, INTT, NATR, GVP, GRVY.

Investing in Stinky Stocks

I use an evaluation system to rank stocks (I’ve written about it extensively here and here and here). But sometimes I get highly ranked stocks on my list that I really don’t want to buy. I won’t name any names here, but one company that was ranked number one or two on my list sells products that are complete crap, in my opinion, through agents whom they pay very little; in addition, their officers are, in my book at least, more or less crooks, with shady histories.

What I always like to do in these cases is to see if there are some factors that I’m overlooking, something in their financial statements that really damns this company. I like to learn from situations like this. But in this case, the financials looked superb, and the technicals were right too. So I just held my nose and bought a large number of shares, following my system. I actually put about 8.5% of my investments into this one company, or about 38% of my yearly salary.

That was in late May. Shares of the stock are now selling for more than double what I bought them for. I sold some of my shares at a profit of over 100% shortly before the earnings report, but the report was great, so I’m buying them back. This lousy, horrible, awful company has a way to go yet.

If I had exercised my discretion (i.e. trusted my gut) rather than blindly following my proven system, I wouldn’t have bought a single share in this company. That’s why it’s very important to be comfortable with your system. If it’s giving you a lot of stocks that you’re uncomfortable buying and it’s not making you rich, you need to do some more work on it. That’s a better approach than giving up on it and following your gut. Be discretionary about the process, not about the stocks that the process gives you.

But how do you trust the financial reports that unscrupulous companies issue? The key is to use a lot of metrics that ensure those reports are more or less honest—or at least of better quality than most companies. You don't just look at earnings: you look at sales and operating income and free cash flow and gross profit. You look at the stability of their operating margin, their accruals, their Altman Z-score, late reporting, quarterly sales stability, short interest, share turnover, and so on. If you evaluate companies carefully, it's like checking under the hood of a used car before you buy it.

When I set the amount I’m going to buy of a stock, I use an Excel spreadsheet that makes a few minor adjustments. Some of those adjustments depend on trading difficulties—if a stock has a big bid-ask spread or is very thinly traded, I’ll deduct a few points and buy fewer shares. But what I used to do is to award a company extra points or deduct points based on reviews on Glassdoor, which are written by companies' employees. It’s time-consuming to go through these, but Glassdoor does offer some interesting metrics, so long as enough people have written about the company (if it gets fewer than 25 reviews, it’s probably best not to look at them).

But I no longer consult Glassdoor. The reason for my investing success lies in my adherence to a carefully designed probability-based system which discovers things about companies that are not already reflected in their price. My edge lies in the numbers, not the looks. If I think a company’s products are lame or their management is crazy or they’re outdated or gimmicky, no doubt my opinion is shared by a large number of other investors, and that’s why the company’s price is low. The same is true if the common perception is that the management has no idea what they’re doing and it’s a terrible place to work.

If your system points to undervalued companies, it’s your job to ignore all the sentiment that justifies those prices, and to trust that you’ve found a diamond in the rough. Your biggest winners are always going to be the stocks that have been underestimated. Don’t underestimate them yourself. Instead, tweak your system so that you’re more comfortable buying them—perhaps in slightly smaller quantities.

Now there’s a behavioral issue involved as well. Take this scenario (which is mine):

You’ve lived all your life, over half a century, never getting paid more than $100K a year. You’ve saved diligently and you’ve invested wisely. You have $700K to invest in stocks. Your best model has you putting 6% to 8% into each position, and it’s a model that really works, that consistently beats the market big time in real time. So now you’re putting half a year’s salary into a hold-your-nose stock. You tell yourself it’s all about the process, and you’re doing fine.

And then someone asks you, “So, what companies are you investing in these days?”

You tell her.

“XXX is your #1 stock?” she says. “Are you kidding? Well, as long as it’s only a small position, I suppose it can’t hurt too bad.”

You tell her how much you own of this company.

“What?” she says. “You’ve put $45,000 into an unscrupulous company that rips off its franchises and sells snake oil? Are you nuts?”

“Well,” you say, “I also have a lot invested in YYY.”

“YYY bills their customers for thousands of dollars for a product that should cost $50 and then refuses to return their calls. And their CEO is a shady guy who once fired an employee because she was black. OK, that’s only two companies. What else do you own?”

You tell her. “There’s company ZZZ,” you explain, “which basically deals in stealth ads, the kind that get into your computer and pop up when you don’t want them to. And then there’s the mining company that mistreats its workers. And then, and then . . .”

I’m not about to stop putting huge sums of money into stinky stocks, but I have to have a very dark sense of humor about it.

CAGR since 1/1/16: 51%.

My top ten holdings right now: AUDC, PERI, OSIR, PCOM, FNJN, INTT, PMD, LFVN, GVP, GRVY.

How to Obtain Leverage Without Margin or Loans

Tamara buys a stock market index (VTI) and reinvests her dividends. She doesn’t use leverage. She began investing exactly ten years ago, and has made 178% on her investments, for an annualized return of 10.76%. Her initial $100,000 investment is now worth $278,000.

Jessika buys the same stock market index and reinvests her dividends. But she does use leverage, at 1.5X, with a 10% margin carry cost and a minimum maintenance margin of 35%. You’d think she’d make quite a bit more than Tamara, right? But no. Starting at the same point in time as Tamara, she gets a margin call after seven months. And even if she had avoided that margin call in 2009, her total return is still only 172%, for an annualized return of 10.56%. Tamara still wins, because leverage is not cheap in this world.

What if Jessika had used 2X leverage? Her equity would have fallen below zero in March 2009. The only way Jessika could have made more money than Tamara is if there had been no margin call and her margin carry cost had been below 10%. But there’s a psychological cost to consider as well: the standard deviation of her returns would have been almost double that of Tamara’s.

If you make the right deal, leveraging your returns can be quite profitable. Let’s say that Jessika had found a broker that didn’t make margin calls, gave her 1.75X leverage, and charged only 2% interest. At the end of ten years, she would have made 259%, for an annualized return of 13.64%. Her initial $100,000 would be worth $359,000.

But finding a broker like that would have been very hard, if not impossible.

Jessika could, of course, have taken out a personal or home equity loan. The problem there is that she would have had to pay a portion of the total (loan plus interest) every month, and if her home equity loan had been big enough, she would have lost her house after seven months. If she had obtained a ten-year loan for $50,000 at 6%, putting the entire amount into VTI and paying $555 a month for the privilege, she would end up with $276,268 at the end of ten years, which is still lower than Tamara’s total.

What if Jessika had simply bought a 2X leveraged ETF like SSO instead? Well, she would have received a return of 323%, or 15.52% annualized, and her $100,000 would be worth $423,000. But she would have lagged Tamara for the first five years after her buy and suffered a drawdown of 77%. Using leverage is highly risky, and leveraged ETFs are not recommended for long-term holding.

I’m going to suggest a very different approach for Jessika. I’m going to suggest that she use leverage by investing in companies that are using their leverage wisely. To get leverage safely, invest in companies that use leverage, but make sure their earnings are high enough to cover their debts.

First, we need to define leverage. For investors, leverage is straightforward: it’s the sum of the amount you have and the amount you borrowed divided by the amount you have. If you have $100,000 and you’re borrowing $50,000, your leverage is 1.5X. Similarly, for a public company, leverage is total assets divided by total equity. But this isn’t nearly as straightforward, because there are plenty of companies with zero or negative equity. How do you measure their leverage?

Let’s look at it mathematically. Leverage = assets/equity, so 1/leverage = equity/assets. Since equity = assets – liabilities, equity/assets = (assets – liabilities)/assets = 1 – liabilities/assets. So leverage = 1/(1 – liabilities/assets).

Now liabilities divided by assets is what’s commonly known as the debt ratio. And it’s clear from the above formula that the higher the debt ratio, the higher the leverage. If the debt ratio is 0.5, leverage is 2X. If the debt ratio is 0.8, leverage is 5X. If the debt ratio is 0.95, leverage is 20X. And if the debt ratio is greater than 1, then leverage is off the charts.

Given this, I’ve designed an index for Jessica: the Leverage 100. These are the hundred stocks on the market with the highest debt ratios (and therefore the highest amount of leverage), so long as their price is over $1.00 per share, market cap is over $100 million, EBITDA is greater than zero, and debt-to-EBITDA is less than ten. (Just so that nobody accuses me of cherry-picking, these are nice round numbers and well-established criteria. And yes, I also wanted all the limits to be made up of 1’s and 0’s. Just for fun.)

(In case you’re unfamiliar with these terms, EBITDA stands for earnings before interest, taxes, depreciation, and amortization. Debt-to-EBITDA is the ratio that banks and credit agencies look at when deciding if a company is borrowing too much. Companies with debt-to-EBITDA ratios over five often get lower credit ratings. All of the companies I’ve looked at whose bonds have CCC ratings right now have debt-to-EBITDA ratios of five or higher.)

With quarterly equal-weight reconstitution and 0.25% slippage costs, the ten-year returns of the Leverage 100 are impressive: 384%, or 17.09% annualized. Jessika would have made more money investing in this index than with any of her other options: her $100,000 would have grown to $484,000, leaving Tamara in the dust.

Do you want more than ten-year returns? Well, I can only backtest back to 1999, but the Leverage 100 has annualized returns of 14.03% since then, compared to VTI’s 7.04% (or the equal-weight S&P 500’s 9.02%). And if we reduce the number of stocks in the Debt 100 to the Debt 50 or the Debt 20 or the Debt 10, choosing the stocks with the very highest debt ratios, the ten-year returns go up: to 20.90%, 26.29%, and 30.45% annualized, respectively. (If you’d like to play around with this and you subscribe to Portfolio123, here’s the screen and here’s the simulation.)

What were these miracle stocks Jessika would have invested in? Seven stocks have been in the index for ten years running: Cincinnati Bell (CBB), Choice Hotels (CHH), Dennys (DENN), Dun & Bradstreet (DNB), Domino’s Pizza (DPZ), National CineMedia (NCMI), and Sally Beauty (SBH); AutoZone (AZO), Unisys (UIS), and Vector Group (VGR) have been in it almost as long. The current top ten are Domino’s (DPZ), Yum Brands (YUM), Wingstop (WING), Aspen Technology (AZPN), Nathan’s Famous (NATH), MSG Networks (MSGN), Weight Watchers (WTW), Mechel (MTL), Northern Oil and Gas (NOG), and Verisign (VRSN).

These high-debt-ratio companies are getting tremendous leverage. At the moment, every single stock in the Leverage 100 has a debt ratio greater than one, which means a practically infinite amount of leverage. Back in 2008, when Jessika was first investing, the Leverage 100 included 46 stocks with debt ratios less than one, so that you could quantify their leverage, which ranged from 16X to 2300X. But now, negative equity companies rule.

I should say a word or two about the negative equity phenomenon, which Travis Fairchild at O’Shaughnessy Asset Management has written about at length here. (I’ve also written about it at length here; this article explains why you should favor companies with high debt over companies with high equity.) Fairchild points out that negative equity companies have outperformed the market in 57% of rolling three-year periods over the last twenty-five years (unlike me, he includes companies with extremely low or negative EBITDA, which worsens his results). He rightly points out that some of the reasons these companies have negative equity are that their balance sheets understate the value of their intangible assets, that their long-term assets are depreciated too fast, and that their use of buybacks and dividends create a decrease in equity that can “accelerate distortions.” But what Fairchild doesn’t look at is these companies’ use of debt (and certain non-debt liabilities) as leverage to power their growth. In fact, the word “debt” appears nowhere in his paper.

Since negative equity companies have low total assets to begin with, it’s begging the question to use assets or equity in a measure of these companies’ debt. So let’s compare their debt load to their market cap instead. The median debt-to-market-cap ratio of the 126 negative-equity companies that currently have $100 million market caps and debt-to-EBITDA ratios under ten is 0.70; the median debt-to-market-cap ratio of the S&P 500 is 0.24, and the median ratio of the Russell 3000 is 0.25. By absolutely any measure, negative equity companies are awash in debt. And that’s why they thrive—not because their assets are understated.

As long as the debt-to-EBITDA ratio of these companies is reasonable, banks and bondholders are not going to be knocking on their doors for repayment. These companies have interest expenses, of course, but those expenses are usually pretty modest. The median trailing twelve-month interest expense of the Leverage 100 right now, expressed as a percentage of each company’s total debt, is 5.37%, and though that number was somewhat higher ten years ago (7.34%), interest expenses for public companies are in general a lot lower than what your broker charges.

Now some would argue that the reason these companies are getting such high returns is that they’re undervalued. In other words, the returns aren’t driven by leverage, they’re driven by investor mispricing. But I’m afraid that argument doesn’t hold water. The median EV/EBITDA of the Leverage 100 is 10.43; the median of the S&P 500 is 10.65. The difference is negligible, as is the difference in their median P/E ratios. It would indeed be hard to argue that Domino’s, Wingstop, Aspen Technologies, Weight Watchers, or Verisign are value stocks: by any conventional measure, they’re certainly not. Rather, they are companies that have figured out how to use massive amounts of leverage to their advantage.

John Rekenthaler, the vice president of research at Morningstar, has written that “purchasing securities on margin, at retail interest rates . . . is wiser than renting furniture with monthly payments—but only barely.” Instead, he recommends “investing in securities [that] put more than 100% of their assets to work.” That’s indeed the best way to get leverage to work for you.

CAGR since 1/1/16: 52%.

My top ten holdings right now: AUDC, FNJN, PCOM, GRVY, INTT, IRMD, MSON, ZYXI, KEQU, PMD.

When Is Investing Like Gambling?

Last May, Kit Chellel wrote a very interesting article for Bloomberg News about Bill Benter, who won $900 million betting on horse races. The races he bet on were run on a parimutuel system, where odds are updated in proportion to how bettors bet, with the house simply skimming a commission off the top.

One passage in the article leaped out at me:

Buried in stacks of periodicals and manuscripts, [Benter] found what he was looking for—an academic paper titled “Searching for Positive Returns at the Track: A Multinomial Logit Model for Handicapping Horse Races.” Benter sat down to read it, and when he was done he read it again.

The paper argued that a horse’s success or failure was the result of factors that could be quantified probabilistically. Take variables—straight-line speed, size, winning record, the skill of the jockey—weight them, and presto! Out comes a prediction of the horse’s chances. More variables, better variables, and finer weightings improve the predictions.

It struck me that that’s exactly what I’m doing when I trade.

The stock market is a bit like a parimutuel system. In parimutuel betting, all bets are placed in a pool, taxes and the house take are skimmed off the top, and the pool is shared by the winning bettors.

Let me give an example. Let’s say five horses are racing, and right before the race is run, all bets have been placed. $100 has been placed on horse #1, $200 has been placed on horse #2, $300 on horse #3, and so on. Altogether, $1500 has been bet. Let’s say the taxes and the take amount to 10%, leaving $1350 in the pool. If horse #5 wins, then those who bet on that horse will take home $1350 divided by $500, or a payout ratio of 2.7 to 1. If horse #1 wins, on the other hand, those who bet on that horse will take home $1350 divided by $100, or 13.5 to 1.

How is this like the stock market? Because in both cases, prices are set purely by the bidders, the traders, the buyers and sellers. The key to winning in a parimutuel betting system—just like the key to winning in the stock market—is to wield an advantage over other bettors/investors through better information/data and/or a better strategy.

Just like Bill Benter did, a wise investor can take factors that can be quantified, weight them, and come up with a prediction of a stock’s chances. The more and better variables, the better the predictions.

This has been my practice: to use as many and as good variables as possible, to weight them well, and to look at every decision I make in probabilistic terms. I’m betting on twenty-seven stocks right now, stocks that I think will be winners not only because they’re primed to beat other stocks, but because I’m using formulae that few other investors use. I’m interested not only in the future performance of the companies I invest in but in the behaviors of other investors in those companies, just as Benter was interested not only in the performance of the horse he bet on, but in the betting behavior of his competitors.

The relationship between gambling and investing is made explicit in the abstract to the 1986 paper that Bill Benter read: “This paper investigates fundamental investment strategies to detect and exploit the public’s systematic errors in horse race wager markets” (emphases added).

At some point, gambling and investing can become interchangeable. Bill Benter was a gambler. But what about Edward O. Thorp, one of the greatest investors in history? Fundamentally, he was a gambler too.

Thorp started out playing blackjack. He proved, mathematically, that the odds could be in his favor if he counted cards, and in his 1966 book Beat the Dealer he was the first to show exactly how it could be done. When Thorp placed his bets at a blackjack table using his method, was he gambling or investing?

“The overlap of interest between gambling and the stock market is very high,” Thorp once said. “It’s an amazing phenomenon. But there are so many similarities and so much one can teach you about the other. Actually, gambling can teach you more about the stock market than the other way around. Gambling provides an analytically simpler world, and you can see principles and test theories.”

Thorp went on to derive the Black-and-Scholes options pricing model a few years before Black and Scholes (he decided to keep it secret in order to make money on it). Between 1969 and 1988 his Princeton Newton Partners firm made 19.1% annually, with a positive performance in 227 out of 230 months. Frederik Vanhaverbeke, in his book Excess Returns, points out that the probability of getting this kind of performance by pure chance is smaller than the probability that one would find a specific atom by looking in a random place on earth. Over twenty-nine years, Thorp’s compound annual return was almost 20%.

Now a lot of gambling has nothing to do with investing, and a lot of investing has nothing to do with gambling. Gambling based on odds set by a money maker rather than by other gamblers (as in most sports betting these days), gambling on slot machines, gambling on lottery tickets—these have little in common with investing. Dividend investing and fixed-income investing have little in common with gambling.

But I would argue that the point when successful gambling and successful investing become interchangeable comes when your aim is to beat the market, you take a purely systematic approach, you never let your emotions get in the way, and you let the data do the work.

If you take a rigorous probabilistic approach and put in lots of practice and hard work, it’s not that difficult to beat the house.

CAGR since 1/1/16: 52%.

Top ten holdings right now: LFVN, FNJN, IRMD, PCOM, AUDC, MGIC, PERI, MSON, ZYXI, MNDO.

A Systematic Evaluation of Ten Stocks

I use an automated evaluation system to choose what stocks to buy and sell. It has worked well for me, producing returns of 45% in 2016, 58% in 2017, and 28% so far this year (annualized, that’s 56%). My own system is designed for microcap investing, but I have produced a variation of the system for general use, the Stock Evaluator, which you can read about here and here and subscribe to here.

In this article I want to give ten practical examples of how the system works, using ten stocks, five of which I own and five of which I’d advise you to sell quickly if you own them. The five stocks I own, which the Stock Evaluator ranks 99 or 100, are:

• Audiocodes (AUDC), an Israeli tech company that specializes in VOIP (note: I began writing this article before AUDC’s fabulous earnings announcement on 7/24, and everything in this article reflects its previous numbers);
• Finjan Holdings (FNJN), which owns a lot of cybersecurity patents;
• LifeVantage (LFVN), which develops and markets “neutraceutical” dietary supplements and skin-care products;
• Points International (PCOM), a Canadian company that manages loyalty programs; and
• PFSWeb (PFSW), an IT consulting firm.

The five stocks whose price I think will tank, which the Stock Evaluator ranks 0, are:

• Aurora Cannabis (ACBFF), a Canadian producer and distributor of medical marijuana;
• Akoustis Technologies (AKTS), which manufactures radio frequency filters for mobile phones;
• Carvana (CVNA), a used-car online marketplace;
• GDS Holdings (GDS), a Chinese data-center manufacturer; and
• Vivint Solar (VSLR), a solar energy provider.

Let me say at the outset that I don’t really care about the quality of these companies’ products. I personally think LifeVantage’s products are garbage, but the stock has doubled in price since I bought it and I think it’s going to go up some more; and I’m a strong supporter of medical marijuana and solar energy, but I think Aurora Cannabis and Vivint Solar are overpriced companies with bad prognoses. Other authors have written about these companies in depth, and look at many more aspects of their businesses than I do. I’m only crunching numbers here. I don’t go into as much depth into these companies’ merits and faults as other Seeking Alpha contributors normally do. But my practice of trusting in numbers gleaned from earnings reports and other sources, and made available to me through Portfolio123, has served me well.

For the sake of simplicity, I’m going to break down the main factors I use into four categories: growth, quality, sentiment/technical, and value. Let’s tackle growth first, since it comes first alphabetically. Growth factors look at the change in a company’s earnings and sales over time.

In the first column is each stock’s estimated EPS growth, which I calculate by taking the current quarter’s estimated EPS, subtracting the reported EPS for the same quarter last year, and dividing by the absolute value of the latter. There’s a pretty big divide between the good stocks and the bad stocks here, with the exceptions of GDS, which is showing healthy growth, and LFVN, for which no EPS estimate is available. In the second column is actual income growth, which I calculate by taking the most recent quarter’s net income, subtracting that of the same quarter last year, and dividing by the absolute value of the latter (I adjust the income figures by subtracting a fraction of the “special items” reported). Once again, you can see a major difference between the bad stocks and the good ones. In the third column is a figure representing change in operating margin. This is the median difference between each of the last twelve quarters and the same quarter the previous year. The best option would be a number in the range of 0% to 3%. As you can see, ACBFF, AKTS, VSLR, and FNJN give me alarmingly high and low numbers here. In three of these companies, income growth is outpacing sales growth to an alarming degree, and in the case of AKTS, income is falling far faster than sales. In the fourth column is sales acceleration. This is a rather complicated factor. You first measure the sales growth by comparing this quarter to the same quarter last year. Then you measure it by comparing the last twelve months to the twelve months before that. Lastly, you take the difference between those two numbers and divide it by the second. All the good stocks have accelerating sales, while three of the bad stocks have decelerating sales. In the last column is the rank, by sector, from 0 to 100, of the sales growth over the last three years. What I’m looking for here is a number close to 70. Sales growth that is extremely high—like that of CVNA, GDS, VSLR, and FNJN—is likely going to result in some disappointment down the line, and poor sales growth like that of ACBFF, AKTS, AUDC, and LFVN is not very promising. The best stocks in this column are PFSW and PCOM.

Now let’s turn to quality. These are factors that have nothing to do with a stock’s price, trading volume, or change in earnings or sales.

In the first three columns are various accrual measures. I want these to be negative, with the lower the better, and indeed all the good stocks have negative accruals across the board. The first two columns measure the difference between operating cash flow and net income, divided by total assets; the third measures the difference between the last twelve months’ net operating assets and that of the previous twelve months, divided by average total assets. CVNA is too young a company for me to have much data, but its one-year accruals are terrible. The difference between the balance-sheet accruals for the bad and good stocks is particularly notable. Ideally, the change in the cash conversion cycle between one year and another shouldn’t be more than three months, and you can see that VSLR, AUDC, PCOM, and PFSW are within that range. The rest of the stocks are presenting somewhat worrisome numbers here. Free cash ROA is the most recent quarter’s free cash flow (net cash flow from operations plus net cash flow from investments) divided by total assets. The bad stocks all have negative numbers, the good stocks all positive. The reason for all the N/As in the gross margin column is that all these bad stocks are less than five years old. The number here is the company’s gross margin minus the industry average—a great measure of a company’s “moat.” I’m looking for positive numbers here, so the figures for PCOM and PFSW are less than ideal. Net operating assets to total assets is my number-one quality ratio (I’ve written about it here). I want the number here to be low—definitely under 0.5. Indeed it is for all the good stocks, and it’s too high for all the bad ones. Lastly, I’d rather invest in a company that’s reducing its share count after splits than one that’s increasing it. This measure is the current share count divided by the share count a year ago, adjusted for splits. The amount by which ACBFF, CVNA, and GDS have increased their share count is troubling.

Now we turn to technical and sentiment measures.

I would rather invest in a stock in an industry with some momentum, so the numbers in the first column for CVNA, GDS, FNJN, PCOM, and PFSW are encouraging, while those for ACBFF and VSLR are dismal. Because most of these are small and microcap stocks, price volatility, as measured by the standard deviation of the daily returns over the last three months, is pretty high. AUDC, though, is a nice exception. I wrote about share turnover here, and once again AUDC is posting some nice low numbers, while CVNA is damn scary. And the short interest in all of the bad stocks is way too high for my liking—though CVNA, with short interest at 55% of its shares outstanding, could be ripe for a short squeeze were its other numbers not so dismal.

Now we turn to value.

EVA is economic value added, a measure devised by Joel Stern in 1983 for maximizing value at firms for which he consulted. Basically, EVA is the company’s net operating profit after taxes minus the product of the weighted average cost of capital and the economic capital employed. I like to measure the EVA of companies I invest in and divide that by their market cap. Most of these companies have negative EVAs, but FNJN’s EVA is outstanding compared to the company’s price. Forward earnings yield and forward sales yield are basically the current year’s earnings and sales estimates divided by the market cap. You can see the numbers are far better for the good stocks than the bad stocks on the whole, with the exception of CVNA’s forward sales yield. The price to sales ratio (trailing twelve months) for the bad stocks is astonishingly high, with the exception of CVNA, while for the good stocks it’s less than 2. Gross profit to enterprise value is one of my mainstays, and you can see it’s far better for the good stocks than the bad. AUDC’s ratio of R&D to market cap is quite strong, while that of all the “bad stocks” except AKTS is pretty terrible. Price to tangible book value is a somewhat problematic ratio, but in the extremes it’s a good measure of overpriced and underpriced companies. It’s essential to measure this against other companies in the industry, and by this measure FNJN is particularly strong and AKTS and CVNA particularly weak. Unlevered free cash flow to enterprise value is the foundation of discounted cash flow analysis, and you can see quickly that all the bad firms fall down on this measure, while AUDC, FNJN, and PCOM are posting some very healthy ratios. I also look at dividend yield and payout ratios, but none of these ten stocks pays dividends (though AUDC announced one after this article was mostly written).

By weighting these various factors, along with others, and comparing the values to those of other companies (sometimes in the same sector or industry), I come up with a final score from 0 to 100. As you can see, even the best companies can post some bad numbers on some factors, and even the worst can post some good ones. What’s important is the aggregate score; the diversity of factors ensures that a diversity of companies will score well.

I’ve written before that buying a stock is like buying a used car (though perhaps not from Carvana), in that the most important thing to do is to look under the hood. That’s what the evaluation process can be compared with. Evaluating stocks using proven measures like the ones I’ve highlighted in this article should be an essential tool for all stock market traders and investors. These are, of course, not the only measures one should use, and savvy accountants and analysts may use entirely different ones. But no matter which measures you use, I think it wouldn’t be too difficult to come to an agreement that five of the stocks I’m highlighting in this article are a lot better buys than the other five.

CAGR since 1/1/16: 52%.

My top ten holdings right now: LFVN, FNJN, IRMD, PCOM, PERI, MGIC, NTWK, ZYXI, TRIB, MSON.

Ultimate Omega: The Best Risk-Adjusted Performance Measure?

In our anxiety to weigh the possibility of high returns against the risk of losing money—or the “risk” of high variability—we investors have, over the years, come up with over a dozen measures of “risk-adjusted returns.” The most commonly used are the Sharpe ratio and Jensen’s alpha, but I have found a number of others equally or more useful, including the information ratio, median excess returns, and the omega ratio. It is this last that I’d like to turn my attention to today.

Omega was conceived in 2002 by Con Keating and William F. Shadwick; you can find one of their original papers here. I’ll quote from it at length:

Omega . . . employs all the information contained within the return series. . . . It can be used to rank and evaluate portfolios unequivocally. All that is known about the risk and return of a portfolio is contained within this measure. . . . This function is, in a rigorous mathematical sense, equivalent to the returns distribution itself, rather than simply being an approximation to it. It therefore omits none of the information in the distribution and is as statistically significant as the returns series itself. As a result, Omega is ideally suited to the needs of financial performance measurement where what is of interest to the practitioner is the risk and reward characteristics of the return series. . . . In use, Omega will show markedly different rankings of funds, portfolios or assets from those derived using Sharpe ratios, Alphas or Value at Risk, precisely because of the additional information it employs.

Omega can be used to compare all sorts of returns, not just equity returns, but the returns have to have some variability. For a fund that simply returns a steady 0.1% per month, the omega function is useless.

There’s an omega ratio and an omega function. The ratio varies depending on your choice of a “hurdle rate,” or an expected rate of return. The omega function tracks the omega ratios for all possible hurdle rates.

The omega ratio is simple to calculate. You choose a hurdle rate of return. This could be zero, the risk-free rate, the median or mean return of a comparable benchmark, or simply a percentage return you’d really like to see. You then take the returns (monthly, weekly, or annual) of your portfolio, strategy, or fund and subtract that hurdle rate to get adjusted returns. Lastly, you sum up all the adjusted returns that are greater than zero, and divide by the absolute value of the sum of all the adjusted returns that are less than zero. (If the “hurdle rate” is zero, you get the gain-to-pain ratio, which was delineated by Jack Schwager in Appendix A of his 2012 book Hedge Fund Market Wizards.)

Through experimentation, I have found that setting the hurdle rate to the median return of whatever benchmark you’re using is a pretty good way to compare the future returns of a backtested strategy. I like this better than the simple gain-to-pain ratio. I also like to take the product of the ratio at three different hurdle rates: 0%, the median monthly return, and twice the median monthly return. A strategy whose omega ratio beats all others at all three of those points is a strategy that is highly likely to perform well going forward.

There is no one standard hurdle rate; the omega function is the continuous function of omega ratios as the hurdle rate increaces. Usually performance measures are associated with a single number, not a function or a series of numbers or a choice between various numbers depending on your expected rate of return. You can estimate the equation for the omega function, but an equation is necessarily more complicated than the single number that a Sharpe ratio or alpha consists of.

The omega function is basically a reconfigured histogram, but it’s far easier to read and process. You don’t have to worry about tails, skew, and kurtosis: all the information is right there in one simple curve. The Sharpe ratio and the information ratio are based on the assumption that returns are normally distributed; they can therefore fail when returns have asymmetric data. But omega takes all the moments of distribution into account.

There are many other things you can learn from the omega function. To illustrate, let’s compare the omega ratios of some mutual funds. I’ve chosen five at random here: XEXDX, Eaton Vance Tax-Advantage Bond; LAIEX, Lord Abbott International Opportunities Fund; HFQIX, Janus Henderson Global Equity Income Fund; HAIHX, Hartford Health Care HLS Fund; and MPGFX, Mairs and Power Growth Fund. Here is what their performance looked like over the last eight years if you’d invested $100 in each.

From this chart, it looks like HAIHX performed the best and XEXDX the worst, but it also looks like HAIHX is the riskiest in terms of variability of returns.

Now let’s look at their omega function:

As you can see, if the hurdle rate is 0%, the omega ratios (or gain-to-pain ratios) are 0.63, 1.70, 1.62, 2.01, and 2.22. This means, for instance, that the sum of the positive returns of HAIHX over the last three years is twice as large as the sum of the negative returns, while the sum of the negative returns of XEXDX is larger than the sum of the positive ones. As the hurdle rate increases, the omega ratios decrease, which is what you would intuitively expect. (Just a note: these are typical ratios for monthly returns; the ratios for yearly returns tend to be a lot higher and for weekly returns a lot lower.)

Now, the steeper an omega curve, the less “risky” it is, in the sense that it has fewer extreme gains and losses. This is because as you move the hurdle rate from one number to another, if the returns are mostly clustered around the median return, the drop-off is going to be pretty steep; if the returns are all over the place, moving the hurdle rate isn’t going to make such a big difference. So the mutual fund with the most extremes (the shallowest slope) is indeed HAIHX, and the one with the least is XEXDX. You can see this better if you look at the graph in logarithmic scale, where the curves become relatively straight lines.

There’s something else important on these graphs. Take a look at where each of the lines intersects y = 1 (on either graph). XEXDX does so at –0.42% (off the left side of the chart), LAIEX at 0.91%, HFQIX at 0.65%, HAIHX at 1.51%, and MPGFX at 1.15%. This is the average monthly return of each fund.

Now the omega function can be closely approximated by the exponential function y = b*e^mx, where b is the gain-to-pain ratio (the omega ratio at a hurdle rate of 0%) and m is the logarithmic slope of the curve (i.e. the linear slope if you use the logarithms of the omega ratios at each point). Here are the exponential functions approximated for the five mutual funds:

XEXDX: 0.63e^–111.3x

LAIEX: 1.70e^–56.5x

HFQIX: 1.62e^–74.9x

HAIHX: 2.01e^–48.0x

MPGFX: 2.22e^–69.3x

This gives us additional information: if we want our returns to have low variability, we can choose not only on the basis of the omega ratio at our given hurdle rate(s), but also of the logarithmic slope, with more extreme numbers being better. Especially if you’re hedging or using margin, variability can be very important.

So I suggest taking the product of the omega ratio at 0%, the omega ratio at the median benchmark return, the omega ratio at twice the median benchmark return, and the logarithmic slope (which you can calculate quickly from just those three ratios without having to extend the line). I call this number the “ultimate omega.”

You can see that the choice of mutual funds will be somewhat different if we take this approach. If we look at the omega ratio only at these three points, we’ll choose HAIHX; but if we also look at the logarithmic slope, using ultimate omega, MPGFX looks like a better bet.

If you’re using Excel, here’s how to calculate the ultimate omega given a sequence of returns, whether they be weekly, monthly, or yearly. Remember that this is a comparison tool, and that results will be very different if you’re using different time periods.

Let’s say your returns are in column A. In column B, subtract the median benchmark return from the column A returns. In column C, subtract the median benchmark return from the column B returns. Now in cell D1 type =SUMIF(A:A,">0")/-SUMIF(A:A,"<0"); in cell D2 type =SUMIF(B:B,">0")/-SUMIF(B:B,"<0"); and in cell D3 type =SUMIF(C:C,">0")/-SUMIF(C:C,"<0"). In cell E1, type 0; in cell E2, put in the median benchmark return; and in cell E3, put in twice the median benchmark return. Now in cell F1, type =PRODUCT(D1:D3,-SLOPE(LN(D:D),E:E)). That will be the ultimate omega.

I often perform what I call “correlation studies,” in which I backtest a number of different strategies using multiple in-sample and out-of-sample time periods, and then correlate the various performance measures during the in-sample periods with the actual returns of the out-of-sample periods. I recently performed such a study that I think may be the best one I’ve done. I took, at random, fifty different ranking systems from the over 7,000 public ranking systems that Portfolio123 users have created, and combined each with a different stock universe (whose rules screen out certain stocks, usually low-liquidity ones along with others based on various criteria). I then ran simulations of each one, holding the top fifty-ranked stocks, with a monthly rebalance and 0.25% slippage, from 1/1/1999 to today. I then compared the total returns of each strategy over six different “out-of-sample” five-year periods with the risk-adjusted returns of the same strategy over adjoining eight-year periods, as shown in the chart below.

I found that the risk-adjusted measures that correlated the most strongly with the out-of-sample total returns were, hands-down, the various omega ratios. I’ve put the results below, bolding the highest correlations for each period. (I used monthly returns, measured daily, for all the measures. “Omega 1” is the ratio after subtracting the median benchmark return, “omega 3” is the product of the first three ratios, “omega 1s” multiplies omega 1 by the logarithmic slope, and “omega 3s” is ultimate omega.)

Based on these results, I think that in the future, “ultimate omega” will be the measure I will turn to most frequently when deciding upon the optimal investment strategy. After all, it contains more information about in-sample returns than any other performance measure, so no wonder that it correlates so well with out-of-sample returns.

CAGR since 1/1/2016: 53%

Top ten holdings right now: FNJN, LFVN, PCOM, PERI, NTWK, TRIB, ZYXI, MCHX, MNDO, GSB.

In our anxiety to weigh the possibility of high returns against the risk of losing money—or the “risk” of high variability—we investors have, over the years, come up with over a dozen measures of “risk-adjusted returns.” The most commonly used are the Sharpe ratio and Jensen’s alpha, but I have found a number of others equally or more useful, including the information ratio, median excess returns, and the omega ratio. It is this last that I’d like to turn my attention to today.

Omega was conceived in 2002 by Con Keating and William F. Shadwick; you can find one of their original papers http://www.all-in-or-out.com/An%20Introduction%20to%20Omega.pdf here. I’ll quote from it at length:

[quote] Omega . . . employs all the information contained within the return series. . . . It can be used to rank and evaluate portfolios unequivocally. All that is known about the risk and return of a portfolio is contained within this measure. . . . This function is, in a rigorous mathematical sense, equivalent to the returns distribution itself, rather than simply being an approximation to it. It therefore omits none of the information in the distribution and is as statistically significant as the returns series itself. As a result, Omega is ideally suited to the needs of financial performance measurement where what is of interest to the practitioner is the risk and reward characteristics of the return series. . . . In use, Omega will show markedly different rankings of funds, portfolios or assets from those derived using Sharpe ratios, Alphas or Value at Risk, precisely because of the additional information it employs.

Omega can be used to compare all sorts of returns, not just equity returns, but the returns have to have some variability. For a fund that simply returns a steady 0.1% per month, the omega function is useless.

There’s an omega ratio and an omega function. The ratio varies depending on your choice of a “hurdle rate,” or an expected rate of return. The omega function tracks the omega ratios for all possible hurdle rates.

The omega ratio is simple to calculate. You choose a hurdle rate of return. This could be zero, the risk-free rate, the median or mean return of a comparable benchmark, or simply a percentage return you’d really like to see. You then take the returns (monthly, weekly, or annual) of your portfolio, strategy, or fund and subtract that hurdle rate to get adjusted returns. Lastly, you sum up all the adjusted returns that are greater than zero, and divide by the absolute value of the sum of all the adjusted returns that are less than zero. (If the “hurdle rate” is zero, you get the gain-to-pain ratio, which was delineated by Jack Schwager in Appendix A of his 2012 book Hedge Fund Market Wizards.)

Through experimentation, I have found that setting the hurdle rate to the median return of whatever benchmark you’re using is a pretty good way to compare the future returns of a backtested strategy. I like this better than the simple gain-to-pain ratio. I also like to take the product of the ratio at three different hurdle rates: 0%, the median monthly return, and twice the median monthly return. A strategy whose omega ratio beats all others at all three of those points is a strategy that is highly likely to perform well going forward.

There is no one standard hurdle rate; the omega function is the continuous function of omega ratios as the hurdle rate increaces. Usually performance measures are associated with a single number, not a function or a series of numbers or a choice between various numbers depending on your expected rate of return. You can estimate the equation for the omega function, but an equation is necessarily more complicated than the single number that a Sharpe ratio or alpha consists of.

The omega function is basically a reconfigured histogram, but it’s far easier to read and process. You don’t have to worry about tails, skew, and kurtosis: all the information is right there in one simple curve. The Sharpe ratio and the information ratio are based on the assumption that returns are normally distributed; they can therefore fail when returns have asymmetric data. But omega takes all the moments of distribution into account.

There are many other things you can learn from the omega function. To illustrate, let’s compare the omega ratios of some mutual funds. I’ve chosen five at random here: XEXDX, Eaton Vance Tax-Advantage Bond; LAIEX, Lord Abbott International Opportunities Fund; HFQIX, Janus Henderson Global Equity Income Fund; HAIHX, Hartford Health Care HLS Fund; and MPGFX, Mairs and Power Growth Fund. Here is what their performance looked like over the last three years if you’d invested $100 in each. (I’m doing this for the simplicity of illustration alone; if I were actually thinking of investing in these funds I’d look at a lot more than three years of returns.)

[5 mutual fund returns]

From this chart, it looks like HAIHX performed the best and XEXDX the worst, but it also looks like HAIHX is the riskiest in terms of variability of returns.

Now let’s look at their omega function:

[omega function of 5 mutual funds]

As you can see, if the hurdle rate is 0%, the omega ratios (or gain-to-pain ratios) are 0.63, 1.70, 1.62, 2.01, and 2.22. This means, for instance, that the sum of the positive returns of HAIHX over the last three years is twice as large as the sum of the negative returns, while the sum of the negative returns of XEXDX is larger than the sum of the positive ones. As the hurdle rate increases, the omega ratios decrease, which is what you would intuitively expect. (Just a note: these are typical ratios for monthly returns; the ratios for yearly returns tend to be a lot higher and for weekly returns a lot lower.)

Now, the steeper an omega curve, the less “risky” it is, in the sense that it has fewer extreme gains and losses. This is because as you move the hurdle rate from one number to another, if the returns are mostly clustered around the median return, the drop-off is going to be pretty steep; if the returns are all over the place, moving the hurdle rate isn’t going to make such a big difference. So the mutual fund with the most extremes (the shallowest slope) is indeed HAIHX, and the one with the least is XEXDX. You can see this better if you look at the graph in logarithmic scale, where the curves become relatively straight lines.

[omega function of 5 mutual funds log scale]

There’s something else important on these graphs. Take a look at where each of the lines intersects y = 1 (on either graph). XEXDX does so at –0.42% (off the left side of the chart), LAIEX at 0.91%, HFQIX at 0.65%, HAIHX at 1.51%, and MPGFX at 1.15%. This is the average monthly return of each fund.

Now the omega function can be closely approximated by the exponential function y = b*e^mx, where b is the gain-to-pain ratio (the omega ratio at a hurdle rate of 0%) and m is the logarithmic slope of the curve (i.e. the linear slope if you use the logarithms of the omega ratios at each point). Here are the exponential functions approximated for the five mutual funds:

XEXDX: 0.63e^–111.3x

LAIEX: 1.70e^–56.5x

HFQIX: 1.62e^–74.9x

HAIHX: 2.01e^–48.0x

MPGFX: 2.22e^–69.3x

This gives us additional information: if we want our returns to have low variability, we can choose not only on the basis of the omega ratio at our given hurdle rate(s), but also of the logarithmic slope, with more extreme numbers being better. Especially if you’re hedging or using margin, variability can be very important.

So I suggest taking the product of the omega ratio at 0%, the omega ratio at the median benchmark return, the omega ratio at twice the median benchmark return, and the logarithmic slope (which you can calculate quickly from just those three ratios without having to extend the line). I call this number the “ultimate omega.”

[omega scores 5 mutual funds]

You can see that the choice of mutual funds will be somewhat different if we take this approach. If we look at the omega ratio only at these three points, we’ll choose HAIHX; but if we also look at the logarithmic slope, using ultimate omega, MPGFX looks like a better bet.

If you’re using Excel, here’s how to calculate the ultimate omega given a sequence of returns, whether they be weekly, monthly, or yearly. Remember that this is a comparison tool, and that results will be very different if you’re using different time periods.

Let’s say your returns are in column A. In column B, subtract the median benchmark return from the column A returns. In column C, subtract the median benchmark return from the column B returns. Now in cell D1 type =SUMIF(A:A,">0")/-SUMIF(A:A,"<0"); in cell D2 type =SUMIF(B:B,">0")/-SUMIF(B:B,"<0"); and in cell D3 type =SUMIF(C:C,">0")/-SUMIF(C:C,"<0"). In cell E1, type 0; in cell E2, put in the median benchmark return; and in cell E3, put in twice the median benchmark return. Now in cell F1, type =PRODUCT(D1:D3,-SLOPE(LN(D:D),E:E)). That will be the ultimate omega.

I often perform what I call “correlation studies,” in which I backtest a number of different strategies using multiple in-sample and out-of-sample time periods, and then correlate the various performance measures during the in-sample periods with the actual returns of the out-of-sample periods. I recently performed such a study that I think may be the best one I’ve done. I took, at random, fifty different ranking systems from the over 7,000 public ranking systems that Portfolio123 [https://www.portfolio123.com/?sref=27297] users have created, and combined each with a different stock universe (whose rules screen out certain stocks, usually low-liquidity ones along with others based on various criteria). I then ran simulations of each one, holding the top fifty-ranked stocks, with a monthly rebalance and 0.25% slippage, from 1/1/1999 to today. I then compared the total returns of each strategy over six different “out-of-sample” five-year periods with the risk-adjusted returns of the same strategy over adjoining eight-year periods, as shown in the chart below.

[in sample out of sample]

I found that the risk-adjusted measures that correlated the most strongly with the out-of-sample total returns were, hands-down, the various omega ratios. I’ve put the results below, bolding the highest correlations for each period. (I used monthly returns, measured daily, for all the measures. “Omega 1” is the ratio after subtracting the median benchmark return, “omega 3” is the product of the first three ratios, “omega 1s” multiplies omega 1 by the logarithmic slope, and “omega 3s” is ultimate omega.)

[correlation study]

Based on these results, I think that in the future, “ultimate omega” will be the measure I will turn to most frequently when deciding upon the optimal investment strategy. After all, it contains more information about in-sample returns than any other performance measure, so no wonder that it correlates so well with out-of-sample returns.

In our anxiety to weigh the possibility of high returns against the risk of losing money—or the “risk” of high variability—we investors have, over the years, come up with over a dozen measures of “risk-adjusted returns.” The most commonly used are the Sharpe ratio and Jensen’s alpha, but I have found a number of others equally or more useful, including the information ratio, median excess returns, and the omega ratio. It is this last that I’d like to turn my attention to today.

Omega was conceived in 2002 by Con Keating and William F. Shadwick; you can find one of their original papers http://www.all-in-or-out.com/An%20Introduction%20to%20Omega.pdf here. I’ll quote from it at length:

[quote] Omega . . . employs all the information contained within the return series. . . . It can be used to rank and evaluate portfolios unequivocally. All that is known about the risk and return of a portfolio is contained within this measure. . . . This function is, in a rigorous mathematical sense, equivalent to the returns distribution itself, rather than simply being an approximation to it. It therefore omits none of the information in the distribution and is as statistically significant as the returns series itself. As a result, Omega is ideally suited to the needs of financial performance measurement where what is of interest to the practitioner is the risk and reward characteristics of the return series. . . . In use, Omega will show markedly different rankings of funds, portfolios or assets from those derived using Sharpe ratios, Alphas or Value at Risk, precisely because of the additional information it employs.

Omega can be used to compare all sorts of returns, not just equity returns, but the returns have to have some variability. For a fund that simply returns a steady 0.1% per month, the omega function is useless.

There’s an omega ratio and an omega function. The ratio varies depending on your choice of a “hurdle rate,” or an expected rate of return. The omega function tracks the omega ratios for all possible hurdle rates.

The omega ratio is simple to calculate. You choose a hurdle rate of return. This could be zero, the risk-free rate, the median or mean return of a comparable benchmark, or simply a percentage return you’d really like to see. You then take the returns (monthly, weekly, or annual) of your portfolio, strategy, or fund and subtract that hurdle rate to get adjusted returns. Lastly, you sum up all the adjusted returns that are greater than zero, and divide by the absolute value of the sum of all the adjusted returns that are less than zero. (If the “hurdle rate” is zero, you get the gain-to-pain ratio, which was delineated by Jack Schwager in Appendix A of his 2012 book Hedge Fund Market Wizards.)

Through experimentation, I have found that setting the hurdle rate to the median return of whatever benchmark you’re using is a pretty good way to compare the future returns of a backtested strategy. I like this better than the simple gain-to-pain ratio. I also like to take the product of the ratio at three different hurdle rates: 0%, the median monthly return, and twice the median monthly return. A strategy whose omega ratio beats all others at all three of those points is a strategy that is highly likely to perform well going forward.

There is no one standard hurdle rate; the omega function is the continuous function of omega ratios as the hurdle rate increaces. Usually performance measures are associated with a single number, not a function or a series of numbers or a choice between various numbers depending on your expected rate of return. You can estimate the equation for the omega function, but an equation is necessarily more complicated than the single number that a Sharpe ratio or alpha consists of.

The omega function is basically a reconfigured histogram, but it’s far easier to read and process. You don’t have to worry about tails, skew, and kurtosis: all the information is right there in one simple curve. The Sharpe ratio and the information ratio are based on the assumption that returns are normally distributed; they can therefore fail when returns have asymmetric data. But omega takes all the moments of distribution into account.

There are many other things you can learn from the omega function. To illustrate, let’s compare the omega ratios of some mutual funds. I’ve chosen five at random here: XEXDX, Eaton Vance Tax-Advantage Bond; LAIEX, Lord Abbott International Opportunities Fund; HFQIX, Janus Henderson Global Equity Income Fund; HAIHX, Hartford Health Care HLS Fund; and MPGFX, Mairs and Power Growth Fund. Here is what their performance looked like over the last three years if you’d invested $100 in each. (I’m doing this for the simplicity of illustration alone; if I were actually thinking of investing in these funds I’d look at a lot more than three years of returns.)

[5 mutual fund returns]

From this chart, it looks like HAIHX performed the best and XEXDX the worst, but it also looks like HAIHX is the riskiest in terms of variability of returns.

Now let’s look at their omega function:

[omega function of 5 mutual funds]

As you can see, if the hurdle rate is 0%, the omega ratios (or gain-to-pain ratios) are 0.63, 1.70, 1.62, 2.01, and 2.22. This means, for instance, that the sum of the positive returns of HAIHX over the last three years is twice as large as the sum of the negative returns, while the sum of the negative returns of XEXDX is larger than the sum of the positive ones. As the hurdle rate increases, the omega ratios decrease, which is what you would intuitively expect. (Just a note: these are typical ratios for monthly returns; the ratios for yearly returns tend to be a lot higher and for weekly returns a lot lower.)

Now, the steeper an omega curve, the less “risky” it is, in the sense that it has fewer extreme gains and losses. This is because as you move the hurdle rate from one number to another, if the returns are mostly clustered around the median return, the drop-off is going to be pretty steep; if the returns are all over the place, moving the hurdle rate isn’t going to make such a big difference. So the mutual fund with the most extremes (the shallowest slope) is indeed HAIHX, and the one with the least is XEXDX. You can see this better if you look at the graph in logarithmic scale, where the curves become relatively straight lines.

[omega function of 5 mutual funds log scale]

There’s something else important on these graphs. Take a look at where each of the lines intersects y = 1 (on either graph). XEXDX does so at –0.42% (off the left side of the chart), LAIEX at 0.91%, HFQIX at 0.65%, HAIHX at 1.51%, and MPGFX at 1.15%. This is the average monthly return of each fund.

Now the omega function can be closely approximated by the exponential function y = b*e^mx, where b is the gain-to-pain ratio (the omega ratio at a hurdle rate of 0%) and m is the logarithmic slope of the curve (i.e. the linear slope if you use the logarithms of the omega ratios at each point). Here are the exponential functions approximated for the five mutual funds:

XEXDX: 0.63e^–111.3x

LAIEX: 1.70e^–56.5x

HFQIX: 1.62e^–74.9x

HAIHX: 2.01e^–48.0x

MPGFX: 2.22e^–69.3x

This gives us additional information: if we want our returns to have low variability, we can choose not only on the basis of the omega ratio at our given hurdle rate(s), but also of the logarithmic slope, with more extreme numbers being better. Especially if you’re hedging or using margin, variability can be very important.

So I suggest taking the product of the omega ratio at 0%, the omega ratio at the median benchmark return, the omega ratio at twice the median benchmark return, and the logarithmic slope (which you can calculate quickly from just those three ratios without having to extend the line). I call this number the “ultimate omega.”

[omega scores 5 mutual funds]

You can see that the choice of mutual funds will be somewhat different if we take this approach. If we look at the omega ratio only at these three points, we’ll choose HAIHX; but if we also look at the logarithmic slope, using ultimate omega, MPGFX looks like a better bet.

If you’re using Excel, here’s how to calculate the ultimate omega given a sequence of returns, whether they be weekly, monthly, or yearly. Remember that this is a comparison tool, and that results will be very different if you’re using different time periods.

Let’s say your returns are in column A. In column B, subtract the median benchmark return from the column A returns. In column C, subtract the median benchmark return from the column B returns. Now in cell D1 type =SUMIF(A:A,">0")/-SUMIF(A:A,"<0"); in cell D2 type =SUMIF(B:B,">0")/-SUMIF(B:B,"<0"); and in cell D3 type =SUMIF(C:C,">0")/-SUMIF(C:C,"<0"). In cell E1, type 0; in cell E2, put in the median benchmark return; and in cell E3, put in twice the median benchmark return. Now in cell F1, type =PRODUCT(D1:D3,-SLOPE(LN(D:D),E:E)). That will be the ultimate omega.

I often perform what I call “correlation studies,” in which I backtest a number of different strategies using multiple in-sample and out-of-sample time periods, and then correlate the various performance measures during the in-sample periods with the actual returns of the out-of-sample periods. I recently performed such a study that I think may be the best one I’ve done. I took, at random, fifty different ranking systems from the over 7,000 public ranking systems that Portfolio123 [https://www.portfolio123.com/?sref=27297] users have created, and combined each with a different stock universe (whose rules screen out certain stocks, usually low-liquidity ones along with others based on various criteria). I then ran simulations of each one, holding the top fifty-ranked stocks, with a monthly rebalance and 0.25% slippage, from 1/1/1999 to today. I then compared the total returns of each strategy over six different “out-of-sample” five-year periods with the risk-adjusted returns of the same strategy over adjoining eight-year periods, as shown in the chart below.

[in sample out of sample]

I found that the risk-adjusted measures that correlated the most strongly with the out-of-sample total returns were, hands-down, the various omega ratios. I’ve put the results below, bolding the highest correlations for each period. (I used monthly returns, measured daily, for all the measures. “Omega 1” is the ratio after subtracting the median benchmark return, “omega 3” is the product of the first three ratios, “omega 1s” multiplies omega 1 by the logarithmic slope, and “omega 3s” is ultimate omega.)

[correlation study]

Based on these results, I think that in the future, “ultimate omega” will be the measure I will turn to most frequently when deciding upon the optimal investment strategy. After all, it contains more information about in-sample returns than any other performance measure, so no wonder that it correlates so well with out-of-sample returns.

Why Low Beta Outperforms

For almost fifty years people have written about a “low-beta anomaly,” and despite a lot of literature on the subject, nobody has been able to figure out what exactly causes it.

The Capital Asset Pricing Model (CAPM), which was developed in the 1960s by William Sharpe (the inventor of the Sharpe ratio and the winner of the 1990 Nobel prize in economics) and John Lintner, proposes that the expected return on an asset is the risk-free rate plus the product of the market return and the asset’s beta, or its systemic risk. Beta is calculated as the slope of the linear regression line formed by the asset’s return plotted against the market return. According to this model, the higher the beta, the higher the expected return should be. This is the model that is still used widely in business (for estimating the cost of capital) and among financial advisors in evaluating the performance of portfolios. It’s the centerpiece of many MBA courses, and is one of very few asset-pricing models available. (The main alternative is Arbitrage Pricing Theory, a multi-factor model.)

I’ll try to explain the CAPM in layman’s terms. Choose a stock in the S&P 500. List its monthly returns over a three-year period in one column, and the monthly returns of the S&P 500 in another. Create a scatter plot of those returns, with the stock’s returns on the y-axis and the market returns on the x-axis. Now draw a straight line through that scatter plot that is the best fit according to the least-squares method (in other words, the squares of the vertical distances between the line and all the points is minimized). The slope of that line is the stock’s beta, and the y-intercept is its alpha. If the stock’s beta is 2.0, then every time the market goes up 2%, the stock will go up approximately 4% plus its alpha, and every time the market goes down 2%, the stock will go down approximately 4% minus its alpha. If the stock’s beta is 0.5, then every time the market goes up 2%, the stock will go up approximately 1% plus its alpha, and every time the market goes down 2%, the stock will go down approximately 1% minus its alpha. The CAPM states that in an efficient market, alpha will be equivalent to the risk-free rate and that therefore the higher the stock’s beta, the higher the stock’s return will be. Since beta is a measurement of volatility--high-beta stocks move a lot more than low-beta stocks--CAPM accords with the popular belief that the riskier the investment, the higher the return. And it is meant to apply to other investable assets besides stocks.

Only a few years after its development, however, a fundamental problem with the model emerged. By 1972, Merton Miller (who would share the Nobel Prize with Sharpe) and Myron Scholes (who co-originated the Black-Scholes options pricing model) had shown empirically that high-beta assets tended to have negative alphas and that low-beta assets tended to have positive alphas (and alpha correlates extremely closely with total returns). Their findings were confirmed that same year by Fischer Black (the other co-originator of the options pricing model) and Michael Jensen (who came up with the idea of alpha), and have frequently been confirmed since. Across asset classes and in different markets, alpha and beta are negatively correlated. The “riskier” assets have lower returns than the less risky ones.

A large number of explanations of this “low-beta anomaly” have since been proposed. They include leverage constraints, asset managers’ benchmarking, lottery demand, opinion differences, correction of market-driven overpricing, and so on. All these explanations have one thing in common: they’re behavioral. They look at investor behavior as basically illogical, or flawed in some way, or inefficient. I’m not going to go into these explanations in this article, because they’re all basically wrong.

Instead, I have solved this long-standing problem in a very different way. In this article I am going to show that the solution to this anomaly is purely mathematical and has nothing to do with investor behavior.

Here’s the problem as stated in mathematical terms. If you find the next two paragraphs hard to follow, feel free to skip them. I’ll explain them in simple terms immediately afterwards.

Take n series of incremental values, a­_1,a_2, . . . a_i;b­_1,b_2, . . . b_i,;etc., such that there is a slightly higher probability of each value in each series being positive than negative. Let there be another series, x, which is the average of all the n series: x_i = (a_i + b_i + . . . + n_i)/n.

I am going to show that if you take the linear regression of each series against x (with x being the base variable—the x-axis values—and a through n being the y-axis variables), the correlation of the slopes and the intercepts will be more likely to be negative than positive. The corollary is that if the values in the various series are more likely to be negative than positive, the correlation will be more likely to be positive than negative.

OK, in plain language. Take a bunch of asset returns over a period in which there are more positive returns than negative ones. Let there be a “market” return which is simply the average of all the asset returns. (Just to keep things from getting too complicated, the “market” here is equally weighted with a rebalance that coincides with the measurement period of the assets’ returns.) I am going to prove that if an asset has a higher beta than another, it’s more likely to have a lower alpha, and vice-versa. And I’m also going to prove that if you’re looking at a period in which negative returns outnumber positive ones, the reverse is true.

Now let’s start with the simplest case possible. The entire market is composed only of two assets. For illustration’s sake, I’m going to use a real-life example for a moment. Here are the returns of US Steel (X) and Consolidated Edison (ED) over the last two years.

Now let’s plot the regression of both stocks against the “market” (which consists of the average return of X and ED). We’re going to get two trendlines, both of which slope upward as we go from left to right (I’m using weekly returns here, by the way, and zooming in to focus on the y-intercepts).

The slope of these lines is these stocks’ beta. X is a very high-beta stock and ED is a very low-beta one. The point at which they cross the y-axis is their alpha. As you can see, ED’s alpha is above zero, and X’s is below zero.

Now notice that the two lines intersect to the right of the y-axis, at a point whose x-coordinate is a positive number. That’s why X’s beta is higher while ED’s alpha is higher. You can quickly see that as long as two lines intersect to the right of the y-axis, one’s beta is going to be higher and the other’s alpha is going to be higher. But if the two lines intersect to the left of the y-axis—if the x-coordinate of the intersection is negative—then the line with the higher beta is going to have a higher alpha.

Now let’s get away from real life and go back to pure mathematics. We have two assets and the market consists only of those two assets. And the only information we have about those two assets is two months’ worth of returns. Let’s call the assets mn and pq and the returns m, n, p, and q. The market’s returns will be the average of those returns, or (m + p)/2 and (n + q)/2.

Now where do the regression lines of these two assets intersect? To the right of the y axis or to its left?

The formula for the x-coordinate of two lines given two points on each line is

If we substitute (m + p)/2 for x₁ and x₃ and (n + q)/2 for x₂ and x₄, and m, n, p, and q for y₁, y₂, y₃, and y₄, the formula for the x coordinate of the intersection of the two lines in question can be reduced to (mq – np) / ((m + q) – (n + p)).

Now look closely at that formula. You have the product of two numbers minus the product of two other numbers. And you’re dividing that by the sum of the first two numbers minus the sum of the second two numbers.

If all four of these numbers are positive numbers, it’s pretty obvious that the whole fraction will usually be a positive number. After all, if the product of two numbers is greater than the product of two other numbers, the sum is usually greater too. There are plenty of exceptions (e.g. 1 and 5, 2 and 3), but it’s usually the case. At any rate, if both the sum and the product of m and q are bigger than the sum and the product of n and p, or if both are smaller, we’ll have a positive x-coordinate.

Now let’s assume that m, n, p and q are all greater than zero. What is the probability that the pair with the greater sum has the lesser product or vice-versa?

To start with, the numbers in the pair with the greater product have to fall in order of size between the numbers with the greater sum. Why? Because if the sums are equal, the pair that’s closer together is going to have a higher product.

If one pair is m and q and the other is n and p, the only possible permissible permutations in order of size for solving this problem are [m n p q], [m p n q], [q n p m], [q p n m], [n m q p], [n q m p], [p m q n], and [p q m n]. So that’s eight of the twenty-four possible permutations, or one-third.

Now given four positive numbers in order of size, the probability that the outside two will have a greater sum is dependent on whether the numbers are distributed evenly, normally, or in some other fashion. But we can estimate that it’s about one-half.

Similarly, given four positive numbers in order of size, the probability of the inside two having a greater product is also entirely dependent on how the numbers are distributed. If, for example, the distribution favors higher numbers, it’ll be more than one-half, and if the distribution favors lower numbers, as it would in the case of returns, it’ll be less than one-half. But for convenience’s sake, we can approximate the chance as one-half.

Multiplying one-third, one-half, and one-half will give us a probability of one-twelfth.

Therefore, approximately eleven out of twelve times, if all the returns are positive, the x-coordinate is going to be to the right of the y axis and the asset with the higher beta will have the lower alpha.

But what happens if all the returns are negative? The situation is dramatically switched. Let’s look at that fraction again: (mq – np) / ((m + q) – (n + p)). You multiply two negative numbers and you get a positive number. Now the above fraction is almost always going to have the opposite sign in the numerator and denominator. And that means that the x-coordinate is almost always going to be negative. In fact, it has an approximately eleven in twelve chance of being negative, again depending on the distribution of the numbers.

Now we need to do three things: a) we need to deal with the case of having mixed returns, some positive and some negative; b) we need to expand this scenario to include more than two returns per asset; and c) we need to expand the market to include more than two assets.

It’s pretty clear from the foregoing that if the returns are half negative and half positive, with symmetric distribution around zero, the x-coordinate of the intersection of the two lines is going to be equally likely to be positive and negative, and there will then be no correlation at all between alpha and beta. But if the returns are more positive than negative, then alpha and beta will be negatively correlated, and if the returns are more negative than positive, alpha and beta will be positively correlated. That takes care of a).

Now all straight lines are defined by two points, so it really doesn’t matter if we add more returns. We’re talking about linear regression here. If all the returns are positive, no matter how many there are, we still have an approximately eleven out of twelve chance of the x-coordinate of the intersection being positive. That takes care of b).

Now let’s add more assets. The number of intersections will grow in a triangular way as we add assets, so that with three assets there will be three intersections, with four assets there will be six intersections, with five assets there will be ten, and with n assets there will be (n - 1)(n - 2) intersections.

Remarkably, the chance that any one of those intercepts will be positive, no matter how many assets we add to the mix, if all the returns are positive, is still approximately eleven out of twelve.

Mathematically, here’s why. If we add a new asset, uv, to the mix, with returns u and v, the formula for the intersection of the linear regressions of assets mn and pq becomes (2mq – 2np + mu – pu + qv – nv) / 3((m + q) – (n + p)). This is basically 2/3 times the previous formula with some extra stuff about u and v in it. Without that extra stuff, the probability of the x-coordinate of the intersection being positive is still approximately 11/12, so long as all the numbers are positive. Does adding the u and v stuff change that at all? No, it doesn’t, because each of them are multiplied once by a positive number and once by a negative number. The average of all possible values of mu – pu + qv – nv is precisely zero so long as all the individual returns are positive. That takes care of c), since the same logic can now be applied to negative and mixed additional returns.

I have now conclusively shown that the x-coordinate of the intersection of any two linear regression lines in a set of series of returns with the “market” line being the average of all the others is always going to be more likely to be positive if the returns are more likely to be positive and is going to be more likely to be negative if the returns are more likely to be negative.

Through empirical testing, we can show how the probability of an intercept being positive will change as the proportion of returns are negative. If the average and median return are both zero, the chance of a positive x-coordinate drops from between 85% and 100% (for all positive returns) down to 50%, but not linearly—the curve is s-shaped, and depends entirely on the distribution of returns. Using the distribution properties of the monthly returns of a handful of randomly selected US stocks, here’s what the curve looks like as the returns go from 100% positive to 100% negative.

What does this tell us about the correlation of beta to alpha? Well, statisticians will mostly agree that the best, most robust measure of correlation is Kendall’s tau rather than Spearman’s rho or Pearson’s r. The calculation of Kendall’s tau is quite simple in concept, if difficult in execution. You basically take all the possible pairs of the two values (alpha and beta in this case). Every pair you label as either concordant (if one of the two assets has both a higher alpha and a higher beta) or discordant. Then you take the number of concordant pairs, subtract the number of discordant pairs, and divide by the total number of pairs.

The pairs, in this case, correspond to the x-coordinate of the intersection of the two linear regressions. If the x-coordinate is positive, the pair is discordant, since one line’s beta will be higher and the other line’s alpha will be higher. So if the returns are all positive, depending on their distribution, Kendall’s tau will be approximately (1 – 11)/12, or –0.833. If the returns are all negative, Kendall’s tau will be approximately 0.833. And if the returns are equally distributed between negative and positive, Kendall’s tau will be 0. (In general, Kendall’s tau tends to be significantly closer to zero than Spearman’s rho or Pearson’s r, in case you’re used to thinking of correlations in those terms. A Kendall’s tau of 0.833 would probably be a Spearman’s rho of 0.9 or thereabouts.)

Therefore the Kendall’s correlation of alpha and beta is more likely to be negative the more positive the returns are, and vice-versa.

Now just in case you think I have my math wrong, run an empirical test in Excel. It’ll take about ten minutes. Create a few series of numbers. Create another series (the “market” series) that consists of the average of all those numbers. Use the slope and intercept functions to figure out the slope and intercepts of each series as regressed to the market (the language is “=SLOPE([cells of one series],[cells of “market” series])” and “=INTERCEPT(ditto)”). Then take all those slopes and intercepts and use the correlation function (“=CORREL”) to find the correlation. As long as the numbers are all positive, the correlation will almost always be less than -0.75. As long as the numbers are all negative, the correlation will almost always be more than 0.75. If the numbers are equally positive and negative, the correlation will probably hover close to zero.

Now let’s apply this to the real world of US stock prices. Using Portfolio123 and looking at the S&P 500 between January 1999 and today, I can see that there’s a 56.22% chance that an individual stock had a positive monthly return, which would result in an approximate 56% chance of the x-intercept of any two stocks being positive, which in turn results in a Kendall’s correlation between alpha and beta of -0.12. If we look at the constituents of the Russell 3000 with a price above $1, the chance drops to 54.33%, and the correlation is about -0.08. If we look at inflation-adjusted returns, or returns minus the risk-free rate, the correlation will be much closer to zero, but perhaps you’d then have to move the y-axis to match the base return. At any rate, the general rule applies: if the returns of a member of an asset class are more likely to be positive than negative, the correlation of the alpha and beta of the consituents of that asset class is more likely to be negative than positive.

Now let’s look, for just a moment, at the first part of that rule. Are the returns of investable asset classes more likely to be positive than negative? Well, if they weren’t, nobody would be investing in them.

There are many problems with CAPM. But one of them is a basic misunderstanding of mathematics. CAPM is based on a correlation of risk, as measured by beta, and returns. But since alpha and beta are usually negatively correlated and since alpha is very strongly correlated with returns, the theory completely falls apart. If we want to maintain that risk is associated with higher returns, we need to come up with a very different model for risk than beta.

But looking beyond CAPM, what else can we learn from this mathematical proof? If high alpha is associated with low beta, and if beta is a measure of how dramatically an asset responds to market changes, we should try to invest in assets that do not respond to such market changes. If you’re looking at the stock market, one way to do this is to invest in stocks with low share turnover (see my article Share Turnover, Beta, And Stock Returns).

If we change the “low-beta anomaly” to the “low-beta principle,” we can much more confidently treat low beta as a factor. We can try to avoid high-beta assets and develop portfolios that are relatively impervious to market movements.

Just a few warnings, however. Low-beta is not the same as low-volatility. Most low-volatility indices are based on the standard deviation of the returns, which is very different from beta. Also, the calculation of beta can be tenuous when it comes to assets with a very low correlation to the market--or assets with a lot of outliers in their data.

In conclusion, one of the primary principles of investing is not to follow the herd. High-beta investing is a form of herd-following--one invests in those assets most likely to be affected by market movements. My mathematical proof that high alpha is usually correlated with low beta affirms what most of us have always known about investing: to beat the market, you have to take the road less traveled.

CAGR since 1/1/16: 50%.

My top ten holdings right now: FNJN, MCHX, PCOM, AUDC, ZYXI, LFVN, FFNW, SBFG, AGYS, PERI.

Share Turnover, Beta, and Stock Returns

Share turnover is the volume of a stock traded divided by its shares outstanding (or by its float). In this article I want to show what this metric is good for.

(This article is based loosely on a recent working paper by Maria Kasch, a professor at Humboldt University of Berlin, entitled “Systematic Risk and Share Turnover.” As it’s not a very well-known article, and as it’s not that easy to get through, I thought it would be worthwhile sharing its conclusions in simpler language, and bolstering them with my own observations. I won’t pretend to understand everything in it, though. For someone without a degree in finance, it's tough going.)

For those who have never before looked at share turnover, there’s only a very weak correlation between the size and the share turnover of a company. In the S&P 500, as of Memorial Day, the ten companies with the highest share turnover (I use the median volume over the last three months divided by the current shares outstanding) are Advanced Micro Devices (AMD), Micron Technology (MU), Discovery (DISCA), Macy’s (M), Range Resources (RRC), Under Armour (UAA), Chipotle Mexican Grill (CMG), Foot Locker (FL), Netflix (NFLX), and Kohl’s (KSS); the ten with the lowest are Johnson & Johnson (JNJ), Coca-Cola (KO), Brown-Forman (BF.B), Berkshire-Hathaway (BRK.B), Marsh & McLennan (MMC), Stryker (SYK), Accenture (ACN), Cincinnati Financial (CINF), Danaher (DHR), and Walmart (WMT). To generalize, older, established, and somewhat boring companies (widows and orphans), often with high-priced shares and low short interest, have low share turnover; and cutting-edge, exciting, controversial, highly hyped, turnaround, high-momentum, and/or heavily shorted companies have high share turnover.

Now let’s look at what happens during a shock to the market, and let’s take Black Monday, October 19, 1987, as an example. (The chart below is from Dr. Kasch’s paper.) If you were to sort the stocks in the NYSE and AMEX into deciles according to their share turnover that day and then look at the decrease of each decile that day, you’d get a chart that looks like this (look at the line marked “contemporaneous turnover”):

Interestingly, if you had classified the same set of stocks according to their share turnover over August and September 1987 you would have seen exactly the same effect (look at the line marked “lagged turnover”).

This is a nice illustration of the fact that stocks with lower share turnover are less subject to market shocks, and the higher their turnover, the more they’ll be moved by the market. In other words, low-turnover stocks have lower beta and high-turnover stocks have higher beta. And both their turnover and their beta remain relatively constant over time. Dr. Kasch studied six decades of data, and found a remarkably high and persistent correlation between share turnover and beta. Dr. Kasch excluded NASDAQ stocks from her study, but I have looked at the data of all Russell 3000 stocks over the last two decades and found the same high and persistent correlation.

Now beta is a rough measurement of how closely a stock’s movements resemble those of the market as a whole. And alpha is a measurement of excess returns after beta is taken into account. Beta is the slope of the linear regression between the stock’s weekly or monthly price movements and those of the market, and alpha is the y-intercept. If a stock’s beta is 1, then one should expect that when the market goes up or down 2%, the stock will go up or down 2% plus its alpha. If its beta is 2, when the market goes up or down 2%, the stock will go up or down 4% plus its alpha. If its beta is close to 0, the stock will act completely independently of the market. And if the stock’s beta is –1, when the market goes up 2%, the stock will, on average, go down 2% plus its alpha.

One has to keep in mind that beta, when it comes to individual stocks, does not really work like this because of the relatively low correlation between most individual stocks' price performance and the market as a whole. Beta essentially measures the relationship if the correlation were perfect. If you look at the price chart of most stocks, you won’t see its beta very well. So let’s look at some stocks whose correlation to the market is relatively high: Berkshire Hathaway (BRK.B) has a beta of 1, Cypress Semiconductor (CY) has a beta of 1.8, and Waste Management (WM) has a beta of 0.56. If you look closely at the chart below, you’ll see that the week-to-week price movements of CY tend to exaggerate those of SPY while those of WM tend to be more moderate.

Now why do share turnover and beta go hand-in-hand?

It’s common knowledge that, in general, the larger the price change, the larger the simultaneous increase in volume, and vice versa. This holds true for all asset classes, and is true both of individual assets and the market in general. It’s a function of the axiom that prices and quantities traded are driven by the same forces. And it almost goes without saying that without a large increase in volume, you simply can’t have a large increase or decrease in price. That’s because prices change largely incrementally in a kind of auction. You need a lot of increments for a big price move.

The formula for share turnover is, as I said, the volume traded divided by the number of shares available. Let’s multiply both the top and bottom of that equation by the price per share. Now in the numerator we get dollar volume—the amount of money actually exchanging hands—while in the denominator we get market cap.

If we put everything together, we can see how the price movements in the cap-weighted market as a whole are going to be much more heavily reflected in stocks that experience a high dollar volume compared to their market cap than in stocks that experience a low dollar volume, simply because volume amplifies market-related price movements. Share turnover—average dollar volume divided by market cap—is essentially a measure of investor participation in a company. As Dr. Kasch puts it, “Other things equal, higher investor participation will be associated with a larger amount of capital responding to common shocks. And, other things equal, a larger amount of capital responding to a common shock will result in a stronger price movement.”

As a result, you might guess that stocks with low share turnover would do well in periods with low market returns, and stocks with high share turnover would do well in periods with high market returns. But what actually happens is the precise opposite.

It has long been recognized that low-beta stocks tend to outperform high-beta stocks on a risk-adjusted basis (a phenomenon labeled the low-beta anomaly or the low-volatility anomaly). This is true across international equities and even across asset classes, and it’s been persistent at least since the 1920s. And stocks with low share turnover tend to outperform stocks with high share turnover by an even higher degree than low-beta stocks outperform high-beta ones. If you divided stocks in the Russell 3000 into deciles by their three-month share turnover and rebalanced quarterly, this is what their performance would have looked like since 1999. As you can see, the stocks with really high share turnover drastically underperform, and those with low share turnover outperform.

Why does this happen? There are a number of explanations of the low-beta anomaly, but none of them are terribly convincing. Dr. Kasch’s theory is that because high market returns are more prevalent than low market returns, high-turnover stocks tend to become overpriced rather quickly, and this then offsets their tendency to rise in price. In this case, beta can double as a measure of mispricing. Stocks with low beta or low share turnover are relatively impervious to market-driven price changes, and thus their prices better reflect their worth.

This theory doesn’t convince me at all. I have come up with a simple and elegant mathematical proof that in a market in which returns are mostly positive, low alpha will be correlated with high beta and vice versa. This will be the subject of my next article. The behavior of investors, the intrinsic value of a stock, and the kinds of stocks that exhibit high and low share turnover make no difference at all to the relationship between alpha and beta, which is purely mathematical. The “anomaly” is actually not an anomaly at all, but is built into the relationship between alpha and beta when returns are more often positive than negative. As a bonus, alpha is, mathematically, highly correlated with returns.

Too often when we think about beta as a measure of susceptibility to market increases or decreases we forget to take alpha into account, and the relationship of beta to a stock's returns is meaningless without alpha. If, for example, a stock with a beta of 2 has an alpha of -2%, when the market goes up 2%, the stock will also go up 2%, but when the market goes down 2%, the stock will go down 6%. If during bull markets the relationship of beta and alpha is an inverse one, low-beta stocks will in general outperform high-beta stocks.

To conclude, the behavior of stocks with high and low share turnover is derived from what Dr. Kasch calls “a simple and intuitive fact: A greater investor participation in a stock translates to a greater participation of the stock in market movements.” If you want returns that aren’t very susceptible to larger market movements, that have low beta (or low volatility) and high alpha, by all means avoid high-turnover stocks.

How to Backtest for Superior Out-of-Sample Results

I highly recommend backtesting any portfolio strategy. I do my backtesting using Portfolio123, but there may be other options. I’ve backtested a lot of strategies over the years, and have run a number of correlation studies as well, comparing backtested results during one period to “out of sample” results for a later period in order to figure out the most correlative backtesting methods. Now I want to offer thirteen tips for better backtesting.

1. Double or triple your portfolio size. If you normally hold twenty stocks, run a backtest on a portfolio of fifty. If you normally hold a hundred stocks, run a backtest on two or three hundred.
2. Never run a backtest over a period less than six years long. And studiously ignore all backtest results that are shorter than six years. Jim O’Shaughnessy gives a great example of misleading backtests: over a five-year period, he found that holding the top fifty stocks in terms of annual sales gains produced terrific returns. Those years just happened to be 1964 through 1968; over the long term, it’s a terrible strategy. Six years is my absolute minimum; ten to twenty years is far better.
3. Never backtest using the entire universe of stocks that you’re going to be choosing from. Find some way of splitting it into pieces (half is good) and test each universe separately. Do this several times, and then average the results. Similarly, you can bootstrap your time periods by choosing just half of your weekly or monthly returns, and then average the results. Once again, Jim O’Shaughnessy spells this out well: see his article The Power of Back Testing Investment Strategies. In designing The Stock Evaluator, my Seeking Alpha Marketplace subscription service, I created thirteen different stock universes delimited by size and sector (for example, one universe excludes energy, materials, and industrials, and includes only stocks in the bottom 40% size-wise; another includes only stocks between 40% and 80% by size and excludes discretionary, health care, financials, utilities, and real estate; and so on), then once I had a good strategy for each one, I averaged them all.
4. Ignore the total returns of your backtest. Instead look at more robust portfolio performance measures. I favor three: the omega ratio, median excess returns, and Jensen’s alpha (measured weekly). I’ll explain briefly how to calculate each of these. The omega ratio is also called the gain-to-pain ratio, and there are a few ways to calculate it. I figure out the median return of the benchmark (weekly, monthly, yearly or whatever interval you want to use). I then take the backtested return of my strategy and for each period subtract that benchmark median return. I then add up all the net positive returns and divide by the negative of the sum of the net negative returns. To calculate median excess returns, I take the monthly returns of my backtested strategy and subtract the returns of the benchmark over the same period. I then get the median of those numbers. To calculate Jensen’s alpha, take the weekly returns of your strategy and the weekly returns of the benchmark and find, using regression analysis, the y-intercept, i.e. the expected return of your strategy when the benchmark return is zero. Using total returns instead of these portfolio measures is often very misleading since your strategy could have worked extremely well (or extremely poorly) during a short period and affected your compounded earnings considerably. If you use alternative (and better) portfolio performance measures, you can more easily discern which is the best of your tested strategies. I would not, however, recommend using the Sharpe ratio, which has a multitude of problems (I’ve spelled these out in two of my previous posts, The Ultimate Measure of Portfolio Performance and William F. Sharpe, Beta, and the Paradox of Risk-Adjusted Returns).
5. If you’re combining various factors into a workable system, use increments of at least two or three percent. The difference between a factor weight of 6% and 7% is not worth backtesting. Too much time is wasted trying to decide exactly how much weight to allocate to various factors. Getting those factors right is far more important than their weight.
6. Do different kinds of backtests. I combine the results from a screen that rebalances weekly with those of a rolling backtest that holds for eight weeks. For a system with less turnover, concentrate more on rolling backtests. A straight simulation of a strategy that rebalances quarterly will only have one-thirteenth of the data as a rolling backtest performed weekly. So don’t rely only on precise simulations, but take advantage of other backtesting possibilities.
7. Employ recency bias. The backtest of a strategy over the last twelve years is far more likely to correspond to near-future returns than one performed over the previous twelve years. However, it’s important to remember that while bull markets are often quite similar, bear markets are usually extremely different from each other (see my post on Bear Market Investing).
8. Never rely only on a backtest of a factor in isolation. Instead, incorporate it into your factor set and see if it improves your results or not.
9. Never expect your out-of-sample results to have a compound annual growth rate greater than one-half of that of your best backtested results. In other words, if your backtests are showing a CAGR of 30% per annum, expect no more than 15% going forward. Expecting out-of-sample returns that match in-sample returns is not just unrealistic, it’s a major tool of snake-oil salesmen. The system I use for my everyday investments gives me a backtested nineteen-year CAGR of well over 100%. I know that’s completely unrealistic, I only expect 50% at best, and I know that will vary greatly from year to year. (I got 45% in 2016, 58% in 2017, and my annualized return in 2018 so far is 36%, but I'm pretty sure that one of these years I'm going to be in the red.)
10. Backtest lots of systems and variations and adopt the average or a combination of those that give you the best performance. Don’t just backtest one system and tweak it; and don’t invest in a lot of weak systems hoping that one will outperform.
11. Never derive your rule or factor from the data. Factors have to make intuitive and financial sense first and foremost. Then you can see if the data backs them up.
12. Use reliable data and avoid look-ahead bias. The data on Portfolio123 is reliable, but that on other websites may not be. Make sure there’s no survivorship bias in your backtests, and make extra sure that share count—invaluable for per-share measures—is accurate (it often isn’t, especially for ADRs and stocks that have undergone splits). Make sure that your database avoids look-ahead bias: if an earnings announcement comes out on the evening of the 7th, your backtest should not recommend that you buy that stock on the 8th, since the data from the announcement would probably have taken at least a day or two to be incorporated into the database that you use. You need real point-in-time data.
13. Never include stocks that you wouldn’t have been able to buy. A lot of misleading backtesting is done on stocks with liquidity so low that you wouldn’t actually have been able to buy them in the quantity that your investment strategy requires.

If you have any questions about any of these principles, I’d be glad to answer them in the comments below.

CAGR since 1/1/16: 49%.

My top ten holdings right now: RCKY, IRMD, AUDC, ZYXI, TZOO, TRIB, XOXO, ORN, MCHX, EIGI.

The Three Types of Factors

Academic studies have identified a large number of factors that can be said to have predicted outsized returns over periods of time, depending on how you measure their effectiveness. Various firms have created indices based on a number of these factors, ranging from low volatility to momentum. Beyond that, investors have been looking at factors like the price-to-earnings ratio and the price-to-book ratio for a hundred years or so.

But what most investors overlook is that factors don’t all work the same way.

I classify factors into roughly three categories: direct, distributive, and augmentative. Here’s what I mean.

A direct factor, when tested by deciles over time, produces a chart that looks like this:

This is the performance of unlevered free cash flow to enterprise value in the Russell 3000 with a monthly rebalance and no slippage since 1999.

A distributed factor produces a chart like this:

This is the performance of operating margin growth (the difference between the most recent TTM operating margin and the twelve months before that), again in the Russell 3000 with a monthly rebalance and no slippage since 1999. I call it a distributed factor because the deciles fall into a normal distribution, more or less.

Now if you go long the top quintile of each factor and short the bottom quintile, which is the conventional way to measure the effectiveness of a factor, the first factor, using the Russell 3000 and rebalancing quarterly, will give you a result that looks like this:

And the second will give you a result that looks like this:

Now for most people who look at factors, this second factor clearly doesn’t work. But what if you go long the middle quintile and short the top and bottom deciles? Then you get a chart that looks like this:

That’s the kind of thing you have to do with a distributed factor.

Now let’s look at an augmentative factor: fully diluted market cap, with lower values ranking higher. (Most size factors are augmentative, but many quality factors are too, e.g. accrual ratios.)

Clearly, this is not going to produce good results if we take the top quintile long and the bottom quintile short. And even as a distributed factor, it’s pretty weak, since the middle deciles aren’t much higher than the top and bottom ones.

Now here’s a direct factor, operating income growth (the growth of the most recent quarter’s operating income compared with the same quarter last year):

I’m going to combine this direct factor with the augmentative factor, and weight them 60% operating income growth, 40% fully diluted market cap. Here’s what we get:

An augmentative factor increases the effectiveness of a direct factor.

Two things should be quite clear from this categorization of factors. First, a distributed factor can be converted into a direct factor by privileging middling results rather than high or low results. I do this for a lot of “growth” factors when I evaluate stocks. Second, an augmentative factor can be converted into a direct factor by combining it with another factor. So, for example, I can combine fully diluted market cap with operating income growth by using the former as a denominator and the latter as a numerator, ending up with a modified inverse PEG ratio. This solution, of course, only works if the denominator is always positive, but there are other ways to combine factors mathematically.

The problem with most factor studies is that they look at all possible factors as if they’re direct, and their tests are always along the lines of “go long the top quintile and short the bottom,” or “chart the excess returns of the top quintile over a benchmark.” Recognizing that factors can work in very different ways will increase the number of factors you can use—and your opportunities to use them.

CAGR since 1/1/16: 48%.

My top ten holdings right now: RCKY, IRMD, AUDC, INTT, ZYXI, WSTL, TRIB, XOXO, TZOO, RICK.

The Stock Evaluator Is Being Launched

I am now launching my subscription service, The Stock Evaluator, on Seeking Alpha's Marketplace. I wrote a pitch for it here.

CAGR since 1/1/16: 46%.

My top ten holdings right now: RCKY, INTT, SEAC, CLUB, WSTL, ZYXI, PCOM, AUDC, RICK, III.

 

 

How I Evaluate Stocks

I have long believed that the only way to make money picking stocks is to evaluate each stock on a large number of different criteria. My method has been successful so far, allowing me to make a return of 131% on my investments over the last 29 months (for a CAGR of 41%).

A few weeks ago, I introduced to my followers an “Ideal Stock Evaluation System,” which I hope to offer to subscribers on Seeking Alpha’s marketplace soon. I’m calling it the Stock Evaluator. Subscribers will get a weekly list of over 4,000 stocks, each ranked on a scale of 0 to 100, along with its price, sector, market cap, liquidity, yield, and other information.

In this article and subsequent ones, I want to clarify on what basis I evaluate and rank stocks, suggest some possible uses for the Evaluator, and provide some backtests. Just to be clear: unlike some evaluation systems and all stock screeners, I’m not giving stocks points based on whether they pass certain tests, but instead I’m using a more flexible weighted ranking system that rewards stocks that rank highly on certain metrics compared to others in the same industry, sector, or market.

Here are the top twenty factors that go into the Evaluator, with a word of explanation about each.

1. Projected earnings growth. This is a combination of four measures: the percent change between the current quarter’s earnings estimate and the same quarter last year; the percent change between this fiscal year’s earnings estimate and that of the most recent fiscal year; the company’s profit margin (with lower numbers better); and the company’s return on assets (with lower numbers better). These last two measures appear counterintuitive, but note that I’m not ranking based on weak earnings but on the potential for strong earnings, which can lead to earnings surprises and upward price movement. See my article on this here.
2. Sales growth, acceleration, and stability. I use some complex formulae to look for companies whose sales don’t jump around a lot from quarter to quarter, whose year-to-year sales growth is above average but not unsustainably high, but whose recent sales growth is accelerating. Like the previous factor, this is a combination of four different measures, each of which works well on its own.
3. Price to sales. This metric, especially when looked at in combination with other value ratios, has long been invaluable for comparing companies in the same industry; Jim O’Shaughnessy discussed it well in What Works on Wall Street. I look at both actual sales and projected sales (analyst estimates).
4. Dividend yield, dividend growth, earnings yield, and payout ratio. Using several formulae I compare the indicated annual dividend to the dividend paid last year; calculate the dividend yield and the earnings yield; examine five-year dividend growth; and look at the payout ratio (dividends paid to net income). Companies that pay no dividends get ranked right in the middle between companies with good dividend practices and those with bad (for example, those whose dividend payments exceed their income).
5. Low net operating assets. I look at the ratio of net operating assets to total assets. See my article on this measure here.
6. Low accruals. I look at the two basic measures of accruals: cash flow accruals, which is the ratio of net income minus operating cash flow to total assets; and balance sheet accruals, which is the change in net operating assets divided by average total assets. I look not only at the last year, but at the last three years too.
7. The ratio of R&D expenses to market cap, with higher numbers better. This is a very unusual metric that surprised me when I learned about it. I use it only for stocks in certain sectors; my testing has confirmed that it’s a terrific value ratio for those stocks. Indeed, a paper published in The Journal of Finance back in 2002 found that “companies with high R&D to equity market value (which tend to have poor past returns) earn large excess returns.”
8. Gross profit to enterprise value. My backtests have shown that this is another terrific measure of value. I look mostly at the last three years, but weight it more heavily on the last year.
9. Low share turnover. The ratio of share volume to float is a great measure of volatility. A recent study has demonstrated a very good correlation between beta and share turnover. I plan to devote a future article to this measure.
10. Price to tangible book value. This is an especially valuable measure for companies in the financial sector, but it can profitably be applied to other companies as well.
11. Operating margin stability. Companies that are growing their income but shrinking their sales are companies to avoid. Companies that are growing their sales but shrinking their income are also companies to avoid. I favor companies whose sales growth and operating income growth are in sync. See my article on this measure here.
12. Low short interest. I compare this to other companies in the same industry. Especially in the world of small caps, strong short interest can be a real sign of trouble ahead.
13. Accounting stability. I look primarily at the difference between last year’s cash conversion cycle and this year’s—that difference should be minimal. But I also look at the ratio of the change in accounts receivables to sales. Companies with unstable accounting can be unsafe investments.
14. Low price volatility. Technically, this should be called price variability, but everyone calls it volatility these days. (Properly speaking, volatility is beta.) This is simply the standard deviation of daily price returns.
15. Unlevered free cash flow to enterprise value. The basis for discounted cash flow valuation, this is an extremely important but often overlooked ratio; my research indicates that it works a lot better than the more common EV/EBITDA. Once again I look at both three-year and one-year figures.
16. Industry momentum. I favor stocks in industries whose average price has increased over the past year. The calculation I use here eliminates outliers and ADRs.
17. Free cash flow return on assets. Divide free cash flow by total assets. I like this ratio better than return on capital, return on equity, or other return measures, simply because my backtests show that free cash flow can be a better indicator of a company’s potential than net or operating income. For this measure, though, I use a somewhat unconventional measure of free cash flow: the sum of cash from operations and cash from investments (which is usually a negative number). In other words, I take acquisitions, divestitures, and other investing income into account here, not just capital expenditures. See my article on this here.
18. Gross margin to industry average. If you want to get a bead on whether a company has a strong “moat,” this is a great place to start. The companies with the highest gross margins, compared to the industry average, are the safest from competitors.
19. EVA yield. This is the ratio of economic value added, a measure invented by Joel Stern, to market cap. (I have to tip my cap to Joel Stern, who also came up with the concept of free cash flow.) Although EVA can be an extremely complex calculation, I’ve put in the hours to come up with a workable formula. EVA is a terrific indicator of a company’s health, and comparing it to market cap makes it a great value ratio.
20. PEG and PEG-like ratios. I lump here various measures that compare earnings growth and free cash flow growth to market cap to come up with measures that emphasize both low price and high growth.

 

Other things I look at include sustainable growth (ROE times retention rate), recent earnings growth, price momentum, gross plant to capital expenditures (the higher the better), asset turnover, basic sentiment indicators like earnings estimate revisions and recent earnings surprises, late statements (which are bad), share reduction (buybacks, which are good), employee growth, free cash flow margin, earnings stability, forward earnings yield (p/e), operating margin, return on capital, EV to EBITDA, EV to long-term debt, and EV to sales. I may add additional factors as new research supports change, or vary these somewhat; but I will be implementing changes only incrementally so as not to throw rankings off from week to week.

To conclude, below are a few decile backtests I’ve done on my ranking system using Portfolio123. These show the annualized returns of ten equal portfolios based on stock ranks, with a quarterly rebalance and no slippage, for six different groups of stocks. I have not optimized my system for these groups—in fact, I use exactly the same rules to rank a microcap as a large cap, and only a few of my rules are particular to sectors. (Please note: I did not include REITs in these backtests because I will be offering a different ranking system for those.)

In my next post, I’ll illustrate how investors with very different inclinations can profitably use the Stock Evaluator, and provide some backtested results.

My top ten holdings right now: RCKY, ZYXI, INTT, WSTL, NWY, PCOM, PERI, PBIB, BVX, PTN.

CAGR since 1/1/2016: 47%.

Bear-Market Investing

There is probably more disagreement about how to invest in stocks during a bear market than about anything else in investing. The disagreement centers around three fundamental points.

First, is it better to stick to the same strategy in a bear market as in a bull market simply because it’s impossible to predict when a bear market is going to start or end, and because you don’t want to miss the bounce? Or is it better to use some sort of market-timing signal to switch strategies?

Second, do you put a significant portion of your money into cash or bonds or a hedge, or do you stay just as long as you were during the bull market?

Third, if you stay long, do you switch strategies? This depends on the answer to a related question: can you learn anything about future bear-market strategies from past bear markets, or is every bear market different?

I’ll tackle these questions one by one.

1. Market Timing

First, market timing is difficult and often unreliable. But the anonymous author behind the brilliant Philosophical Economics blog (his Twitter handle is Jesse Livermore, the name of a legendary investor of the early twentieth century who made and lost millions and committed suicide in 1940) came up with a terrific method. It’s well worth your while reading his post In Search of the Perfect Recession Indicator.

Basically, the strategy is to go long unless the unemployment rate is rising and the price trend is falling. Unemployment is rising if the reported rate is above its trailing twelve-month moving average and price trend is falling if the S&P 500 is below its trailing ten-month moving average. “Livermore” found that this indicator beats all others over the period from 1930 to 2016.

So let’s take a close look at how this indicator would have performed over the last forty years.

First of all, there are a large number of false signals. You would have had bear-market signals on November 1, 1979 and April 1, 1980, both false, but only lasting a month. Then you would have been out of the market for the decline in late 1981 and early 1982. You would have remained long through the 1987 crash. You would have been hopping in and out of the market for several months in 1990, getting back in on February 1, 1991, then out again December 1 for a month. You would have left the market on March 1, 2001, when the S&P 500 had already dropped a good 19%, gone back in on April 1, 2002, but just for one month, and finally re-entered on May 1, 2003. You would have then exited on December 1, 2007 and re-entered on July 1, 2009, missing the first four months of the recovery, when the S&P 500 gained 38% from its lowest point. You would have remained long ever since, even through the almost-bear markets of May through October 2011 and May 2015 through February 2016. Still, even with all these false signals, you would be well ahead of someone who stayed long the entire time, assuming that person was invested only in the S&P 500 instead of using a more profitable stock-picking system.

So, yes, market timing is possible. It’s not neat and clean, and it’s hardly foolproof, but, as “Jesse Livermore” has shown, it’s better than simply sticking with an index through thick and thin. And there are far more sophisticated methods of market timing than this one. For some good examples, check out iMarketSignals.com.

But here’s the conundrum. If it were possible to develop a market-timing scheme that enables investors to avoid most bear markets, why would nobody have come up with it forty or fifty years ago? Stock-market indexes and the unemployment rate were both readily available in 1968. So why did nobody come up with this simple system back then?

The answer is complicated. As “Jesse Livermore” points out, the onset of the 1937 and 1945 recessions could not have been predicted by any of the commonly used recession indicators, including the unemployment rate, which only began to rise after the recession had begun and the bear market was well under way. And the strategy does not work very well in other countries, using their unemployment rate. In addition, it has frequently been the case that the onset of a bear market has been a cause of recession rather than the other way around.

But there’s also a question of logic. Let us pretend that the wisdom of the combined unemployment rate and S&P moving-average crossover method of market timing were accepted by 75% of market participants, which would certainly be the case if it could be proven to have actually worked. And let’s say that in July of this year, the unemployment rate started rising, but the S&P 500 was still well above its ten-month moving average (this has happened a number of times over the last fifty years). What would it take for enough market participants to sell their stocks to drive the S&P 500 below its ten-month moving average? Remember that 75% of market participants will believe that while the S&P 500 is still well above its moving average, no bear market will occur. Therefore, any dip in the S&P 500 will be eagerly bought by those market participants, and indeed no bear market will occur. In other words, any market-timing indicator that actually works and which depends on stock prices will render bear markets impossible. The real cause of a bear market is fear, and market-timing confidence and fear are incompatible. So we can take this scenario to the next logical level: if 75% of market participants had faith in the “Jesse Livermore” method of market timing, those same 75% of market participants would soon conclude that a bear market will never happen (or if it did they could get out in time), and the bond market would collapse since stock market indexes would be more lucrative and just as safe.

Now let’s say, on the other hand, that a market-timing method were discovered that was completely independent of stock-market prices. It instead relied purely on other economic indicators, and was proven to have predicted every single bear market since 1929. And let’s say that 75% of investors believed in it. In that case, as soon as the indicators gave the signal, an incredible crash would occur and stocks would lose practically all their value overnight. As a result, most public companies would go bankrupt and the economy would go into a depression the likes of which the world has never seen. There would be, therefore, incredible efforts on the part of governments to jigger those economic indicators so that they would never indicate a bear market. (There may be some parallels here to quantitative easing.) Or perhaps the government would make it impossible to read those indicators by messing with the data or keeping it under wraps. No matter what, this scenario is nightmarish in the extreme, and could be the basis for an excellent dystopian story.

These two scenarios are pretty strong arguments against the existence of a generally acceptable (or proven) market-timing mechanism. If one existed, stock markets would cease to make sense.

2. Strategy in a Bear Market

Now let’s turn to the second question: in a bear market, do you put a significant portion of your money into cash or bonds or a hedge, or do you stay just as long as you were during the bull market?

If you’re investing using index funds and you’re confident you can get the re-entry point right, obviously you want to be out of the market during a bear market and putting your money in short strategies, cash, and/or bonds. If, on the other hand, you doubt your market-timing ability, or you’re confident in your stock-picking prowess, stay long or use a long-short strategy similar to the one hedge funds use.

Now I’ve backtested, using Portfolio123, the strategy that I use for my own stock picking—a microcap value-growth-and-quality strategy—and according to these backtests, it would have been a serious mistake to be out of the market during those periods. Even if my returns had been only half of what my backtests tell me they’d have been (a reasonable assumption), I would have made a lot of money in the first of the millenium’s recessions, and while I would have lost a lot in the second, the recovery in 2009 was quick and dramatic. So that answers the question for me. While using a long-short strategy during both recessions would have made me more money, there are significant costs and risks involved, and timing the re-entry point is very important.

So the answer here depends on the answer to two other questions. Can you time the end of a bear market? And do you have a winning value-based strategy for stock picking that consistently beats the index?

3. What do Bear Markets Have in Common?

Now for the third question: would a successful strategy for one bear market be successful in another?

Well, let’s create six different long-only strategies and test them out. I’m going to create ranking systems for a purely momentum strategy (with three factors), a size strategy (with two factors), a growth strategy (with three factors), and a value strategy (with four factors). The factors within each strategy will have equal weight. Then I’m going to combine two strategies, again equally weighted, at a time and test those against the S&P 500.

The stock universe I’ll test is all stocks on major US exchanges with a median three-month daily dollar volume of $100,000 or more, a minimum market cap of $25 million, and a minimum price of $1.00, excluding REITs and MLPs. The backtest consists of going long on the top-ranked fifty stocks and relabancing monthly, with 0.5% slippage for each rebalance. I’ll use the conventional timing for the bear markets, 3/24/2000 to 10/9/2002 and 10/9/2007 to 3/9/2009.

Here are the results, which are not annualized:

As you can see, by far the best strategy in the 2001 recession was a growth and value strategy, while that would have failed miserably in the 2008 recession. By far the best strategy in the 2008 recession was momentum and value, which did quite well in 2001; but a close second is the growth and momentum strategy, which would have fared miserably in 2001. All three value-based strategies would have done just fine in the 2001 recession, but in the 2008 recession, two of them would have underperformed the S&P 500. I haven’t tried it, but I suspect you’d find similar discrepancies if you added the almost-bear markets of 2011 and 2015.

Another way to look at bear markets is by sector performance. Lawrence Hamtil has helpfully broken down the last five bear markets by sector performance in his post Imagining the Next Bear Market - Part II. In the 1973-75 bear market, the best performing sectors were energy, materials, and staples; in the 1980-82 bear market, they were industrials, materials, and telecom; in the 1990 bear market they were health care and energy; in the 2001 bear market they were staples, materials, and financials; and in the 2008 bear market they were staples, health care, and utilities. In general, materials and staples performed the best, but materials did very badly in the most recent bear market. If you look at what sectors performed the worst, it’s all over the map. In the first bear market it was discretionary and financials; in the second, it was energy (nothing else came close); in the third it was discretionary and financials again; in the fourth it was technology and telecom; and in the fifth it was financials, industrials, and materials. In short, every bear market is very different.

Now as I’ve written in my Seeking Alpha article The Ideal Stock Evaluation System?, I’ve developed a stock evaluation system. If you had used that evaluation system, in the same universe as above, buying stocks ranked 98 or better, you would have beat the market handily in both of the most recent bear markets, earning a total of 100.42% (not annualized) in the 2001 recession and losing only 43.28% in the 2008 recession. And a combined long-short strategy (shorting stocks ranked 2 or worse that are over $1 billion in market cap) would have done even better (if you don’t count interest and other costs): 3,363% in the 2001 recession (no, that’s not a typo: remember all those incredibly overvalued and utterly worthless stocks in 2000?) and a gain of 105.77% in the 2008 recession. But this all depends on perfect timing. If you were a few months late in realizing that the bear market in stocks was over in March 2009—for example, if you were relying on an end-of-month moving-average signal—you would have been better off not shorting anything at all. A long-short strategy was great in the 2001 bear market but only would have worked in the 2008 bear market given very good market-timing skills.

To conclude, the most logical approach, in my opinion, is to remain fully invested in stocks at all times using a sensible low-beta high-alpha stock-picking strategy that consistently beats the market. If you are comfortable with short-selling (I’m not), use the recession indicator that “Jesse Livermore” discussed and split your holdings between long and short positions during those periods, choosing your stocks wisely according to good fundamental techniques. Another way to hedge during a bear market is to buy puts, which, I confess, I’m not sophisticated enough to discuss. If your retirement account doesn’t allow you to pick stocks, go to cash or bonds in that account during the periods that the unemployment-moving-average system outlines. And remember: there’s no way to characterize bear markets—each one is different. How a system performed in one bear market will tell you very little about how it will perform in the next.

My top ten holdings right now: RCKY, TG, WSTL, PBIB, UWN, GTS, FSTR, PTSI, RCMT, FWP.

CAGR since 1/1/16: 50%.

My Models on Portfolio123

I have five designer models on Portfolio123 that you're welcome to subscribe to, and I'm launching a sixth today, which should beat them all hand's down as it's the closest to the one I use for my own investments. It's not identical, though, because Portfolio123 has a minimum price and liquidity requirement that's stricter than my own. It's called "Crazy Returns Microcap Model." Here are the stats for the backtest:

You won't be able to subscribe to this model until June, and it's very expensive. I'll post more about it when it's available. In the meantime, the other models, some of which have lagged their benchmarks since launch but none of which have lost money, can be found here:

small cap model

mid-cap model

large cap model

S&P 1500 model

ultra-low turnover model

My top-ten holdings right now: RCKY, TG, WSTL, PBIB, UWN, GTS, RCMT, MERC, PTSI, FSTR.

CAGR since 1/1/16: 49%.

Predicting EPS Growth

A few weeks ago a question came to me: how can we best predict a company’s earnings growth? So I designed an experiment to answer that question. The experiment is a little complicated, so I’ll discuss it at the end of this article. I’ll instead lead with my results, in reverse order: the factors most likely to predict future earnings growth.

In a tie for fourth and fifth place, with a 25% advantage over a random selection:

Stocks with strong operating earnings growth as measured by comparing the most recent quarter’s operating earnings (or EBIT) to the same quarter last year and dividing by the absolute value of the latter

and

Stocks with strong volume-weighted momentum, as measured by the ratio of the three-week volume-weighted moving average to the ten-month volume-weighted moving average.

On the whole, I found that measurements of past earnings growth were relatively useless for predicting future earnings growth. In fact, there tends to be a reversion to the mean. The stocks whose earnings per share have grown the most over the last twelve months are less likely to exhibit strong growth over the next twelve months than a random selection. But there was one exception: operating income growth, as measured by the most recent quarter. And indeed, if you look at Seeking Alpha’s articles on individual stocks, they very often use precisely this comparison. It’s a damn good one.

As for volume-weighted momentum, the reason this works is that companies with strong growth prospects attract investors, who bid up the price and are increasingly interested in buying shares.

In third place, with 32% and 26% advantages:

Stocks with low cash-flow accruals, as measured by the difference between net income and operating cash flow, divided by total assets (32% advantage); and stocks with low balance-sheet accruals, measured by the difference between the average net operating assets the last twelve months and the previous twelve months, divided by average total assets over the last two years (26% advantage).

If your net income is low or negative but you have good, strong operating cash flows, you’re likely to see a nice increase in earnings in the near future. The same is true if you’re lowering your net operating assets efficiently (see my piece on this measure here).

In second place, with 34% and 33% advantages:

Stocks with a high current quarter’s EPS estimate as compared to the actual (GAAP) EPS the same quarter last year (34% advantage), and stocks with a high current fiscal year’s EPS estimate as compared to the actual (GAAP) EPS last fiscal year (33% advantage). The actual formula is to take the difference between the estimate and the actual and divide by the absolute value of the actual (if that absolute value is less than five cents, then divide by five cents instead).

I don’t pay attention to analyst ratings or target prices. But analysts definitely have a bead on future earnings.

And now, in first place (drum roll, please), with 42% and 41% advantages (the gold medal goes to . . .):

Companies with the lowest net profit margin (42% advantage) and lowest return on assets (41% advantage) are the companies with the highest earnings growth potential.

This may appear confounding at first, but it makes sense. These are companies with very low earnings and very high sales (if you’re looking at profit margin) or very high assets (if you’re looking at ROA). They thus have the highest potential for growth.

Factors that made relatively little difference to growth potential include those based on free cash flow, analyst ratings, asset turnover, and many others. Companies with high returns—whether that be return on capital, return on equity, or high margins—were significantly less likely to experience strong earnings growth than the average company.

Now, of course, there are plenty of other things to look at when considering buying shares in a company than its potential for earnings growth. But it appears to me that investors should be cautious when using measures like ROA, profit margin, and previous EPS growth—which are all negatively correlated with future earnings growth—when looking at which stocks to buy.

Now here’s the experiment. First, I chose a factor. Using Portfolio123, I ranked the stocks in the Russell 3000 according to that factor fifteen months ago, and chose those ranked in the top quintile (20%)—about 600 stocks. Then for each of those stocks I looked at the percentage change between the most recent four quarters’ EPS and that of the previous four quarters. If the stock had more than a 15% increase in EPS, it got a point. (The reason I ranked the stocks fifteen months ago and then looked at trailing twelve-month EPS growth now is because I wanted to make sure there was no overlap between the factor measurement and the EPS reporting.) Now I had a number—out of those 600 stocks in the top quintile, 266 (for example) reported EPS growth higher than 15%. And I could compare that number to a baseline, which would be derived by looking at all the Russell 3000 stocks and dividing the number with EPS growth higher than 15% by five. I then moved the entire experiment back two years, four years, six years, and eight years, and repeated it. And I tested a large number of different factors.

So, considering these criteria, which are the stocks most likely to experience strong EPS growth over the next year?

Well, currently there are no companies in the Russell 3000 that are in the top quintile for all of these measures. But we could use a ranking system instead. If we take the eight winning factors and weight them evenly, the top ten stocks in the Russell 3000 right now are: Crocs (CROX), DMC Global (BOOM), Molina Healthcare (MOH), Twitter (TWTR), Kadmon Holdings (KDMN), Casella Waste Systems (CWST), Fluidigm (FLDM), Splunk (SPLK), Chegg (CHGG), and Envestnet (ENV). Now I would not recommend investing in all these stocks by any means. You not only want growth, but growth at a reasonable price. I do, however, predict that their EPS growth over the next fifteen months will be strong.

As for stocks I would recommend, Russell 3000 stocks with tremendous EPS growth potential that also rank highly in the evaluation system I intend to shortly offer to the public, they are: Verifone Systems (PAY), Diodes (DIOD), Unisys (UIS), L.B. Foster (FSTR), Heidrick & Struggles International (HSII), Bloomin’ Brands (BLMN), Acorda Therapeutics (ACOR), Citrix Systems (CTXS), Orthofix International (OFIX), and Endurance International Group Holdings (EIGI). All of these companies are in the top five percent of both ranking systems.

My top ten holdings right now: RCKY, WSTL, TG, RCMT, PBIB, MERC, UWN, PTSI, FSTR, BCML.

CAGR since 1/1/16: 48%.

The Problem with Small-Cap Value Indexes

Part I: Indexing Idiocy

MSCI’s value index (MGV, VTV) is seriously lagging behind the USA index (EUSA, PBUS). Its ten-year, five-year, three-year, and one-year CAGRs are all lower. The small-cap index (PBSM) is still ahead if you look at its ten-year CAGR, but way behind on its five-year, three-year, and one-year numbers. And MSCI’s small-cap value index (VBR) has been utterly pitiful: its one-year return as of the end of January was 8.94%, compared to 25.54% for the USA index; its ten-year, five-year, and three-year numbers are also really low. All this has prompted remarks among some investors that the advantages of value and small-caps seem to be vanishing.

This all seems like nonsense to me. Value disappearing? Small caps not doing well? I invest only in low-priced small caps and microcaps, and I made 45% in 2016 and 58% in 2017.

Here’s what’s actually going on: not much has really changed.

If you define “value,” as MSCI does, as a combination of low price-to-book, low P/E, and high dividend yield, you’re defining value all wrong. The price-to-book ratio is one of the worst value ratios you can come up with, since it rewards companies with little to no leverage rather than companies that are using their leverage wisely (I’ve written at length about this here). High dividend yield is only a good thing if the company isn’t paying out more than it takes in (I’ve written at length about this here).

And MSCI isn’t the worst offender at all.

Read the fine print as to how Russell defines its value indexes (IUSV, IWD, IWN, IWS, IWX, OVLU, PXLV, PXMV, PXSV, VONV, VTWV). It creates a three-pronged ranking system. Fifty percent is based on the terrible price-to-book ratio. The other fifty percent is made up of a medium-term growth forecast and the company’s five-year-historical sales growth per share, but ranked negatively, so that the companies with least growth potential get ranked the highest. It’s almost as if they’ve designed the index to fail. And, sure enough, it has. Total returns of the Russell 2000 Value index, as of the end of January, are seriously lagging the Russell 3000 by every single measure from one month to ten years.

I’ll admit, there are some smarter value indexes out there. MSCI, to its credit, has its “Enhanced Value Index” (IVLU), which combines price to book and price to forward earnings with enterprise value to cash flow from operations, and rebalances twice yearly. Sure enough, this index beats their other value indices pretty consistently. But its one-year and three-year record still lags behind their USA index, and it only includes mid- and large caps.

I know I’m committing heresy here, but I’m going to come out and say it: most factor-indexed ETFs are based on idiocy. I can’t understand why anyone would want to invest in, say, SLYV (S&P 600 small-cap value). This is an ETF that rebalances annually (exactly the wrong approach for small-cap value, though it makes sense for large-cap value), defines small-cap as less than $2.1 billion (thus including a huge number of mid-caps), and defines “value” by looking only at equity measures and ignoring all enterprise-value-based measures, as well as ignoring all quality measures. That’s not what value investing is. Well, I guess it is now, but it never was until the rise of all these senseless indexes. Value investing involves serious consideration of a lot of fundamentals, not just three common equity-based measures.

OK, this brings up the basic question: what exactly is value investing? As Michael Mauboussin of Blue Mountain puts it, “There has been a simplistic association between value investing and the basic idea of buying statistically cheap stocks.” And that’s not what value investing really is. “At its core, value investing is buying something for less than what it’s worth.” And what it’s worth can’t be determined by a simplistic statistical approach. You can’t just look at a few price ratios and say, “This is a value stock.” You need to look at a stock’s fundamentals from many different angles. “If you do not have the time or inclination to seek value . . . indexing is a reasonable path.” I would say it’s perhaps the only reasonable path. But just don’t call it “value.”

I find indexing essential. I need to have an index to compare my results with. I can’t do regression analysis without an index. I have no beef with people who want to use a value index to analyze their investment strategy. Indexing is a very useful tool.

But using an index as a tool and investing in it are two very different things. Indexing is fantastic for investors who don’t want to spend the time and energy finding mispriced stocks and figuring out when to buy and sell them. It’s cheap, it’s easy, and it works wonders. Just don’t call it value investing.

Small-cap value investing works, always has worked, and always will work. You just have to work extremely hard at it rather than relying on an index.

Part II: A Better Small-Cap Value Index

Now the difference between investing in small caps and large caps is very simple, and consists of two things. First, large caps are more stable, they’re safer, they’re solid, they don’t jump around like mad. Second, almost all sensibly built (i.e. top decile a lot better than bottom decile) ranking systems based on fundamentals will perform better (i.e. larger difference between top and bottom decile) in a small-cap or microcap universe than in a large-cap universe.

To illustrate this, I’ve created, using Portfolio123, a very simple ranking system based on the three factors in the MSCI enhanced value index, equally weighted. Here’s how it performed in four different universes with a minimum price of $3.00 and a quarterly rebalance since 1999. As you can see, the smaller the capitalization, the bigger the difference in performance.

Now I’m going to go a step further. I’m going to create what I would consider an ideal small-cap value index, again using Portfolio123. I’m going to use eight factors, equally weighted (and I’m not going to tell you what they are unless you pay me big bucks). Four of them are based on the price or enterprise value of the stock, three on its quality and/or growth, and one on its size. This index tracks the 500 top-ranked stocks with market caps greater than $100 million and prices greater than $1.00, with a quarterly rebalance. It does include a few large caps, but it’s equally weighted, so companies with a market cap of over $10 billion only make up about 7% of the index.

This index beats all the others hands down. Since January 2000, with slippage costs of 0.5% each time stocks are bought and sold, it has made a CAGR of 19.27%, compared to SPY’s 5.42%. If you had invested in this index beginning in Y2K, you would have earned almost fifteen times what you would have earned if you’d invested in SPY. This index beat SPY in fourteen out of the last eighteen calendar years, and was within 4% of SPY in seventeen (2011 was a bad  year for it).

Of course, hindsight is 20/20, and I doubt I would have come up with this system back in 1999. But regardless, if you’re a fan of factor index investing, it pays to combine lots of factors in one index. And that’s an increasing trend these days. A slew of multifactor ETFs have come out in the last few years, and that’s a very good thing as long as the factors are transparent and sensible and the fees are low.

But why diversify to five hundred stocks? I know that’s what indexing is all about, but it’s really not essential. If I invest in only the top fifty ranked stocks rather than the top five hundred, the standard deviation of my “index” goes up 15% or 20%, but the returns go up to 27.59% annually, meaning that you would have earned fifty times as much as SPY over the last eighteen years.

So, as you can see, I still believe that a dedicated, systematic small-cap value investing strategy is the best strategy to follow. Which is why it’s such a shame that many of the so-called small-cap value ETFs are misleading investors into putting their money into stocks that are set up to fail.

CAGR since 1/1/15: 49%

My top ten holdings right now: SBFG, CTG, WSTL, BCML, ACNB, RCMT, UWN, PFSW, QTRH, FWP.

Equity Versus Debt: A Showdown

The equity multiplier is a simple formula: assets divided by equity. It’s frequently used as a measure of financial leverage, since assets minus equity equals liabilities. Everyone seems to agree that a lower equity multiplier is better. Investopedia:

It is better to have a low equity multiplier, because a company uses less debt to finance its assets.

The higher a company’s equity multiplier, the higher its debt ratio (liabilities to assets), since the debt ratio is one minus the inverse of the equity multiplier. So it follows that a low debt ratio is also a good thing. As YCharts puts it:

Companies in signs of financial distress will often also have high L/A [liabilities to assets] ratios. A company facing declining revenues and poor long-term prospects of growth will be impacted on retained equity. Companies with low L/A ratios indicate a company with little to no liabilities. With some notable exceptions, this is normally a good sign of financial health for the company.

Every single accounting website I’ve seen says the same thing: lower equity multipliers and lower debt ratios are better than higher ones.

The purpose of this article is to challenge this conventional wisdom and to argue the exact opposite: a high equity multiplier—and therefore a high debt ratio—is actually a good thing.

1. The DuPont Identity

The DuPont Identity is a simple formula. You can break down return on equity (net income divided by shareholder’s equity) into three components: net profit margin (net income divided by net sales), asset turnover (net sales divided by average assets), and equity multiplier (average assets divided by average equity).

So let’s take two companies with similar asset turnover and profit margin. Which one will have the higher return on equity? The one with the higher equity multiplier.

I’ll make this concrete. Let’s look at two companies, Kubota (KUBTY) and W. R. Grace (GRA). Both of them have a 58% asset turnover and a net profit margin between 8.5% and 9%. Kubota has an ROE of 11% while Grace has an ROE of 34%. Huge difference, right? That’s because Grace has an equity multipier of 7.5 while Kubota’s equity multiplier is only 2.1.

Now what does Grace’s huge equity multiplier actually mean, though? It means that it has $2.94 billion dollars in assets and $2.55 billion in liabilities. Compare that to Kubota, with $23.3 billion in assets and $12.1 billion in liabilities. In a word, Grace is far more leveraged than Kubota.

Does that mean that Grace is a worse investment, though? Not at all. (Well, I think it is, but not for that reason.) Both companies have about the same debt-to-EBITDA ratio (3.9 for Grace, 3.8 for Kubota). So neither of them are facing a huge risk there.

My point is that when we look at leverage, we have to also look at the other side of the coin: equity. The more a company is leveraged, the less equity it has. Why? Equity is simply total assets minus total liabilities. And according to the Dupont Identity, the lower the equity, the better the investment.

2. The Cost of Capital

One can reach the same conclusion by looking at the cost of capital. The cost of equity is always higher than the cost of debt, and usually significantly so—double or triple in some cases. Debt may be riskier, but it’s a far cheaper method of funding operations.

In case you’re unfamiliar with classical accounting and the weighted average cost of capital, here’s why the cost of equity is always higher than the cost of debt. In what case would you, as an investor, expect a higher return on a bond (debt) than on a stock in the same company? If your answer is “never,” then you’ve got it down and you can skip the rest of this paragraph. But if you have doubts, think of it this way. If the company goes belly up and you’re holding stock in it, that stock is worthless, but if you’re holding debt, you get paid first. Now if people were to expect the same return on a bond as on a share, then nobody would ever buy stocks. The only reason that stocks are ever bought is that they promise higher returns than bonds.

We’ll come back to this in a minute. First, I want to propose a practical experiment. Let’s say you invested in the top 10%, according to their equity multiplier, of stocks in the Russell 3000 with a $100 million market cap or more, a price of $1.00 or more, excluding financials, real estate, and utilities, with a quarterly rebalance since the beginning of 1999. (Because equity can be negative, I’m using as my formula one minus the ratio of total equity to total assets instead of simply total assets divided by total equity.) These are companies with loads of debt and other liabilities and relatively little equity, companies like Home Depot (HD), Boeing (BA), UPS (UPS), ADP (ADP), and Kimberly-Clark (KMB). (My evaluation system, which I outlined in an earlier article, currently gives them scores of 74, 95, 64, 81, and 88 out of 100.) Using Portfolio123, I can simulate this screen. You would have realized a tidy 10.8% annual return.

If, on the other hand, you’d invested in the bottom 10%, the companies with the lowest debt ratio, the lowest equity multiplier, the fewest total liabilities—companies like Alphabet (GOOGL), Facebook (FB), Cognizant Technology (CTSH), Liberty Broadband (LBRDK), and Snap (SNAP) (scores: 87, 64, 94, 2, and 7)—you would have made a piddly 1.9% annual return.

Now I’m going to be even more extreme. I’m going to create two stock screens. One is of companies with negative equity, companies whose liabilities are greater than their assets, like Philip Morris (PM), McDonald’s (MCD), Lockheed Martin (LMT), Colgate-Palmolive (CL), and HP (HPQ) (scores: 86, 84, 61, 93, and 98). The other is of companies with no debt at all, like Intuitive Surgical (ISRG), Monster (MNST), Align Technology (ALGN), Skyworks Solutions (SWKS), and Ulta Beauty (ULTA) (scores: 60, 42, 31, 85, and 37). I’ll use the same modified Russell 3000 universe, but this time I’ll rebalance yearly. Which do you think will outperform?

Well, the debt-free companies will give you an annualized return of 9.83%, for a total return of 498%. That’s not bad at all. (The reason that this is so much better than the companies with extremely high equity multiples is that most of the high-equity companies not only have little to no debt but have very low other liabilities; the debt-free companies, on the other hand, can have large non-debt liabilities, which are very valuable for a company’s prospects. I’ve written a bit about non-debt liabilities here.)

But the negative equity companies will give you an annualized return of 13.33%, for a total return of 989%. You would have earned about twice as much buying these companies as you would have buying the debt-free ones.

So here’s the paradox. How is it that companies with very little equity and, therefore, lots of leverage, outperform companies with no debt at all?

One answer lies in the cost of capital. There are basically three ways a company can fund its continuing operations and its future growth. It can use cash, which has no cost whatsoever; it can use debt, for which it pays interest; or it can sell shares, which costs a great deal of money.

First, there’s the underwriter’s fee, which can range from 5% to 10% of the proceeds—significantly higher than interest on a loan. There are external auditors’ fees and payments to lawyers. There are all the costs attendant to marketing and publicizing the offer. And then there are onerous auditing costs related to satisfying regulations concerning public companies.

But those costs aren’t even part of the cost of equity, which is, theoretically, simply the return the company is supposed to give its investors to pay them for the risk they take by buying shares. This cost is usually fulfilled through share buybacks and dividend payments.

I’ve run some more numbers using Portfolio123. Last year, the companies in the S&P 500, excluding financial and real estate firms because debt means something totally different for them, spent an average of $2.027 billion on share repurchases and dividends, and an average of $406 million on interest payments. OK, we are in a very low-interest-rate environment right now, so let’s look at the same numbers in 2000, when interest rates were far higher than they are now. The discrepancy wasn’t as large, but it’s still significant: these firms spent an average of $476 million on share repurchases and dividends, and only $214 million on interest. To put these figures in perspective, the current average equity of these companies ($12.1 billion) is almost the same as its debt ($11.6 billion), and the same was true back in 2000 ($3.2 billion to $3.3 billion). Clearly the cost of equity is far higher.

Now I’m not saying that companies with negative equity never pay dividends or buy back shares—of course they do, and in spades. But their huge debt load, which is comparatively cheap, gives them a much greater ability to grow. The median EPS increase over the last twelve months of stocks in the modified Russell 3000 universe specified above that had negative equity a year ago is 20.86%; the median EPS increase of those that were debt-free is only 3.38%. Now that is quite a difference indeed.

3. The Risks of Debt and Equity

Now the other major difference between equity and debt financing is risk. Debt is risky—too much debt, and your company will go bankrupt. And according to classical accounting/portfolio theory, equity is basically risk-free—no matter how much equity you issue, you’re not going to go bankrupt by issuing more. So the higher costs of equity have been traditionally balanced by its lower risk, and the lower cost of debt is balanced by its higher risk. That’s the foundation of the Modigliani-Miller theorem, which maintains that capital structure is irrelevant.

But there are two problems with this theory. The first, which has been long recognized and is related only to cost, not to risk, is that the Modigliani-Miller theorem doesn’t take into account the tax benefits of debt. Interest payments are fully deductible; dividends and stock buybacks are not. Therefore, even when taking risk into account, debt financing is better than equity financing.

The second problem is that the theorem doesn’t take into account that equity, especially for small firms, now carries great risk. There’s a terrific interview with Marc Andreessen here which explains exactly how risky it is for a small company to go public nowadays.

But let’s just go with Modigliani-Miller for a moment and assume that we want to mitigate the risk of debt. The best way to do so is to use the debt-to-EBITDA ratio, since this is the ratio most commonly used by credit rating agencies when they’re assessing a company’s solvency. Let’s say you had invested in the non-financial, non-real estate Russell 3000 stocks with a debt-to-EBITDA ratio greater than 8, rebalancing quarterly since 1999. These are companies with lots of debt and low earnings, companies like Tesla (TSLA), Ford (F), ServiceNow (NOW), Alliance Data Systems (ADS), and Cheniere Energy (LNG) (scores: 1, 96, 40, 77, and 1). You would have earned an annualized return of only 2.4%, compared to SPY’s return of 6.21%. And that’s not taking into account all the companies with negative EBITDA—companies like Workday (WDAY), Autodesk (ADSK), Square (SQ), Biomarin (BMRN), and Hess (HES) (scores: 41, 48, 15, 55, and 7)—whose annualized return would have been –2.43%.

I’m going to do another experiment that takes this into account. I’m going to create a system that ranks stocks based on two factors: the equity multiplier (I’ll reverse this and use equity to assets, with lower numbers better, since I want to reward companies with negative equity) and the debt-to-EBITDA ratio (to include negative EBITDA companies and zero-debt companies, I’ll reverse the ratio with a minimum denominator of $1 million and give higher numbers better ranks). This will basically reward companies with very little equity and a decent ability to pay their debts. Just to prove my point, I’m going to weight these two rankings 3-to-1 in favor of the equity multiplier. Now I’m going to test the performance of this system on two universes: the S&P 500 and the Russell 3000 (both excluding financial and real estate firms) based on a monthly rebalance since January 1999. Here’s the result, with the numbers on the left representing annualized percentage returns for each decile:

As you can see, by diminishing the risk factor of debt just slightly, we end up with a very nice ranking system that rewards high-equity-multiplier companies. Just to reiterate, this ranking system would have been exactly the same if it had been based on the debt ratio rather than the equity multiplier. Because of the high cost of equity, high-debt companies outperform as long as their debt doesn’t exceed their earnings by too much.

4. Book Value

I’ve been spending this whole article talking about equity without bringing up a very important identity: equity (assets minus liabilities) = book value. They are exactly the same.

As I’ve shown, as long as you exclude companies with unsustainable debt levels as measured by debt-to-EBITDA, it’s better to invest in companies with a very low book value than companies with a very high book value, at least if you compare that book value to total assets. But if you use the price-to-book ratio, you’re going to be favoring companies with a high book value (relative to their market cap), and therefore a low equity multiplier. And that doesn’t really work very well.

Let’s say you start with the S&P 1500 and exclude financials and real estate companies. Now let’s say you invest only in stocks with a price-to-book ratio of less than 1, rebalancing quarterly, with a 0.5% slippage each rebalancing—stocks like Allergan (AGN), National Oilwell Varco (NOV), Baker Hughes (BHGE), CenturyLink (CTL), and News Corp (NWSA) (scores: 52, 20, 14, 28, and 95). Your total return since 1999 would be 109%, which is half as much as investing in SPY (216%). If instead you had invested only in stocks with a price-to-book ratio greater than 5—companies that today would include Apple (AAPL), Microsoft (MSFT), Amazon (AMZN), Alibaba (BABA), and Johnson and Johnson (JNJ) (scores: 73, 88, 53, 39, and 84)—you would have made 408%. That’s quite a difference.

(The reason I excluded financial and real estate companies from this analysis is that price to tangible book value is a good criteria for valuing companies in the financial sector and price to net asset value—which is often quite close to book value—is a good criteria for those in the real estate sector. Outside those two sectors, however, I think price to book value is worthless.)

What makes this truly pernicious is that a large number of institutions have classified stocks into “growth” and “value” classes, and define “value” as stocks with low price-to-book ratios. I have not come across a more useless definition of value, nor one more contrary to the way value investing really should work. Simply put, the relationship of the market value and the book value of equity tells you almost nothing of any use because it ignores almost everything of importance about the company and treats the entirety of a company’s debt as a problem rather than a possible solution.

One of the great things about enterprise-value-based valuation ratios (EV to EBITDA, unlevered free cash flow to EV, EV to gross profit, etc.) is that the enterprise value of a company is a kind of shorthand for its cost of capital. Remember that EV is market cap plus debt minus cash. Market cap is the market value of equity, and has the highest cost of capital, so it carries a lot of weight in determining EV. Debt in this equation is valued far lower than its market value, since the equation doesn’t include interest payments; this is the right approach since debt has a lower cost of capital. Cash has no cost whatsoever, and can be used to either buy back shares or pay down debt; its weight in EV is negative, which reflects how wonderful it is. In other words, a company’s cost of capital is going to be roughly proportional to its enterprise value. So if you’re worried about the cost of capital, it makes a lot more sense to use enterprise value-based ratios than book value-based ratios when evaluating your stock picks.

So I propose that instead of looking at price to book value as your default balance-sheet ratio to estimate the worth of a company, look at enterprise value to total assets. This ratio is seldom used, but it works very nicely. Here’s how it has worked if you rebalanced stocks in the Russell 3000 (excluding financials, real estate, and stocks under $1.00) monthly since 1999:

5. The Biggest Debt-Related Mistakes Investors Make

In sum, here are the big mistakes that investors commonly make when it comes to looking at a company’s debt (or equity multiplier):

• They determine whether a company is overleveraged by looking at its debt ratio or its equity multiplier. They should instead look at its debt-to-EBITDA ratio.
• They focus only on whether a company is reducing or increasing its debt and not on whether it’s increasing or reducing its equity. The cost of equity is always greater than the cost of debt.
• They use the price-to-book ratio as a shortcut for value instead of looking at a range of other measures.

6. The Paradox of Debt and Equity

Why do we investors make these mistakes? It’s because when we think about debt, we think about household debt, personal debt, credit card debt, the national debt, debtor’s prisons in Dickens novels, student loan debt, collateralized debt obligations, and so on and on. Debt is a bad word. And when we think about equity, we think about the equity we have in our houses, and about stocks, and how they go up and up and yield great returns, and how much fun it is to pick them, and how much more rewarding it’s been investing in equity ETFs than fixed-income ETFs, and so on and on. Equity is a nice word.

But none of these concepts apply to running a successful public company. A public company is entirely different from a person, or a household, or a government. It has equity costs, and we don’t.

So imagine that you're a public company.

You—yes, you, with your credit-card debt, your monthly mortgage payments, and your outstanding student loan—sold, a few years ago, a large percentage of your future earnings, in perpetuity, to other people so that you could afford what you needed at that time. And those people have the power to decide what you do with the rest of your life so that their income from that percentage will be maximized.

There’s really only one parallel to this in contemporary life: if you’re a prostitute, you pay your pimp a percentage of your earnings, and he gets to decide what you wear and how many clients you service and where you get them from. A bygone parallel is the case of a slave who gets to keep a small portion of his or her earnings, which was actually quite common in the eighteenth century. At any rate, in this scenario, someone, or a group of people, basically owns you.

Now if you could save enough money, which would you do first—buy back your future earnings and your decision-making power by paying off the owners, essentially engaging in a massive share buyback? Or pay down your debts? And if you could buy back your future earnings now by maxing out your credit card, wouldn’t you do so, provided your earnings were sufficient to eventually pay it off?

That’s how we should think of equity. Equity, for public companies, is prostitution (or slavery—take your pick). Debt is freedom.

OK, that’s a little extreme. But I wanted to make a point. Don’t put down companies with large debts but decent earnings. Don’t imagine that book value is a good comparison to a stock’s price. Don’t scoff at share buybacks, which reduce equity. Don’t imagine that paying down debt will increase growth. Instead, take a long, hard look at what its debt and equity really mean for a company and its future, and invest accordingly.

7. Postscript: The Future of Equity

I’m no expert in macroeconomics, and I normally avoid writing about it. But I suspect that we’re in a moment when the cost of equity, historically speaking, is at a near-record high and the cost of debt at a near-record low. Interest rates on corporate bonds are so low at this point that investors are putting a larger percentage of their money in stocks than at any time since the dot-com boom. (See this chart, which tracks the allocation to equities among overall investments.) This drives up stock prices, which contributes to the high cost of equity. Then this cost, along with onerous regulations and unlimited short selling, ensures that IPOs, especially of small companies, are drying up altogether (here's an article about that). Meanwhile, also because of the high cost of equity, stock buybacks are at a historic high. This in turn creates a scarcity of investable stocks, which drives up prices even further. It’s a vicious cycle.

This cycle can be broken, however, and surely will be at some point. Regulations on public corporations can be relaxed to encourage private firms to go public. IPO costs can fall because of decreased demand. Interest rates can rise, increasing the cost of debt, moving investment money from stocks to bonds, and lowering the relative cost of equity. Stocks can enter a bear market, prompting equity costs to fall. Any one of these things can precipitate a change, and all four seem somewhat likely to me.

While equity will always be more expensive than debt, the disparity doesn’t have to be as huge as it is right now. But while it is huge—before all these things happen—it pays for individual stock-pickers like you and me to pay far less attention to company debt than most people think we should.

CAGR since 1/1/15: 48%

My top ten holdings right now: HDNG, BBRG, CERC, CTG, NWY, WSTL, UWN, HURC, GSL, BCML.

Philosophers and Poets

I love to read, and when I come across words that strike me as particularly wise, I often write them down. It struck me the other day that some of these words can be applied to investing. So here, in chronological order, are some quotations and their implications.

Heraclitus was one of the first philosophers, even before Socrates, and is perhaps my favorite of them all.

The most beautiful order of the world is still a random gathering of things insignificant in themselves.

Next time you see an especially convincing chart touting some technical analysis or market-timing breakthrough, remind yourself of this.

Hidden connections are stronger than obvious ones.

The connection between the price of a stock and its intrinsic value is obvious. Here is the price, here is what it’s worth, and one should correspond to the other. But this is an extremely weak connection, since the price will shoot up or come crashing down on the slightest provocation. The connection between a company’s free cash flow and its ability to generate growth, on the other hand, is hidden by a multitude of other numbers. And it’s pretty strong. The object of the savvy investor is to uncover hidden connections.

Kohelet is the pseudonym of the author of the book of Ecclesiastes (the title of which is a Latin mistransliteration of that name). This is one of my favorite books of the Bible, and some folks claim it was written by King Solomon, one of my ancestors.

In the day of prosperity be joyful, but in the day of adversity consider: God also hath set the one over against the other, to the end that man should find nothing after him.

I like to paraphrase this as follows: The only reason for God’s actions is to prevent us from predicting them. One could say exactly the same thing about Mr. Market. Think of the current euphoria in equities this way: the real reason for it is to confound money managers.

Dante wrote the Inferno, which traces a visit to Hell, a playground just a few feet under Wall Street. One of the people who live there told him,

                                     . . . we can behold

     Remote things well, for so much light does He

Who rules supreme still grant us; but we are foiled

     When things draw near us, and our intelligence

     Is useless when they are present. . . . (translated by Robert Pinsky)

This denizen must have been an investor, since investors have no idea what the price of a stock will be tomorrow but are absolutely certain that it will be higher a year from now.

Søren Kierkegaard is one of my other favorite philosophers. He wrote an entire book about boredom (Either/Or), and it’s not the least bit boring.

Life can only be understood backwards, but it must be lived forwards.

Now that’s what backtesting is all about. And why getting good out-of-sample performance can be so hard.

Rainer Maria Rilke was a poet full of advice, so he inadvertently founded the self-help movement. He would have been horrified by it, though. One thing he said gives the lie to it all:

We must hold to what is difficult.

Apply this with appropriate seriousness to investing. We’re always presented with easy ways to make money, only to find that they don’t actually work. We must embrace difficulty if we’re going to succeed.

Sugar Ray Robinson was not just the greatest boxer in history, but came up with a line that has long struck me as applicable to all sorts of endeavors:

The best is always fragile.

You can apply that to investing in numerous ways. For instance, your most successful investment is the one most likely to collapse. Or the thing that makes you richest is also the riskiest. Or the peak of your wealth will likely be followed by your biggest drawdown.

This brings me to our next poet, James Merrill, a great American writer. One of his most brilliant lines is:

Au fond each summit is a cul-de-sac.

That’s a great thing to keep in mind the next time your portfolio reaches a new high.

Tom Waits is my last poet/philosopher today. His interviews are as entertaining as his music, and in one of them, he said:

There is no such thing as truth. People who really know what happened aren’t talking. And the people who don’t have a clue, you can’t shut them up.

Yes, we can apply the “people who don’t have a clue” bit to President Trump. But we can also apply it to stock market commentators, economic prognosticators, and all those people trying to pitch you some magic formula that will make you rich. And the “people who really know what happened” have all signed non-disclosure agreements.

As for the words of wisdom of actual investors, well, someone else can give that a shot—and websites like ValueWalk.com do so every day. But I’ll leave you with one aperçu, from George Soros, a man well worth listening to:

The prevailing wisdom is that markets are always right. I take the opposite position. I assume that markets are always wrong.

Amen to that.

My top ten holdings right now: CERC, HDNG, FWP, NWY, WSTL, CTG, ZYXI, BBRG, GSL, HURC.

CAGR since 1/1/2015: 57%.

The Ideal Stock Evaluation System?

This is the title of an article I wrote, posted this morning on Seeking Alpha here. Normally I post my articles on this page too, but in this case I wanted to keep the comments all there. Check it out and add your comments.

My top ten holdings right now: CERC, HDNG, NWY, FWP, WSTL, HURC, BBRG, CTG, LXFR, UWN.

CAGR since 1/1/15: 54%.

Rethinking Free Cash Flow

The term “free cash flow” has a rather curious history, with a variety of shifting meanings over the last thirty-odd years. It has always carried the meaning of cash flow in excess of that required for operations, but the nuances, implications, and use of the term have undergone quite a transformation. I’m going to outline three ways to think about and calculate free cash flow, and argue in favor of the last and most recent.

The term originated with Joel M. Stern in 1972 as an alternative to earnings. Stern initially calculated it as “net operating profits after taxes minus the amount of new capital investment required in order to generate future profits.” It was Stern who suggested subtracting capital expenditures from cash flow when doing discounted cash flow analysis. This is a rough equivalent to Warren Buffett’s “owner earnings,” as spelled out in the appendix to his 1986 shareholder’s letter.

Also in 1986, coincidentally, Michael C. Jensen, published an article called “Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers.” After defining free cash flow as “cash flow in excess of that required to fund all projects that have positive net present values when discounted at the relevant cost of capital” (following Stern’s lead), Jensen wrote, “Such free cash flow must be paid out to shareholders if the firm is to be efficient and to maximize value for shareholders.” Jensen saw free cash flow as a problem rather than a good thing:

Conflicts of interest between shareholders and management over payout policies are especially severe when the organization generates substantial free cash flow. The problem is how to motivate managers to disgorge the cash rather than invest it below the cost of capital or waste it through organizational inefficiencies.

For Jensen, free cash flow couldn’t finance growth, since by definition it was excess to the cash flow needed for growth—it was an inefficiency. Jensen’s theory was widely discussed by scholars and for more than two decades free cash flow remained an inefficiency, a source of “agency costs.” Basically, free cash flow provided managers opportunities to waste money on unprofitable investments. Many papers were written supporting this theory. For the purposes of these papers, free cash flow was generally defined as undistributed cash flow in excess of that needed for positive net present value projects and was calculated as operating income before depreciation minus taxes, interest expense, and total dividends; often capital expenditures were deducted as well. Over the years, though, a revised calculation came into general use: cash flow from operations minus capital expenditures minus dividends paid.

Unlike scholars, investors continued to follow Stern’s idea of using free cash flow as an alternative to earnings in order to evaluate a company’s quality and value. Seth A. Klarman’s brilliant preface to the sixth edition of Graham and Dodd’s Security Analysis, written in 2009, includes the following passage:

While Graham looked at corporate earnings and dividend payments as barometers of a company’s health, most value investors today analyze free cash flow. This is the cash generated annually from the operations of a business after all capital expenditures are made and changes in working capital are considered. Investors have increasingly turned to this metric because reported earnings can be an accounting fiction, masking the cash generated by a business or implying positive cash generation when there is none. Today’s investors have rightly concluded that following the cash—as the manager of a business must do—is the most reliable and revealing means of assessing a company.

In 1988, the Security and Exchange Commission required that companies provide not only a balance sheet and an income statement in their reports but a cash flow statement as well, and the numbers in the three reports had to be reconciled. At some point, this forced investors to start looking at the other items in the investing section of the cash flow statement besides capital expenditures. Doing so led Stephen Penman, for example, to use cash flow from investments rather than capital expenditures to calculate free cash flow in his now standard textbook, Financial Statement Analysis and Security Valuation. Penman is hardly alone in this practice.

The term free cash flow, then, has come to be thought of in three different ways.

1. Stern’s original concept, seconded by Buffett and Klarman: free cash flow as an alternative to earnings per share and the basis for discounted cash flow analysis. These days one usually calculates it by taking cash flow from operations and subtracting capital expenditure—often subtracting only those capital expenditures necessary for maintaining operations. If one is then using this for discounted cash flow analysis, comparing it with the company’s enterprise value, one must add back after-tax interest expense to get unlevered free cash flow.
2. Free cash flow as an inefficiency, as in Jensen’s 1986 article. Here one starts with the above definition and then subtracts dividends paid.
3. The sum total of all cash flows from operations and investments (in the cash flow statement, cash flows from investments are the negative of Penman’s term cash investments). In essence this means subtracting not only capital expenses but also acquisitions, and adding back divestitures and various other investment-related income.

When I’m not doing discounted cash flow analysis—when I’m looking at free cash flow growth, free cash flow margin, free cash flow to assets, or free cash flow to price—I prefer definition #3, which puts me in the minority of value investors. Basically this definition makes no distinction between capital expenses and acquisitions. There's a strong case to be made, especially when it comes to tech and pharmaceutical companies, that this distinction no longer applies. And if we treat acquisitions as capital expenditures, why should divestitures not diminish capital expenditures?

It has been argued that acquisitions are usually one-time expenditures, but I've found that not to be the case. If you screen on Portfolio123 for companies that reported acquisitions over the last year, well over half (as high as 80%, depending on what universe you look at) also reported acquisitions either the year before or the year before that.

What about cash from other investing activities? Let’s take Bloomin’ Brands, for example. In 2016, the company reported over $530 million in cash proceeds from sale-leaseback transactions—basically, they sold 153 restaurants at fair market value. Now when all those restaurants had been originally bought or built, the cost had been accounted as capital expenditures, and was deducted from free cash flow. So when they were sold, why shouldn’t that be added to the company’s free cash flow?

On a more basic level, if we’re using free cash flow as Seth Klarman suggests we do—as a way to “follow the cash”—does it make sense to ignore acquisitions, divestitures, and other investment activity? How exactly does one justify deducting the purchase of a building from free cash flow but not the purchase of a subsidiary? Especially if the subsidiary will contribute more immediately to operating income than the building?

Interestingly, Stephen Penman’s problem with discounted cash flow analysis is that, as he writes, “GE earned one of the highest stock returns of all U.S. companies from 1993–2004, yet its free cash flows are negative for all years except 2003. . . . During the years 1996–2000, [Starbucks’] stock price more than doubled. Yet the free cash flows are consistently negative.” I can provide plenty of more up-to-date examples of companies whose annual free cash flows have been negative for five years running while their price has doubled: Netflix, Baidu, Cheniere Energy, Diamondback Energy, Cimarex Energy, Alnylam, Exelixis, Seattle Genetics, SMI, Amerco, and so on. These companies are consistently spending more on investments than they’re getting from operations.

But what else do these companies have in common? They usually either have terrible earnings or terrible total-debt-to-EBITDA ratios. In fact, if you take the fifty largest companies (excluding those in the financial, real estate, and utilities sector) with negative free cash flows over each of the last five years but whose price has doubled nonetheless, an astonishing forty of them (80%) reported either a negative EBITDA or a debt-to-EBITDA ratio greater than 4.0 in their most recent annual report. If you look at the S&P 500 as a whole, only 16% of companies outside those three sectors reported negative EBITDAs or debt-to-EBITDA ratios greater than 4.0. In other words, the negative free-cash-flow companies really need to generate some positive free cash flow in order to increase their earnings and/or pay down their debts. I'm not saying that companies can't succeed with consistently negative free cash flows—clearly Netflix, Baidu, SMI, Amerco, and InterXion, all of which have decent debt-to-EBITDA ratios, have. But it's much harder to do so.

I recently created a simple ranking system based on a company’s recent free cash flow. Every company is ranked equally on five factors: the ratio of its trailing twelve-month free cash flow to its total assets, its total sales, and its fully diluted market cap; its year-to-year free cash flow growth; and the ratio of its unlevered free cash flow to its enterprise value. For all of these I used the contemporary definition of free cash flow as cash flow from operations plus cash flow from investments, with the exception of the last, for which I used the more conventional definition of unlevered free cash flow as cash flow from operations minus capital expenditures plus after-tax interest expense. Using Portfolio123, I then looked at the performance of this ranking system on stocks in the S&P 1500 (excluding utilities, REITs, and MLPs) with a one-month rebalance since January 1999. The result (including dividends) is below. As you can see, it's definitely worthwhile taking free cash flow into account when investing.

Lastly, I’d like to recommend five undervalued companies with good, healthy cash flows that I think are worth investing in: Forward Pharma (FWP), Points International (PCOM), Cambium Learning Group (ABCD), Triple-S Management (GTS), and Bayer (BAYRY).

My top ten holdings right now: CERC, HDNG, FWP, NWY, LXFR, KTEC, UWN, WSTL, SEAC, UTSI.

CAGR since 1/1/2015: 54%.

My Favorite Balance-Sheet Ratio

In this piece I want to drill down deep into a ratio that I find extremely useful in assessing potential investments: the ratio of net operating assets (NOA) to total assets (the lower, the better). It’s my favorite balance-sheet ratio.

In a 2004 paper entitled “Do Investors Overvalue Firms with Bloated Balance Sheets,” David Hirshleifer, Kewei Hou, Siew Hong Teoh, and Yinglei Zhang came to the following conclusion: “In our 1964–2002 sample, net operating assets scaled by beginning total assets is a strong negative predictor of long-run stock returns. Predictability is robust with respect to an extensive set of controls and testing methods.” Their data seems convincing to me.

The ratio has produced similar results for the last twenty years too. I divided companies in the Russell 1000 into deciles depending on the ratio of NOA to total assets, with a monthly rebalance since January 1999, and looked at their price performance, using data available from Portfolio123. Here are the results, with the right-most decile having the lowest ratio. (The left-most bar is the return of the S&P 500 without dividends; the other bars include dividends.)

Hirshleifer et al. explain their conclusions by invoking investor behavior: “The financial position of a firm with high net operating assets superficially looks attractive, but is deteriorating, like an overripe fruit ready to drop from the tree.”

But there are other ways to explain this phenomenon. Like Wallace Stevens did in “Thirteen Ways of Looking at a Blackbird,” I’m going to look at eight different ways to define or calculate NOA.

1. This is the basic definition: subtract operating liabilities from operating assets, and you get NOA. Operating assets are the total assets minus cash and equivalents; operating liabilities are the total liabilities minus total debt.

Let’s look at an imaginary company that has ten widgets in its inventory valued at $10 apiece, a factory valued at $100, $50 in cash, and $100 in debt. Its NOA, then, is $200, compared to $250 in total assets, for an NOA ratio of 0.8. Now let’s say it sells five of its widgets for $20 in cash apiece, and it creates five more widgets at $10 apiece, deferring the cost of doing so (on the balance sheet, it has $50 in payables). Its NOA is now $150, compared to $350 in total assets, for a ratio of 0.43. As you can see, as you do business wisely, you reduce your NOA.

Now let’s look at another company that starts from an identical position but does business a bit differently. It sells its five widgets but doesn’t get paid up front (on the balance sheet, it now has $100 in receivables), and creates five more widgets using its cash reserve of $50. Both companies have a net income of $50, $200 in equity, and $100 in debt. But company B’s net operating assets will be $300, with an NOA ratio of 1.

Now which company is in a better financial position? Company A has $150 in cash and company B has none. Company A can pay off its receivables, pay down its debt, and/or invest in more widget production; company B can’t do anything until it gets paid, borrows more money, or issues more shares.

2. The current NOA is the NOA at the firm’s inception plus the accumulated balance-sheet accruals since then.

The CFA Institute defines accruals in two different ways, one based on the cash-flow statement, and the other based on the balance sheet. The balance sheet accruals number is simply the increase in NOA from one period to the next. It therefore follows that NOA is the sum of all the accruals over the history of the firm in addition to whatever operating assets the firm started with. A company with low accruals is going to have lower NOA than it used to, so a company with low or negative NOA is going to be one with historically low accruals.

3. NOA is the sum of all debt, all equity, and all non-controlling interest, minus cash and equivalents.

What is the ideal way to finance the ongoing operations of your company? Clearly, the answer is with cash. Cash has no costs. Debt has interest costs and risk; equity dilutes the ownership of your company and has high costs due to investor expectations. Therefore, the more of your assets are in cash and equivalents and the less are in debt and equity, the lower your cost of continuing operations will be.

4. NOA can be calculated by subtracting cash, equivalents, and non-debt liabilities from total assets.

You can rank companies, as Hirschleifer et al. and I did above, on the ratio of net operating assets to total assets, with the lower values getting higher ranks. But you could alternatively rank companies on the ratio of cash and equivalents and non-debt liabilities to total assets, with higher values getting higher ranks, and come up with the exactly the same rankings. I’ve just explained why a company with plenty of cash is primed to grow, but what about non-debt liabilities? These consist primarily of accounts payable, deferred liability charges, and minority interest; also included might be accrued expenses, deferred revenue, deferred taxes, and commercial paper. These liabilities are often investable in the short term, and they cost nothing. They’re very roughly equivalent to what Warren Buffett calls, in insurance companies, “float.” To quote from the Berkshire Hathaway Owner’s Manual, “Berkshire has access to two low-cost, non-perilous sources of leverage that allow us to safely own far more assets than our equity capital alone would permit: deferred taxes and ‘float,’ the funds of others that our insurance business holds because it receives premiums before needing to pay out losses. . . . Better yet, this funding to date has been cost-free. Deferred tax liabilities bear no interest. . . . Neither item, of course, is equity; these are real liabilities. But they are liabilities without covenants or due dates attached to them. In effect, they give us the benefit of debt—an ability to have more assets working for us—but saddle us with none of its drawbacks.”

5. For a company with a price-to-book ratio of 1, NOA is exactly the same as enterprise value (EV). EV is defined as market capitalization plus preferred equity plus non-controlling interest minus cash and equivalents plus total debt; NOA can be defined in exactly the same way except by substituting book value, or common equity, for market cap.

In every EV-based valuation ratio—EV to EBITDA, EV to gross profit, EV to sales, or the classic of discounted cash flow analysis, unlevered free cash flow to EV—the lower the enterprise value, the better. So it stands to reason that if a company’s price-to-book ratio is more or less 1, the lower the NOA, the better.

6. Since common equity is the sum of net operating and net financial assets, NOA is equivalent to common equity minus net financial assets. Financial assets (as opposed to operating assets) are cash and equivalents; financial liabilities are debt, preferred equity, and non-controlling interest; and net financial assets is the difference between them.

Of all a company’s sources of capital, common equity has the highest cost. So a company with a low ratio of common equity to net financial assets is probably going to be healthier than a company with a high ratio. Remember that in DuPont analysis, return on equity is profit margin times asset turnover times the ratio of assets to equity. Clearly having a lot more assets than common equity is a good thing.

7. Today’s NOA is last year’s (or quarter’s or decade’s) NOA plus accumulated net operating profit after taxes (NOPAT) since then minus accumulated free cash flow (defined as the sum of cash flow from operations and cash flow from investments—the latter is usually a negative number). Using the same logic as I used in definition 2, NOA is therefore the accumulated NOPAT since the company’s inception minus its accumulated free cash flow. These equivalences come from Stephen Penman’s book Financial Statement Analysis and Security Valuation; his accounting reformulations depart from GAAP in many instances, so if you stick to GAAP numbers, your calculation of NOA based on NOPAT and free cash flow will be a bit off. However, in 90% of the Russell 1000, the difference between this definition and the previous definitions is less than 10%.

This is the crux of Hirshleifer et al.’s argument: “When cumulative net operating income (accounting value added) outstrips cumulative free cash flow (cash value added), subsequent earnings growth is weak. In this circumstance, we argue that investors with limited attention overvalue the firm, because naïve earnings-based valuation disregards the firm’s relative lack of success in generating cash flows in excess of investment needs.” They put it another way too: “Net operating assets are a cumulative measure of the discrepancy between accounting value added and cash value added—‘balance sheet bloat.’ An accumulation of accounting earnings without a commensurate accumulation of free cash flows raises doubts about future profitability.”

Companies with higher NOA ratios tend to have higher earnings at the present time, simply because of their accumulated profit. But their growth potential is significantly lower than companies with low NOA ratios.

From this understanding Hirshleifer et al. derive an eighth equivalence:

8. NOA is the accumulated accruals since the company’s inception (as measured by the difference between NOPAT and cash flow from operations) plus the accumulated investment in operating assets (the negative cash flow from investments).

There’s nothing wrong with having deep investment in operating assets, but a company with a history of negative accruals is able to convert cash into earnings much faster than one with a history of positive accruals.

I’ll close by naming twenty-one companies with very low or negative net operating assets that may be worth investing in. These are all stable companies with signs of healthy growth and are, in my opinion, undervalued; they’re all pretty cash-rich too. They are: Bank Butterfield and Son (NTB), Barrett Business Services (BBSI), BayCom (BCML), CorVel (CRVL), Forrester Research (FORR), Fortinet (FTNT), Forward Pharma (FWP), Grupo Aeropuertuario del Pacifico (PAC), Heritage Commerce (HTBK), HP (HPQ), Humana (HUM), Insperity (NSP), Lazard (LAZ), Plumas Bancorp (PLBC), Points International (PCOM), Royal Bank of Canada (RY), Timberland Bancorp (TSBK), Trend Micro (TMICY), TrustCo Bank (TRST), United Security Bancshares (UBFO), and XO Group (XOXO).

My top ten holdings right now: CERC, HDNG, KTEC, CNCE, LXFR, NWY, SEAC, FWP, UTSI, WSTL.

CAGR since 1/1/16: 51%.

The Abominable Anomalousness of the Anomaly Analogy

The other night I asked my son, a high school student who knows next to nothing about economics or the stock market, “Which is more likely to grow faster, a small company or a large company?” He answered, “A small company.” Then I asked him, “Which will rise in price faster, a company whose price is cheap compared to what it earns, or a company whose price is expensive?” He answered, “The cheap one.”

An anomaly is a strange or unusual occurrence, a deviation from the rule. Academics talk of the fact that small firms grow faster than large firms as a “size anomaly.” The fact that cheap stocks usually rise in price faster than expensive stocks is a “value anomaly.” But are these really “anomalies”? Or, like my high-school student suggested, are they in the very nature of firms?

I don’t want to go into the whole history of the efficient market hypothesis (EMH), the capital asset pricing model, and the application of Thomas Kuhn’s paradigm-shift theory to them, which is why these things are called “anomalies.” Instead I want to look at the big metaphor (the analogy) behind the term.

Back in 1972, Eugene Fama proposed that we could work with a model of “a capital market that is efficient in the sense that prices at every point in time fully reflect available information.” He has stuck with his theory of an efficient market, and even won the Nobel prize for it in 2013. Basically, the EMH views the stock market as a rather well-oiled machine. An anomaly, then, is analogous to a gear that’s gone slightly out of place.

I’d like to propose a different metaphor. The stock market is a badly oiled contraption, stuck together with cellophane tape and staples, and full of rust spots and leaks and broken parts. Its pricing mechanism is terrible and inefficient, and it runs a crazy, circuitous, and illogical course. Why? Because many of the price movements in stocks are based on the quirks of human behavior rather than on sound financial sense.

In this model, what the academics call an “anomaly” is really a thing in the machine that actually works the way it’s supposed to.

The reason movements in stock prices are so confoundedly difficult to predict is not because they’re efficient and reflect all known information, but because they are the products of thousands of small overreactions, unfulfilled expectations, and misguided second guesses. Rather than cancelling each other out, as Fama suggests, these behavioral quirks make stock prices far more volatile than they should be, and make them move in entirely unexpected directions.

This is where the savvy investor gets an advantage. By looking at the general principles behind this machine, she can see through all the smoke, hear through all the noise, and figure out approximately what certain stocks are doing and what they’re likely to do in the future.

Fama’s view of the stock market is Orwellian. In 1984, war is peace, freedom is slavery, and ignorance is strength. For Fama, a common-sense principle is an anomaly. So let me list, in alphabetical order, four of the many “anomalies,” or common-sense principles, that really govern the stock market:

1. The accruals anomaly. Companies with low accruals—whose earnings are backed by real cash transactions in the present—are more likely to do well than companies whose earnings are all predicated on future cash flows.
2. The size anomaly. Small companies generally grow faster than large companies.
3. The stability anomaly. Companies whose sales and earnings grow at a modest but steady rate are more likely to keep growing at a modest but steady rate than companies that are growing or shrinking extremely fast. Similarly, companies with big changes in margin—in other words, that are increasing their sales while decreasing their earnings, or increasing their earnings while decreasing their sales—are more likely to fall in price than companies that keep their margins steady by increasing both their sales and their earnings.
4. The value anomaly. Stocks whose price is low compared to similar companies with similar sales, earnings, and free cash flow are more likely to increase in price than stocks whose price is high.

All of these principles should either be immediately apparent after a few moments’ thought or can be easily explained in a paragraph or two. One doesn’t need elaborate models of stock behavior or decades worth of backtests to come to these conclusions.

Now these are not precisely the same anomalies that Fama and his accomplice Kenneth R. French talk about. Their “value anomaly” is based on book value alone, which even Benjamin Graham thought was a silly idea. Their “momentum anomaly” makes even less sense. But the size and accruals “anomalies” are very similar to theirs.

So if these are general principles rather than anomalies, what are the real anomalies in stock market behavior? Or are there any?

Let’s go back to my model of the stock market as a huge but terribly inefficient machine held together with matchsticks and glue. What would qualify as a “strange or unusual occurrence” for such a machine? Even a total breakdown, as happened in 1929 and 2008, wouldn’t be an anomaly. Nor would various other inefficiencies, like the overvaluation of “momentum” stocks, the huge jumps in price after earnings reports that showcase unsustainable growth, the huge drops in price when a firm decides to issue a few extra shares, and so on.

No, the only real “anomaly” in today’s stock market is the dominance in popular opinion of the academic view that the stock market is a well-oiled machine, that stock prices just reflect all available information, and that inefficiently priced stocks simply don’t exist.

My top ten holdings right now: SMMT, CVV, HDNG, ALSK, LXFR, VHI, QNST, ACNB, ELMD, GSL.

CAGR since 1/1/2016: 44%.

The Perils of High Growth

Operating margin is very simply defined: operating income divided by sales.

If a company’s operating margin is growing, then either its income is rising, its sales are slowing, or both. If its operating margin is shrinking, then either its income is falling, its sales are rising, or both. This isn’t much of a problem if the margin is shrinking or growing by a few percentage points. But a ten percent rise or fall in operating margin can indicate some serious problems. Because what you’d really like to see is a company whose sales are rising and whose income is rising too. In other words, you don’t really want to see operating margin grow or shrink very much. I’d much rather invest in a company with a stable operating margin than a rapidly growing one.

The stability of operating margin is just one of many metrics that are usually overlooked by investors, metrics that I have found extraordinarily useful in my investing.

Take a look at the following three quantile charts, which I created on Portfolio123. The first measures the performance of the Russell 3000 since 1999 if you group stocks into deciles by operating margin growth, trailing twelve months minus previous twelve months, rebalancing monthly with no transaction costs. The second does the same except for asset growth: the ratio of the TTM total assets to that of the previous twelve months. The third does exactly the same but for sales rather than assets.

In each case, you see a parabolic graph; in each case the highest performance was in a middle decile, and the highest and lowest deciles performed worst. This is especially true for sales--notice how the decile with the highest sales growth not only performed worst of all deciles, but actually lost a considerable amount of money, and the fifth decile beat the market by an annualized seven percent. The reason is simple: extremely high growth is usually unsustainable.

You’ll get similar parabolic graphs if you measure year-on-year ROE growth, profit margin growth, book value growth, employee growth, income growth, and change in the cash conversion cycle. The only year-on-year growths I’ve found that look more like an upward slope are in dividends and free cash flow. Only in those cases is higher growth really better.

So don’t invest in companies that boast an operating margin twenty percent higher than last year’s, or sales fifty percent higher than last year’s, or that have doubled their assets through acquisitions. Companies with middling growth rates are the best investments.

My ten largest holdings right now: SMMT, CVV, ALSK, HDNG, SONS, ELMD, LXFR, PRTS, ACNB, KMDA.

CAGR since 1/1/2016: 44%.

How Long Should You Hold a Microcap?

Value investing is probably at least a hundred years old: it was already a long-established practice by the time Benjamin Graham and David Dodd published the first edition of Security Analysis in 1934. And one of its central tenets is patience. One buys a stock that appears cheap and one waits patiently for it to rise in price to a level that approximates its intrinsic value. This could take years, and often does.

Let’s say you bought all the stocks in the S&P 500 and held them for four years. When would be the optimal time to sell each one? When their price is the highest, of course. The chart below plots the number of bars that it takes S&P 500 stocks to reach their four-year peak. (I obtained this data, and the data in the rest of the article, from Portfolio123 by screening every two years since 1999 for stocks that were in the S&P 500 or microcap universe four years earlier, so it therefore does not include stocks that no longer existed after four years). The bar on the right shows the most recent five months; that’s when 38% of the stocks reached their highest points. And no doubt most of those went (or will go) still higher.

Now the chart below repeats the same experiment with microcaps. The result is markedly different. 25% of the microcaps reached their peaks within five months of purchase, and another 25% reached their peaks within the last five months. Not only that, but the four-year survivorship rate for microcaps is only 74%—compared to 90% for the S&P 500—due to a higher level of mergers, acquisitions, and bankruptcies; if one were to take that into account, the percentage that reach their peaks four years after purchase would be markedly smaller.

And what kinds of peaks are they? Well, the average peak among that 25% that achieved their high within five months was an increase of 52% over the purchase price. Of course, one would have to be superhuman to sell at exactly the right point, but considering that peak was achieved an average of 43 bars (two months) after purchase, your superhuman stock seller would achieve a CAGR of over 1,000%. By contrast, the average high among the microcaps that lasted close to four years was an increase of 212% over the purchase price, which makes for a CAGR of 34%. There’s a huge survivorship issue here too, which I wasn’t able to take into account—a lot more microcaps are going to survive for 43 bars than for four years.

All this suggests that the optimal holding period for microcaps is significantly shorter than that for large caps—in fact, it’s only about two or three months.

Microcap investors have a host of advantages over other investors, which I’ve detailed here and Jim O’Shaughnessy has detailed here. But to reap the maximum profit from those advantages, it’s best not to play the buy-and-hold game. Over the last two years I’ve doubled my money by investing in microcaps. I would not have done half as well if I hadn’t sold most of my holdings within a few months. Patience is indeed essential to successful value investing, but with microcaps impatience may be more profitable.

My ten largest holdings right now: VHI, AVDL, ALSK, CVV, CRNT, ELMD, SMMT, GSL, CTG, KMDA.

CAGR since 1/1/2016: 47%.

13 Investment Rules to Break

Rule 1. Never lose money (Warren Buffett’s first rule). You’re going to lose money. What makes the difference is how you react. Do you lose your cool and compound your losses? Or do you react in a disciplined, focused manner and learn from your mistakes? If you spend all your time trying to avoid losing money, you’ll never make any in the first place.

Rule 2. Never buy high, never sell low. Never say never. Try to buy low and sell high but make room for exceptions. Establish a system that will give you sell signals when a better opportunity arrives. Following that system can mean selling low. And sometimes coming late to the table—after the price has already risen—is better than missing the meal altogether.

Rule 3. Set a goal for every trade. Don’t do this, please. Investing requires flexibility. Sell your positions only when a better opportunity arises—or when you need the money for something more important.

Rule 4. Never add to a losing position. If you buy a diamond ring and then the price goes down, what do you do—sell the ring or buy another? If stock in a good company is getting cheaper, especially if it’s for a dumb reason, buy more.

Rule 5. You can’t beat the market, so invest in index funds. You can indeed beat the market if you invest wisely and put in the time and effort to develop a good system. Proponents of the Efficient Market Hypothesis say that people who beat the market consistently must be doing so by chance. Frederik Vanhaverbeke, in his book Excess Returns, puts that argument to rest. He names 67 investors and traders who made annual compound returns of more than 15% over periods of at least ten years. He writes:

It was not home runs and leverage that drove these returns. Virtually all of these returns were achieved through diversified portfolios with significant turnover across periods ranging from 10 to almost 60 years. . . . The most striking example of consistency is Edward Thorp, who posted gains in 227 of the 230 months that he ran an investment partnership between 1969 and 1988. Assuming the probability of a positive gain in any particular month is about 0.6 (as has been the case historically), the probability that someone can achieve this level of consistency or better [purely by chance] is 6 × 10^–46. This is only a few orders of magnitude higher than the probability that one would find a single specific atom by looking in a random place on earth. It is therefore safe to say that Thorp was not just lucky.

Rule 6. Keep it simple, stupid. Well, if you’re stupid, I guess you have to keep it simple. I hope you’re not. Companies and their stocks are not simple creatures, and treating them as if they are is a big mistake. Acknowledge complexity and approach investing accordingly.

Rule 7. Don’t try to outperform the market. Yes, that’s actually a rule suggested by a writer for lifehack.org in an article entitled “Eight Investing Rules You Need to Follow to Make You Rich.” She comments, “This is one of my favorite investing rules.” I wonder if she tells her kids not to try to get A’s.

Rule 8. Back up your fundamental analysis with technical analysis. Buying a stock is like buying a used car. The most important thing is to look under the hood. The least important thing is to compare the price you’re paying with the fifty-day simple moving average.

Rule 9. Keep your winners and sell your losers. It’s usually more profitable to do it the other way around because of mean reversion. Let’s say you buy $10,000 each of two stocks on the same day and a month later one has risen 20% and the other has fallen 20%. The loser is more likely to rise over the next month than the winner (I tested this, using both the Russell 3000 and the S&P 1500 since 1999, on Portfolio123). Sell the $2,000 you made on the winner and invest it in the loser.

Rule 10: If prices are rising, go long; if prices are falling, go short. Prices may be rising or falling today, but you have no idea what they’ll do tomorrow. They turn on a dime. If you short the market when prices are falling you’ll be missing out on your best opportunities when prices start to rise, as well as risking a lot more than you would by just holding what you have.

Rule 11. Always keep a significant portion of your money in cash. And miss out on compounding? If you’re convinced that a) there are no good stocks to buy right now; b) the market is about to crash; or c) you don’t want to miss an opportunity if a stock you’re watching unexpectedly falls in price, then go ahead and keep some cash in a safe place. But don’t make it a habit. Park your money in investments with a margin of safety instead. And remember, if you need cash, you can always quickly sell your least favored stock.

Rule 12: The trend is your friend. The trend is actually your enemy. Never follow trends—in life or investing. It’s the surest way to lose money. Stock prices revert to the mean. Buck the trend as much as you can.

Break these rules. And when you’ve finished, find some more to break.

But there’s one rule you should never break:

Rule 13: Make your own rules. Make absolutely sure they work. And then stick to them, making only minor modifications, through thick and thin.

My ten largest holdings right now: VHI, ALSK, AVDL, CRNT, SMMT, CVV, ELMD, AMSWA, GSL, KMDA.

CAGR since 1/1/2016: 48%.

The Ultimate Measure of Portfolio Returns

Sharpe ratio. Information ratio. Jensen's alpha. Compound annual growth rate (CAGR). Average monthly or annual returns (or excess returns). These are the five major ways that people measure portfolio performance. I've already discussed these at length in a previous article. But I want now to offer something new—and better. This performance measure is simpler, more elegant, more robust, and, most importantly, more predictive than any other I've investigated. And I've investigated a lot of them.

I recently ran the following correlation study. Using Portfolio 123, I developed forty different ranking strategies, each consisting of five equally weighted factors. One, for example, ranked stocks on the past three years' accruals (the lower, the better), trailing twelve months' operating margin, price to sales, price to tangible book value, and unlevered free cash flow to enterprise value; another ranked stocks on annual EPS growth, operating income growth, free cash flow to assets, market cap (the lower, the better), and gross profit to enterprise value. For each strategy, I measured the returns of holding the fifty top-ranked stocks in the Russell 3000, rebalancing once a month with 0.5% slippage, for the following eight-year periods: December 1999 to December 2007 and August 2009 to August 2017.

I then correlated the ranks of these strategies over the two periods according to seven different measures. Here are the results. (I repeated this experiment with the S&P 1500 and the results were very similar; I also have obtained similar results with other universes and time periods.)

The measure that beats them all, hands down, is median excess return.

The median excess return is not the median of the return minus the median of the benchmark. It is the median of the strategy's excess returns over the benchmark, measured monthly (or weekly), which is usually an entirely different number. (The average excess return, on the other hand, is the same either way you measure it.)

Why is median excess return more predictive of future returns than other performance measures? It's because of two essential features. First, it's very closely tied to the benchmark, and, as I pointed out in my previous article, there is nothing more correlative between the returns of two periods than their relationship to the benchmark (best measured by beta). Second, it effectively ignores outliers--those months with huge positive or negative returns--which have a very strong impact on other performance measures, but which are relatively useless for predicting future returns.

To illustrate the advantages of median excess return over Jensen's alpha, let's take FAIRX, the Fairholme Fund, which has a very actively managed and focused approach. Here is its five-year return including dividends compared to that of SPY, the S&P 500 ETF, assuming you invested the same amount in each fund. (I'm using the monthly adjusted close as given by Yahoo Finance, though this may not match other sources.)

You'll notice that FAIRX had a loss of 46% in November 2015, followed by a 48% rise in December (due to a massive dividend payment) and another 29% rise the following October.

FAIRX's alpha, measured over the last five years, is 4.60%. See the chart below. Alpha is the intercept of the ordinary least squares (OLS) linear regression of the returns of the fund plotted against the returns of the benchmark. The intercept is at 0.375%, which annualized is 4.60%.

So according to Jensen's alpha, FAIRX performed better than SPY. But according to every other performance measure I can think of, FAIRX performed worse than SPY. FAIRX's median excess return, for example, is –0.74%, or –8.56% annualized. Looking at the first chart, which do you think is more representative of FAIRX's five-year performance?

Why is FAIRX's alpha so high? It's because of those three outliers—the 46% loss and the 48% and 29% gains—the three dots on the second chart that are way outside the center. If you eliminate those from the data, FAIRX's alpha falls to –4.51% annualized. If you eliminate only the 48% rise, the alpha falls to –14.71%. Outliers have a huge impact on alpha. On the other hand, they don't affect the median excess return much at all. Eliminating the 48% rise lowers the median excess return from –8.56% to –9.09%, as does eliminating all three outliers.

A number of alternate methods of linear regression are more robust than alpha derived from the ordinary least squares, which gives much more weight to points that are on the outer edges of the grid than to points that are closer to the center. One is least absolute deviation (LAD) regression. Instead of drawing a line that minimizes the sum of the squares of the vertical distances to the observed points, you minimize the sum of the vertical distances. To stick to the example above, the LAD alpha would be –0.56% annualized, and the slope (beta) would be 0.78, which is steeper than the OLS beta of 0.61.

Another alternate method is Theil-Sen regression. Basically, you connect every single observed point to all the other points. Then you take the median slope of all those little lines to get your beta. Lastly, to get alpha, you take the median of all the values of y­­_i – mx­_i, where m is your beta. Now when m is one, the Theil-Sen alpha is the same as the median excess return. When m is less than one, the median excess return will exceed the Theil-Sen alpha, which means that aiming for the highest median excess return will favor low-beta strategies over high-beta strategies. In general, a high median excess return-based strategy does well in both bull and bear markets. Since we're probably near the end of a bull market, that's not a bad place to stand.

Calculating Theil-Sen alpha is actually what inspired me to calculate median excess returns. Most of the strategies I was testing had betas close to one, so the differences between Theil-Sen alpha and median excess returns were tiny. And the latter was a whole lot easier to compute. You see, unfortunately, both Theil-Sen and LAD regression are computationally difficult. You can calculate OLS alpha by hand or with a calculator. (You take the product of the sum of the squares of the x values and the sum of the y values, subtract the product of the sum of the x values and the sum of the products of the x and y values, then divide all that by the difference between the number of points times the sum of the squares of the x values and the square of the sum of the x values. Now say that three times fast.) Calculating LAD regression involves estimating the line hundreds of times to find the best fit, and in rare cases you'll find two best fits. (Happily, you can download an Excel plug-in that does this for you here.) Calculating Theil-Sen alpha becomes extremely cumbersome if you have lots of points; if you have a hundred pieces of data, you have to calculate the slopes of almost five thousand lines and take their median, and if you have five hundred pieces of data, you'll need to calculate a quarter of a million slopes. I normally work with thirteen-bar returns over eighteen years, measured daily, so that's over four thousand points, or eight million slopes.

Calculating median excess returns is a hell of a lot simpler than any of that. And the results are excellent. But why are they better than CAGR, the Sharpe ratio, or the information ratio?

Once again, outliers play a huge role in all three measures. Take, for example, the following chart, which shows the performance of my own investments since November 2015 (when I started evaluating stocks based on a ranking system at Portfolio 123) compared to SPY, the S&P 500 ETF.

 

Now look at my returns the summer before last. In June, July, and August 2016 I made 7.82%, 4.88%, and 14.69%—enormous monthly gains. Why? In part it's because I hold only fifteen to twenty stocks at a time, and one of them, Lantheus Holdings (LNTH), went from $1.94 when I bought it at the end of March to $9.36 when I sold it in early September. Now that is an outlier.

Should LNTH's crazy outperformance—a 482% rise—really be counted in full in any estimation of my future returns? Do I really deserve an alpha of 36% or a CAGR of 43%? A Sharpe ratio of 2.33? An information ratio of 1.74? Or is my median excess return—1.35% per month, or 17.4% annualized—more representative of my actual performance?

Their sensitivity to outliers isn't the only problem with these conventional measures of performance. CAGR and the Sharpe ratio are uncorrelated to any benchmark. They measure absolute returns. Since the most persistent quality of returns is their relationship to the benchmark, that seems like an absurd way of thinking about performance.

As for the information ratio, which is also based on excess monthly returns, its weaker predictive performance is in large part due to the fact that using standard deviation as a denominator in a fraction is always going to result in a grave distortion of your data. This idea of mine goes against everything you learn in basic statistics and finance classes—not only does it invalidate the Sharpe and information ratios, it invalidates t-tests and Z-scores and Sortino ratios and probably a dozen other things beloved by quants worldwide. But I have five good reasons for it.

1. Unfortunately, stock market returns are not normally distributed. Here is an excellent article on how assuming a normal distribution completely messes up expectations for standard deviation.
2. Measuring standard deviation relies on the distance from the mean, and the mean is never a good measure for returns. A 50% gain followed by a 33% loss brings you a total gain of 0%, but a mean of 8.5%. Do this a lot and your standard deviation will be measuring the distance from a number that is far higher than it should be.
3. Standard deviation is, like alpha, an OLS measure, giving far more weight to outliers than they deserve.
4. Placing standard deviation in the denominator gives it far more weight than it should have based on its persistence, which is relatively low. In other words, the correlation of the standard deviation of a strategy or fund or portfolio between two different periods is not very high—certainly not high enough to use it as the denominator in a fraction, which has a huge impact on your measure.
5. You can't meaningfully apply the measure when you're dealing with certain kinds of funds with extremely low standard deviations (e.g. short-term bond funds), as the ratio blows up sky-high.

But that was a digression. To get back to median excess returns, I wanted to make sure this measure had real-life applications, so I did another experiment. I took fifty actively managed mutual funds with the same manager for the last twenty-odd years, funds like the Franklin MicroCap Value Fund (FRMCX), the RBC Small Cap Core Fund (RCSIX), and the Bridgeway Aggressive Investors 1 Fund (BRAGX). I looked at their monthly returns going back to January 1996 and performed a four-pronged eight-year rolling correlation test, comparing their 1996-2004 returns with their 2004-2012 returns, their 1998-2006 returns with their 2006-2014 returns, and so on. As a benchmark, I used the Vanguard Total Stock Market Index Fund (VTSMX). I then deleted funds whose adjusted returns had a 0.99 correlation to those of the benchmark, because including ranking results for funds like those would be irrelevant and confusing. I was left with forty funds.

Here are my results:

These results were pretty consistent whether I used thirty, forty, or fifty funds.

Here median excess returns were not as correlative as simple median returns (I attribute that to the fact that comparing a large-cap and a microcap fund to the same benchmark is bound to cause mischief). But both of them were more correlative than any other measure. Now if you want high performance, you'd probably be better off choosing the fund with the worst average yearly return than the one with the best median return. Don't look to me for an explanation of why funds that outperform in one decade usually underperform in the next and vice-versa. But the two things that are pretty consistent about their performance are beta (which had a correlation of 0.47) and median returns. LAD alpha performs pretty well too, but every other measure had a zero or negative correlation to the same measure in the next period. These measures have very low persistence.

Now is anyone besides me using median excess returns as a performance measure these days?

Well, yes and no. You see the term crop up a lot when folks are measuring the performance of a large group of funds. Vanguard, for instance, uses it in their papers to compare the median excess return of "go anywhere funds" to a benchmark, or their actively managed funds to those of other companies. But nobody is talking about it as a way to compare just one fund or strategy to another; unless I'm overlooking someone, nobody is suggesting that it replace alpha or the Sharpe ratio as a standard measure of portfolio performance.

So I guess that's my job. Go for it, ladies and gentlemen. I think you'll find your results will be significantly better than average.

My ten largest holdings right now: AVDL, CRNT, ALSK, ELMD, AMSWA, CVV, VHI, SMMT, KMDA, BBRG.

CAGR since 1/1/2016: 50%.

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In Favor of Backtest-Driven Investing Strategies

1. When we decide whether or not to buy a stock, or choose what stock to invest in, we pay attention to certain aspects of that stock (low price-to-sales ratio, for example, or strong earnings growth), and we favor stocks with those aspects in part because we’ve learned that such stocks tend to outperform. We are thus informed in our stock choices by past performance data.
2. Because we want to be thus informed, and because we have no data for the future, we must mine the past for as much data as possible. Past data might indeed show, for example, that companies with strong earnings growth and a low price-to-sales ratio tend to do better than other companies. Or it might show the opposite. If, on the other hand, we think past data is useless for getting good future results, it might be better for us not to invest at all. Investing without data is like throwing darts blindfolded: you might still hit the target, but you’re not focused on it, and you might hit something else entirely.
3. The question then becomes how to best use this data. A simulation of a strategy, also known as a backtest, is a way to test the probability of a desired result on the assumption that the data pertaining to the past is more or less the same as the data pertaining to the future. That assumption is extremely problematic, especially since every backtest necessarily involves only a finite set of past data, and since misuse of that data can be psychologically gratifying. But relying on data without backtesting it blinds one to potential pitfalls. For example, past data shows that stocks with low value ratios tend to outperform, but only a backtest will show that following a pure value strategy will result in long periods of underperformance and is subject to far worse drawdowns than a strategy that mixes value with other traits.
4. The components of an investment strategy must be formulated not just from observation of data but from understanding why the data shows what it shows. If there is no coherent explanation based on sound principles of analysis for a conclusion drawn from data, that conclusion should be discarded.
5. The best way to find out whether a backtesting procedure will produce strong results is to do correlation studies. Develop fifty different strategies and see how well their simulated results correlate over many different time periods using different procedures. For example, a five-stock simulation will probably be less correlative than a fifty-stock simulation. A two-year simulation will probably be less correlative than an eight-year simulation. Alpha will probably be more correlative to forward returns than the information ratio. And so on. The best backtesting procedure will be the one that produces the most correlative results.
6. Because stock-market returns have never been in the least predictable, strategy returns are even less predictable. We should never try to estimate a strategy’s return. What we can do, though, is make a reasonable claim that, based on past returns, correlation studies, and robust simulations tested across different data sets, certain strategies are more likely to produce a profit than others. We should be able to assign a level of confidence to the probability that one strategy will outperform another. And we should invest in the strategy or strategies that have the best chance of outperforming.

My ten largest holdings right now: BGFV, CTG, BASI, MEIP, ODC, TATT, EGY, ELMD, TGB, FNJN.

CAGR since 1/1/2016: 56%. One-year return: 75%.