invest(igations)

How to Be a Great Investor, Part Nine: Position Sizing

This article is the ninth 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 One: Be Numerate,” “Part Two: Understand Value,” “Part Three: Properly Assess Strategy,” “Part Four: Compare Effectively,” “Part Five: Think Probabilistically,” “Part Six: Update Your Views Effectively,” “Part Seven: Beware of Behavioral Biases,” and “Part Eight: Know the Difference Between Information and Influence” for previous installments. And please keep in mind that although I’m basing my work on Mauboussin’s, I am departing from his ideas on occasion.

Mauboussin writes, “success in investing has two parts: finding edge and fully taking advantage of it through proper position sizing. Almost all investment firms focus on edge, while position sizing generally gets much less attention.”

This is because position sizing is a forbidding concept. If you try mean-variance portfolio optimization or using the Kelly criterion to decide how much to put into each stock you own, you’re likely to get bogged down in remarkably complex computations with results that are indefinite at best.

Position sizing has to answer two main questions: how many positions should you hold? and how much of your portfolio should you allocate to each position? The answers are complicated by the following considerations:

• If you have a very good stock-picking strategy, the fewer positions you’re in, the higher the returns will be.
• If you have a mediocre stock-picking strategy, the fewer positions you’re in, the lower your returns will be.
• If you invest in low-liquidity stocks, the fewer positions you take, the more market impact your buys and sells are going to have.
• The fewer positions you’re in, the greater the variance of your returns will be.

Given this, it might seem more sensible to invest in a hundred stocks than ten. But practically every backtest will show you otherwise. So what do you do?

I can’t answer that question for everyone. There’s no one-size-fits-all approach to position sizing. Instead, I’ll give you my approach, even though I’m sure it’s not suitable for everyone.

In my personal accounts, I currently own shares in 24 companies, with weights ranging from 8.2% to 0.7%. My top ten stocks account for 59% of my holdings.

Many great investors take an even more concentrated approach. I’ll quote from Excess Returns by Frederik Vanhaverbeke:

Joel Greenblatt usually put about 80% of his funds in no more than eight stocks. Eddie Lampert holds about eight major positions at a time. And Glenn Greenberg has a rule that he will not buy a stock if he is not willing to put at least 5% of his assets in it. . . . Warren Buffet states that for relatively small portfolios (< $200 million), he would put about 80% of his portfolio in five stocks. . . . In his private portfolio he is even willing to go up to 75% in one single stock.

But Vanhaverbeke also notes, “[High] portfolio concentration obviously only makes sense for true stock pickers. It does not make sense, for instance, for quantitatively driven investors.” And I’m one of the latter. I view my portfolio concentration as moderate; many investors I know have a very low portfolio concentration, owning fifty to a hundred stocks at any one time.

My position-sizing formula has three components.

1. Rank. Because I use a ranking system to decide what stocks to buy and sell, one component is based on rank: the higher the rank, the more I put into the stock. Since stocks change rank positions over time, I gradually increase or decrease my investment in a stock as it moves.
2. Liquidity. To diminish market impact, I invest less in stocks with very low liquidity.
3. Industry concentration. If I’m invested in more than a certain number of stocks in any one industry, I’ll lower the weights of those stocks.

Here’s how I came up with the number of stocks to invest in and how much to invest in each one. I ran out-of-sample backtests over the last three or four years on various ranking systems that I formulated back in 2015, 2016, and early 2017, adjusting the costs per transaction higher for fewer positions taken. I then looked at the position-sizing approach that would have given me the highest out-of-sample alpha for each system and averaged them all. Some of them would have performed best with very high concentrations, others would have performed best with lower concentrations. The average gave me a formula that I’m pretty pleased with.

Here’s the nitty-gritty of the formula I use. I first give each stock a number of points based on its rank. The actual formula is 47 * (4.7 – ln (rank + 12)), but if you simplify that to 101 – rank, there’s not much difference. Either way, if a stock is ranked #1 it gets 100 points, and if a stock is ranked #100, it gets close to 0. The major difference is that with the log-based formula, the ranking goes down more steeply for highly ranked stocks. So when a stock is ranked, say, #35, using my formula, it gets 40 points, but with the 101 – rank formula, it gets 66.

I then adjust these numbers for liquidity—if a stock has low liquidity, the number of points may go down by 20. I also adjust them lower if I own more than four stocks in one industry: in that case, the total number of points for those stocks are diminished so that they add up to what they would if I only owned four companies in that industry. Once I’ve settled on the final number of points for each stock, I apportion my total investment accordingly, and if there is a major difference between the ideal apportionment and my current apportionment, I buy and sell to rebalance my positions. If a stock I don’t own turns up in my top ten or top twelve, I sell bottom-ranked and overweight positions in order to free up enough money to buy the new stock. If there’s nothing for me to buy, I don’t sell, no matter how low a stock ranks.

Obviously, this technique is not for everyone. You may do better with a modified Kelly criterion or a mean-variance optimization formula. Or you may have an entirely different approach that works well for you. (If so, I’d love to learn about it in the comments below.) At any rate, many people put too little thought into position sizing. It can make a huge difference in one’s returns.

Here’s an example. I’m going to use an eleven-factor ranking system that I designed back in December 2015 and backtest it, using Portfolio123, on the Russell 3000 since then (starting in January 2016).

If I bought the top 20 stocks in equal weight and sold them when the rank went below 50, buying and selling monthly without rebalancing, I would have made an annualized return of 13.47%. If I’d bought the top 25 stocks instead, the return goes up to 15.88%, and if I’d bought the top 40 stocks, the return goes down to 11.38%. That gives me a good range to start with.

Now what if I had used my ranking formula to determine the portfolio weight? The top 20 return goes up 195 basis points to 16.32%, the top 25 goes up 165 basis points to 17.53%, and the top 40 goes up 240 basis points to 13.78%. In each case, the return is higher than for equal weights.

Why is this? Well, consider that four out of my eleven factors are value factors. Thus, when a stock falls in price relative to other stocks, it gets a higher rank, and when it increases in price relative to other stocks, the rank falls. But if you don’t resize your portfolio, when a stock falls in price, it has a lower weight, and when it rises in price, it has a higher weight. So rebalancing by rank, if you use value factors, does exactly the opposite of what the portfolio would do naturally.

With rank-based position sizing, your biggest bets are always on the stocks with your highest expectations. If you use a multi-factor ranking system to lower risk, this can produce significantly better returns than other methods would.

My CAGR since 1/1/16: 29%.

My top ten holdings right now: PCTI, MTBC, ELMD, ECOM, III, ESALY, MHH, ACU, PDEX, DL.

Why Momentum Works

The Evidence: Momentum Works

As a factor, momentum—the idea that a stock’s relative returns over the past six to twelve months have a tendency to persist over the next six to twelve months—has proved remarkably resilient. Academics first recognized this factor in the early 1990s, and its return premium has since been verified over the past 220 years (no, this is not a typo) of US equity data. As Clifford Asness and his colleagues documented in a 2014 paper entitled “Fact, Fiction, and Momentum Investing,” there has been over 25 years of out-of-sample evidence of momentum, in forty countries, and even in a dozen other asset classes.

Using Portfolio123, I looked at the performance of the Russell 3000 since 1999 if divided into deciles according to momentum over various lookback periods, with monthly rebalancing. I then calculated the slope of those deciles (with the lowest decile getting an x value of 1% and the highest 10%), and also looked at the difference between the top decile and the bottom decile. Here are the results:

It’s pretty clear that over short periods (4 weeks or less) and long periods (5 years or more), price returns revert to the mean; over six- and twelve-month periods, momentum prevails.

(I should add that when looking at momentum decile returns, the difference between the top three deciles is minimal but the difference between the bottom three is huge. Momentum, like many factors, is more effective at identifying losing stocks than winning ones.)

The Explanations So Far

Yet there has been no general agreement on why momentum works. As Asness and his colleagues write, most of the theories fall into two categories: risk-based and behavioral. I’ll outline these theories briefly.

Behavioral explanations explain momentum as either an underreaction or a delayed overreaction. In other words, either momentum happens because new information filters into the market and then the market takes some time to catch up with it, or because investors chase returns, providing a feedback loop that chases prices higher.

These explanations, of course, contradict each other. The second might explain momentum well if it were a two-to-four-week phenomenon, but price returns tend to revert over such a short period. As for the first explanation, why would it take six months for information to filter into the market? Why wouldn’t it take two weeks? The only explanation for momentum that can make sense has to be one that explains why momentum works well if using a six-to-twelve-month lookback and does not work well for shorter or longer periods.

The risk-based explanations are, first, that high-momentum stocks face greater cash-flow risk because of their growth prospects, and second, that they face greater discount risk because of their investment opportunities. Both would give them a higher cost of capital. These explanations make more sense to me than the behavioral ones, but not much. At least they conform with the six-to-twelve-month outlook. But they seem like a stretch. And the second explanation is incompatible with the risk-based explanation for the value factor. In general, I don't like risk-based explanations for factors because I don't believe that risk and return have a linear relationship, and because many factors work because they reduce risk.

I think there are some alternative explanations that are quite a bit simpler. The first is regulatory; the second is just common-sense.

Alternative Explanations

1. Tax law encourages investors to sell losing positions.
2. Companies that outperform are more likely to continue to outperform than companies that underperform, and companies that underperform are more likely to continue to underperform than companies that outperform. Since companies that outperform tend to increase in price and companies that underperform tend to fall in price, momentum is a natural consequence of the persistence of performance.

Both these reasons make sense with the six-to-twelve-month optimal lookback period for momentum strategies, and are compatible with long- and short-term price reversal.

Let’s drill down a little deeper into each one.

The Taxation Explanation

Tax law currently encourages investors to sell losing positions and to hold winning positions, thus contributing to momentum. Taxation of capital gains has been a constant in the United States for over one hundred years, and is imposed in a large majority of other countries as well. A capital gain is the result of selling a winning position; a capital loss reduces capital gains. So there has been some tacit governmental encouragement to sell losing positions and hold onto winning ones.

Let’s look at how this works. You invest in two stocks, A and B. After a while, A posts a gain and B posts a loss. Now let’s say you want to sell A. Without capital gains taxes, your decision to sell A would be completely independent of your decision to sell or hold onto B. But given capital gains, it makes much more sense to sell B at the same time as you sell A. Thus capital gains taxation contributes significantly to negative stock momentum.

Because capital gains taxes are calculated on a year-to-year basis, and because most institutions tend to hold stocks for about a year, this explanation conforms pretty well with the six-to-twelve-month optimal lookback period for the momentum factor.

The flaw in this explanation is that it only covers the last hundred years or so, and some studies show that momentum was a factor even before then.

The Performance Explanation

What’s a good measurement for performance? Clearly, one that correlates well with future price increases but actually is independent from price.

I’ve chosen free cash return on assets, measured quarterly to avoid any data infiltration. Companies with a high ratio of free cash flow to total assets tend to perform well; companies with a low ratio tend to perform poorly. There are plenty of other performance measures that one could choose instead. But please note that I didn’t test a bunch of factors and then choose one that I thought would persist. I chose this factor because it correlates well with future price increases and therefore, in my opinion, signifies something about company performance.

Indeed, this ratio measured at one point in time and measured again 12 months later has a correlation ranging from 0.6 to 0.9, which is astonishingly high for a ratio based solely on one quarter's data. But measured over a five-year period, the correlation range drops to 0.2 to 0.4, depending on what that five-year period is.

According to my second explanation, momentum is a proxy for company performance. If a company’s performance is strong, its price is going to rise. If its performance continues to be strong, its price will continue to rise. Therefore, a company whose price is rising now is likely to have a rising price a year from now, and a company whose price has risen over the last year is likely to experience a continued rise in price simply due to the momentum of its performance. And the exact reverse is true for companies with poor performance.

The flaw in this explanation is that it doesn’t account for mean reversion after five years—or after four weeks.

But there’s a solution to this. Price returns in general tend to revert to the mean because their movements often appear to be random, and mean reversion is a characteristic of all random variables. (The farther a random variable is from the mean, the more probable it is that it will reverse course.) Price returns are not random, strictly speaking, but they do have many of the characteristics of random variables.

The momentum of company performance is so strong in the six-to-twelve-month period, however, that it overrides that mean-reversion tendency. Performance momentum in a four-week period is meaningless since one usually measures performance by looking at quarterly statements; performance momentum over five years is simply not strong enough to overcome the natural tendency of price returns to mean revert.

Implications of the Quality Theory of Momentum

The quality theory of momentum, stated in different words, is: If returns are, in part, a sign of company performance, and if relative company performance tends to persist over a certain period—i.e., there is a positive correlation between company performance in two different periods—then the returns over those two different periods will show a stronger resistance to their natural tendency to revert to the mean than over two periods for which the correlation of company performance is weak or difficult to measure.

I admit, that’s a mouthful. But it seems logical.

Momentum, then, is a proxy for company performance. If one can find good measures of company performance that are independent of stock prices but correlate well with future returns, then those measures are preferable to momentum measures. And thankfully, there are dozens of such measures.

One can break down factors into six main types.

1. Value: the ratio of something in a company’s financial statements to its price.
2. Quality: the ratio of something in a company’s financial statements to another thing in a company’s financial statements (this group of factors includes many growth measures).
3. Size: a measure of how big or small a company is.
4. Momentum: a measure of the relative returns of a stock over a certain period of time.
5. Sentiment: factors that indicate the feelings of investors about a company.
6. Volatility: factors that measure deviation and beta, along with other measures of price and volume that have to do with risk.

There are, of course, a few factors that don’t fit into any of those categories, but not many.

My takeaway from the Quality Theory of Momentum is that one should emphasize quality factors over momentum factors because the latter are secondary in nature and the former are primary. In the systems I use to choose stocks, value factors have a combined weight of 15% to 20%, quality factors have a combined weight of 45% to 50%, while momentum factors only have a combined weight of between 5% and 10%. (Size and volatility factors also each have combined weights of between 5% and 10%, while sentiment factors have a combined weight of between 10% and 15%.)

There are, however, certain elements of a company’s quality that are immeasurable. Financial statements go a long way in outlining to investors how a company is doing, but not all the way. There are always some pesky unquantifiable factors. And that’s why momentum can be so useful as a proxy for quality. One ignores momentum—especially negative momentum—at one’s peril.

CAGR since 1/1/16: 32%.

My top ten holdings right now: ELMD, MHH, ACU, MTBC, CO, PDEX, IESC, CMCL, WSTG, ECOM.

How to Be a Great Investor, Part Eight: Know the Difference Between Information and Influence

This article is the eighth 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 One: Be Numerate,” “Part Two: Understand Value,” “Part Three: Properly Assess Strategy,” “Part Four: Compare Effectively,” “Part Five: Think Probabilistically,” “Part Six: Update Your Views Effectively,” and “Part Seven: Beware of Behavioral Biases” for previous installments. And please keep in mind that although I’m basing my work on Mauboussin’s, I am departing from his ideas on occasion.

Mauboussin breaks down two functions of the price of a stock. First, it tells us (gives us information about) how much the market believes a stock is worth. Second, it acts as an influence upon buyers: if a price is rising, people want to get in on the rise and buy; if a price is falling, investors are more likely to want to sell. The task of a great investor is to learn how to separate the two, subscribe only to the information, and ignore the influence. I’ll let Mauboussin explain:

Investing is an inherently social exercise. As a result, prices can go from being a source of information to a source of influence. This has happened many times in the history of markets. Take the dot-com boom as an example. As internet stocks rose, investors who owned the shares got rich on paper. This exerted influence on those who did not own the shares and many of them ended up suspending belief and buying as well. This fed the process. The rapid rise of the dot-com sector was less about grounded expectations about how the Internet would change business and more about getting on board. Negative feedback ceded to positive feedback, which pushes a system away from its prior state.

I’d like to look at the difference between information and influence in a more scientific, less anecdotal manner. Let’s look at companies that experienced a change in price in a four-week period that was 20% more than that of the benchmark. We’ll limit this experiment to the Russell 3000 and exclude biopharma companies, as these big price jumps are common when a drug is approved or shut down. And we’ll only look at stocks whose latest earnings release was over four weeks ago and whose next earnings release is over four weeks away. The source of my research is www.Portfolio123.com.

If information prevails, we should see a large percentage of these companies revert to their former prices; if influence prevails, we should see the new prices sticking.

Over the last twenty years, stocks from this group whose price has risen 20% more than the benchmark see an average decline of 0.83% in the next four weeks (compared to an increase of 0.79% for all stocks); stocks that have declined 20% see an average increase of 1.69% in the next four weeks.

Now let’s classify price changes based on earnings releases as information and price changes not based on earnings releases as influence. This is, of course, too broad a classification—there is plenty of information happening between earnings releases, and some of the hoopla surrounding earnings releases should be classified as influence or noise. But let’s keep things simple for the moment. If information is more relevant than influence, major price changes that happen right after earnings releases should be stickier than major price changes between earnings releases.

I’ve already given you the numbers for the stocks with major price changes between earnings releases—they tend, on the whole, to revert. But stocks with major price changes around earnings releases act differently. Those with an excess 20% jump in the four weeks that include an earnings release tend to gain an additional 1.61% over the next four weeks; stocks with an excess 20% loss tend to mean revert with a 1.15% gain, but this is significantly less than the mean reversion of stocks that have dropped 20% without an earnings release (1.69%), and significantly less than all stocks with an excess decline of 20% (1.41%).

Here are the numbers:

Just to make the difference even clearer, here are all those numbers annualized.

Now, obviously, there are far more sophisticated ways to look at large price changes than whether or not they’re related to earnings announcements. But I wanted to give you these numbers to emphasize the main point: when you’re looking at a change in the price of a stock, it’s very important to try to figure out whether it’s related to the underlying value of the stock or if it’s just noise/influence. If it’s the latter, the price change is much more likely to revert.

Too many investors look only or primarily at the price of a stock. But because the price of a stock reflects a huge amount of information about it, it’s not going to give you many clues as to whether it’s going to rise or fall.

There are two ways to capitalize on the price of a stock—when you believe that the information informing the price is wrong and when you believe that the price is based on noise or influence rather than on the information. Both of these are very difficult projects.

Because public companies have to disclose so much information, and because the SEC is pretty good at policing it, it’s difficult to find instances of the information being wrong. And differentiating information from influence can be quite difficult. If a stock you’re interested in seems quite cheap or expensive and there’s very little to indicate why it’s so cheap or expensive, will a recent price move tell you much? Probably not.

But there is a third way to make money on stocks: to anticipate changes in information. And the best way to do this is to look at what the company is actually doing rather than looking at its price. I’m not saying one should disregard the price altogether, but examining how a company is allocating its capital, looking at its patterns of revenue generation, tracing its cash flow, and so on can indicate to a savvy investor what price future information might justify.

CAGR since 1/1/16: 32%.

My top ten holdings right now: IESC, NRC, ELMD, MHH, CO, INFU, ACU, SPNS, WSTG, CMCL.

Misbehaving Factors

The conventional method of finding out whether or not a factor works is to look at the performance of the top (or bottom) ten or twenty percent of stocks ranked according to that factor and then subtract the bottom (or top) ten or twenty percent. One should then buy stocks that rank highly on that factor and sell (or short) stocks that rank near the bottom.

But there are a lot of factors for which it makes more sense for middling values to be best. You have to think each factor through logically.

Change in profit margin (net income divided by revenue/sales) is one such factor. The companies whose margin has risen the most over the last year have decreasing sales and increasing income; companies whose margin has fallen the most have decreasing income and increasing sales. Neither of those is a good thing. If your income is increasing but your sales are falling, your income increase will be unsustainable and you’ll be setting yourself up for a fall (or maybe you’re cooking the books). If your sales are increasing but your income is falling, you’re likely using your revenue inefficiently.

Using the S&P 1500 and monthly rebalancing, I created, using Portfolio123, a decile-by-decile graph of how stocks have fared on this factor over the last twenty years:

Sales growth is another such factor. Companies with unsustainable sales growth are usually punished by the market. Here’s a chart using the same parameters as the previous one, except looking at sales growth rather than margin growth. I bet you could look at a hundred years of data and see this play out well.

These are what I like to think of as “misbehaving factors.” They’re giving you the middle finger, challenging you to deal with them.

It’s absolutely vital to think every factor through. Ask yourself: Are stocks that have super high (or super low) factor X really more likely to outperform than stocks that have middling factor X? You’ll often find yourself answering: Well, not necessarily.

But what should we do with factors like this? Should we simply ignore them? Should we combine them with other factors to see if the pattern will change? Or should we favor middling values?

When I started evaluating stocks back in 2015, I decided to concentrate on factors that had the most impact, that made the most difference. Here was my thinking.

I wanted to evaluate every stock I bought from as many angles as possible. Obviously, I couldn’t hope to evaluate stocks on absolutely everything—there were certain factors I tried for which it made little sense to evaluate a stock. I wanted to look at the factors that showed the largest discrepancies between high and low forward performance, no matter where those discrepancies showed up on the chart—at one end or in the middle. And while it may be “data-mining” to estimate an optimal rank or value for a factor, that still may be more logical than settling on the highest/lowest value or ignoring the factor altogether.

So that’s what I did. I created ranking systems in which I favored low values for some factors, high values for others, and middling values for yet others. Since nobody else at the time was favoring middling values for anything, that gave me an edge. And I went on to triple my money in less than three years. Of course, there may be absolutely no relationship between using middling rankings and tripling my money. But both in backtests and out of sample, this technique seems to improve results.

Just because some factors “misbehave,” don’t count them out. If you want to really evaluate every stock you buy from every major angle, leaving out a factor with a large significance (a big difference between the highest and lowest decile performance) can have a worse effect on your returns than including a factor that, it turns out, doesn’t “work.” Feel free to leave out factors that honestly don’t make much difference. But if you see a factor with a huge variation in returns between deciles, you probably want to avoid stocks in the top and bottom deciles and favor stocks in the middle few. That will help make every stock you pick a real treasure.

CAGR since 1/1/16: 32%.

My top ten holdings right now: IESC, NRC, ELMD, CO, INFU, MHH, KBAL, SPNS, ACU, CMCL.