invest(igations)

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.