Active investing: another look at luck vs. skill

Two days after posting my white paper, The Inconvenient Truth About Active Investing, an article appeared in the the Wall Street Journal bearing the provacative title "Top Mutual Funds: Luck or Skill?". Is it possible that Sam Mamudi (the WSJ reporter) has been reading Smart Nest Egg?...uhhh, doubtful. But the coincidence speaks to the relevance of this topic.

The focus of Mamudi's article is a new study by Eugene Fama (University of Chicago) and Ken French (Dartmouth College). The study looks for evidence of skill among active mutual fund managers by dissecting the returns of 3,278 U.S. equity mutual funds from 1984 through 2006. To summarize, Fama and French use regression analysis to isolate the return earned by each fund beyond what should have been earned by exposure to specific risk factors. This excess return is known in market parlance as alpha and the presence of alpha has generally been thought to indicate manager skill.

Though they found that many active managers generated alpha between 1984 and 2006, the Fama/French study asks a much more probing question: Do these funds produce enough alpha to provide conclusive evidence that the active managers are skilled, or is it possible they just got lucky? The following example will help illustrate what they mean.

A random example

Suppose we invest $100 in a fund that can deliver only one of two possible outcomes in a given year, a 20% gain or 20% loss, and that both outcomes are equally likely. In other words, the outcome of the investment in any given year is symmetric (plus or minus 20%) and completely random (both events are equally likely to occur). Intelligence and skill have no bearing on the outcome for this investment. We can't change the odds of success by doing more research or trading more astutely. Furthermore, because the outcomes are symmetric and random, the expected return on this investment over time is zero, that is, over time, we would expect gains and losses to offset each other.

At the end of the first year our investment will be worth either $120 or $80. This either-or outcome is called a binomial process and we can represent it in a diagram as follows:

During the second year, our investment will once again return either +20% or -20%. Therefore, at the end of the second year, our account has three possible values: $144, $96, or $64. We can diagram these outcomes and their associated probabilities by extending our previous diagram in this manner:

Now let's suppose we hold onto this investment for 10 years. Drawing a binomial process of this magnitude starts to become a bit cumbersome, but we can plot the range of potential outcomes and their associated probabilities on a chart as follows:

Examing the chart reveals some interesting characteristics of this investment. First, as we would expect given the symmetric and random nature of the investment's returns, we are most likely to experience very little return on this investment. In other words, the value of our account after 10 years is most likely to be very close to our original $100 investment. Second, there are some scenarios that could produce returns that are dramatically better than average. Clearly, we would be richer if we experienced one of the dramatically better scenarios, but it would not mean we were any smarter or more skillful. We would simply be lucky.

Now suppose 10,000 investors each put $100 into our investment.  Given the distribution of our hypothetical investment, we would expect to see several hundred investors with outstanding 10-year performance, including 10 with perfect records. Of this group of 10,000 investors, the number expected to experience each possible outcome is given in the following table. 

If someone didn't understand the investment's underlying properties, they might try to rank order the skill of the 10,000 investors by the group in which each investor is found. For example, they might judge investors in Group A to be more skilled than those in Group K. They might devise some sort of method for tracking the historical performance of different investors to see which deliver better risk-adjusted returns. More than likely the investors in Group A would go start a hedge fund and use their track record to attract an exclusive clientele of well-heeled, but naive, investors. But all those efforts would be misguided because the difference in results acheived by Group A investors and Group K investors has nothing to do with differences in skill or intelligence. The results are purely random.

Mistaking luck for skill is a very common fallacy that plagues many investment organizations. I remember a discussion I overheard some years ago when I was a mutual fund manager at American Express. Two senior managers were discussing the investments of another veteran manager. One expressed concern about the amount of risk in the portfolio to which the other replied, "Yes, but it's hard to argue with success."

The bottom line to this example is that alpha is not an unambiguous indication of skill. Sometimes alpha is just fancy name for luck. I call this luck-generated alpha  "phantom alpha" to distinguish it from "true alpha", or alpha that arises from skillful management.

The Fama/French findings

The Fama/French study builds on the fact that some alpha we observe is phantom alpha. They postulate that skill, if it exists, would be apparent by a higher incidence of alpha among active managers than the incidence of phantom alpha we would expect to see in a zero-alpha world. In other words, if active managers really had skill, they would systematically produce more alpha than we would expect dumb luck to produce.

Without going into the gory details of the Fama/French methodology, here is what they found. While some of the highest performing active managers exhibit some skill, their performance advantage is swamped by the additional costs associated with their management. After costs are considered, there is no evidence of true alpha. You can see this by comparing the following two graphs from their study.

The chart in Figure 1 compares the actual alphas with those expected in a zero-alpha world net of all management fees. The universe of managers is divided into percentiles corresponding to the strength of their relative alphas. The horizontal axis is the amount of observed alpha. The blue line shows actual alpha levels for various percentile managers and the red line shows the amount of phantom alpha (my term) we would expect to see in a zero-alpha world.

Looking over Figure 1, we can see that active manager alphas lay uniformly to the left of the phantom alpha line. Only at the highest percentiles are actual alphas close to phantom alphas and then only barely. Among the upper percentile mangers there is no evidence that they produce alpha, net of fees, beyond what we would expect to see from random market activity. On the other hand, among the lower percentiles, there is sobering evidence of truly terrible managers (i.e. managers that produce more negative alpha than we would expect to see.)

Data Source: Dimensional

But what happens when we remove the impact of fees? Is it possible that managers have skill, but the mutual fund companies siphon off the economic value of their skill in the fees they charge? Figure 2 reveals the answer.

Data Source: Dimensional

The data in Figure 2 indicate skill among managers in the extreme right tail. In fact, 90 percent of the managers in the 90th percentile delivered alpha above the pure chance level. What does this mean? It means there are some managers with skill, but the investors don't benefit from it. This, of course, begs the question: who are these managers really serving?

Perhaps I should leave it to Fama and French to state their own conclusion:

...the evidence says that for the vast majority of funds true alpha is negative. And even for the top percentiles of [managers], strong past performance is probably due to chance. Going forward, the estimates of true alpha for the top performers is close to zero - about the same as for an efficiently managed portfolio of passive funds.

I encourage interested readers to dig through the Fama and French study. To make their findings more accessible to us mere mortals, Fama and French wrote a summary for Dimensional Fund Advisors. For those who want to read the original, you can find it at the Social Security Research Network.