Active Management: How Important is Luck?

This month, as part of our never ending quest to expose the numerous myths, legends and fallacies that surround active investment management, we have set our sites on a simple question: What role does luck play in successful active investment management? Common sense tells most people that luck's role is far from insignificant: think of your reaction the last time your cousin Ralph loudly regaled party guests with tales of his latest stock market conquest. If you are like most people, you were probably quietly mumbling "lucky bastard" or some similar compliment as you headed off in search of another (stronger) drink.

Well, we have good news -- you were right. And we have the numbers to prove it.

Before we start, ask yourself this apparently simple question. Consider a situation in which there are ten active investment managers, and one of them (Manager A) has been ranked number one in terms of cumulative performance after one year. What are the chances that he or she will still be ranked number one after three, five, or ten years? If you are like most of us, you probably said ten percent. If someone told you that Manager A had been ranked number one or two in terms of cumulative performance (that is, compound annual returns) after ten years, you would probably conclude that this showed that he or she had some real investment management skills. You might even consider paying him or her a fee well in excess of what you would pay an index fund manager, in the expectation of earning superior returns on your investment.

Unfortunately, you could be making a big mistake.

Here is the experiment we ran. We constructed a world in which there were ten investment managers. To establish a baseline situation, we assumed that none of them had any active management skill -- that is, the returns each manager earned in any given year were randomly drawn from the historical distribution of returns for the Wilshire 5000 Index between 1971 and 2000 (average return of 14.5%, with a standard deviation of 18.0%). In other words, each manager's performance was solely due to luck. The question we asked was a simple one: what was the probability that a manager who ranked number one in terms of returns after one year would still rank number one in returns after three, five, and ten years? To answer this question, we ran 25,000 simulations. In each simulation, we randomly generated 100 returns (10 managers times ten annual returns for each), and calculated the compound annual returns and rankings after one, three, five and ten years.

The results shocked us.

After three years, the probability that the manager who was ranked number one (out of ten) after one year would still be number one was 53.5%. The probability that he or she would be ranked number one or two was 73.8%. The probability of being in the top five was 94.5%.

The probability that this manager would still be ranked number one (based on compound annual rate of return) after five years was 46.4%. The probability of being ranked number one or number two after five years was 67.4%, while the probability of being in the top five was 92.2%.

After ten years, the probability of being ranked number one was still 40.4%, the probability of being ranked number one or number two was 61.3%, and the probability of being in the top five was 89.6%.

In short, investment management appears to be a non-linear phenomenon, in which the power of compounding causes long term performance ranking to display a very high sensitivity to initial conditions.

What are we to make of this?

First and foremost, these data seem to suggest that pure luck plays a much bigger role in active investment management success than anybody wants to acknowledge. And of course, given the amount of fees paid to active investment managers, nobody is in any rush to admit this. But these numbers suggest that luck alone plays a very big role in determining which mutual fund ranks at the top of the "best returns after one, three, five and ten years" league tables.

The second point is perhaps more shocking than the first. Consider the accumulated research findings (some of which are available in the Investment Research section of this site) with respect to what is called the "persistence" of mutual fund returns, or the likelihood that this year's top performing fund will be next year's top performing fund. Most of the academic research that has been done in this area has found that persistence is either minimal or non-existent. As an August 2000 research study done for the U.K.'s Financial Services Authority put it, "the conclusion from an examination of the literature is that repeat performance (if there is any), is both small in the size of the effect and short lived." And yet blind luck alone suggests that we should find strong evidence of it. What is going on? In light of the academic research findings and our experimental data, one is forced to conclude that many active managers are delivering worse performance than one would expect if they were simply picking stocks at random. That is, not only do the great majority of active managers fail to add value in excess of the fees they charge, but many actually appear to be destroying it in substantial amounts.

The final conclusion flows from the first two: in a world in which most active managers appear to be doing worse than luck alone would predict, while charging high fees, the case for low cost index investing is clearly very strong indeed.