The notion that mutual fund investors are better off in index funds than in actively managed funds is challenged in a new paper from Wharton finance professor Andrew Metrick and graduate students Klaas Baks of Brown University and Jessica Wachter of Harvard University.

Financial advisors and analysts often point out that index funds, which invest in Standard & Poor’s list of 500 large corporations, do better than funds that are actively directed by professional managers. In fact, just 6% of those professionally managed funds have, over the past five years, outperformed funds that are pegged to the S&P 500.

But there is the matter of that sage 6%. If there were a way to figure out which managers are likely to beat the market in the future, the investor stands a chance of maximizing returns. Metrick, Baks and Wachter don’t provide a practical way for the average investor to figure out who those six percenters are, but they do show that even if only one in 1,000 can beat the S&P consistently, the potential returns make it worthwhile to search for that one.

Their paper, entitled "Should Investors Avoid All Actively Managed Mutual Funds?" uses a statistical technique known as Bayesian analysis (after the 18th Century English mathematician Thomas Bayes) to prove their point. If one starts with a prediction about the likelihood of an event, Bayesian methodology allows one to use the history of an event to continually revise that prediction. Put in other words, Bayesian analysis is a means of calculating, from the number of times an event has occurred or not occurred, the probability that it will happen in future attempts.

In the case of actively managed funds, the paper applies Bayesian theory to show that every month of successful performance increases the likelihood that a manager will continue that success.

A New York Times article published in October 1999 on the Metrick-Baks-Wachter study gives this example of Bayesian analysis: If 10% of a collection of coins is weighted so that they come up heads 75% of the time when tossed, could you tell whether one of the coins, selected randomly, was one of the loaded coins? No – but you could increase the odds of identifying it as loaded if you were allowed to flip it a few times. If the first flip comes up heads, then the odds that it is one of the loaded coins increases from 10% to 14.3%. Each successive flip that comes up heads will increase the probability that the coin is loaded.

In the case of actively managed funds, the odds that a manager could consistently beat the market were unknown. But Bayesian analysis must start with an initial probability figure, so the researchers estimated that number. To be on the conservative side, they assumed that two-hundredths of 1%, or one in 5,000 fund managers, had the ability to consistently beat the market. They applied those assumptions to 1,437 active fund managers of diversified mutual funds in the U.S., over an average of 51 months, using data drawn from the Center for Research in Security Prices (CRSP). The researchers examined managers rather than the funds they worked for because they considered that it is the manager, not the funds themselves, that is primarily responsible for exceptional returns.

Just as even weighted coins will sometimes come up tails, the superior managers didn’t always beat the S&P benchmark. They did it enough times, however, to make it apparent that the rare highly skilled manager is worth looking for.

According to Times financial reporter Mark Hulbert, the researchers found that five fund managers or management teams beat the market consistently: Shelby Davis of Davis New York Venture, by 4.1%; Ralph Wanger, Charles P. McQuaid and Terrance M. Hogan of the Acorn Fund, 3.4%; Stephen A. Lieber of the Evergreen Fund, 3.2%; Robert A. Lange of Lindner Growth, 3.2%; and Charles Albers of Guardian Park Avenue, 2.9%.

Unfortunately, those results will be of little help to investors. At the time of the paper, CRSP data covered the period from 1963 to 1996, and most of the superior managers identified have since moved on. Of those managers, the only ones still managing the same fund are Acorn’s Wanger and McQuaid (Hogan having since left). Moreover, because of the abstruse mathematical analysis required, the average investor would not be able to duplicate it.

The study backs up conventional wisdom in that it found that the average active fund underperforms index funds. Moreover, it did not disprove the hypothesis that fund managers who achieve exceptional results are just lucky. The analysis does show, however, that it is rash to argue that investors should avoid all actively managed funds.

There is no correct model by which fund manager performance can be evaluated, and Metrick, Baks and Wachter do not pretend to offer one. Investors may be best advised to use simple rules of thumb for evaluating funds and their managers if they do not have the statistical analysis prowess and computer savvy to carry off advanced investment strategies. Nonetheless, the method provides a new way to evaluate performance that is at distinct odds with conventional thinking about indexed funds.