Mutual Fund Performance: Luck or Skill?

I. INTRODUCTION Fundamental finance principles, along with common sense, dictate that investors take account of both risk and return, yielding some measure of positive risk-adjusted returns that also account for all transaction costs and/or management fees. In other words, investors seek positive alphas ([alpha]'s), i.e., risk and cost-adjusted positive returns. Many investors turn to professionals in search of such gains. According to the Investment Company Fact Book (2011), almost 30% of world's wealth is invested in mutual funds: $25 trillion of the $85 trillion total world-wide investible wealth. About 44% of individual wealth in the U.S., $12 trillion, is invested in mutual funds. Mutual funds charge management fees that appear to reduce total return to investors. Many mutual funds either do not beat the market or fail to outperform their chosen benchmarks. Indeed, while Fama and French (2010) note "the aggregate portfolio of actively managed U.S. equity mutual funds is close to the market portfolio, but the high costs of active management show up intact as lower returns to investors," they document existence of genuine inferior and superior performance at the negative and positive extremes. Results herein mirror those of Fama and French (2010), though a probability approach leads to the results herein versus the bootstrap method used by them. Experiments involving many successive trials with multiple subjects, demonstrate a positive probability that a subject will win several times in a row merely due to luck, not skill. For example, while the probability that a person flips a coin and ends up with 10 heads in a row is less than one in a thousand (1/1032 = 0.098%), such strings of luck do occur, and when they do, it is not skill on the part of the person flipping the coin. Some of the thousands of investment funds may end up the "winners" for prolonged periods of time. Naturally, investors need to know whether streaks of superior performance are due to skill. The analysis herein demonstrates that such streaks exist within the family of mutual funds and are due to skill, not luck. The main contention of this paper relies on detecting the existence of skill with the generalized binomial distribution, using an established analogy with winning in sports. Money managers are usually well-educated and even skilled, as are professional athletes. Competition alone in sports dictates that not all professional teams can win; though as noted in more detail below, the most highly skilled teams appear to win more often. In contrast, a good deal of prior evidence indicates that a majority of actively managed mutual funds fail to outperform passively managed index funds. According to Berk and Green (2004), the apparent lack of investment skill has "led researchers to raise questions about the rationality of investors who place money with active managers despite their apparent inability to outperform passive strategies and who appear to devote considerable resources to evaluating past performance of managers. " This paper contributes to this important debate about luck vs. skill. Using a novel statistical approach based on the Generalized Binomial Distribution (Drezner and Farnum, 1993), this paper investigates whether some mutual funds provide positive [alpha]'s over time as a result of skill. The approach demonstrates, in contrast to a large degree of the extant evidence, that skilled fund managers do exist--persistence in superior performance cannot be attributed to luck. This paper's results suggest important practical implications. The lack of convincing evidence that mutual funds provide superior performance dramatically influences the investing habits of individuals. The lack of such evidence along with such straightforward factors as the ease of trading ETFs and lower management costs for ETFs have most likely led to the growth of ETFs and a relative decline in mutual funds in recent years. …