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Chicago Booth BUSF 35150 - Luck versus Skilll in the Cross Section of Mutual Fund Returns

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THE JOURNAL OF FINANCE•VOL. LXV, NO. 5•OCTOBER 2010Luck versus Skill in the Cross-Section of MutualFund ReturnsEUGENE F. FAMA and KENNETH R. FRENCH∗ABSTRACTThe aggregate portfolio of actively managed U.S. equity mutual funds is close tothe market portfolio, but the high costs of active management show up intact aslower returns to investors. Bootstrap simulations suggest that few funds producebenchmark-adjusted expected returns sufficient to cover their costs. If we add backthe costs in fund expense ratios, there is evidence of inferior and superior performance(nonzero true α) in the extreme tails of the cross-section of mutual fund α estimates.THERE IS A CONSTRAINT on the returns to active investing that we call equi-librium accounting. In short (details later), suppose that when returns aremeasured before costs (fees and other expenses), passive investors get passivereturns, that is, they have zero α (abnormal expected return) relative to passivebenchmarks. This means active investment must also be a zero sum game—aggregate α is zero before costs. Thus, if some active investors have positiveα before costs, it is dollar for dollar at the expense of other active investors.After costs, that is, in terms of net returns to investors, active investmentmust be a negative sum game. (Sharpe (1991) calls this the arithmetic of activemanagement.)We examine mutual fund performance from the perspective of equilibriumaccounting. For example, at the aggregate level, if the value-weight (VW) port-folio of active funds has a positive α before costs, we can infer that the VWportfolio of active investments outside mutual funds has a negative α.Inotherwords, active mutual funds win at the expense of active investments outsidemutual funds. We find that, in fact, the VW portfolio of active funds that investprimarily in U.S. equities is close to the market portfolio, and estimated beforeexpenses, its α relative t o common benchmarks is close to zero. Since the VWportfolio of active funds produces α close to zero in gross (pre-expense) returns,α estimated on the net (post-expense) returns realized by investors is negativeby about the amount of fund expenses.The aggregate results imply that if there are active mutual funds with posi-tive true α, they are balanced by active funds with negative α. We test for the∗Fama is at the Booth School of Business, University of Chicago, and French is at the AmosTuck School of Business Administration, Dartmouth College. We are grateful for the comments ofJuhani Linnainmaa, Sunil Wahal, Jerry Zimmerman, and seminar participants at the Universityof Chicago, the California Institute of Technology, UCLA, and the Meckling Symposium at theUniversity of Rochester. Special thanks to John Cochrane and the journal Editor, Associate Editor,and referees.19151916 The Journal of FinanceR existence of such funds. The challenge is to distinguish skill from luck. Giventhe multitude of funds, many have extreme returns by chance. A common ap-proach to this problem is to test for persistence in fund returns, that is, whetherpast winners continue to produce high returns and losers continue to under-perform (see, e.g., Grinblatt and Titman (1992), Carhart (1997)). Persistencetests have an important weakness. Because they rank funds on short-term pastperformance, there may be little evidence of persistence because the allocationof funds to winner and loser portfolios is largely based on noise.We take a different tack. We use long histories of individual fund returnsand bootstrap simulations of return histories to infer the existence of superiorand inferior funds. Specifically, we compare the actual cross-section of fund αestimates to the results from 10,000 bootstrap simulations of the cross-section.The returns of the funds in a simulation run have the properties of actualfund returns, except we set true α to zero in the return population from whichsimulation samples are drawn. The simulations thus describe the distributionof α estimates when there is no abnormal performance in fund returns. Com-paring the distribution of α estimates f rom the simulations to the cross-sectionof α estimates for actual fund returns allows us to draw inferences about theexistence of skilled managers.For fund investors the simulation results are disheartening. When α is es-timated on net returns to investors, the cross-section of precision-adjusted αestimates, t(α), suggests that few active funds produce benchmark-adjusted ex-pected returns that cover their costs. Thus, if many managers have sufficientskill to cover costs, they are hidden by the mass of managers with insufficientskill. On a practical level, our results on long-term performance say that true αin net returns to investors is negative for most if not all active funds, includingfunds with strongly positive α estimates for their entire histories.Mutual funds look better when returns are measured gross, that is, before thecosts included in expense ratios. Comparing the cross-section of t(α) estimatesfrom gross fund returns to the average cross-section from the simulations sug-gests that there are inferior managers whose actions reduce expected returns,and there are superior managers who enhance expected returns. If we assumethat the cross-section of true α has a normal distribution with mean zero andstandard deviation σ ,thenσ around 1.25% per year seems to capture the tailsof the cross-section of α estimates for our full sample of actively managed funds.The estimate of the standard deviation of true α, 1.25% per year, does notimply much skill. It suggests, for example, that fewer than 16% of funds haveα greater than 1.25% per year (about 0.10% per month), and only about 2.3%have α greater than 2.50% per year (about 0.21% per month)—before expenses.The simulation tests have power. If the cross-section of true α for gross fundreturns is normal with mean zero, the simulations strongly suggest that thestandard deviation of true α is between 0.75% and 1.75% per year. Thus, thesimulations rule out values of σ rather close to our estimate, 1.25%. The powertraces to the fact that a large cross-section of funds produces precise estimatesof the percentiles of t(α) under different assumptions about σ , t he standarddeviation of true α. This precision allows us to put σ in a rather narrow range.Luck versus Skill in Mutual Fund Returns 1917Readers suggest that our results are consistent with the predictions of


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