In examining the question of luck versus skill in actively managed equity mutual funds, the authors start from the perspective of equilibrium accounting. They assume that active management is a zero-sum game and if some active managers have positive α before costs, it is at the expense of other active managers. The authors use long histories of individual fund returns and the results of 10,000 bootstrap simulations of return histories to infer the existence of superior and inferior funds. They compare the distribution of α estimates from the simulations with the cross-section of α estimates for actual fund returns.

The data are from the CRSP database. The authors eliminate index funds, include only funds that invest primarily in U.S. common stocks, and focus on the period after 1983 because of selection bias in the 1962–83 data as a result of a substantial number of funds not reporting monthly returns. They rely mainly on their own three-factor regression model as the main benchmark for their analysis, although they also include results for Carhart’s four-factor model, which includes momentum return as well as the authors’ constructions of size and value-growth returns.

The authors look at monthly returns from 1984 to 2006 on equal-weighted (EW) and value-weighted (VW) portfolios of the funds chosen for their sample. In aggregate, the active funds show little exposure to value-growth and momentum factors, and although smaller funds seem more inclined to invest in small stocks than large funds do (as shown by the EW portfolio compared with the VW one), total dollars invested in active funds show little tilt toward small stocks.

Looking at the intercepts in the estimates of EW and VW returns relative to passive benchmarks, the authors find that the three-factor and four-factor intercepts for the net returns are negative. This finding suggests that on average, active managers lack sufficient skill to cover the costs that active funds impose on investors. Market return alone explains 99 percent of the variance in the monthly VW fund return; active mutual funds in aggregate thus mimic, before expenses, market portfolio returns. The high expense ratios of active mutual funds then reduce the return to investors.

To measure whether active managers have any skill in achieving expected returns that differ from those of comparable passive benchmarks, the authors look at gross returns. Because of issues of error and bias in measuring trading costs, they opt to use gross returns that include costs other than those captured in expense ratios as well as the typically small revenues from securities lending. The results of the tests on gross returns suggest that in aggregate, active funds show sufficient skill to produce expected returns that cover some or all of the costs missed in expense ratios and do not produce returns that are either above or below those of passive benchmarks.

To evaluate whether superior and inferior managers balance one another out to produce α estimates close to zero in the aggregate, the authors set up simulations that use individual fund returns. The tests include funds that reached $5 million in assets under management (AUM) and keep including funds once they have reached that level of AUM. The authors only include funds that appear in the database for at least five years before the end of the sample period to avoid including a large number of new funds with short return histories.

The tests use bootstrap simulations on returns that have the properties of actual fund returns, except that true α is set to 0 for every fund. The authors perform 10,000 simulation runs to produce 12 distributions of t-statistics, t(α), for a world in which true α is 0. For net returns, setting true α to 0 implies that every active fund manager has sufficient skill to generate expected returns that cover all costs; for gross returns, it implies that every active fund manager has just enough skill to generate expected returns that cover the costs not included in expense ratios.

For net returns, the results of the tests confirm that skill sufficient to cover costs is rare. Below the 80th percentile, the three-factor t(α) estimates for actual net fund returns are better than those from the simulation in less than 1 percent of the net simulation runs. Analyzing the extreme right tail percentiles against the benchmark, the authors conclude that a portfolio of low-cost index funds would perform about as well as a portfolio of the top three percentiles of past active winners and better than the rest of the active fund universe. The tests on gross returns point to the presence of skill, both positive and negative, at the extreme tails of the cross-section.

The authors explain that the more positive results in other research, which suggest that many of the best funds have more than sufficient skill to cover costs, are because of a different simulation approach and different rules for including funds in the simulation tests.