When they study the performance of mutual funds, researchers must correct for survivorship bias effects. The author argues that this effort to correct for survivorship bias introduces a bias in the opposite direction, which results in estimated mutual fund alphas being understated.
The author investigates the existence and magnitude of what he calls “reverse survivorship bias.” Investors will abandon a mutual fund when the fund’s posterior mean (i.e., true alpha) falls below a certain negative alpha. But researchers who correct for survivorship bias use estimated alphas calculated from average risk-adjusted returns. Because estimated alphas are averages, they must fall below the negative alpha (where investors abandon the fund) before the posterior mean reaches the same point. This difference between the estimated alpha and true alpha is the reverse survivorship bias. One estimate of the magnitude of this bias, based on a four-factor model, is 43 bps.
How Is This Research Useful to Practitioners?
Poor performance by mutual fund managers can be explained by a lack of skill or by bad luck. Thus, alpha estimates for managers who are unlucky but still skillful may provide too harsh a view. Conceptually, reverse survivorship bias seems to have useful implications for assessing the skills of mutual fund managers as well as hedge fund managers, pension fund managers, and individual investors. But as the author notes, inferring skill from longevity for mutual fund managers involves the same issues as inferring CEO skill from longevity. He concludes that no simple and effective solution to the problem of reverse survivorship bias exists and leaves the development of one to future researchers.
How Did the Author Conduct This Research?
The author uses mutual fund data, beginning in January 1984, from the CRSP database. Alphas are estimated from regressions based on the capital asset pricing model, three-factor Fama and French model, and four-factor Carhart model. Alpha estimates are used to examine the relationship between fund returns and the disappearance of funds as well as the impact of both on the size of the survivorship bias. Funds are classified by year of disappearance; 10% of funds do not survive 4 years, and about one-third do not survive 10 years. The alpha estimates of surviving mutual funds are considerably better than those of nonsurviving funds. For example, alpha estimates for funds that survive five years are 0.19%, whereas alpha estimates for funds that do not survive five years are –4%. These results are consistent regardless of the method used to estimate alphas.
To estimate the magnitude of the reverse survivorship bias, the author uses two approaches. In the first method, he performs a regression analysis that compares alpha estimates from two sources: a fund-by-fund estimate of alphas and alpha estimates derived from the four-factor model. This method yields a reverse survivorship bias between 0.46% and 0.62% a year.
In the second method, he derives mutual fund characteristics directly from observed data using a structured learning model. These characteristics are then compared with simulated findings, which results in an estimate of the reverse survivorship bias that is reasonably consistent with the regression-based estimate of 43 bps per year.
Although the concept of reverse survivorship bias, as it has been developed so far, would seem to have applicability largely for academic studies of investment performance, one byproduct of the study has a useful implication for practitioners. Specifically, the author notes the high degree of difficulty in assessing manager skill based solely on past returns. Although he offers no advice on how to proceed, his observation suggests that other aspects of the due diligence process are important in manager selection.