Survivorship bias and attrition effects in measures of performance persistence
We generate samples of fund returns calibrated to match the U.S. mutual fund industry and simulate standard tests of performance persistence. We consider a variety of alternative return generating processes, survival criteria, and test methodologies. When survival depends on performance over several periods, survivorship bias induces spurious reversals, despite the presence of cross-sectional heteroskedasticity in performance. In samples which are largely free of survivorship bias, look-ahead biased methodologies and missing returns still affect statistics. In samples with no true persistence, the spurious persistence caused by survivorship bias in the presence of single-period survival criteria never reaches the magnitude found in recent empirical studies. When fund returns are truly persistent, the simulations reveal an attrition effect, distinct from survivorship bias. The systematic disappearance of poor performers causes mean persistence measures to differ from those in a hypothetical sample in which funds never disappear, even in tests which incorporate all data on disappearing funds. The magnitude and direction of this effect depends on the return generating process. We also examine the specification and power of the persistence tests. The t-test for the difference between top and bottom portfolios ranked by past performance is the best specified under the null and among the most powerful against the alternatives we consider.
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