The J-Shape of Performance Persistence Given Survivorship Bias

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Abstract
Performance may enhance survival probability. When it does, the induced lack of randomness challenges robust and unbiased inference. If survivors are sorted into two groups based on past performance, spurious persistence has been demonstrated if variance in performance is heterogeneous. However, as we show both theoretically and with simulations, if performance is categorized finely, the spurious persistence will be J-shaped; that is, at the bottom better performance in one period “predicts” worse performance for another period. We propose a simple t-test applied to the quadratic coefficient in a regression to distinguish between a spurious J-shape and monotonic patterns. Mutual funds, our example, exhibit the monotonically increasing pattern produced by true performance persistence. Performance may enhance survival probability. When it does, the induced lack of randomness challenges robust and unbiased inference. If survivors are sorted into two groups based on past performance, spurious persistence has been demonstrated if variance in performance is heterogeneous. However, as we show both theoretically and with simulations, if performance is categorized finely, the spurious persistence will be J-shaped; that is, at the bottom better performance in one period “predicts” worse performance for another period. We propose a simple t-test applied to the quadratic coefficient in a regression to distinguish between a spurious J-shape and monotonic patterns. Mutual funds, our example, exhibit the monotonically increasing pattern produced by true performance persistence. Performance may enhance survival probability. When it does, the induced lack of randomness challenges robust and unbiased inference. If survivors are sorted into two groups based on past performance, spurious persistence has been demonstrated if variance in performance is heterogeneous. However, as we show both theoretically and with simulations, if performance is categorized finely, the spurious persistence will be J-shaped; that is, at the bottom better performance in one period “predicts” worse performance for another period. We propose a simple t-test applied to the quadratic coefficient in a regression to distinguish between a spurious J-shape and monotonic patterns. Mutual funds, our example, exhibit the monotonically increasing pattern produced by true performance persistence.

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