The J-Shape of Performance Persistence Given Survivorship Bias

Survivorship in a panel sample may depend on performance. The lack of randomness introduced challenges unbiased robust inference. If variance of performance over time is heterogeneous, spurious performance persistence may be observed in samples of survivors (Brown, Goetzmann, Ibbotson and Ross, 1992). However, we show that if the categorization of performance is sufficiently fine, the spurious persistence will be J-shaped. This pattern can be distinguished from the monotonic increasing pattern produced by true performance persistence (which has been observed with mutual funds). We confirm the emergence of the J-shape with simulations. A simple t-test applied to the quadratic coefficient in a regression enables us to distinguish between the J-shaped and monotonic patterns