On the Stability of Performance Measures Over Time

Abstract

Performance persistence is a relevant issue when evaluating the predictability of future results of managed portfolios. A related crucial aspect is the stability over time of the measure used to assess the performance, defined as the degree of association between the rankings of financial assets induced by the performance measure throughout subsequents periods. In this work a general class of possible criteria to measure stability is proposed. Then, the attention is focused on a specific index, whose asymptotic expected value and variance are derived under the null hypothesis of absence of stability. Furthermore, two statistical tests for evaluating the significance of stability are discussed. An application to a large set of US equity mutual funds shows that stability may remarkably vary, as the performance measure or the time widow width where it is computed change.