ABSTRACT
Chapter 3 considers the distribution of the Sharpe ratio when the assumptions of i.i.d normal returns are violated. The bias and variance of the Sharpe ratio are computed when returns are drawn from elliptically distributed returns, from heteroskedastic normal returns, and from autocorrelated normal returns. In each case it is shown there is little impact on the mean and variance of the Sharpe. The asymptotic distribution of the Sharpe ratio is given for general returns. This result is used to support Frequentist and Bayesian inference on functions of several Sharpe ratios. Concentration inequalities are given which bound the probability that the Sharpe exceeds a given amount. The effect of survivorship bias on the Sharpe is given, and it is argued that the Sharpe can be meaningfully computed even when moments of the returns distribution do not exist. Many of these results are then shown for the ex-factor Sharpe ratio. An empirical study is described that compares the usual and higher-order standard errors of the Sharpe ratio.
