ABSTRACT
Chapter 2 considers the statistical properties of the Sharpe ratio when returns are independent and identically distributed, drawn from a normal distribution. The connection between the Sharpe ratio and the t-statistic are used whenever possible to recycle results about the t-test into equivalent results about the Sharpe ratio. The distribution of the Sharpe is given, as well as moments. The bias of the Sharpe is considered. The lambda-prime distribution, which is the confidence distribution for the Sharpe ratio, is discussed. Standard errors for the Sharpe are given, and Frequentist confidence intervals are discussed. Frequentist hypothesis testing using the Sharpe ratio is explored, including power under the alternative. These tests are expanded to the “ex-factor” Sharpe. The likelihood ratio test for the Sharpe is presented. The Bayesian update for the Sharpe ratio based on a Normal Inverse Gamma conjugate prior is discussed. Bayesian credible intervals are presented.
