ABSTRACT
Chapter 4 considers the problem of “overoptimism”, wherein one has selected one among many assets based on having the largest observed Sharpe ratio. Several techniques are introduced to deal with the bias of the observed Sharpe of the selected asset. First the basic techniques of Multiple Hypothesis Testing are introduced and applied to the problem. The Bonferroni correction is analyzed for the case where returns have a common positive correlation. Hypothesis testing against one-sided alternatives is considered, using the asymptotic normal approximation of the distribution of the Sharpe. Hansen's log-log correction is applied to the problem. Finally, conditional inference is considered, including application of the “polyhedral lemma”. The power of the various methods are compared. Tukey's post hoc test is adapted to produce a means of clustering assets with “honestly” significantly different Sharpes.
