Optimal portfolio choice using the maximum Sharpe ratio

Abstract

Choosing a portfolio from among the enormous range of assets now available to an investor would be facilitated if we could locate the return–risk ratio of a particular allocation along a spectrum of possibilities. A comparison between portfolio choices can tell us, for example, whether it is better to select a suboptimal portfolio from a large class of assets or to perform a Markowitz optimal procedure on a subset of the assets. A common criterion for this assessment is the expected return-to-risk tradeoff as measured by the Sharpe ratio. Given that the ideal, maximized Sharpe ratio must be estimated, we develop, in this paper, an approach that enables us to assess ex ante how close a given portfolio is to this ideal. For this purpose, we derive the large-sample distribution of the maximized Sharpe ratio, as obtained from sample estimates, under very general assumptions. This distribution then represents the spectrum of possible optimal return–risk trade-offs that can be constructed from thedata. We illustrate applications of the theory by analyzing a large sample of US companies, comparing constant-correlation and momentum strategies with the optimal strategy. Simulations based on this data are also given for illustration.