Sharpe Portfolio Using a Cross-Efficiency Evaluation

Abstract

The Sharpe ratio is a way to compare the excess returns (over the risk-free asset) of portfolios for each unit of volatility that is generated by a portfolio. In this paper, we introduce a robust Sharpe ratio portfolio under the assumption that the risk-free asset is unknown. We propose a robust portfolio that maximizes the Sharpe ratio when the risk-free asset is unknown, but is within a given interval. To compute the best Sharpe ratio portfolio, all the Sharpe ratios for any risk-free asset are considered and compared by using the so-called cross-efficiency evaluation. An explicit expression of the Cross-Efficiency Sharpe Ratio portfolio is presented when short selling is allowed.