  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-Eficiency Sharpe ratio portfolio is presented when short selling is
allowed.
