Sharpe portfolio using a cross-efficiency evaluation

TL;DR

This paper introduces a robust method for constructing Sharpe ratio portfolios when the risk-free rate is unknown, using cross-efficiency evaluation to compare portfolios across a range of possible risk-free assets.

Contribution

It proposes a novel robust Sharpe ratio portfolio model that accounts for uncertainty in the risk-free asset using cross-efficiency evaluation, with explicit solutions for portfolios allowing short selling.

Findings

The robust portfolio maximizes the Sharpe ratio over an interval of risk-free rates.

Explicit expression derived for portfolios with short selling allowed.

The method improves portfolio comparison under risk-free rate uncertainty.

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