Maximizing excess return per unit variance: a novel investment management objective

Abstract

I propose a novel investment objective for portfolios fully invested in risky assets only. The new objective is based on achieving the highest possible excess return per unit of variance. The optimal portfolio is a linear combination of the tangent portfolio and the minimum variance portfolio where the weights are inversely proportional to the standard deviation of the return of each portfolio. Using a standard factor model of securities’ returns, I provide an empirical application of the optimal portfolio and show that it performs quite well out-of-sample relative to the maximum Sharpe ratio portfolio as well as the minimum variance portfolio.