Portfolio Optimization: The Case for Rank and Sign in Expected Returns

Abstract

The portfolio theory literature has long strived for perfection when it comes to estimating expected returns. In this paper we develop a theoretical framework which shows that perfect (known) expected returns may not be necessary for (optimal) portfolio optimizations. Using simulated data, we show that results from a portfolio constructed using perfect expected returns do not outperform those whose results are "shocked." Our findings suggest that optimizations using correctly ranked expected returns outperform portfolios whose expected returns are known. We confirm these results empirically using option-recovered expected idiosyncratic returns which outperform other benchmark portfolio optimization models.

Keywords: Portfolio theory, expected returns, mean-variance, ranking, recovery theorem

JEL Classification: G12, G13, G14, G17