On the Economic Value of Alphas

Abstract

Assets with nonzero alphas are supposed to provide performance improvement relative to the benchmark portfolios. However, when the mean and covariance matrix of asset returns are estimated with errors, it is unclear whether the performance improvement can be realized. In this paper, we analyze the out-of-sample performance of a sample optimal portfolio constructed based on the benchmark portfolios and a set of assets with nonzero alphas. We show that while this sample optimal portfolio continues to have positive out-of-sample alpha, due to estimation errors, it fails to outperform the benchmark portfolios in terms of mean-variance utility for estimation windows typically used in the literature. Under the i.i.d. normality assumption, we derive the unconditional distribution of the out-of-sample return of the sample optimal portfolio and analytically study the behavior of this portfolio, offering insights on the effect of estimation risk. We further consider a strategy that optimally combines the sample optimal portfolio with the benchmark portfolios. The combining strategy consistently outperforms the benchmark portfolios, providing a reliable way to realize the economic value of alphas.

Keywords: Alpha, optimal portfolio, estimation risk, combining portfolio

JEL Classification: G11