On the Economic Value of Alphas

Abstract

In this paper, we examine the benefit of incorporating test assets with nonzero alphas into an optimal portfolio when the mean and covariance matrix of asset returns are estimated with errors. Under the normality assumption, we derive the distribution of out-of-sample return of a portfolio that is optimized based on sample mean and covariance matrix. We show that as long as the benchmarks are not ex ante efficient, this sample optimal portfolio will generate positive alpha relative to the benchmarks. However, due to estimation errors, we need a very long estimation window for the sample optimal portfolio to outperform the benchmarks. We further consider a strategy that optimally combines the risk-free asset, the sample optimal portfolio, and the sample optimal portfolio based on just the benchmarks. This combining strategy consistently outperforms the benchmarks, providing a reliable way to realize the economic value of nonzero alphas.