On the Economic Value of Alphas

77 Pages Posted: 15 Mar 2011 Last revised: 28 May 2019

See all articles by Raymond Kan

Raymond Kan

University of Toronto - Rotman School of Management

Xiaolu Wang

Iowa State University

Date Written: May 25, 2019


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

Suggested Citation

Kan, Raymond and Wang, Xiaolu, On the Economic Value of Alphas (May 25, 2019). Available at SSRN: https://ssrn.com/abstract=1785161 or http://dx.doi.org/10.2139/ssrn.1785161

Raymond Kan (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S3E6
416-978-4291 (Phone)
416-971-3048 (Fax)

Xiaolu Wang

Iowa State University ( email )

2167 Union Drive
Ames, IA 50011
United States

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