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Optimal Portfolio Choice with Parameter Uncertainty

Published online by Cambridge University Press:  06 April 2009

Raymond Kan and
Guofu Zhou
Raymond Kan
Affiliation:
kan@chass.utoronto.ca, Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario M5S 3E6, Canada
Guofu Zhou
Affiliation:
zhou@wustl.edu, Olin School of Business, Washington University, St. Louis, MO 63130.
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Abstract

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In this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical results show that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance. We further show that with parameter uncertainty, holding the sample tangency portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the estimation risk. In particular, we show that a portfolio that optimally combines the riskless asset, the sample tangency portfolio, and the sample global minimum-variance portfolio dominates a portfolio with just the riskless asset and the sample tangency portfolio, suggesting that the presence of estimation risk completely alters the theoretical recommendation of a two-fund portfolio.

Information

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 42 , Issue 3 , September 2007, pp. 621 - 656
Copyright
Copyright © School of Business Administration, University of Washington 2007

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