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The Impact of Estimation Error on Portfolio Selection for Investors with Constant Relative Risk Aversion

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  • Bengtsson, Christoffer

    (Department of Economics, Lund University)

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    Abstract

    This paper examines the impact of estimation error in a simple single-period portfolio choice problem when the investor has power utility and asset returns are jointly lognormally distributed. These assumptions imply that such an investor selects portfolios using a modified mean-variance framework where the parameters that he has to estimate are the mean vector of log returns and the covariance matrix of log returns. Following Chopra and Ziemba (1993), I simulate estimation error in what are assumed to be the true mean vector and the true covariance matrix and the impact of estimation error is measured in terms of percentage cash equivalence loss for the investor. To obtain estimation error sizes that are similar to the estimation error sizes in actual estimates, I use a Bayesian approach and Markov Chain Monte Carlo Methods. The empirical results differ significantly from Chopra and Ziemba (1993), suggesting that the effect of estimation error may have been overestimated in the past. Furthermore, the results tend to question the traditional viewpoint that estimating the covariance matrix correctly is strictly less important than estimating the mean vector correctly.

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    File URL: http://project.nek.lu.se/publications/workpap/Papers/WP03_17.pdf
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    Bibliographic Info

    Paper provided by Lund University, Department of Economics in its series Working Papers with number 2003:17.

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    Length: 26 pages
    Date of creation: 10 Nov 2003
    Date of revision: 29 Apr 2004
    Handle: RePEc:hhs:lunewp:2003_017

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    Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund,Sweden
    Phone: +46 +46 222 0000
    Fax: +46 +46 2224613
    Web page: http://www.nek.lu.se/en
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    Related research

    Keywords: Portfolio selection; Estimation risk; Markov Chain Monte Carlo;

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    1. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, 08.
    2. Olivier Ledoit & Michael Wolf, 2001. "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection," Economics Working Papers 586, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    4. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-42.
    5. Ohlson, J. A. & Ziemba, W. T., 1976. "Portfolio Selection in a Lognormal Market When the Investor Has a Power Utility Function," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(01), pages 57-71, March.
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