**Working Papers, Department of Economics, Lund University**
# No 2003:17:

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

*Christoffer Bengtsson*
**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.

**Keywords:** Portfolio selection; Estimation risk; Markov Chain Monte Carlo; (follow links to similar papers)

**JEL-Codes:** G11; (follow links to similar papers)

26 pages, November 10, 2003, Revised April 29, 2004

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