On the Estimation Error in Mean-Variance Efficient Portfolio Weights

19 Pages Posted: 28 Oct 2004

See all articles by Frans de Roon

Frans de Roon

Tilburg University - Department of Finance

Date Written: October 25, 2004

Abstract

This paper derives the asymptotic covariance matrix of estimated mean-variance efficient portfolio weights, both for gross returns (without a riskfree asset available) and for excess returns (in excess of the riskfree rate). When returns are assumed to be normally distributed, we obtain simple formulas for the covariance matrices. The results show that the estimation error increases as the risk aversion underlying the portfolio decreases and as the (asymptotic) slope or Sharpe ratio of the mean-variance frontier increases. For the tangency portfolio, there is an additional estimation risk because the location of the tangency portfolio is not known beforehand. The empirical analysis of efficient portfolios based on the G7 countries indicates that the estimation error can be big in practice. It also shows that the standard errors that assume normality are usually very close to the standard errors that do not assume normality in returns, except for portfolios close to the Global Minimum Variance portfolio.

Keywords: Portfolio choice, estimation error, international finance

JEL Classification: G11, G15

Suggested Citation

de Roon, Frans A., On the Estimation Error in Mean-Variance Efficient Portfolio Weights (October 25, 2004). Available at SSRN: https://ssrn.com/abstract=610002 or http://dx.doi.org/10.2139/ssrn.610002

Frans A. De Roon (Contact Author)

Tilburg University - Department of Finance ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 1 3466 8361/3025 (Phone)
+31 1 3466 2875 (Fax)

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