Incorporating Estimation Risk in Portfolio Choice

We propose an adjustment in mean-variance portfolio weights to incorporate uncertainty caused by the fact that, in general, we have to use estimated expected returns.The adjustment amounts to using a higher pseudo risk-aversion rather than the actual risk-aversion.The difference between the actual and the pseudo risk-aversion depends on the sample size, the number of assets in the portfolio, and the curvature of the mean-variance frontier.Applying the adjustment to international portfolios, we show that the adjustments are nontrivial for G5 country portfolios and that they are even more important when emerging markets are included.We also show that, in the case of time-varying expected country returns, our adjustment implies a signifficantly smaller variability in portfolio weights than is commonly believed.

[1]  Michael W. Brandt,et al.  Variable Selection for Portfolio Choice , 2001 .

[2]  Philippe Jorion Bayesian and CAPM estimators of the means: Implications for portfolio selection , 1991 .

[3]  Stephen J. Brown,et al.  Estimation risk and optimal portfolio choice , 1980 .

[4]  W. Ziemba,et al.  The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice , 1993 .

[5]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

[6]  H. Markowitz Mean—Variance Analysis , 1989 .

[7]  Stephen J. Brown The Effect of Estimation Risk on Capital Market Equilibrium , 1979, Journal of Financial and Quantitative Analysis.

[8]  Campbell R. Harvey,et al.  PREDICTABLE RISK AND RETURNS IN EMERGING MARKETS , 1999 .

[9]  H. White,et al.  Data‐Snooping, Technical Trading Rule Performance, and the Bootstrap , 1999 .

[10]  Vijay S. Bawa,et al.  The effect of estimation risk on optimal portfolio choice , 1976 .

[11]  John Matatko,et al.  Estimation risk and optimal portfolio choice , 1980 .

[12]  Campbell R. Harvey,et al.  Emerging Equity Market Volatility , 1995 .

[13]  Jeffrey L. Coles,et al.  On Equilibrium Pricing under Parameter Uncertainty , 1995, Journal of Financial and Quantitative Analysis.

[14]  F. D. Roon,et al.  Testing for Mean-Variance Spanning with Short Sales Constraints and Transaction Costs: The Case of Emerging Markets , 2001 .

[15]  Philippe Jorion International Portfolio Diversification with Estimation Risk , 1985 .

[16]  Bruno Gerard,et al.  International Asset Pricing and Portfolio Diversification with Time‐Varying Risk , 1997 .

[17]  W. Sharpe,et al.  Mean-Variance Analysis in Portfolio Choice and Capital Markets , 1987 .

[18]  Philip H. Dybvig Short Sales Restrictions and Kinks on the Mean Variance Frontier , 1984 .

[19]  Philippe Jorion Bayes-Stein Estimation for Portfolio Analysis , 1986, Journal of Financial and Quantitative Analysis.

[20]  C. B. Barry PORTFOLIO ANALYSIS UNDER UNCERTAIN MEANS, VARIANCES, AND COVARIANCES , 1974 .

[21]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[22]  Stephen J. Brown,et al.  Estimation Risk and Simple Rules for Optimal Portfolio Selection , 1983 .

[23]  Bruce G. Resnick,et al.  More on Estimation Risk and Simple Rules for Optimal Portfolio Selection , 1985 .