Estimation Risk and Portfolio Selection in the Lower Partial Moment

Abstract

Portfolio selection models generally assume that the investor knows the parameters of the probability distribution of security returns. In practise the investor must, however, employ estimates of the necessary parameters. In this paper we investigate the effect of estimation risk on the efficient frontier in the lower partial moment framework. The results of the average difference between the actual and estimated portfolios show that the estimated portfolios are biased predictors of the actual portfolios. However, the estimates of the optimal portfolios can be improved. If our concern is the uncertainty in the optimal portfolio weights, then a bootstrap approach should be used to improve the optimizations. On the other hand, if our concern is related to the risk and portfolio mean returns of the optimized portfolios, then a James-Stein approach should be used . ∗I thank seminar participants at Lund University, at the Nordic Econometric meeting , Uppsala, 1999, and at the 28th Annual Conference of Economists, Melbourne, 1999, for valuable comments.