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Portfolio choice and estimation risk : a comparison of Bayesian approaches to resampled efficiency
(2002)
Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. Several approaches to incorporate estimation risk into portfolio selection are suggested in the earlier literature. These papers regularly discuss heuristic approaches (e.g., placing restrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class of estimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985, 1986), which is probably the most popular estimator. We will show that optimal portfolios based on the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficient frontier with a higher risk aversion. We quantify this increase in risk aversion. Furthermore, we review a relatively new approach introduced by Michaud (1998), resampling efficiency. Michaud argues that the limitations of MV efficiency in practice generally derive from a lack of statistical understanding of MV optimization. He advocates a statistical view of MV optimization that leads to new procedures that can reduce estimation risk. Resampling efficiency has been contrasted to standard Markowitz portfolios until now, but not to other approaches which explicitly incorporate estimation risk. This paper attempts to fill this gap. Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are compared in an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochastic dominance.
The classical approaches to asset allocation give very different conclusions about how much foreign stocks a US investor should hold. US investors should either allocate a large portion of about 40% to foreign stocks (which is the result of mean/variance optimization and the international CAPM) or they should hold no foreign stocks at all (which is the conclusion of the domestic CAPM and mean/variance spanning tests). There is no way in between.
The idea of the Bayesian approach discussed in this article is to shrink the mean/variance efficient portfolio towards the market portfolio. The shrinkage effect is determined by the investor's prior belief in the efficiency of the market portfolio and by the degree of violation of the CAPM in the sample. Interestingly, this Bayesian approach leads to the same implications for asset allocation as the mean-variance/tracking error criterion. In both cases, the optimal portfolio is a combination of the market portfolio and the mean/variance efficient portfolio with the highest Sharpe ratio.
Applying both approaches to the subject of international diversification, we find that a substantial home bias is only justified when a US investor has a strong belief in the global mean/variance efficiency of the US market portfolio and when he has a high regret aversion of falling behind the US market portfolio. We also find that the current level of home bias can be justified whenever-regret aversion is significantly higher than risk aversion.
Finally, we compare the Bayesian approach of shrinking the mean/variance efficient portfolio towards the market portfolio to another Bayesian approach which shrinks the mean/variance efficient portfolio towards the minimum-variance portfolio. An empirical out-of-sample study shows that both Bayesian approaches lead to a clearly superior performance compared to the classical mean/variance efficient portfolio.