Optimal Portfolio Selection Under the Estimation Risk in Mean Return

This thesis investigates robust techniques for mean-variance (MV) portfolio optimization problems under the estimation risk in mean return. We evaluate the performance of the optimal portfolios generated by the min-max robust MV portfolio optimization model. With an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, minmax robust portfolios equal to the ones from the standard MV model based on the nominal mean estimates but with larger risk aversion parameters. With an interval uncertainty set for mean return, min-max robust portfolios can vary significantly with the initial data used to generate the uncertainty set. In addition, by focusing on the worst-case scenario in the mean return uncertainty set, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjusting the conservatism level of min-max robust portfolios can only be achieved by excluding poor mean return scenarios from the uncertainty set, which runs counter to the principle of min-max robustness. We propose a CVaR robust MV portfolio optimization model in which the estimation risk is measured by the Conditional Value-at-Risk (CVaR). We show that, using CVaR to quantify the estimation risk in mean return, the conservatism level of CVaR robust portfolios can be more naturally adjusted by gradually including better mean return scenarios. Moreover, we compare min-max robust portfolios (with an interval uncertainty set for mean return) and CVaR robust portfolios in terms of actual frontier variation, portfolio efficiency, and portfolio diversification. Finally, a computational method based on a smoothing technique is implemented to solve the optimization problem in the CVaR robust model. We numerically show that, compared with the quadratic programming (QP) approach, the smoothing approach is more computationally efficient for computing CVaR robust portfolios

How much foreign stocks? : Bayesian approaches to asset allocation can explain the home bias of US investors

US investors hold much less foreign stocks than mean/variance analysis applied to historical data predicts. In this article, we investigate whether this home bias can be explained by Bayesian approaches to international asset allocation. In contrast to mean/variance analysis, Bayesian approaches employ different techniques for obtaining the set of expected returns. They shrink sample means towards a reference point that is inferred from economic theory. We also show that one of the Bayesian approaches leads to the same implications for asset allocation as mean-variance/tracking error criterion. In both cases, the optimal portfolio is a combination the market portfolio and the mean/variance efficient portfolio with the highest Sharpe ratio. Applying the Bayesian approaches to the subject of international diversification, we find that substantial home bias can be explained 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 falling behind the US market portfolio. We also find that the current level of home bias can justified whenever regret aversion is significantly higher than risk aversion. Finally, we compare the Bayesian approaches to mean/variance analysis in an empirical out-ofsample study. The Bayesian approaches prove to be superior to mean/variance optimized portfolios in terms of higher risk-adjusted performance and lower turnover. However, they not systematically outperform the US market portfolio or the minimum-variance portfolio

Consistency and heterogeneity of individual behavior under uncertainty

By using graphical representations of simple portfolio choice problems, we generate a very rich data set to study behavior under uncertainty at the level of the individual subject. We test the data for consistency with the maximization hypothesis, and we estimate preferences using a two-parameter utility function based on Faruk Gul (1991). This specification provides a good interpretation of the data at the individual level and can account for the highly heterogeneous behaviors observed in the laboratory. The parameter estimates jointly describe attitudes toward risk and allow us to characterize the distribution of risk preferences in the population