Estimation risk: an introduction; Estimation risk and optimal choice under uncertainty: a selective review; Estimation risk and optimal portfolio choice: a selective review; The effect of estimation risk on optimal portfolio choice.

The issue of estimation risk is of particular interest to the decision-making processes of portfolio managers who use long-short investment strategies. Accordingly, our paper explores the question of whether a VaR constraint reduces estimation risk when short sales are allowed. We find that such a constraint notably decreases errors in estimates of the expected return, standard deviation, and VaR of optimal portfolios. Furthermore, optimal portfolios in the presence of the constraint are substantially closer to the 'true' efficient frontier than those in its absence. Finally, we provide VaR bounds and confidence levels for the constraint that lead to the best out-of-sample performance.

We propose a new adjustment in mean-variance portfolio weights to incorporate uncertainty caused by the fact that, in general, we have to use estimated expected returns when determining optimal portfolios. The adjustment amounts to using a higher pseudo risk-aversion rather than the actual risk-aversion and has a straightforward interpretation. 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. We show how short sales constraints and time-varying expected returns are incorporated in our framework. 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. The exclusion of short sales is found to have a further important impact on the adjusted portfolio weights. In case expected country returns are time- varying, our adjustment induces a significantly smaller variability in portfolio weights that is commonly found.

In Das, Markowitz, Scheid, and Statman (2010), an investor divides his or her wealth among mental accounts with short selling being allowed. For each account, there is a unique goal and optimal portfolio. Our paper complements theirs by considering estimation risk. We theoretically characterize the existence and composition of optimal portfolios within accounts. Based on simulated and empirical data, there is a wide range of account goals for which such portfolios notably outperform those selected with the mean-variance model for plausible risk aversion coefficients. When short selling is disallowed, the out performance still typically holds but to a considerably lesser extent.

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.

Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.