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.

In spite of theoretical benefits, Markowitz mean-variance (MV) optimized portfolios often fail to meet practical investment goals of marketability, usability, and performance, prompting many investors to seek simpler alternatives. Financial experts Richard and Robert Michaud demonstrate that the limitations of MV optimization are not the result of conceptual flaws in Markowitz theory but unrealistic representation of investment information. What is missing is a realistic treatment of estimation error in the optimization and rebalancing process. The text provides a non-technical review of classical Markowitz optimization and traditional objections. The authors demonstrate that in practice the single most important limitation of MV optimization is oversensitivity to estimation error. Portfolio optimization requires a modern statistical perspective. Efficient Asset Management, Second Edition uses Monte Carlo resampling to address information uncertainty and define Resampled Efficiency (RE) technology. RE optimized portfolios represent a new definition of portfolio optimality that is more investment intuitive, robust, and provably investment effective. RE rebalancing provides the first rigorous portfolio trading, monitoring, and asset importance rules, avoiding widespread ad hoc methods in current practice. The Second Edition resolves several open issues and misunderstandings that have emerged since the original edition. The new edition includes new proofs of effectiveness, substantial revisions of statistical estimation, extensive discussion of long-short optimization, and new tools for dealing with estimation error in applications and enhancing computational efficiency. RE optimization is shown to be a Bayesian-based generalization and enhancement of Markowitz's solution. RE technology corrects many current practices that may adversely impact the investment value of trillions of dollars under current asset management. RE optimization technology may also be useful in other financial optimizations and more generally in multivariate estimation contexts of information uncertainty with Bayesian linear constraints. Michaud and Michaud's new book includes numerous additional proposals to enhance investment value including Stein and Bayesian methods for improved input estimation, the use of portfolio priors, and an economic perspective for asset-liability optimization. Applications include investment policy, asset allocation, and equity portfolio optimization. A simple global asset allocation problem illustrates portfolio optimization techniques. A final chapter includes practical advice for avoiding simple portfolio design errors. With its important implications for investment practice, Efficient Asset Management 's highly intuitive yet rigorous approach to defining optimal portfolios will appeal to investment management executives, consultants, brokers, and anyone seeking to stay abreast of current investment technology. Through practical examples and illustrations, Michaud and Michaud update the practice of optimization for modern investment management.

Embracing finance, economics, operations research, and computers, this book applies modern techniques of analysis and computation to find combinations of securities that best meet the needs of private or institutional investors.

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.