Journal Article

MEAN-VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN

Lai, Tze Leung, Xing, Haipeng, Chen, Zehao

2011

Overview

Markowitz's celebrated mean-variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counterintuitive asset allocation weights; this has been referred to as the \"Markowitz optimization enigma.\" After reviewing different approaches in the literature to address these difficulties, we explain the root cause of the enigma and propose a new approach to resolve it. Not only is the new approach shown to provide substantial improvements over previous methods, but it also allows flexible modeling to incorporate dynamic features and fundamental analysis of the training sample of historical data, as illustrated in simulation and empirical studies.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: Bayes estimators / Calculus of variations and optimal control / Covariance matrices / efficient frontier / empirical Bayes / Estimators / Exact sciences and technology / Financial portfolios / General topics / Investors / Linear inference, regression / Markowitz’s portfolio theory / Mathematical analysis / Mathematics / Modeling / Observational studies / Probability and statistics / Probability theory and stochastic processes / Sciences and techniques of general use / Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) / Statistical variance / Statistics / stochastic optimization / Time series / Time series models