Mean--variance portfolio optimization when means and covariances are unknown

Details Mean--variance portfolio optimization when means and covariances are unknown Mean--variance portfolio optimization when means and covariances are unknown

2011-08-04

arxiv.org/abs/1108.0996v1

Annals of Applied Statistics 2011, Vol. 5, No. 2A, 798-823

Statistics

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Published in at http://dx.doi.org/10.1214/10-AOAS422 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/10-AOAS422

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 counter-intuitive 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.

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