Markowitz's celebrated mean--variance portfolio optimization theory assumesthat the means and covariances of the underlying asset returns are known. Inpractice, they are unknown and have to be estimated from historical data.Plugging the estimates into the efficient frontier that assumes knownparameters has led to portfolios that may perform poorly and havecounter-intuitive asset allocation weights; this has been referred to as the"Markowitz optimization enigma." After reviewing different approaches in theliterature to address these difficulties, we explain the root cause of theenigma and propose a new approach to resolve it. Not only is the new approachshown to provide substantial improvements over previous methods, but it alsoallows flexible modeling to incorporate dynamic features and fundamentalanalysis of the training sample of historical data, as illustrated insimulation and empirical studies.
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