  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.
