Markowitz Portfolio Construction at Seventy
arxiv(2024)
Abstract
More than seventy years ago Harry Markowitz formulated portfolio construction
as an optimization problem that trades off expected return and risk, defined as
the standard deviation of the portfolio returns. Since then the method has been
extended to include many practical constraints and objective terms, such as
transaction cost or leverage limits. Despite several criticisms of Markowitz's
method, for example its sensitivity to poor forecasts of the return statistics,
it has become the dominant quantitative method for portfolio construction in
practice. In this article we describe an extension of Markowitz's method that
addresses many practical effects and gracefully handles the uncertainty
inherent in return statistics forecasting. Like Markowitz's original
formulation, the extension is also a convex optimization problem, which can be
solved with high reliability and speed.
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