Morningstar vs. Michaud Optimization

Abstract

Classical linear constrained Markowitz (1952, 1959) mean-variance (MV) optimization has been the standard for defining portfolio optimality for more than fifty years. However, Markowitz efficient portfolios are known in practical application to be unstable and highly sensitive to estimation error in risk-return inputs. Michaud optimization (1998, 2008a, 2008b) is a U.S. patented generalization of linear constrained Markowitz MV efficiency that uses modern statistical resampling technology to address estimation error and instability in portfolio optimization. The Morningstar® Encorr® software also features a portfolio optimization procedure that uses the terms “resampling” and “resampled frontiers.” In this report we discuss the similarities and differences of the two methods and illustrate the results using identical inputs and portfolio optimality criteria. We show that the procedures are fundamentally different and the results typically very dissimilar. While the Michaud portfolios are investment intuitive, stable, and well diversified across the entire efficient frontier the Morningstar portfolios are often inconsistent with sensible perceptions of diversification and generally reflect serious limitations as alternatives to MV optimization limitations. The lack of theoretical framework for the procedure and the non-uniqueness of the solutions defeats Morningstar claims of superior investment value relative to Markowitz or Michaud optimality.