Extreme mean-variance solutions: Estimation error versus modeling error

Without short-sales constraints, mean-variance (MV) and power-utility portfolios generated from historical data are often characterized by extreme expected returns, standard deviations, and weights. The result is usually attributed to estimation error. I argue that modeling error, that is, modeling the portfolio problem with just a budget constraint, plays a more fundamental role in determining the extreme solutions and that a more complete analysis of MV problems should include realistic constraints, estimates of the means based on predictive variables, and specific values of investors’ risk tolerances. Empirical evidence shows that investors who utilize MV analysis without imposing short-sales constraints, without employing estimates of the means based on predictive variables, and without specifying their risk tolerance miss out on remarkably remunerative investment opportunities.