Mean-Variance Analysis, the Geometric Mean, and Horizon Mismatch

The investment horizon plays a crucial role in portfolio selection: For horizons approximately up to a year, one can safely employ the mean-variance (M-V) rule. Moreover, if investment consultants use monthly rates of return to derive the M-V efficient set and the investor horizon is longer but smaller than one year, the economic cost induced by this horizon mismatch is negligible. For longer horizons, the M-V rule deviates substantially from expected utility maximization and the economic cost induced by employing the M-V rule is substantial. For relatively long horizons (say 20 or 30 years), despite the argument that with myopic preference the horizon does not matter, small stocks dominate large stocks by the maximum geometric mean (MGM) rule and, in practice, also by expected utility for all economically relevant preferences, as there is almost first-degree stochastic dominance (AFSD).