Massaging Mean-Variance Inputs: Returns from Alternative Global Investment Strategies in the 1980s

This paper explores the impact of adjustments to the inputs on total returns, terminal wealth, and portfolio turnover in an unconstrained monthly mean-variance (MV) asset allocation over time. It is well known that MV allocations are very sensitive to small forecast errors in the means and covariances. This sensitivity is especially pronounced for errors in means. One way to control this sensitivity to forecast errors is to use Stein estimation. We examined three naive applications of Stein estimation for six individual country stock indexes, five country bond indexes and five cash indexes.

This study has two major conclusions. First, any of the suggested adjustments to inputs dominate the results of an unadjusted-input MV optimization. Adjusted-input portfolios have higher mean return, less variance and greater terminal wealth than unadjusted-input portfolios. Second, these improvements become even greater with transaction costs.