Horses for Courses: Mean-Variance for Asset Allocation and 1/N for Stock Selection

Abstract

For various organizational reasons, large investors typically split their portfolio decision into two stages - asset allocation and stock selection. We hypothesise that mean-variance models are superior to equal weighting for asset allocation, while the reverse applies for stock selection, as estimation errors are less of a problem for mean-variance models when used for asset allocation than for stock selection. We confirm this hypothesis for US data using Bayes-Stein with no short sales and variance based constraints. Robustness checks with four other types of mean-variance model (Black-Litterman with three different reference portfolios, minimum variance, Bayes diffuse prior and Markowitz), and a wide range of parameter settings support our conclusions. We also replicate our core results using Japanese data, with additional replications using the Fama-French 5, 10, 12 and 17 industry portfolios and equities from seven countries. In contrast to previous results, but consistent with our empirical results, we show analytically that the superiority of mean-variance over 1/N is increased when the assets have a lower cross-sectional idiosyncratic volatility, which we also confirm in a simulation analysis calibrated to US data.