The Role of Cross-Sectional Dispersion in Active Portfolio Management

Abstract

We show that relaxing one of modern portfolio theory's standard modeling assumptions--that stock returns are uncorrelated--leads to the result that cross-sectional dispersion replaces time-series volatility in many of the key technical expressions in the theory of active portfolio management. Cross-sectional dispersion is shown to be the relevant volatility variable in the derivation of the set of optimal active portfolio weights, and the appropriate scaling factor in the formulation of a manager's set of expected returns. Additionally, we show that mis-estimation of cross-sectional dispersion can have significant adverse affects on investor utility. Accurate forecast of both cross-sectional dispersion and manager skill are essential to building high-performance portfolios that meet ex ante risk and expected return expectations.