The Role of Cross-Sectional Dispersion in Active Portfolio Management
Weigand, Robert A.
Sapra, Steven G.
Gorman, Larry R.
Washburn University. School of Business
Kaw Valley Bank
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.