The Role of Cross-Sectional Dispersion in Active Portfolio Management

Abstract:     
We derive and interpret the main results of Modern Portfolio Theory and the Theory of Active Portfolio Management from the perspective that, for active investors, the cross-sectional dispersion of returns is more relevant as a measure of risk than time series volatility. We show that all key measures of portfolio risk - total, systematic and idiosyncratic - are positively related to return dispersion, with dispersion primarily affecting idiosyncratic risk. Moreover, active portfolio returns are a function of managers’ skill and cross-sectional dispersion, with realized dispersion acting as a leverage factor for realized skill. Regardless of their level of skill, however, active managers will tend to reduce their active weights as the cross-sectional dispersion of returns increases. While higher levels of dispersion represent opportunities to earn
higher active returns, managers’ information ratios are expected to remain unchanged, as realized tracking error is expected to vary proportionately with dispersion and managers’ active returns. Absolute return investors are therefore more likely to benefit from tactically adjusting the activeness of their strategies with the level of return dispersion.

Number of Pages in PDF File: 25

Keywords: Dispersion, Active Management, Volatility, IC

JEL Classification: G11, G14

Accepted Paper Series