The Fundamental Law of Active Management: Redux

41 Pages Posted: 10 Feb 2016 Last revised: 5 Oct 2018

See all articles by Zhuanxin Ding

Zhuanxin Ding

AlphaFocus Investment Research, LLC

R. Douglas Martin

University of Washington

Date Written: October 2, 2018


We develop a fundamental law of active management based on cross-section factor models for residual returns where the latter have unconditional mean zero and the factor exposures have zero mean and unit variance. Under our model framework the factor returns are cross-sectional information coefficients IC(t) that vary randomly over time with constant mean and variance. The fundamental law holds for portfolio managers who use conditional expectation of the residual returns and the associated conditional covariance matrix as inputs to active quadratic utility portfolio optimization. The fundamental law formula shows that the optimal portfolio’s information ratio (IR) is positively related to the mean of IC(t) and the number of assets N in the portfolio selection universe, inversely related to the volatility of IC(t), and is an absolute upper bound on IR as N tends to infinity. Support for our choice of factor model and our fundamental law is provided by an empirical study showing that significantly higher IR values are obtained using our choice of factor model as compared with IR values using an industry standard factor model.

Keywords: the fundamental law of active management, information coefficient, information ratio, factor model, time series, cross section

JEL Classification: G1, C1, C2, C3, C5

Suggested Citation

Ding, Zhuanxin and Martin, R. Douglas, The Fundamental Law of Active Management: Redux (October 2, 2018). Available at SSRN: or

Zhuanxin Ding (Contact Author)

AlphaFocus Investment Research, LLC ( email )

P. O. Box 8306
Rancho Santa Fe, CA 92067
United States
1-858-461-1076 (Phone)

R. Douglas Martin

University of Washington ( email )

Applied Mathematics & Statistics
Seattle, WA 98195
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics