The fundamental law of active management: Redux

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 ICt 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 ICt and the number of assets N in the portfolio selection universe, inversely related to the volatility of ICt, 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.