Generalized Information Ratio

Alpha-based performance evaluation may fail to capture correlated residuals due to model errors. This paper proposes using the Generalized Information Ratio (GIR) to measure performance under misspecified benchmarks. Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of residual covariance matrix. GIR nests alphas and Information Ratio as special cases, depending on the amount of information used in the residual covariance matrix. We show that GIR is robust to various degrees of model misspecification and produces stable out-of-sample returns. Incorporating residual correlations leads to substantial gains that alleviate model error concerns of active management.