# Generalized Information Ratio

## TL;DR

The paper introduces the Generalized Information Ratio (GIR), a new performance metric that accounts for residual correlations and model errors, providing more robust and stable evaluation of active investment strategies.

## Contribution

It develops the GIR as a unified measure that generalizes alphas and Information Ratio, addressing residual correlation issues in performance evaluation.

## Key findings

- GIR is robust to model misspecification.
- Incorporating residual correlations improves out-of-sample stability.
- GIR offers substantial performance gains over traditional metrics.

## Abstract

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.

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Source: https://tomesphere.com/paper/1803.01381