 This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ). GIR translates residual covariance information into adjusted alphas and nests alphas and Information Ratio as special cases . Simulation results show that GIR is robust to  model misspecification and produces stable out-of-sample returns. The gain of using GIR is substantial when the fund pool is large; however, a longer history of fund returns is required for accurate estimation of high-dimensional residual covariance matrix .
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 %DIFDELCMD < }%%% %DIFDELCMD < }%%% . 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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Alpha-based performance evaluation may fail to capture correlated residuals due to model errors.
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using
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evaluate the performance of active portfolios under misspecified models
measure performance under misspecified benchmarks
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the
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(GIR =
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\Sigma
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^(-1/2)
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\alpha
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). GIR translates residual covariance information into adjusted alphas and
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. Simulation results
, depending on the amount of information used in the residual covariance matrix. We
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various degrees of
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The gain of using GIR is substantial when the fund pool is large; however, a longer history of fund returns is required for accurate estimation of high-dimensional residual covariance matrix
Incorporating residual correlations leads to substantial gains that alleviate model error concerns of active management