Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing beta pricing models have the same population R2. This provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application which demonstrates the importance of our new results when applied to a variety of asset pricing models.

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Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, that is, expected returns are exactly linear in asset betas. This assumption can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R 2 and develop a test of whether two competing linear beta pricing models have the same population R 2. This test provides a formal alternative to the common heuristic of simply comparing the R 2 estimates in evaluating relative model performance. Finally, we provide an empirical application, which demonstrates the importance of our new results when applied to a variety of asset pricing models. JEL classification: G12

Over the years, many asset pricing studies have employed the sample cross‐sectional regression (CSR) R2 as a measure of model performance. We derive the asymptotic distribution of this statistic and develop associated model comparison tests, taking into account the impact of model misspecification on the variability of the CSR estimates. We encounter several examples of large R2 differences that are not statistically significant. A version of the intertemporal capital asset pricing model (CAPM) exhibits the best overall performance, followed by the Fama–French three‐factor model. Interestingly, the performance of prominent consumption CAPMs is sensitive to variations in experimental design.

We show how to conduct asymptotically valid tests of model comparison when the extent of model mispricing is gauged by the squared Sharpe ratio improvement measure. This is equivalent to ranking models on their maximum Sharpe ratios, effectively extending the Gibbons, Ross, and Shanken (1989) test to accommodate the comparison of nonnested models. Mimicking portfolios can be substituted for any nontraded model factors, and estimation error in the portfolio weights is taken into account in the statistical inference. A variant of the Fama and French (2018) 6-factor model, with a monthly updated version of the usual value spread, emerges as the dominant model.