Estimating Asset Pricing Models in the Presence of Cross-Sectionally Correlated Pricing Errors

Abstract

In this study, we propose an adversarial learning approach to the asset pricing model estimation problem which aims to find estimates of factors and loadings that capture time-series covariations while minimizing the worst-case cross-sectional pricing errors. The proposed estimator is defined by a novel min-max optimization problem in which finding a solution is known to be difficult. This contrasts with other related estimators that admit a well-defined analytic solution but do not effectively account for correlations among the pricing errors. To this end, we propose an approximate algorithm based on the alternating optimization procedure and empirically demonstrate that our proposed adversarial estimation framework outperforms other existing factor models, especially when the explanatory power of the pricing model is limited.

Keywords

• adversarial machine learning
• asset pricing model
• factor model
• min-max optimization