Board of Governors of the Federal Reserve System

December 2012

Firm Characteristics and Empirical Factor Models: A Data-Mining Experiment

Leonid Kogan and Mary Tian

Abstract:

"A three-factor model using the standardized-unexpected-earnings and cashflow-to-price factors explains 15 well-known asset pricing anomalies." Our data-mining experiment provides a backdrop against which such claims can be evaluated. We construct three-factor linear pricing models that match return spreads associated with as many as 15 out of 27 commonly used firm characteristics over the 1971-2011 sample. We form target assets by sorting firms into ten portfolios on each of the chosen characteristics and form candidate pricing factors as long-short positions in the extreme decile portfolios. Our analysis exhausts all possible 351 three-factor models, consisting of two characteristic-based factors in addition to the market portfolio. 65% of the examined factor models match a larger fraction of the target return cross-sections than the CAPM or the Fama-French three-factor model. We find that the relative performance of the complete set of three-factor models is highly sensitive to the sample choice and the factor construction methodology. Our results highlight the challenges of evaluating empirical factor models.

Keywords: Anomalies, factor model, data-mining, firm characteristic

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