Some Characteristics Are Risk Exposures, and the Rest Are Irrelevant

We use a new method to estimate common risk factors and loadings in the cross section of asset returns. The method, Instrumented Principal Components Analysis (IPCA), allows for time-varying loadings in a latent factor return model by introducing observable characteristics that instrument for the unobservable dynamic loadings. If the characteristics’expected return relationship is driven by compensation for exposure to latent risk factors, IPCA will identify the corresponding latent factors. If no such factors exist, IPCA infers that the characteristic effect is compensation without risk and allocates it to an “anomaly” intercept. Studying returns and characteristics at the stock-level, we find that three IPCA factors explain the cross section of average returns significantly more accurately than existing factor models and produce characteristic-associated anomaly intercepts that are small and statistically insignificant. Furthermore, among a large collection of characteristics explored in the literature, only seven are statistically significant in the IPCA specification and are responsible for nearly 100% of the model’s accuracy. ∗We thank Svetlana Bryzgalova (discussant), John Cochrane, Stefano Giglio, Lars Hansen, Serhiy Kozak, Toby Moskowitz, Andreas Neuhierl, Dacheng Xiu and audience participants at AQR, ASU, Chicago, Duke, Minnesota, SoFiE, and the St. Louis Federal Reserve for helpful comments. We are grateful to Andreas Neuhierl for generously sharing data with us. Corresponding author contact information: bryan.kelly@chicagobooth.edu, (773) 702-8359.