Nber Working Paper Series Characteristics Are Covariances: a Unified Model of Risk and Return

We propose a new modeling approach for the cross section of returns. Our method, Instrumented Principal Components Analysis (IPCA), allows for latent factors and time-varying loadings 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 four 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 eight are statistically significant in the IPCA specification and are responsible for nearly 100% of the model's accuracy. Bryan Kelly Yale School of Management 165 Whitney Ave. New Haven, CT 06511 and NBER bryan.kelly@yale.edu Seth Pruitt Department of Finance W.P. Carey School of Business Arizona State University Tempe, AZ 85287-3906 seth.pruitt@asu.edu Yinan Su University of Chicago Booth School of Business 5807 S. Woodlawn Avenue Chicago, IL 60637 yns@uchicago.edu One of our central themes is that if assets are priced rationally, variables that are related to average returns, such as size and book-to-market equity, must proxy for sensitivity to common (shared and thus undiversifiable) risk factors in returns. Fama and French (1993) We have a lot of questions to answer: First, which characteristics really provide independent information about average returns? Which are subsumed by others? Second, does each new anomaly variable also correspond to a new factor formed on those same anomalies? ... Third, how many of these new factors are really important? Cochrane (2011)