Characteristics are covariances: A unified model of risk and return

Bryan T. Kelly, Seth Pruitt, Yinan Su

Research output: Contribution to journalArticlepeer-review

124 Scopus citations


We propose a new modeling approach for the cross section of returns. Our method, Instrumented Principal Component 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 five 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 ten are statistically significant at the 1% level in the IPCA specification and are responsible for nearly 100% of the model's accuracy.

Original languageEnglish (US)
Pages (from-to)501-524
Number of pages24
JournalJournal of Financial Economics
Issue number3
StatePublished - Dec 2019


  • Anomaly
  • Conditional betas
  • Cross section of returns
  • Factor model
  • Latent factors
  • PCA

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Economics and Econometrics
  • Strategy and Management


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