Estimating latent asset-pricing factors

Abstract

We develop an estimator for latent factors in a large-dimensional panel of financial data that can explain expected excess returns. Statistical factor analysis based on Principal Component Analysis (PCA) has problems identifying factors with a small variance that are important for asset pricing. We generalize PCA with a penalty term accounting for the pricing error in expected returns. Our estimator searches for factors that can explain both the expected return and covariance structure. We derive the statistical properties of the new estimator and show that our estimator can find asset-pricing factors, which cannot be detected with PCA, even if a large amount of data is available. Applying the approach to portfolio data we find factors with Sharpe-ratios more than twice as large as those based on conventional PCA and with smaller pricing errors.