Factors That Fit the Time Series and Cross-Section of Stock ReturnsI
Martin Lettau
Haas School of Business, University of California at Berkeley, Berkeley, CA 94720,
lettau@berkeley.edu,NBER,CEPR
Markus Pelger
Department of Management Science & Engineering, Stanford University, Stanford, CA 94305,
mpelger@stanford.edu
Abstract
We propose a new method for estimating latent asset pricing factors that fit the time series and
cross-section of expected returns. Our estimator generalizes principal component analysis (PCA)
by including a penalty on the pricing error in expected returns. Our approach finds weak factors
with high Sharpe ratios that PCA cannot detect. We discover five factors with economic meaning
that explain well the cross-section and time series of characteristic-sorted portfolio returns. The
out-of-sample maximum Sharpe ratio of our factors is twice as large as with PCA with substantially
smaller pricing errors. Our factors imply that a significant amount of characteristic information is
redundant. (JEL C14, C52, C58, G12)