Factor Models for Asset Pricing

This paper develops a complete methodology for inference on asset pricing models, that are linear in latent risk factors, valid when the number of assets diverges but the time series dimension is fixed, possibly very small

We cast the factor model within the Arbitrage Pricing Theory of Ross (1976) and show how to exploit the no-arbitrage condition to identify the latent risk factors that are robust to the presence of pricing errors. In turn, this permits to develop an inferential procedure for the associated risk premia and for the stochastic discount factor, corresponding to the Arbitrage Pricing Theory, spanned by the latent risk factors.

Our set up can be naturally extended to handle time-varying factor models, allowing for time-variation in risk premia and of the stochastic discount factor.

From a technical point of view, under this sampling scheme with fixed time series dimension, we derive a consistent estimator for the number of risk factors and establish the asymptotic distribution of their PCA estimator, with asymptotically valid standard errors, when loadings, idiosyncratic risk and the number of risk factors are potentially time-varying. Several Monte Carlo experiments corroborate our theoretical findings.

An empirical application based on individual asset returns data demonstrates the powerfulness of the methodology, allowing to tease out the empirical content of the time-variation stemming from asset pricing theory.