Latent Factor Analysis in Short Panels

TL;DR

This paper introduces a new pseudo maximum likelihood method for latent factor analysis in short panels, allowing for more flexible assumptions and providing a powerful test for the number of factors, with applications to stock return data.

Contribution

It develops a novel estimation and testing approach for latent factors in short panels without sphericity or Gaussianity assumptions, and applies it to financial data to analyze risk components.

Findings

Systematic risk explains much of the variance in bear markets.

Total and idiosyncratic volatilities show an increasing trend.

Multiple factors, not just observed ones, drive systematic risk.

Abstract

We develop a pseudo maximum likelihood method for latent factor analysis in short panels without imposing sphericity nor Gaussianity. We derive an asymptotically uniformly most powerful invariant test for the number of factors. On a large panel of monthly U.S. stock returns, we separate month after month systematic and idiosyncratic risks in short subperiods of bear vs. bull market. We observe an uptrend in the paths of total and idiosyncratic volatilities. The systematic risk explains a large part of the cross-sectional total variance in bear markets but is not driven by a single factor and not spanned by observed factors.