Latent Factor Analysis in Short Panels

ArXiv ID: 2306.14004 “View on arXiv”

Authors: Unknown

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.

Keywords: Factor Analysis, Maximum Likelihood, Systematic Risk, Idiosyncratic Risk, Panel Data

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail

  flowchart TD
    A["Research Goal<br>Latent Factor Analysis in Short Panels<br>Without Sphericity or Gaussianity"] --> B["Methodology<br>Pseudo Maximum Likelihood (PML) +<br>Asymptotically Uniformly Most Powerful Test"]
    B --> C["Data Input<br>Large Panel of Monthly<br>U.S. Stock Returns"]
    C --> D{"Computational Process<br>Apply PML to Short Subperiods<br>Bear vs. Bull Markets"}
    D --> E["Key Findings<br>1. Uptrend in Total & Idiosyncratic Volatilities<br>2. Systematic Risk Dominates in Bear Markets<br>3. Systematic Risk Not Spanned by Observed Factors"]