Factor models with many assets: strong factors, weak factors, and the two-pass procedure

TL;DR

This paper analyzes the challenges of estimating risk premia in linear factor models with many assets, especially when some factors are weak and errors are cross-sectionally dependent, proposing a robust new estimation method.

Contribution

It introduces a novel sample-splitting instrumental variables estimator that is consistent under weak factors and cross-sectional dependence, improving upon the traditional two-pass method.

Findings

The new estimator is robust to weak factors and error dependence.

Simulation results confirm improved accuracy over traditional methods.

Reanalysis of empirical data demonstrates practical effectiveness.

Abstract

This paper re-examines the problem of estimating risk premia in linear factor pricing models. Typically, the data used in the empirical literature are characterized by weakness of some pricing factors, strong cross-sectional dependence in the errors, and (moderately) high cross-sectional dimensionality. Using an asymptotic framework where the number of assets/portfolios grows with the time span of the data while the risk exposures of weak factors are local-to-zero, we show that the conventional two-pass estimation procedure delivers inconsistent estimates of the risk premia. We propose a new estimation procedure based on sample-splitting instrumental variables regression. The proposed estimator of risk premia is robust to weak included factors and to the presence of strong unaccounted cross-sectional error dependence. We derive the many-asset weak factor asymptotic distribution of the proposed estimator, show how to construct its standard errors, verify its performance in simulations, and revisit some empirical studies.