Single-Index Quantile Factor Model with Observed Characteristics

Abstract

We propose a characteristics-augmented quantile factor (QCF) model in which unknown factor loading functions are linked to a large set of observed individual-level (e.g., bond- or stock-specific) covariates via a single-index projection. The single-index specification offers a parsimonious, interpretable, and statistically efficient way to nonparametrically characterize the time-varying loadings, thereby circumventing the curse of dimensionality in flexible nonparametric models. Employing a three-step sieve estimation procedure, the QCF model exhibits superior in-sample and out-of-sample performance in simulations. We derive asymptotic properties for the estimators of the latent factors, loading functions, and index parameters. In an empirical study, we analyse the dynamic distributional structure of U.S. corporate bond returns from 2003 to 2020. Our approach outperforms bench-mark models, including the quantile Fama-French five-factor model and the quantile latent factor model, especially in the tails (τ = 0.05, 0.95). The model uncovers state-dependent risk exposures influenced by characteristics such as bond and equity volatility, coupon rate, and spread. Finally, we offer economic interpretations of the latent factors.