Single-Index Quantile Factor Model with Observed Characteristics

TL;DR

This paper introduces a new quantile factor model that links factor loadings to observed covariates via a single-index approach, improving interpretability and efficiency in modeling time-varying risk exposures.

Contribution

It develops a characteristics-augmented quantile factor model with a single-index structure, offering a parsimonious and interpretable way to nonparametrically model loadings while avoiding high-dimensional issues.

Findings

The model achieves high in-sample and out-of-sample accuracy in simulations.

It outperforms benchmark models in empirical analysis of U.S. corporate bonds.

Reveals state-dependent risk exposures driven by various bond and equity characteristics.

Abstract

We propose a characteristics-augmented quantile factor (QCF) model, where 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, while avoiding the curse of dimensionality in flexible nonparametric models. Using a three-step sieve estimation procedure, the QCF model demonstrates high in-sample and out-of-sample accuracy in simulations. We establish asymptotic properties for estimators of the latent factor, loading functions, and index parameters. In an empirical study, we analyze the dynamic distributional structure of U.S. corporate bond returns from 2003 to 2020. Our method outperforms the benchmark quantile Fama-French five-factor model and quantile latent factor model, particularly in the tails ($\tau=0.05, 0.95$). The model reveals state-dependent risk exposures driven by characteristics such as bond and equity volatility, coupon, and spread. Finally, we provide economic interpretations of the latent factors.