Augmented Factor Models with Applications to Validating Market Risk Factors and Forecasting Bond Risk Premia

49 Pages Posted: 23 Mar 2016 Last revised: 24 Sep 2018

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Yuan Ke

Princeton University - Department of Operations Research & Financial Engineering (ORFE)

Yuan Liao

Rutgers, The State University of New Jersey - New Brunswick/Piscataway

Date Written: March 22, 2016

Abstract

We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the Fama-French factors. In diffusion index forecasts, identified factors are strongly related to several directly measurable economic variables such as consumption-wealth variable, financial ratios, and term spread. With those covariates, both the factors and loadings are identifiable up to a rotation matrix even only with a finite dimension. To incorporate the explanatory power of these covariates, we propose a smoothed principal component analysis (PCA): (i) regress the data onto the observed covariates, and (ii) take the principal components of the fitted data to estimate the loadings and factors. This allows us to accurately estimate the percentage of both explained and unexplained components in factors and thus to assess the explanatory power of covariates. We show that both the estimated factors and loadings can be estimated with improved rates of convergence compared to the benchmark method. The degree of improvement depends on the strength of the signals, representing the explanatory power of the covariates on the factors. The proposed estimator is robust to possibly heavy-tailed distributions. We apply the model to forecast US bond risk premia, and find that the observed macroeconomic characteristics contain strong explanatory powers of the factors. The gain of forecast is more substantial when the characteristics are incorporated to estimate the common factors than directly used for forecasts.

Keywords: Huber loss, Heavy tails, Forecasts, Fama-French factors, Large dimensions

JEL Classification: C38, C53, C58

Suggested Citation

Fan, Jianqing and Ke, Yuan and Liao, Yuan, Augmented Factor Models with Applications to Validating Market Risk Factors and Forecasting Bond Risk Premia (March 22, 2016). Available at SSRN: https://ssrn.com/abstract=2753404 or http://dx.doi.org/10.2139/ssrn.2753404

Jianqing Fan

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Yuan Ke

Princeton University - Department of Operations Research & Financial Engineering (ORFE) ( email )

Sherrerd Hall, Charlton Street
Princeton, NJ 08544
United States

Yuan Liao (Contact Author)

Rutgers, The State University of New Jersey - New Brunswick/Piscataway ( email )

94 Rockafeller Road
New Brunswick, NJ 08901
United States

HOME PAGE: http://rci.rutgers.edu/~yl1114

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