Time-varying risk aversion and forecastability of the US term structure of interest rates

Highlights

• Study predictive power of risk aversion for the term structure of US treasuries.

• Consider three latent factors, level, slope and curvature.

• Apply daily data within a quantiles-based framework.

• Predictive gains stem from risk aversion for the tails of the distributions.

• Predictive gains are significant for the three latent factors at all horizons.

Abstract

We analyse the out-of-sample forecasting ability of a time-varying metric of risk aversion for the entire term structure of US Treasury securities as reflected by the three latent factors, level, slope and curvature. Daily data cover the out-of-sample period 22nd June 1988 to 3rd September 2020 within a quantiles-based framework. The results show statistically significant forecasting gains emanating from the inclusion of risk aversion for the tails of the conditional distributions of the quantiles-based models of the level, slope and curvature factors. The forecasting gains are shown in lower mean squared forecast errors at horizons of one-day, one-week, and one-month-ahead.

Introduction

The role of the United States (US) Treasury securities as a traditional “safe haven” cannot be overemphasized enough given their strong ability to provide investors with valuable portfolio diversifications and hedging benefits at times of heightened market stress during which investors’ risk appetite turns sour, i.e., risk aversion increases (Kopyl and Lee, 2016; Habib and Stracca, 2015; Hager, 2017), as witnessed during the current pandemic of COVID-19. The safe haven nature of US Treasury securities is partially due to the significant lack of default risk fuelled by the vast revenue stream the US government generates, accounting for over 20 percent of global output (Bouri et al., 2020). Given this, a pertinent question to analyse would be whether risk aversion contains predictive power for the US government bond market. Understandably, accurate predictability of movement in Treasury securities is an important issue not only for bond investors, but also for policymakers, as an understanding of the evolution of future interest rates helps in the fine tuning of monetary policies.In spite of the importance of this issue, the forecasting ability of risk aversion for movements of US Treasury securities is limited to the recent work of Çepni et al. (2020a), possibly due to the lack of a robust time-varying measure of risk aversion, given that it is a latent variable and needs to be estimated.¹ These authors find that a metric of time-varying risk aversion (as developed by Bekaert et al. (2019)) obtained from observable financial information which distinguishes time variation in economic uncertainty (the amount of risk) from time variation in risk aversion (the price of risk), predicts (and increase in) monthly US bond premia associated with maturities of 2 to 5 years relative to 1 year, based on a conditional mean-based predictive regression model.² Our objective is to build on this study by examining the forecasting ability of risk aversion for the entire term structure of interest rates for the US. For this purpose, we relate risk aversion to the term structure of interest rates, using the well-established framework of Nelson and Siegel (1987). This model summarizes the entire term structure into three latent yield factors, level, slope, and curvature, which, in turn, are considered the only relevant factors that characterize the yield curve (Litterman and Scheinkman, 1991). The factor model of the term structure involving interest rates associated with US Treasury securities of maturities 1 to 30 years in combination with risk aversion, enables us to characterize the responses of the yield curve to risk aversion, and calculate the entire yield curve movement in the wake of changes in the risk appetite of investors.

Specifically, we rely on daily estimates of the measure of risk aversion proposed by Bekaert et al. (2019) for the period 30th May 1986 to 3rd September 2020, and relate them to the corresponding daily movements of the level, slope and curvature of the yield curve using a quantiles-based framework. The quantile regression model goes beyond the mean-based regression model used by Çepni et al. (2020a), allowing us to test for predictability emanating from risk aversion over the entire conditional distribution of the level, slope and curvature of the yield curve. Given that the period of study involves the zero lower bound (ZLB) situation of interest rates in the US in the wake of the “Great Recession” and following the outbreak of the coronavirus, the use of a quantiles-based framework makes perfect sense, since different quantiles (without having to specify an explicit number of regimes as in a Markov-switching model) can capture the various phases of the 3 latent factors accurately, with the lower, median, and upper quantiles corresponding to low, normal, and high interest rates, respectively. Understandably, high-frequency prediction of the conditional distribution of the term structure of interest rates, unlike the monthly conditional mean-based predictions produced by Çepni et al. (2020a), would allow for the timely and state (regime)-specific design of optimal portfolios involving US government bonds by investors. Furthermore, using the daily information of predictability, policymakers can gauge where the low-frequency real and nominal variables in the economy are headed by feeding the information into mixed-frequency models (Caldeira et al., 2020), given that the entire yield curve is considered a predictor of economic activity (Hillebrand et al., 2018), and, in turn, undertake appropriate monetary policy decisions.

To the best of our knowledge, this is the first paper to study the forecasting ability of risk aversion at daily frequency for the entire conditional distribution of the level, slope and curvature factors characterizing the complete term structure of interest rates of the US. Note that Campbell (2008) points out that the ultimate test of any predictive model (in terms of econometric methodologies and the predictors used) is its out-of-sample performance. Given this, while we present the in-sample analysis (in the Appendix), our focus is on out-of-sample forecastability of the three factors based on the information-content of the time-varying metric of risk aversion.

The rest of the paper is presented in three sections. Section 2 describes the data and the predictive quantile regression approach. Section 3 provides the main results. Section 4 offers some concluding remarks.