Term structure determinants of time‐varying risk of 1‐year bond returns

• Author: Revansiddha Basavaraj Khanapure
• DOI: http://doi.org/10.1111/fire.12222
• Published date: 01 August 2020
• Date: 01 August 2020

DOI: 10.1111/fire.12222

ORIGINAL ARTICLE

Term structure determinants of time-varying risk

of 1-year bond returns

Revansiddha Basavaraj Khanapure

Jindal School of Management, University of Texas

at Dallas, Richardson, Texas

Correspondence

RevansiddhaBasavaraj Khanapure, Jindal School

ofManagement, University of Texasat Dallas,

800W Campbell Rd, JSOM 14.218, Richardson,

TX75080.

Email:khanapure@gmail.com and

rbk160130@utdallas.edu

Abstract

Termstructure drivers of 1-year bond premia and conditional bond

return risk are distinct. Consequently, the Cochrane–Piazzesi fac-

tor captures aggregate price of risk and not the amount of risk in 1-

year bond returns. One linear combination of forward ratescaptures

most of the variation in bond return risk across maturities. Interest

rate levelcaptures substantial amount of variation in the conditional

return risk, a finding consistent with rising inflation uncertainty with

level of inflation and interest rates. The 4-5 yield spread, an impor-

tant positive predictor of bond return premia, has an opposing but

limited impact on the conditional volatility.

KEYWORDS

bond return volatility, interest ratevolatility, risk management, yield

curve

JEL CLASSIFICATIONS

E43, E44, G12, G17, G19

1INTRODUCTION

Literature provides strong evidence in favor of time variation in expected excess returns of bonds. Fama and Bliss

(1987), Campbell and Shiller (1991), and Cochrane and Piazzesi (2005) show that linear combinations of bond yields

or forward rates predict excessbond returns. Cochrane and Piazzesi (2005) provide strong evidence in favor of com-

mon component in the time variation of expected excessreturns across maturities. They find that a single tent-shaped

linear combination of forward rates captures most of the variation in the expected 1-year excessreturns of bonds of

2- to 5-year maturities. The tent-shaped factor is able to predict the excessreturns with more than 30% R2.Also,Fama

and French (1989) find a common component in the time variation of expected excessreturns on bonds and stocks.

These papers suggest that the time variation in the expected excessreturns of bonds is explained, at least partially, by

a time-varying aggregate price of risk. In addition, Wachter(2006) shows that external habit preferences can generate

a positive forecasting relation between the yield spread and bond excessreturns.

Cochrane and Piazzesi (2005) suggest their tent-shaped Cochrane–Piazzesi factor,the driver of conditional mean

of 1-year excess bond returns, to be a strong candidate for aggregate price of risk. However,note that equilibrium

Financial Review.2020;55:365–384. wileyonlinelibrary.com/journal/fire c

2019 The Eastern Finance Association 365

366 KHANAPURE

asset pricing models obtain variation in the expected excess returns as a result of variation in the aggregate/market

price of risk or variation in the amount of risk associated with investment in the asset or both. This precludes a con-

clusive interpretation of the driver of the expectedexcess returns (the driver of conditional mean) as the market price

of risk. The Cochrane–Piazzesi factor, the common component in conditional mean, could in fact be proxying varia-

tion in the amount of risk or, in other words, the conditional volatility.In fact, Boyd, Hu, and Jagannathan (2005) and

Andersen, Bollerslev, Diebold, and Vega(2007) show that stock returns, interest rates, and exchange rates have dif-

ferent responses to macroeconomic news over the business cycle, thus suggesting the existence of a business cycle

component to the variation in the second moments of returns.

In this paper, I extractthe term structure drivers of both the conditional volatility and conditional mean of 1-year

excessbond returns and compare the two. I follow Cochrane and Piazzesi (2005) and conduct these tests for bonds of

2- to 5-year maturities. I show that information in the term structure explains a substantial amount of variation in the

conditional volatilities of excess returns. I also show that a single linear combination of forward rates captures most

of the time variation in the conditional volatilities of excess returns across maturities. This single factor is, however,

different from the tent-shaped Cochrane–Piazzesi factor that drives the conditional mean. I test the extent to which

the variation in the expectedexcess returns is due to the variation in the conditional volatility. I test the hypothesisthat

the same linear combination of forward rates drives both the conditional mean and the conditional volatility.The test

reveals that such a restriction severelyimpedes the ability to forecast the conditional volatility (and produces a model

that is a significant misfit to the data). I therefore conclude that the term structure drivers of the conditional mean and

the conditional volatility are not the same. This shows that the tent-shaped Cochrane–Piazzesi factor that drives the

conditional mean captures the market price of risk and not the conditional volatility,and as a result, this factor can be

used for pricing the cross-section of asset returns.

I use forward rates as the primitives representing the term structure information. The specifications in terms oflog

conditional volatilities help avoidrestrictions on the coefficients of the forward rates. The conditional volatility specifi-

cation in terms of the short rate and the spreads of the forward rates(relative to the short rate) reveals that the overall

level of interest rates captures most of the variation in conditional volatilities. The conditional volatility specification

withoutthe short rate is strongly rejected. In addition, spreads do also contribute a nontrivial but smaller amount to the

variation of the conditional volatility. These finding are consistent with dominance of inflation uncertainty for deter-

mining the volatility of excessbond returns.

I distill the information in the term structure for forecasting the conditional volatility into two components: (1) the

short rate; and (2) a factor formed from the spreads. The spread factor is a linear combination of the spreads of 5- and

4-year forward rates relative to the short rate. The loading is excessivelytilted toward a positive contribution by the

5-year forward rate spread. Cochrane and Piazzesi (2005) note that the 4-5 yield spread is important for forecasting

the 1-year excessreturns of all maturities. The same 4-5 yield spread has an opposing effect on the conditional volatil-

ity.However, the short rate drivesboth the expected excess returns and the conditional volatility in the same direction,

though the short rate dominates the conditional volatility variation. The opposing effects of spreads and the domi-

nance of short rate for the conditional volatilityvariation leave the drivers of the conditional mean and the conditional

volatility out of sync.

Glosten, Jagannathan, and Runkle (1993) suggest that the short rate reflects aggregate economic uncertainty in

addition to expectations of future inflation and the real interest rate. Kim and Nelson (1999) and McConnell and

Perez-Quiros (2000) show that the post-1981 period is characterized by significantly lower real and nominal macroe-

conomic volatility. This shift in macroeconomic volatility does not affect the ability of the short rate to forecast the

conditional volatility.

The study closest to this paper is Viceira (2012). Viceira (2012) focuses on only the realized second moments of

returns at 3- to 12-month horizons on a bond with a fixed 5 years to maturity and the time variation in business cycle

proxies. Note that these realized volatilities do not correspond to volatilities of 1-yearbond returns, the main subject

of this paper.I focus on the 1-year excess returns of bonds of 2- to 5-year maturities for which Cochrane and Piazzesi

(2005) find compelling evidence in favor of a common component in the expectedexcess returns. Viceira (2012) uses