A comprehensive look at the return predictability of variance risk premia

• Date: 01 April 2018
• Author: Bart Frijns,Tai‐Yong Roh,Suk Joon Byun
• Published date: 01 April 2018
• DOI: http://doi.org/10.1002/fut.21882

Received: 8 August 2017

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Accepted: 26 August 2017

DOI: 10.1002/fut.21882

RESEARCH ARTICLE

A comprehensive look at the return predictability of variance

risk premia

Suk Joon Byun

1

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Bart Frijns

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Tai-Yong Roh

2

1

Graduate School of Finance, Korea

Advanced Institute of Science and

Technology, Business School, Hoegiro,

Dongdaemoon-gu, Seoul, Korea

2

Department of Finance, Auckland University

of Technology, Auckland, New Zealand

Correspondence

Tai-Yong Roh, Department of Finance,

Auckland University of Technology, Private

Bag 92006, 1142 Auckland, New Zealand.

Email: tai-yong.roh@aut.ac.nz

Funding information

National Research Foundation of Korea

Grant, Grant number: NRF-2016-

S1A5B5A01023251

The discrepancy between in-sample and out-of-sample predictability of common

predictorsfor asset returns has been widely discussed in the literature.We examine the

out-of-sample predictability and its economic significance of Variance riskpremium

(VRP), which recently has shown empirical success in predicting asset returns in-

sample. Extensive analysis indicates strong out-of-sample predictability of the VRP

for U.S. stock index, currencies, credit index, and equity portfolios. However, we do

not find any evidence for predictability of bond and commodity markets. We

demonstrate economic significance by providing profitable market timing strategies

exploiting the out-of-sample forecasting power of the VRP in a real time setting.

KEYWORDS

asset allocation, economic significance of predictability, macroeconomic uncertainty, return

predictability, variance risk premium

JEL CLASSIFICATION

G12, G14

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INTRODUCTION

Since the work of Bollerslev et al. (2009), several studies have shown the empirical success of the variance risk premium (VRP)

—the difference between model-free implied variance and realized variance—in predicting aggregate U.S. stock market returns.

(Bollerslev, Marrone, Xu, & Zhou, 2014; Bollerslev, Tauchen, & Zhou, 2009; Drechsler & Yaron, 2011). This measure is

attractive not only because of its good predictive power for short-term stock returns, but also because it avoids issues of spurious

regressions and biased estimates when forecasting returns with common predictors, which follow a near unit root process (e.g.,

Ferson, Sarkissian, & Simin, 2003; Stambaugh, 1999). Bollerslev et al. (2014) show that the VRP is a robust predictor of

international equity market returns, and various studies have assessed the predictive relation between the VRP and returns on

other assets, such as bonds and currencies (Aloosh, 2012; Londono & Zhou, 2017; Mueller, Vedolin, & Zhou, 2011).

Most papers focusing on return predictability of the VRP assess this predictive relation in-sample, not out-of-sample. These

studies assess the robustness of return predictability of the VRP in the relation to finite sample biases, inclusion of alternative

variables, or various proxies for VRP, but they do not discuss their economic significance. Assessing out-of-sample (OOS)

performance, however, is crucial when determining the existence of the return predictability (Butler, Grullon, & Weston, 2005;

Campbell & Thompson, 2008; Goyal & Santa-Clara, 2003; Goyal & Welch, 2008; Maio, 2014). For instance, Goyal and Welch

(2008) show that many common return predictors work poorly out-of-sample, generating low or negative OOS R

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Consequently, it has almost become a standard to conduct OOS tests when developing new variables to predict returns (Cooper

& Priestley, 2009; Maio, 2014; Møller & Rangvid, 2015; Rangvid, 2006).

In this paper, we assess whether the return predictability of the VRP holds out-of-sample, and do so by focusing on

various asset classes, such as bond, commodities, and currencies as well as the U.S. stocks (specifically, we consider

J Futures Markets. 2018;38:425–445. wileyonlinelibrary.com/journal/fut © 2017 Wiley Periodicals, Inc.

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the U.S. stock index, six representative equity portfolios, a CDS index, 12 foreign currencies, six commodity indices, and

bonds with various maturities and default risk). We perform OOS tests following Goyal and Welch (2008) and construct a

trading strategy based on 1-month ahead OOS predictability similar to Campbell and Thompson's (2008). We find that a

market timing strategy that exploits the OOS forecasting power of the VRP on U.S. index returns generates a certainty

equivalent return (CER) of 1.89% p.a. and produces higher Sharpe ratio than that of a buy-and-hold strategy (0.32 vs.

0.18). The OOS forecasting power is robust to issues of parameter uncertainty, sensitivity of forecasting schemes, and

market frictions.

For the other asset classes, we find that the VRP positively predict currency and CDS index returns, and negatively predicts

excess returns of long-term bonds with low default risk. The predictive relation between VRP and future currency returns exists

for 9 of the 12 currencies both in- and out-of-sample. The gains obtainable from that predictability are economically significant

for most currencies, but smaller than those associated with equity markets. In contrast, we find only a weak OOS predictive

relation between the VRP and future excess returns of Treasury bonds and Aaa-rated corporate bonds, which is not economically

significant. There is no significant predictive relationship between VRP and commodity indices. The VRP positively predicts the

excess returns of various equity portfolios both in- and out-of-sample. Applying an asset allocation framework to assess the

economic significance, we document that a strategy based on the return predictability of the VRP yields a higher annualized

Sharpe ratio than a no-predictability benchmark (0.69 vs. 0.56).

Our research contributes to a gr owing body of literature on th e role of the VRP as a fundamental fa ctor driving

movements in various markets ar ound the world. Based on the theoreti cal framework developed by Bolle rslev et al. (2009),

the risk factor embedded in the VR P captures general macroecon omic uncertainty and varies in dependently from the

consumption growth risk, whic h is the main focus of long-run risk models (Bansal & Yaron, 20 04). Mueller et al. (2011) find

a predictive relation betw een the VRP and excess bond r eturns in-sample. Londono and Zhou (2017) and Aloosh ( 2012)

study the in-sample relation bet ween the VRP and excess foreign exch ange returns, while Wang, Zhou, an d Zhou (2013)

conduct a similar analysis on cred it spreads. We comprehensiv ely re-examine the in-sample pr edictive relation between the

VRP and the excess returns o f various assets, but exten d this work by assessing out-of -sample predictive powe r for a larger

set of assets over a substantia lly longer time period.

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Furthermore, we study the econom ic significance of the predict ive

power of the VRP for the excess returns of va rious assets. Our analysis at equi ty portfolio level also contribu tes to the

literature on portfolio al location in equity markets. Fleming, Kirby, and Ostd iek (2001) investigate volatility timing in equity

markets. Karstanje, Sojli, Tham, and van der Wel (2013) evaluate the economic value of liquidity timing in equity markets.

Our work relates to the latter, w hich analyzes the economic si gnificance of return predicta bility rather than forecast ing

volatility.

The remainder of this paper is structured as follows. In section 2, we analyze the OOS forecasting power and its economic

significance of VRP for the S&P500 index. In section 3, we extend our analysis to other asset classes such as currencies,

commodities, and bonds. Section 4 provides new evidence of return predictability of the VRP for equity portfolios and construct

a market timing strategy an under asset allocation framework. Section 5 concludes.

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BASIC SETUP AND THE OUT-OF-SAMPLE FORECASTING POWER OF VRP

ON THE U.S. STOCK INDEX

In this section, we assess the economic significance of OOS forecasting power of the VRPfor the S&P500 by considering several

portfolio performance measures. We also conduct several robustness checks about the economic significance against the issues

of parameter uncertainty, sensitivity of forecasting schemes, and the market friction such as transaction or borrowing costs. Our

sample covers the period from 1990 to 2013, which includes three NBER recession periods. The basic predictive regression for

the main analysis is given as

re

t;tþq¼aqþbqxtþut;tþqð1Þ

where re

t;tþqis the excess market return over qperiods and xtis the forecasting variable known at time t.

1

Our work relates to Chen, Shen, Wang, and Zuo (2015) who examine the OOS predictability and its economic significance of the VRP for excess returns

on international equity indices. Our study differs from theirs in that we focus on a range of different asset classes, and we use a much more extensive set

of portfolio performance measures.

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