Is aggregate volatility a priced risk factor?

• Published date: 01 September 2021
• Author: Stanley Peterburgsky
• Date: 01 September 2021
• DOI: http://doi.org/10.1111/irfi.12299

ORIGINAL ARTICLE

Is aggregate volatility a priced risk factor?

Stanley Peterburgsky

Department of Finance, Brooklyn College,

New York, New York

Correspondence

Stanley Peterburgsky, Brooklyn College, 2900

Bedford Ave, New York NY 11210.

Email: speterburgsky@brooklyn.cuny.edu

Abstract

This study shows that the relationships between sensitivity

to changes in aggregate volatility and expected return on

stocks documented by Ang et al. (Journal of Finance, 2006,

61, 259–299) for the 15-year period from 1986 to 2000

have disappeared in the following 15-year period. Aggregate

volatility betas in the portfolio preformation month have not

predicted postformation returns. Alphas from time-series

regressions of excess returnson the high-minus-low sensitiv-

ity to aggregate volatility portfolio with respect to the

CAPM, the Fama–French three-factor model, and the Fama–

French five-factor model have not been statistically different

from zero. Finally, the price of aggregate volatility risk has

not been statistically different from zero. Analysis based on

high-frequency data support these results. Thus, the impor-

tance of aggregate volatility as a factor in the presence of

well-known factors such as SMB and HML appears to be

unclear.

KEYWORDS

aggregate volatility, VIX

JEL CLASSIFICATION

G12

1|INTRODUCTION

Merton (1973) shows that a conditional CAPM model implies an unconditional multifactor model where the addi-

tional risk factors arise due to conditional covariances between stock returns and unanticipated changes in state vari-

ables that affect returns. Over the years, various risk factors have been proposed, including the well-known small

Received: 3 September 2017 Revised: 1 February 2019 Accepted: 21 January 2020

DOI: 10.1111/irfi.12299

© 2020 International Review of Finance Ltd. 2020

International Review of Finance. 2021;21:843–864. wileyonlinelibrary.com/journal/irfi 843

market capitalization minus big market capitalization (SMB) and high book-to-market ratio minus low book-to-market

ratio (HML) factors in Fama and French (1993) and, more recently, the robust profitability minus weak profitability

(RMW) and conservative investment policy minus aggressive investment policy (CMA) factors in Fama and French

(2015). Chen (2002) develops a model of stock returns in which market volatility is time-varying

1

and demonstrates

that stocks that perform poorly when market volatility rises earn a risk premium. The reason for the risk premium is

that investors prefer to hedge against a possible rise in market volatility and require higher compensation (even after

controlling for market beta) to hold stocks that do not provide a hedge. Motivated by Chen's (2002) theoretical

framework, a number of papers examine the relationship between sensitivity to changes in market volatility (also

known as aggregate volatility risk, variance risk) and average returns.

Most studies in the option pricing literature find that aggregate volatility risk carries a negative risk premium

(e.g., Arisoy, Salih, & Akdeniz, 2007; Bakshi & Kapadia, 2003; Carr & Wu, 2009; Da & Schaumburg, 2011). However,

these studies do not control for nonmarket risk factors, such as SMB and HML. Failure to control for known risk fac-

tors can cause redundant factors to appear nonredundant.

Ang, Hodrick, Xing, and Zhang (2006) approach the issue of aggregate volatility risk from a different angle. Using

equity portfolios, they document a number of cross-sectional relationships between sensitivity to changes in aggre-

gate volatility and expected returns. First, they find that portfolios of stocks sorted on sensitivity to changes in

aggregate volatility predict future returns, with lower aggregate volatility loadings associated with higher future

returns. Second, they show that stocks with lower aggregate volatility loadings generate higher alphas with respect

to the CAPM and the Fama–French three-factor model than stocks with higher loadings. Finally, using a Fama and

MacBeth (1973) procedure, they document that aggregate volatility risk carries a negative premium. In investigating

whether these relationships continue to hold in recent data, I find that all have disappeared in the post-Ang et al.

(2006) period. Specifically, aggregate volatility betas in the portfolio preformation month have not predicted post-

formation returns. Alphas from time-series regressions of long/short high-minus-low aggregate volatility beta portfo-

lio returns with respect to the CAPM, the Fama–French three-factor model, and the Fama–French five-factor model

have not been statistically different from zero. Finally, the price of aggregate volatility risk has not been statistically

different from zero. These findings are supported by results based on high-frequency data. Additionally, I present

evidence that the price of aggregate volatility risk may be asymmetric, with only increases in aggregate volatility car-

rying a premium.

The rest of this article is organized as follows. In Section 2, I discuss the data, explain the portfolio construction

methodology, and report summary statistics. In Section 3, I present my main findings on the (lack of) relationships

between sensitivity to changes in aggregate volatility and expected returns on stocks documented by Ang et al.

(2006) in the years following their sample period. In Section 4, I examine the robustness of my results and explore

potential asymmetries in the pricing of aggregate volatility risk. In Section 5, I use high-frequency data to reexamine

the relationships between sensitivity to changes in aggregate volatility and expected returns. Finally, I summarize my

research and offer concluding remarks in Section 6.

2|DATA, PORTFOLIO CONSTRUCTION, AND SUMMARY STATISTICS

This study uses data from a numb er of sources to assess the im portance of sensitivity of st ocks to changes in

aggregate volatility for as set pricing. Daily stock return s and number of shares outstanding ( for computing mar-

ket capitalization) are fr om the Center for Research in Se curity Prices (CRSP). The VI X index

2

is from Chicago

Board Options Exchange. Fac tor returns and risk-free rat es are from Ken French's websi te (http://mba.tuck.

dartmouth.edu/pages/f aculty/ken.french/data_ library.html). Market-t o-book ratios use book value s of common

stock from Compustat. Final ly, high-frequency marke t volatility data are from Heb er, Lunde, Shephard, and

Sheppard (2009).

844 PETERBURGSKY