Consumption Volatility Risk

• Author: LARS‐ALEXANDER KUEHN,OLIVER BOGUTH
• DOI: http://doi.org/10.1111/jofi.12058
• Date: 01 December 2013
• Published date: 01 December 2013

THE JOURNAL OF FINANCE •VOL. LXVIII, NO. 6 •DECEMBER 2013

Consumption Volatility Risk

OLIVER BOGUTH and LARS-ALEXANDER KUEHN∗

ABSTRACT

We show that time variation in macroeconomic uncertainty affects asset prices. Con-

sumption volatility is a negatively priced source of risk for a wide variety of test portfo-

lios. At the firm level, exposure to consumption volatility risk predicts future returns,

generating a spread across quintile portfolios in excess of 7% annually.This premium

is explained by cross-sectional differences in the sensitivity of dividend volatility to

consumption volatility. Stocks with volatile cash flows in uncertain aggregate times

require higher expected returns.

IT HAS LONG BEEN recognized that the volatility of macroeconomic quantities,

such as consumption and output, varies over time.1Surprisingly, the impact of

consumption growth volatility on asset prices has received little attention in

empirical tests of consumption-based pricing models2—most papers use only

the first moment of consumption growth (e.g., Lettau and Ludvigson (2001),

Parker and Julliard (2005), and Yogo (2006)). The contribution of this paper

is to show that exposure to time-varying consumption volatility leads to a

risk premium that can be explained by cross-sectional differences in cash flow

loadings. Stocks with volatile dividends in uncertain aggregate times require

higher expected returns.

∗Oliver Boguth is with the W. P. Carey School of Business at Arizona State University. Lars-

Alexander Kuehn is with the Tepper School of Business at Carnegie Mellon University. We thank

Murray Carlson; Alexander David; Wayne Ferson; Adlai Fisher; Lorenzo Garlappi; Cam Harvey;

Burton Hollifield; Lars Lochstoer; Monika Piazzesi; Lukas Schmid; Amir Yaron; Motohiro Yogo;

Lu Zhang; seminar participants at Berkeley, Carnegie Mellon University, University of British

Columbia, and Wharton; as well as conference participants at the 2009 Annual Meetings of the

Western Finance Association, European Finance Association, and Northern Finance Association,

the 2009 North American Summer Meetings of the Econometric Society, the 2009 Centre for

Economic Policy Research Gerzensee Summer Symposium on Financial Markets, and the 2010

Annual Meeting of the American Economics Association for valuable comments. We also thank

Kenneth French for providing data on his website.

1See, among others, Cecchetti and Mark (1990), Kandel and Stambaugh (1990), and Kim and

Nelson (1999).

2Notable exceptions are Bansal, Kiku, and Yaron (2007), who estimate the conditional first

and second moments of consumption growth as affine functions of financial data, and Tedongap

(2007), who uses a GARCH process for consumption volatility. Other contributions testing the

consumption-based capital asset pricing model (Consumption-CAPM) using realized consumption

growth include Campbell (1996), Campbell and Vuolteenaho(2004), Bansal, Dittmar, and Lundblad

(2005), Lustig and Nieuwerburgh (2005), and Jagannathan and Wang (2007).

DOI: 10.1111/jofi.12058

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2590 The Journal of Finance R

Toguide our empirical exercise, we follow the work of Kandel and Stambaugh

(1991), Bansal and Yaron (2004), and Lettau, Ludvigson, and Wachter (2008).

The representative agent has recursive Epstein and Zin (1989) preferences and

the conditional first and second moments of consumption growth follow Markov

chains with unobservable states. These preferences imply that the agent’s esti-

mates of the conditional first and second moments of consumption growth are

priced. More specifically,when the elasticity of intertemporal substitution (EIS)

is greater than the inverse of the coefficient of relative risk aversion (RRA), the

agent prefers that intertemporal risk due to unobservable Markov states be

resolved sooner rather than later. As a result, the agent demands a negative

price of risk for shocks to the conditional volatility of consumption growth, im-

plying that high expected returns are associated with both low return exposure

and high cash flow volatility exposure to consumption volatility.

Following Hamilton (1989), we estimate a Markov chain for the first and sec-

ond moments of consumption growth. While we retain the common assumption

that the representative agent has preferences over total consumption, defined

as the sum of nondurable and service consumption expenditures, we improve

state identification by using both components of consumption separately in the

estimation. In particular, we assume that both service consumption growth as

well as changes in the share of service to total consumption follow Markov

chains. Total consumption growth is obtained by aggregating the two compo-

nents, and therefore follows the same process. The precision of the resulting

estimates is increased as indicated by reduced standard errors.

Our first empirical evidence on the pricing of consumption volatility is based

on market prices of risk obtained from regressions of average excess returns on

estimated loadings on log consumption growth, as well as changes in the per-

ceived mean and volatility of consumption growth using portfolios. To alleviate

the critique of Lewellen, Nagel, and Shanken (2010), we use not only the 25

Fama–French portfolios sorted on size and book-to-market but also portfolios

sorted on industry and book-to-market as well as net share issuance (NSI) and

size. Surprisingly, our empirical analysis shows no evidence that beliefs about

the mean consumption growth are priced. Consumption growth volatility, how-

ever, is robustly priced in the cross-section. Importantly, the price of volatility

risk is negative, consistent with preference for early resolution of uncertainty.

This is a crucial assumption in the long-run risk framework of Bansal and

Yaron (2004) and our findings strongly support it.

We also study the relation between risk loadings and future returns at the

firm level as emphasized by Ang, Liu, and Schwarz (2010). To obtain time-

varying risk loadings, we run rolling quarterly time-series regressions of in-

dividual stock returns on consumption growth as well as innovations in be-

liefs for the mean and volatility of consumption growth. Evidence from both

Fama–MacBeth regressions and portfolio sorts suggests that loadings on ex-

pected consumption growth do not help to explain future returns. Loadings on

consumption growth volatility,however, significantly negatively forecast cross-

sectional differences in returns. This firm level evidence thus corroborates the

negative price of consumption volatility risk (CVR) estimated from portfolios.