Estimating Oil Risk Factors Using Information from Equity and Derivatives Markets

• Published date: 01 April 2015
• Author: I‐HSUAN ETHAN CHIANG,JACOB S. SAGI,W. KEENER HUGHEN
• DOI: http://doi.org/10.1111/jofi.12222
• Date: 01 April 2015

THE JOURNAL OF FINANCE •VOL. LXX, NO. 2 •APRIL 2015

Estimating Oil Risk Factors Using Information

from Equity and Derivatives Markets

I-HSUAN ETHAN CHIANG, W. KEENER HUGHEN, and JACOB S. SAGI∗

ABSTRACT

We introduce a novel approach to estimating latent oil risk factors and establish

their significance in pricing nonoil securities. Our model, which features four factors

with simple economic interpretations, is estimated using both derivative prices and

oil-related equity returns. The fit is excellent in and out of sample. The extracted oil

factors carry significant risk premia, and are significantly related to macroeconomic

variables as well as portfolio returns sorted on characteristics and industry. The

average nonoil portfolio exhibits a sensitivity to the oil factors amounting to a sixth

(in magnitude) of that of the oil industry itself.

FEW,IF ANY,COMMODITIES have been the focus of more attention for their per-

ceived economic significance than oil. While there is strong evidence relating

oil prices to the business cycle, the nature of the relationship is nonlinear, time-

varying, and difficult to attribute to any single source such as political uncer-

tainty, cartel decisions, or global economic conditions (see Hamilton (2003)and

Barsky and Kilian (2004)). Despite its prominence in the business media and

economics literature, and despite the well-documented role of business cycles in

asset pricing, academic research has largely failed to find consistent evidence

that oil is an important determinant of cross-sectional asset prices.1This paper

introduces a new model and method to estimate latent oil risk factors using

∗Ethan Chiang and Keener Hughen are from the Belk College of Business, University of North

Carolina at Charlotte. Jacob Sagi is from the Kenan-Flagler Business School, University of North

Carolina at Chapel Hill. We are grateful to seminar participants at HEC Paris, the University of

Colorado, the University of Florida, the University of Maryland, and the 25th Annual Conference

of the Financial Markets Research Center at Vanderbilt University for their useful comments.

We particularly benefited from comments by Gurdip Bakshi, Bernard Dumas, Pete Kyle, Chris

Leach, Andy Naranjo, Sugata Ray, Georgios Skoulakis, Zijun Wang, the editor (Cam Harvey) and

anonymous referees. Jun Chen provided excellent research assistance. Ethan Chiang and Keener

Hughen acknowledge the support of the Belk College Summer Research Grant. Jacob Sagi thanks

The Nickell Faculty Fund for financial support.

1Attempts to use Fama and MacBeth (1973) type regressions to deduce oil risk premia from the

cross-section of asset prices have yielded insignificant results (e.g., Chen, Roll, and Ross (1986)).

Direct estimates of risk premia for oil factors using oil derivative price dynamics have yielded mixed

results, but even when they have come up significantly there has been no attempt to connect such

results to cross-sectional asset pricing. Confounding this, Huang, Masulis, and Stoll (1996) find

virtually no relation between futures returns and U.S. stock market returns. On the other hand,

Ferson and Harvey (1993) find that a five-factor model including oil risk performs better than a

single-factor model in predicting the returns of global equity markets. Complementing this finding,

DOI: 10.1111/jofi.12222

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770 The Journal of Finance R

noisy price information from both equity and derivative markets. Put simply,

we extract four distinct oil price components and find that these are important

in explaining the movement of asset prices and macroeconomic fundamentals.

While similar models and techniques have been used to explore the valuation

of commodity derivatives, we are the first to tie the methodology to the pric-

ing of equities.2In particular, the studies that find significant risk premia in

oil-related factors (e.g., Casassus and Collin-Dufresne (2005) and Trolle and

Schwartz (2009)) have not established whether these risk premia are economi-

cally relevant outside oil derivative markets. The oil factors we extract appear

to have an economically and statistically significant relationship with macroe-

conomic variables such as real GDP, industrial production, unemployment,

inflation, and market uncertainty (the VIX). Our four oil factors explain 23.6%

of the variance of oil industry returns beyond what can be explained using mar-

ket returns alone, and this oil risk exposure is associated with a risk premium

of 5.3%. The magnitude of oil risk exposure exhibited by nonoil characteristic

and industry portfolios is on average about a sixth of that of the oil industry,

and compensated by a commensurate risk premium. Overall, our work can be

seen as a new approach to Ross’s (1976) Arbitrage Pricing Theory (APT) em-

ploying structural models together with data from several linked markets to

extract a less noisy set of fundamental and systematic pricing factors.

In our econometric specification, the log-price of oil is affected by four distinct

components. One can be thought of as transient while another may be viewed as

persistent. The drift in the persistent component is itself a factor, reflecting the

long-run trend in oil prices. Finally, the fourth component drives the stochastic

volatility of oil prices (known to exhibit heteroskedasticity). Thus, each of our

model’s components has a ready interpretation in terms of fundamental news

affecting oil prices, which is potentially important in sorting out how oil shocks

impact the macroeconomy (see Hamilton (2003) and Barsky and Kilian (2004)).

We estimate the model using oil futures prices and option-implied variance,

augmented with returns on oil-related stocks. The latter can be an important

source of information about oil prices that may not be captured by short-dated

derivatives. The model is estimated using 30 years of daily data on futures,

options, and equity returns, fitting derivative prices and returns very well

both in and out of sample. The latent factors identified by our estimation

methodology carry significant risk premia, both statistically and economically,

with magnitudes of unconditional annual Sharpe ratios as high as 0.43. Of the

Backus and Crucini (2000) observe that oil shocks are important determinants of relative price

movements in international markets.

2Related derivative pricing models include Casassus and Collin-Dufresne (2005), Gibson and

Schwartz (1990), Hughen (2010), Schwartz (1997), Schwartz and Smith (2000), and Trolle and

Schwartz (2009). Recent studies linking oil prices and price volatility to oil equities include

Elyasiani, Mansur, and Odusami (2011), Oberndorfer (2009), and Ramos and Veiga (2011). Our

more structural approach to extracting the factors allows us to obtain a better fit to oil equity

prices over a longer horizon, simultaneously fit to oil derivative prices, uncover the risk premia

associated with the oil factors, link oil factors to the macroeconomy, and demonstrate the factors’

relationship with the broader cross-section of equities.

Estimating Oil Risk Factors from Equity and Derivatives Markets 771

four, the oil volatility factor appears to be the most related to nonoil variables,

including the macroeconomic variables mentioned earlier as well as the Fama-

French (2003) factors.

The paper makes several contributions to the literature. First, we demon-

strate that stock prices contain important information about fundamentals,

such as commodity prices, that is not contained in commodity derivatives.

By combining information from both markets, we explain oil-related security

prices and returns better than traditional asset pricing approaches. Second,

our model and the estimation methodology are important to the real options

literature, where valuation relies disproportionately on an accurate descrip-

tion of persistent dynamics and stochastic volatility. Third, we demonstrate

that oil shocks are systematic and command nontrivial prices of risk. Finally,

among the types of news about oil, our approach identifies shocks affecting the

magnitude of uncertainty in oil prices as most important to the macroeconomy

and cross-section of expected returns.

We do not presume that oil (combined with the market) spans all pricing

factors. The paper seeks to provide insights to anyone who believes that oil

plays an important role in the pricing of securities—regardless of whether one

is motivated by ad hoc or general equilibrium considerations to include oil in an

empirical asset pricing model. Our study suggests that stochastic oil volatility

is as important, if not more so, for the macroeconomy than oil price itself.

The study also suggests that permanent and temporary oil price shocks have

different effects on asset prices. In that sense, the paper is best viewed as a

thorough attempt to study how oil risks are linked to oil and nonoil securities

rather than as a prespecified factor model like that of Chen, Roll, and Ross

(1986). Our approach and findings complement recent work that explicitly

models the role of oil in the pricing of securities (see Baker and Routledge

(2012) and Ready (2012,2013)).

The paper is structured as follows. Section Iintroduces our four-factor model,

describing its dynamics, derivative prices, and the link between equity returns

and the model risk factors. Section II describes the data we employ and the esti-

mation methodology (Markov chain Monte Carlo, MCMC). Section III presents

the estimation results and the cross-sectional analysis of the extracted latent

factors. Section IV concludes. Appendices A to D contain details of the model

derivation and estimation procedure. A supplementary Internet Appendix con-

tains further information.3

I. Model

Our goal is to estimate oil-relevant state variables from observed prices of

oil futures, options, and equities. To do so efficiently, we look for a specification

admitting closed-form solutions for futures and option prices in terms of fun-

damental state variables. Following the literature on term structure modeling

for interest rates and commodities, we opt for an affine specification (see, e.g.,

3The Internet Appendix may be found in the online version of this article.