Oil jump risk

• Published date: 01 August 2020
• Date: 01 August 2020
• Author: Craig Pirrong,Nima Ebrahimi
• DOI: http://doi.org/10.1002/fut.22129

J Futures Markets. 2020;40:1282–1311.wileyonlinelibrary.com/journal/fut1282

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© 2020 Wiley Periodicals LLC

Received: 17 December 2019

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Accepted: 1 May 2020

DOI: 10.1002/fut.22129

RESEARCH ARTICLE

Oil jump risk

Nima Ebrahimi

1

|Craig Pirrong

2

1

Department of Finance, Tulane

University, New Orleans, Louisiana

2

Department of Finance, University of

Houston, Houston, Texas

Correspondence

Nima Ebrahimi, Tulane University,

Goldring Woldenberg Hall I, 7 McAlister

Drive, New Orleans, LA 70118.

Email: nebrahimi@tulane.edu

Abstract

The risk premium associated with large upside jumps in oil market is a significant

driver of the cross‐section of stock returns from 1986 to 2014. In contrast to

previous research, variance risk is priced only when we do not control for jumps.

Upward jumps are priced in tight supply‐demand conditions but not in more

abundant supply periods. There is some evidence that downward jumps are priced

in abundant supply conditions but not in tight conditions. Innovations in risk

neutral jumps have predictive power for important economic indicators, including

notably consumption growth. This helps explain the pricing of jump risks.

KEYWORDS

cross‐section of stock returns, downside jump risk premium, portfolio selection, upside jump risk

premium, variance risk premium

1|INTRODUCTION

Large oil price spikes and drops have been the subject of a substantial amount of research in finance and economics during

the recent decades. More recently, scholars have examined the effect of time variation in oil price volatility on asset prices.

Ebrahimi and Pirrong (2018) have extended this study to quantify the effects of time variation in higher moments (skewness

and kurtosis) on asset prices. In this article, we extend further that inquiry by investigating how upward and downward

jumps, which drive skewness and kurtosis, affect asset returns, and whether these factors have predictive power over real

variables (e.g., gross domestic product [GDP] growth) and measures of oil market fundamentals.

The main motivation is that our previous research shows that in a competition among variance, skewness, and

kurtosis, variance loses its significance in explaining cross‐section of stock returns after controlling for skewness and

kurtosis. In addition, we find that the kurtosis effect explains more of the the cross‐section of stock returns and retains

its significance through different subperiods and different option maturities. Since upside and downside jumps in oil

prices can affect skewness and kurtosis, in this article we attempt to provide a deeper understanding of what drives the

explanatory power of higher oil return moments for the cross‐section of stock returns.

There are several reasons why we are focusing on oil market in this paper. A series of articles stretching back

decades have shown that oil price shocks have macroeconomic effects, and affect stock returns (Engemann, Kliesen, &

Owyang, 2011; Hamilton, 1996,2003,1983; Kilian, 2009; Kilian & Park, 2009; Kilian & Vigfusson, 2017,2013).

Moreover, options on crude oil futures are highly liquid, and therefore, we can use them to construct reliable

estimates of different measures of oil price risk. Among commodities, crude oil derivatives are the most liquid. In

particular, it is possible to use option prices from this liquid market to calculate implied variances, and estimates of the

(risk neutral) probabilities of downward and upward jumps. It is also possible to use options portfolios that are hedged

against certain risks to estimate how each of these factors is priced by investors. For example, the returns on an oil

futures option portfolio that is hedged against variance risk measures the premium that investors demand to bear the

upside and downside jumps.

The connection between oil market conditions, oil prices, and macroeconomic activity suggests that measures of oil

price risk, and investor preferences regarding these risks, may have some power to predict oil market fundamentals and

macroeconomic activity (Gao, Hitzemann, Shaliastovich, & Xu, 2016). Furthermore, this connection between oil market

conditions and economic activity, and the connection between economic activity and equity risk premia, suggests that

oil price risk measures may be priced factors: therefore, we also explore whether oil risk premia affect the cross‐section

of equity returns (Christoffersen & Pan, 2017; Feuno et al., 2017).

Identifying the causal relationship between oil prices and macroeconomic variables is challenging. As discussed by

Alquist, Kilian, and Vigfusson (2013), the real price of oil has been endogenous to the world's economic condition since 1974:

the economic conditions of the oil‐importing countries have a direct effect on the real price of oil and vice versa. This is what

makes it very hard to identify the causal relationship between the oil price and macroeconomic conditions in industrialized,

oil‐importing economies. Furthermore, as proposed by Hamilton (2003), if we suppose that the major oil price fluctuations

are the result of the disruptions in oil production which is mainly caused by exogenous geopolitical tensions in the Middle

East such as the 1973 Yom Kippur War, the 1973–1974 oil embargo, Iranian Revolution of 1979, and the Persian Gulf War of

1990–1991, we can identify the impact of oil price shocks on macroeconomic activity. However, as pointed out by different

papers (e.g., Kilian, 2014) there is some evidence that demand shocks arising from the macroeconomy impact oil prices:

Barsky and Kilian (2001). This two‐way causation makes identification challenging.

An approach to the endogeneity problem is to use option prices to disentangle the supply and demand effects and to

use the exogenous supply‐driven component to see if it can predict the macroeconomic variables and explain the cross‐

sectional variation of stock returns. Specifically, the prices of relatively short maturity (e.g., 60 days), deep out‐of‐the‐

money call options can be used to measure of the probability of large upward jumps in oil prices. Such large jumps are

most likely to be caused by exogenous supply shocks like those emphasized by Hamilton. Conversely, deep out‐of‐the‐

money puts measure the likelihood of large downward jumps in prices. Such jumps are sometimes caused by severe

economic contraction, and hence downward jumps are a potential proxy for demand‐side shocks (e.g., the Asian Crisis

of 1998, or the Financial Crisis of 2008–2009); since large price declines can also be the result of supply shocks (e.g., the

Saudi increase in output in 1986, or 2014, or the Shale Revolution), however, the identification of downward jumps with

demand shocks and is not as clearcut as the identification of upward jumps with supply shocks.

Our results fall into three categories. First, we show that the risk premia help explain the cross‐section of equity

returns. After controlling for the downside and upside risk premia, the variance risk premium is not a significant risk

factor in the cross‐section of stock returns over the 1986–2014 period. Moreover, the upside risk premium is the most

significant factor and the high‐low upside jump risk portfolio portfolio earns an average monthly return of −0.50%,

which is economically quite large. The same pattern holds in subsamples using different break points, with the major

exception that the upside jump risk premium loses its explanatory power after 2008, but the variance risk premium is

more significant in this period. This is the era of “shale revolution”during which the domestic oil production of the

United States grew substantially.

Second, we evaluate power of variance, upside jump, and downside jump risk premia to predict important mac-

roeconomic variables. We show that the risk premia and their lags are able to predict considerable amount of variation

in GDP growth, consumption growth, and investment growth. The results show that the upside and downside risk

premia are important predictors of macroeconomic variables and adding them to our model increases the predictive

power of the model considerably. The predictive power of the risk premium variables for macro variables is consistent

with, and helps to explain, why these premia are priced factors.

Finally, we show that the premia have power to predict some of the salient measures of oil market fundamentals.

The results show that downside and upside risk premia predict oil futures returns, oil inventory growth, and oil demand

growth. We also observe that the upside jump premium predicts Organization of the Petroleum Exporting Countries

(OPEC's) aggregate production growth.

2|DATA AND METHODOLOGY

Options prices can be used to estimate the compensation for bearing different types of price risk. For example, a

delta–gamma hedged option portfolio is hedged against changes in prices, but exposed to changes in variance, and

hence returns on this portfolio compensate investors for bearing variance risk. In the same fashion, the returns of the

delta–vega hedged portfolio of options measures jump risk probabilities (in the risk neutral measure), as it is hedged

against the risks of price (delta) and variance (vega).

EBRAHIMI AND PIRRONG

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