The optimal hedge strategy of crude oil spot and futures markets: Evidence from a novel method

• Author: Yue‐Jun Zhang,Lu‐Tao Zhao,Ya Meng,Yun‐Tao Li
• Published date: 01 January 2019
• DOI: http://doi.org/10.1002/ijfe.1656
• Date: 01 January 2019

RESEARCH ARTICLE

The optimal hedge strategy of crude oil spot and futures

markets: Evidence from a novel method

Lu‐Tao Zhao

1,2

| Ya Meng

1

| Yue‐Jun Zhang

3,4

| Yun‐Tao Li

1

1

School of Mathematics and Physics,

University of Science and Technology

Beijing, Beijing, China

2

Center for Energy and Environmental

Policy Research, Beijing Institute of

Technology, Beijing, China

3

Business School, Hunan University,

Changsha, China

4

Center for Resource and Environmental

Management, Hunan University,

Changsha, China

Correspondence

Dr. Prof. Yue‐Jun Zhang, Business School,

Center for Resource and Environmental

Management, Hunan University,

Changsha 410082, China.

Email: zyjmis@126.com

Funding information

National Natural Science Foundation of

China, Grant/Award Number: 71322103,

71431008, 71403014, 71521002, 71774051;

National Program for Support of Top‐

notch Young Professionals, Grant/Award

Number: W02070325; Hunan Youth

Talent Program and China Scholarship

Council, Grant/Award Numbers:

201606465017 and 201606135020;

Changjiang Scholars Program of the Min-

istry of Education of China, Grant/Award

Number: Q2016154

Abstract

Hedging is an important measure for investors to resist extreme risks and

improve their profits. This paper develops a FIGARCH–EVT–copula–VaR

model to derive hedge ratio when hedging crude oil spot and futures markets,

overcoming the limitations of static models and simple dynamic models in

existing literature. The empirical results indicate that the FIGARCH–EVT–

copula–VaR model is superior to the other three commonly used models based

on four criteria: mean of returns, variance of returns, ratio of mean to variance

of returns, and hedging effectiveness. Comparatively, the new model has supe-

rior performance to other three models during the sample period and can be

used by investors to obtain excellent hedging effect.

KEYWORDS

copula, EVT, FIGARCH model, oil price, optimal hedge ratio, VaR

1|INTRODUCTION

Maintaining the stability of energy market prices and

ensuring energy security have become important issues

among various countries and regions. Meanwhile, oil

price changes may affect the stability of other economic

and financial environments such as stock markets (Phan

et al., 2015; Y. J. Zhang & Yao, 2016). An important step

in addressing these issues is to establish stable financial

markets in the energy field using, for example, energy

futures markets.

In an energy futures market, an energy company can

lock its profits and costs (to reduce losses caused by

energy price volatility) by means of an important mea-

sure—“hedging”(Y. J. Zhang & Chen, 2018). The key to

formulating a reasonable hedging strategy is to determine

the “hedge ratio”of spot and futures markets, which

directly affects the hedging effect. Therefore, if the value

is unreasonable, the strategy will fail to hedge the risk

properly and may bring about greater losses.

In the beginning, static models are often used to cal-

culate hedge ratios in literature (Y. J. Zhang & Wu,

Received: 14 April 2018 Revised: 29 August 2018 Accepted: 9 September 2018

DOI: 10.1002/ijfe.1656

186 © 2018 John Wiley & Sons, Ltd. Int J Fin Econ. 2019;24:186–203.wileyonlinelibrary.com/journal/ijfe

2018). These, however, are not able to describe the long‐

term relevance and dynamicity of the problem. Later,

some simple dynamic models have also been employed,

but they tend to ignore the tail features of financial time

series or correlativity of spot and futures returns, being

unable to depict the series correlation. Swanson and

Caples (1987) prove that autocorrelation in residual series

leads to excessive over‐estimation of the optimal hedge

ratio in the least squares (LS) model. Myers and

Thompson (1989) solve the autocorrelation problem

using a vector autoregressive (VAR) model but ignore

the cointegration relationship of spot and futures series.

Besides, Ghosh (1993) considers the short‐term dynamic

relationship in the error correction model (ECM), which

is unable to accurately calculate the optimal hedge ratio.

It is well known that financial time series have many

important characteristics, for example, long‐term rele-

vance and dynamicity. Some decades ago, Engle (1982)

proposed the ARCH model, after which, many similar

models are derived. Although these models have

accounted for the shortcomings of the static models, they

still fail to solve the problem of leptokurtosis of financial

time series. For this reason, this paper uses the extreme

value theory to fit the tails (Hsu et al., 2008). Besides, spot

and futures returns should be taken into consideration

together by a copula function due to the correlativity

between the two series (Nelsen, 2006). Based on an

analysis of existing literature, this paper proposes a more

appropriate method to obtain hedge ratios.

Besides the shortcomings of the static models and

simple dynamic models, there are also some properties

exist in oil returns series, such as non‐linear autocorrela-

tion, heteroscedasticity, and long‐term dependence,

which make traditional models no longer efficient

enough. Under this circumstance, this paper determines

the optimal hedge ratio of energy futures by combining

the FIGARCH–EVT–copula model with the Value‐at‐

Risk (VaR) method, which outperforms some other

traditional models and provides the best hedging effect

at different confidence levels. Specifically, first, this paper

employs the FIGARCH model to fit the time series to

describe the long‐term relevance and dynamicity. Then,

it uses the extreme value theory (EVT) method to model

the observations of tails to better capture the probability

of extreme events. After that, the paper uses a copula

function to describe the dependence of crude oil spot

and futures returns. Finally, it employs the VaR method

to measure the market extreme risk and investigate the

hedge ratio. The advantage of the combined method

proposed in this paper is that it considers the long‐term

relevance and dynamicity of the time series. The empiri-

cal results show that the model has a better hedging

effect, which enables energy investors to acquire more

returns but less risks; moreover, it provides a better

understanding of the market extreme risk brought about

by energy price changes, becoming a useful support of

reasonable investment decision making.

The rest of this paper is organized as follows. Section

2 presents a review of relevant literature. Section 3 gives

the methods and data. Section 4 introduces the empirical

results and analysis, and Section 5 concludes the paper

and puts forward several suggestions for investors.

2|RELEVANT LITERATURE

REVIEW

Johnson (1960) first proposes the concept of hedge ratio of

commodity futures and also gives an LS formula for it.

Then, Ederington (1979) proposes a hedging model based

on the LS method to linearly fit the changes in spot and

futures prices. He develops a mathematical programming

scheme to determine the optimal hedge ratio by means of

minimizing the portfolio variance. Heaney and Poitras

(1991) use the spot prices and futures prices to estimate

the hedge ratio using the ordinary least square regression.

Afterwards, Miffre (2004) made a great improvement by

using the conditional ordinary least square method to

reduce the basic risk of a portfolio by incorporating condi-

tional information. The LS model was, at one time, the

main hedging method used by investors. However, the

model does not take the correlation between different

residual series into consideration, and so its prediction

effectiveness is not good. In order to investigate the

impact of autocorrelation of the residual series on the

hedging effect, Swanson and Caples (1987) use the long‐

term foreign‐exchange market to carry out an empirical

analysis. Their results indicate that the autocorrelation is

far too high to allow the optimal hedging ratio to be esti-

mated (more precisely, it exaggerates the hedging effect).

Due to the serious nature of this problem, solving the

autocorrelation issue has become a very important

research direction. In order to eliminate autocorrelation

in residual series, Myers and Thompson (1989) introduce

the bivariate VAR model to estimate the hedge ratio, with

some success. However, the VAR model also ignores the

cointegration relationship between the spot and futures

prices series. Many studies, for example, W. Yang and

Allen (2004) and K. M. Wang et al. (2011), subsequently

compare the VAR model with other hedging models.

Ghosh (1993) develops an ECM based on

cointegration theory in order to make up for the deficien-

cies in the VAR model (which ignores cointegration

between spot and futures prices). ECM considers the non-

stationary, short‐term dynamic relationship and long‐

term equilibrium relationship between spot and futures

ZHAO ET AL.187