Hedging systematic risk in the commodity market with a regime‐switching multivariate rotated generalized autoregressive conditional heteroskedasticity model

• Author: Donald Lien,Hsiang‐Tai Lee,Her‐Jiun Sheu
• Date: 01 December 2018
• Published date: 01 December 2018
• DOI: http://doi.org/10.1002/fut.21959

Received: 30 January 2018

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Revised: 23 June 2018

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Accepted: 1 July 2018

DOI: 10.1002/fut.21959

RESEARCH ARTICLE

Hedging systematic risk in the commodity market

with a regime‐switching multivariate rotated generalized

autoregressive conditional heteroskedasticity model

Donald Lien

1

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Hsiang‐Tai Lee

2

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Her‐Jiun Sheu

3

1

Department of Economics, University of

Texas, San Antonio, Texas

2

Department of Banking and Finance,

National Chi Nan University, Taiwan,

China

3

Department of Finance, Ming Chuan

University, Taiwan, China

Correspondence

Hsiang‐Tai Lee, Department of Banking

and Finance, National Chi Nan

University, No. 1, University Rd., Puli,

Nantou Hsien, 54561 Taiwan, China.

Email: sagerlee@ncnu.edu.tw

Abstract

In this paper, a regime‐switching multivariate rotated BEKK generalized

autoregressive conditional heteroskedasticity (GARCH; RS‐MRBEKK) model

for optimal futures hedging is proposed. The basic structure of the RS‐MRBEKK

model is to rotate returns with spectral decomposition and fit the rotated

returns with a Markov regime‐switching BEKK covariance structure that is

computationally attractive for modeling higher‐dimensional regime‐switching

GARCH dynamics. The empirical results reveal that adding additional

commodity index futures to capture the commodity price comovement under

regime switching improves hedging performance. The more parsimonious

RS‐MRBEKK is statistically no worse than the conventional nonrotated

regime‐switching BEKK, illustrating the usefulness of RS‐MRBEKK in higher‐

dimensional hedging applications.

KEYWORDS

commodity index futures, market systematic risk, Markov regime switching, multiple‐futures

hedging, rotated BEKK GARCH

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INTRODUCTION

The global commodity markets have exhibited increased volatility in recent years, and risk management on extreme

commodity price movement has received considerable attention in the literature. Derivative securities, particularly

commodity futures, serve as an important instrument for hedging commodity price risk. A considerable body of

research has investigated the hedging effectiveness of commodity futures (Baillie & Myers, 1991; Carbonez, Nguyen, &

Sercu, 2011; Chang, McAleer, & Tansuchat, 2011; Choudhry, 2009; Cifarell & Paladino, 2015; Fernandez, 2008; Haigh &

Holt, 2000; Lee, 2009b; Lee & Yoder, 2007a; Lien & Yang, 2008; Moschini & Myers, 2002; Pan, Wang, & Yang, 2014;

Park & Shi, 2017; Sephton, 1993). Most of these articles apply an array of multivariate generalized autoregressive

conditional heteroskedasticity (GARCH) models to capture the time‐varying joint distribution of spot and futures

returns to estimate the time‐varying minimum variance hedge ratio (MVHR). However, implementing an optimal

futures hedging strategy with a state‐independent GARCH model does not consider the effect of changing market

states.

Recent studies recognize that the relationship between spot and futures returns is characterized by regime shifts

(Sarno & Valente, 2000, 2005a, 2005b). The implication is that to estimate the MVHR, the regime‐switching property of

the joint distribution of spot and futures returns must be considered. A number of multivariate regime‐switching

J Futures Markets. 2018;38:1514–1532.wileyonlinelibrary.com/journal/fut1514

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© 2018 Wiley Periodicals, Inc.

models have been applied to estimate the regime‐switching time‐varying MVHR (Alizadeh & Nomikos, 2004; Alizadeh,

Huang, & van Dellen, 2015; Alizadeh, Nomikos, & Pouliasis, 2008; Dark, 2015; Lai, Sheu, & Lee, 2017; Lee, 2009a;

2009b; 2010; Lee & Yoder, 2007a, 2007b; Lien, 2012; Pan et al., 2014; Sheu & Lee, 2014; Yan & Li, 2017). Most of these

studies apply a variety of regime‐switching GARCH models to capture the state‐dependent time‐varying covariance

dynamics of spot and futures returns. A general finding is that regime‐switching GARCH models are superior to their

state‐independent counterparts in implementing futures hedging strategies in terms of both percentage variance

reduction and expected utility gain.

However, most of these regime‐switching GARCH hedging models are bivariate and use only the corresponding

futures to hedge the price risk of underlying assets. This is partly because multiple‐futures hedging under regime

switching involves the estimation of a higher‐dimensional regime‐switching GARCH model, which may be

overparameterized and may encounter the convergence problem. Several facts suggest the potential benefits of

simultaneously hedging the idiosyncratic and systematic risks of agricultural commodities with both corresponding

futures and commodity index futures. First, agricultural commodities tend to move together (Geoffrey Booth & Ciner,

2001; Byrne, Fazio, & Fiess, 2013; Dawson & White, 2002; Malliaris & Urrutia, 1996; Pindyck & Rotemberg, 1990;

Stevens, 1991; Yang, 2001) because agricultural commodities are subject to the same economic fundamentals; some

agricultural commodities are dominated by the common regional weather conditions and the common effects of

government farm and regulation policies. All these factors might drive the prices of agricultural commodities to move

together. Second, the intercommodity spread might also play a role in commodity comovement. For example, recent

studies have discovered significant evidence of volatility spillover between crude oil and agricultural commodities, thus

concluding that the tightened interdependence between energy and agricultural commodities is induced by the recent

development of the biofuel industry (Du, Yu, & Hayes, 2011; Natanelov, Alam, McKenzie, & Van Huylenbroeck, 2011;

Wu, Guan, & Myers, 2011). Third, the potential diversification benefits of investing in the segmented commodity

markets have led to the rapid growth of commodity index investment. Commodities might become increasingly

correlated with each other due to this financialization process (Steen & Gjolberg, 2013; Tang & Xiong, 2012). A number

of studies have investigated hedging performance by considering the effects of commodity price comovement

(Fernandez, 2008; Haigh & Holt, 2002). Haigh and Holt (2002) studied crude oil, heating oil, and unleaded gasoline

futures simultaneously and found that taking account of volatility spillovers between these markets resulted in

significant reductions in price volatility. Fernandez (2008) analyzed a portfolio of metals from the London Metal

Exchange and concluded that neglecting cross correlations led to biased estimates of the optimal hedge ratios and

degrees of hedging effectiveness. However, these multiple‐futures hedging studies do not consider the possible regime‐

switching effect.

In this paper, a regime‐switching multivariate rotated BEKK GARCH (RS‐MRBEKK) model is proposed to

estimate the regime‐switching time‐varying MVHR. RS‐MRBEKK is a regime‐switching extension of the state‐

independent multivariate rotated ARCH (RARCH) model (Noureldin, Shephard, & Sheppard, 2014) and is more

parsimonious than the traditional regime‐switching BEKK GARCH model, which makes the higher‐dimensional

regime‐switching hedging strategy more feasible to implement. This paper investigates whether simultaneously

hedging the idiosyncratic and systematic risks of the agricultural commodity spot prices using both agricultural

commodity futures and S&P Goldman Sachs Commodity Index (GSCI) commodity index futures improves hedging

effectiveness. This paper’s contribution is 2‐fold. First, the proposed RS‐MRBEKK model allows the covariance

dynamic to be both time‐varying and state‐dependent while economizing on the number of parameters. Second,

the effectiveness of multiple‐futures hedging under regime switching is investigated. The more flexible

RS‐MRBEKK model exhibits superior hedging performance compared with state‐independent or nonrotated

GARCH models.

The rest of the paper is organized as follows: The specification of the RS‐MRBEKK model is presented in Section 2;

Section 3 provides the estimation procedure of the RS‐MRBEKK model; this is followed by measurement of hedging

performance, data description, and empirical results in Section 4; the paper concludes with a summarization of the

findings in Section 5.

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RS‐MRBEKK MODEL

Most existing regime‐switching GARCH hedging models are bivariate. This might be because the higher‐dimensional

regime‐switching GARCH model is normally overparameterized and encounters the convergence problem.

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