Optimal Futures Hedging Under Multichain Markov Regime Switching

• DOI: http://doi.org/10.1002/fut.21583
• Author: Hsiang‐Tai Lee,Her‐Jiun Sheu
• Date: 01 February 2014
• Published date: 01 February 2014

OPTIMAL FUTURES HEDGING UNDER

MULTICHAIN MARKOV REGIME SWITCHING

HER‐JIUN SHEU and HSIANG‐TAI LEE*

Most of the existing Markov regime switching GARCH‐hedging models assume a common

switching dynamic for spot and futures returns. In this study, we release this assumption and

suggest a multichain Markov regime switching GARCH (MCSG) model for estimating state‐

dependent time‐varying minimum variance hedge ratios. Empirical results from commodity

futures hedging show that MCSG creates hedging gains, compared with single‐state‐variable

regime‐switching GARCH models. Moreover, we find an average of 24% cross‐regime

probability, indicating the importance of modeling cross‐regime dynamic in developing optimal

futures hedging strategies. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:173–202, 2014

1. INTRODUCTION

The estimation of time‐varying minimum variance hedge ratio (MVHR) for optimal futures

hedging has been widely investigated in the past two decades. The rationale behind the

estimation of a dynamic hedge ratio is that empirically spot and futures returns are

characterized by time‐varying distributions (Baillie & Myers, 1991; Kroner & Sultan, 1993).

To estimate time‐varying MVHR, one has to estimate the conditional second moments of spot

and futures return series. A variety of multivariate GARCH models have been applied to

implement dynamic hedging strategies (Alexander & Barbosa, 2008; Baillie & Myers, 1991;

Brooks, Henry, & Persand, 2002; Ederington & Salas, 2008; Gagnon, Lypny, & McCurdy,

1998; Kroner & Sultan, 1993; Lien & Yang, 2008; Park & Switzer, 1995). Although these

GARCH models capture the time‐varying covariance structure of spot and futures returns, the

hedging strategies developed with these models do not take account of the possible regime‐

shifting effect caused by changing state of the market (Alizadeh & Nomikos, 2004; Lee &

Yoder, 2007).

The existence of regime shifts in the relationship between spot and futures data series is

demonstrated in a series papers of Sarno and Valente (2000, 2005a, 2005b). They find that

regime‐switching model captures the time‐series property of spot and futures price

movements better than simple linear models. The implication of this finding is that to

improve the futures hedging effectiveness, we might have to take into account the possible

regime shifts in estimating optimal hedge ratio. A number of multivariate Markov regime

switching GARCH models have been proposed for dynamic futures hedging (Alizadeh &

Nomikos, 2008; Lee, 2009, 2010; Lee & Yoder, 2007). The covariance structures estimated

Her‐Jiun Sheu and Hsiang‐Tai Lee are Professors in the Department of Banking and Finance, National Chi

Nan University, Nantou, Taiwan.

*Correspondence author, Department of Banking and Finance, 1, University Road, Puli, Nantou, National Chi Nan

University, Taiwan 54561. Tel: (886) 49‐2910960 ext. 4648, Fax: (886) 49‐2914511, e‐mail: sagerlee@ncnu.edu.tw

Received July 2012; Accepted September 2012

The Journal of Futures Markets, Vol. 34, No. 2, 173–202 (2014)

© 2012 Wiley Periodicals, Inc.

Published online 9 November 2012 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21583

with these models are not only time‐varying but also state‐dependent. Accordingly, hedge

ratios estimated with these regime‐switching GARCH models, the so‐called regime‐switching

time‐varying MVHR, are also time‐varying and state‐dependent. A general finding is that

incorporating regime‐switching effect in GARCH models improves hedging effectiveness

compared with conventional state‐independent GARCH models.

Although these multivariate Markov regime switching GARCH‐hedging models capture

the state‐dependent time‐varying covariance structure of spot and futures returns, for

simplicity, they restrict all data series to follow same switching dynamic governed by one

common state variable. This excludes the possibility that spot and futures returns might follow

different switching dynamics governed by different state variables. For instance, it is possible

that the spot return is in the high (low) volatility state and meanwhile the futures return is in

the low (high) volatility state. Although spot and futures prices have same fundamentals and

are closely related, their speed of echoing new or unexpected information might be different.

Some articles find that futures markets generally reflect new information more rapidly than

spot markets because futures generally do not require delivery of the commodity and can be

implemented with low upfront fees (Figuerola‐Ferretti & Gonzalo, 2010; Kavussanos &

Nomikos, 2003; Silvapulle & Moosa, 1999).

1

Because of the discrepancy in the speed of

responding to temporary shocks, there are situations that futures market has responded to

shocks and exhibits higher volatility but meanwhile the spot market remains in the low

volatility state. Moreover, when futures market has fully reflected unexpected information and

returns to tranquil regime, spot market might be still in turmoil and exhibits higher volatility.

In this study, we suggest a multichain Markov regime switching GARCH (MCSG) model to

estimate optimal hedge ratios. MCSG allows the switching dynamic of spot and futures

returns to be governed by different state variables and captures the cross‐regime dynamic.

Otranto (2005) is the first to propose a multichain Markov switching (MCMS) model

such that different data series have different regime structures follow a multichain Markov

process. MCMS model, however, does not incorporate regime switching GARCH effect in the

volatility process. The property of state‐dependent GARCH volatility is frequently observed in

the spot and futures returns and is an important feature in developing optimal hedging

strategies (Alizadeh & Nomikos, 2008; Lee, 2009, 2010; Lee & Yoder, 2007). In this study, we

suggest an MCSG model for futures hedging. MCSG is an extension of MCMS such that

volatility dynamics in MCSG follow a regime‐switching GARCH process. In this study, we

compare the hedging effectiveness of MCSG with a number of single‐state‐variable regime‐

switching GARCH models, including the regime‐switching constant correlation (RSCC)

GARCH (Pelletier, 2006) and three state‐dependent time‐varying correlation GARCH

models: the Markov regime‐switching varying‐correlation (RSVC) GARCH (Lee &

Yoder, 2007), the full‐switching dynamic conditional correlation (FSDCC) GARCH

(Lee, 2010) and the Markov regime switching correlated (RSCor) GARCH (Christodoulakis

& Satchell, 2002; Lee, 2012).

The remainder of the study is organized as follows. The specification of MCSG is

presented in Section 2. In Section 3, we give the estimation procedure of MCSG. The formula

of computing MVHR and the measurements of hedging performance are described in

Section 4. This is followed by discussions of data and empirical results. A conclusion ends the

study.

1

Some other studies, however, conclude that spot prices tend to discover new information more rapidly than futures

prices (Chen & Gau, 2010; Yang, Yang, & Zhou, 2012). Debate of the information dominance between spot and

futures markets is not the main focus of this study. Either view, however, reveals that there are asynchronous

responses of spot and futures markets to new information. Thisshows the importance of modeling switching dynamic

of spot and futures returns with different state variables to capture the cross regime dynamic.

174 Sheu and Lee