Estimation and Hedging Effectiveness of Time‐Varying Hedge Ratio: Nonparametric Approaches

• Date: 01 October 2016
• Author: Haiqi Li,Sung Y. Park,Rui Fan
• Published date: 01 October 2016
• DOI: http://doi.org/10.1002/fut.21766

Estimation and Hedging Effectiveness

of Time-Varying Hedge Ratio:

Nonparametric Approaches

Rui Fan, Haiqi Li, and Sung Y. Park*

Many studies have estimated the optimal time-varying hedge ratio using futures, with most

employing a bivariate generalized autoregressive conditional heteroscedasticity (BGARCH)

model or a random coefficient model to estimate the time-varying hedge ratio. However, it

has been argued that when the variability of the estimated time-varying hedge ratio is large,

this ratio’s hedging performance is not as good as that of the unconditional (constant) hedge

ratio. This study proposes a nonparametric estimation approach to estimate and evaluate the

optimal conditional hedge ratio. This method produces a time-varying hedge ratio with less

volatility than those obtained from the BGARCH and random coefficient models. Weevaluate

the hedging performance of the various models using soybean oil, corn, S&P 500, and Hang

Seng futures indices. The empirical results support the proposed nonparametric approach in

terms of both in-sample and out-of-sample performance. ©2015 Wiley Periodicals, Inc. Jrl

Fut Mark 36:968–991, 2016

1. INTRODUCTION

Estimating an optimal hedge ratio and evaluating hedging effectiveness are important issues

in the futures market. This information helps investors to select appropriate positions in the

futures market to offset the risk from corresponding holdings in the spot market. As a result,

many studies have discussed methods for evaluating optimal static (unconditional) and time-

varying (conditional) hedge ratios. The most widely used optimal hedge ratio is the minimal-

variance ratio, defined as the covariance between the spot and futures returns divided by

the variance of the futures returns. This ratio can be estimated conveniently by the ordinary

least squares (OLS) method (see Ederington, 1979; Figlewski, 1984). However, recent study

reveals the downsides of using simple OLS hedge ratio in several aspects. For example,

Brooks, ˇ

Cern`

y, and Miffre (2012) argue that simple OLS hedge ratio fails to incorporate

the higher moments properties of most financial asset return series and demonstrate that

the out-of-sample performance of the hedging strategy which considers the information in

the higher moments is better than the performance using OLS method. Another problem

pointed out by Ghosh (1993) and Lien (1996) is that the classic least square regression

Rui Fanis at the Department of Economics, University of Illinois at Urbana-Champaign, Champaign, Illinois,

USA. Haiqi Li is at the College of Finance and Statistics, Hunan University, Changsha, Hunan, China.

Sung Y. Park is at the School of Economics, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul,

Korea. We would like to thank the anonymous referee for many pertinent comments and suggestions. How-

ever,we retain the responsibility for any remaining errors. This project was supported by the National Natural

Science Foundation of China (NSFC) (No. 71301048).

JEL Classification: C32, G13

*Correspondence author,School of Economics, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul, Ko-

rea. Tel: +82-2-820-5622, e-mail: sungpark@cau.ac.kr.

Received January 2015; Accepted October 2015

The Journal of Futures Markets, Vol. 36, No.10, 968–991 (2016)

©2015 Wiley Periodicals, Inc.

Published online 18 December 2015 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21766

Estimation and Hedging Effectiveness of Hedge Ratio 969

ignores the disequilibrium error in the short-term dynamics. Lien (1996) shows that the

omission of the co-integration relationship leads to a smaller hedging position and, therefore

yields a relatively poor hedge performance. Subsequent studies, such as Lien (2004, 2009),

provide further evidence of the reduction in hedging effectiveness caused by omitting the

error correction term. These findings suggest that an error correction model (ECM) should be

used when estimating optimal (unconditional) hedge ratios. However, this method has been

criticized for ignoring the time-varying changes in the joint distribution of spot and future

prices. As a result, alternative methods for estimating optimal time-varying hedge ratios,

such as the random coefficient model or the bivariate generalized autoregressive conditional

heteroscedasticity (GARCH) model, are more widely used.

Previous studies, such as Cecchetti, Cumby, and Figlewski (1998), Baillie and Myers

(1991), and Myers (1991), argue that the time variation of optimal hedge ratio may come from

the conditional heteroscedasticity in the spot and futures returns. Thus, multivariate ARCH

or GARCH models have been adopted to estimate conditional hedge ratios, for example,

by Baillie and Myers (1991), Brooks, Henry, and Persand (2002), Kavussanos and Nomikos

(2000b), Harris and Shen (2003), Hsu, Tseng, and Wang (2008), Miffre (2004), and Park

and Jei (2010). Other related studies include those of Myers (1991), Kroner and Sultan

(1993), Park and Switzer (1995), Garcia, Roh, and Leuthold (1995), Bera, Garcia, and Roh

(1997), and Moschini and Myers (2002), among many others. In contrast, Grammatikos

and Saunders (1983) regard the optimal hedge ratio as a random state variable that follows

an autoregressive or other stochastic process. In this case, the optimal hedge ratio can be

estimated using the random coefficient model (RCM), as discussed in Bera, Garcia, and Roh

(1997), Lee, Yoder, Mittelhammer, and McCluskey (2006), and Chang, Lai, and Chuang

(2010). Kavussanos and Nomikos (2000b) show that these conditional hedge ratios provide

larger variance reduction than static hedge ratios.

Despite the success of the above methods and their various extensions, the time-varying

hedging strategy does not always provide better hedging effectiveness than the static hedging

strategy does. Recent studies show that the conditional hedge ratios estimated by GARCH

or random coefficient models are too volatile to outperform the static optimal hedge ratio

in terms of the out-of-sample performance (Kavussanos & Nomikos, 2000a; Lien, 2002,

2005, 2008). Lien (2002) finds that the conditional hedging strategy cannot outperform the

OLS hedging scheme. Lien (2008) provides a theoretical proof that the OLS hedging strategy

dominates any dynamic strategy in terms of the post-sample hedging performance. Moreover,

Kavussanos and Nomikos (2000a) find that the hedge ratio has to be sufficiently volatile to

outperform the OLS strategy. However, using various flexible GARCH models, Park and Jei

(2010) present empirical evidence of an inverse relationship between the variability of the

hedge ratio and hedging effectiveness, while Lien (2010) analyzes the inverse relationship

between hedge ratio variability and hedge performance from a theoretical point of view.

Consequently, a conditional hedge strategy with a high degree of variability is unlikely to

outperform the OLS hedging scheme. In practice, a series of volatile hedge ratios is even more

problematic, since the corresponding hedging strategy requires frequent rebalancing of the

portfolios and, consequently, much higher transaction costs. Therefore, it seems that there

exists a trade-off between the construction of flexible models and the hedging effectiveness

of such models. Salvador and Arog´

o (2014) show that a regime-switching bivariate GARCH

model outperforms static models in both an in-sample and an out-of-sample analysis. In

this study, we propose a new method of managing the high degree of volatility of the time-

varying optimal hedge ratio. Weuse nonparametric models to estimate a smooth time-varying

optimal hedge ratio. This hedging strategy offers the flexibility of time-varying hedge ratios,

but with lower volatility, which generates better in-sample and out-of-sample performance

than conventional hedging strategies do.