By

Nafiu Bashir Abdussalam

Department of Economics

Bayero University, Kano

+2347037880962

nafiu_bashir@yahoo.com

And

Jamaladeen Abubakar

Department of Mathematics and Statistics

Hussaaini Adamu Federal Polytechnic, Kazaure

+2348034067081

ajafuntua@yahoo.com

RISK ANALYSIS USING HEDGING STRATEGY IN CRUDE OIL PRODUCTION: EMPIRICAL EVIDENCE FROM DYNAMIC

MULTIVARIATE GARCH

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

• PAPER’S OUTLINE

• INTRODUCTION & RESEARCH MOTIVATION

• RECEIVED KNOWLEDGE

• ECONOMETRIC TOOLS EMPLOYED & THE ESTIMATION TECHNIQUES

• RESULTS & DISCUSSION

• CONCLUSION

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

• INTRODUCTION AND RESEARCH MOTIVATION

• Crude oil price risk is increasingly significant in determining the optimal crude oil production in the global oil market.

• Importantly, crude oil is exposed to price fluctuations as a results of unexpected jumps in global oil demand, a decrease in the capacity of crude oil production and refinery capacity, petroleum reserve policy, OPEC spare capacity and policy, major regional and global economic crises, and geopolitical risks.( Roengchai, 2010).

• Hedging is identified as a strategies used by oil companies to minimizes the volatility in the price movement in the global market.

• Daniel(2001), Chen et al (2003), Lien and Tse (2002), asserted that hedging strategies can substantially reduce oil price volatility without significantly reducing returns, and with the added benefit of greater predictability and certainty.

• The widely used ARCH due to Engle(1982) and GARCH following Bollerslev (1986) seem to be heavily used models for estimating time-varying OHRs, and a number of applications .

MGARCH MODELING IN CRUDE OIL PRICE RISK…….. • INTRODUCTION AND RESEARCH MOTIVATION

• The study derives its motivation from the dynamic volatility in the construction of OHR. Most of the earlier researches constructed time-invariant hedge ratio (See, for example, Ederington (1979), Figlewski (1985) and Myers and Thomson (1989) ).

• However, it can be argued that financial asset returns volatility, covariance and correlations are time-varying with persistence dynamics, and rely on techniques such as conditional volatility(CV) and stochastic volatility (SV) models.

• Interestingly, Bailers and Myers (1991) claim that, if the joint distribution of cash prices and futures prices change over time, estimating a constant hedge ratio may not be appropriated.

• In this study, the researchers employs estimation techniques that allows dynamics to be time-varying, hence, the MGARCH Models.

MGARCH MODELING IN CRUDE OIL PRICE RISK…….. • INTRODUCTION AND RESEARCH MOTIVATION

• This paper identifies two key gaps:

(a) On one hand, so many studies did not focus on OHR or the design of an optimal hedging strategy based on a wide range of models using time varying volatility models of VEC (initially due to Bollerslev, Engle, and Wooldridge, 1998) Diagonal VEC (DVEC), BEKK (named after Baba, Engle, Kraft and Krooner, 1995), Constant Conditional Correlation Model CCC ( Bollerslev, 1990), Dynamic Conditional Correlation Model DCC (Tse and Tsui, 2002, and Engle, 2002), VARMA-GARCH (Ling and McAleer, 2003) and VARMA-AGARCH (McAleer et al, 2009)

(b) On the other hand, this study will compare the OHR of three different crude oil benchmark, namely, OPEC, WTI and BRENT and identifies the best OHR by determining their hedging effective index (HE).

• The research is motivated to use time-varying models to model the OHR of the three crude oil benchmarks.

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

• RECEIVED KNOWLEDGE

• 2.1 Empirical Evidence

• In the literature, research has been conducted on the volatility of crude spot, forward and futures returns.

• Lanza et al. (2006) applied the constant conditional correlation (CCC) model of Bollerslev (1990) and the dynamic conditional correlation (DCC) model of Engle (2002) for West Texas Intermediate (WTI) oil forward and futures returns.

• Similarly, Manera et al. (2006) used CCC, the vector autoregressive moving average (VARMA-GARCH) model of Ling and McAleer (2003), the VARMA- Asymmetric GARCH model of McAleer et al. (2009), and DCC to spot and forward return in the Tapis market.

• Recently, Chang et al. (2009a, 2009b, 2009c) estimated multivariate conditional volatility and examined volatility spillovers for the returns on spot, forward and futures returns for Brent, WTI, Dubai and Tapis to aid risk diversification in crude oil markets.

MGARCH MODELING IN CRUDE OIL PRICE RISK…….. • 2.2 Conceptual Issues

• Concept of Hedged portfolio can be defined as a portfolio that combines return series on futures and spotprices (Hull, 2009).

•Consider, for example, The OPEC’s return portfolio of spot and futures

position can be defined as:

•Johnson (1960) defined the variance of the returns of the hedged

portfolio, conditional on the available information set at time , is

given by:

•Taking the partial derivative of equation (2) with respect to and equating to zero and solving for, yields the OHRt conditional on the

information set available at

•)

MGARCH MODELING IN CRUDE OIL PRICE RISK…….. From the multivariate conditional volatility model, the conditional covariance matrix is obtained, such that the OHR is given as:

• Hedging effectiveness index is used to measure the performance of OHR. Generally, there are two approaches used to compare the OHR performance using multivariate conditional volatility models. Ku et al. (2007) defined hedging effectiveness as:

• …………………………………………….. (5)

•Alternatively, in order to construct an optimal portfolio design that minimizes risk without lowering expected returns, and applying the methods of Kroner and Ng (1998) and Hammoudeh et al. (2009), the optimal portfolio weight of crude oil spot/futures holding is given by:

•……………………………………………….. (6)

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

•Where () is the weight of the spot (futures) in a one dollar portfolio of crude oil spot/futures at time t.

•The literature reviewed and the conceptual issues raised indicate that the research has identified gaps and intends to fill in the gaps using the most recently econometric methodology.

•Therefore, it is worth noting that, conditional volatility models are the best methods to understand the dynamic process.

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

• DATA MEASUREMENT & ECONOMETRIC TOOLS

• 3.1 Data Measurement

• I apply log-difference transformation to convert data into continuously compounded returns using

• The data covers runs from a period of 30,2002, October to 07, 2013, February which gives a total of 2605 observation.

• It is worth noting that the data is a high frequency data as it is reported daily.

• The data is obtained from the DataStream database, Energy Information Administration and OPEC statistical bulletin.

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

• Data Description

Mean Min Max SD CV Skew Kurt JB

RFO -0.019 6.597 -7.128 1.078 -0.017 0.082 7.748 2448.53

RSO -0.020 4.508 -5.261 0.926 -0.021 0.173 5.539 712.56

RFB -0.021 5.674 -7.126 1.053 -0.020 0.002 7.302 2008.15

RSB -0.022 7.310 -7.873 0.970 -0.023 0.037 7.907 2613.03

RFW -0.020 4.965 -5.550 0.969 -0.020 0.140 5.650 770.57

RSW -0.019 6.597 -7.128 1.078 -0.017 0.082 7.748 2448.53

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

Oct 30, 2

002

Feb 26, 2

003

Jun 25, 2003

Oct 22, 2

003

Feb 18, 2

004

Jun 16, 2004

Oct 13, 2

004

Feb 09, 2

005

Jun 08, 2005

Oct 05, 2

005

Feb 01, 2

006

May 31, 2

006

Sep 27, 2

006

Jan 24, 2

007

May 23, 2

007

Sep 19, 2

007

Jan 16, 2

008

May 14, 2

008

Sep 10, 2

008

Jan 07, 2

009

May 06, 2

009

Sep 02, 2

009

Dec 30, 2

009

Apr 28, 2

010

Aug 25, 2

010

Dec 22, 2

010

Apr 20, 2

011

Aug 17, 2

011

Dec 14, 2

011

Apr 11, 2

012

Aug 08, 2

012

Dec 05, 2

0120

20

40

60

80

100

120

140

160

FUTURE PRICE (OPEC)SPOT PRICE(OPEC)FUTURE PRICE(BRENT)SPOT PRICE(BRENT)FUTURE PRICE (WTI)SPOT PRICE (WTI)

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

3 117 231 345 459 573 687 801 915 1029 1143 1257 1371 1485 1599 1713 1827 1941 2055 2169 2283 2397 2511

-10

-8

-6

-4

-2

0

2

4

6

8

10

Series1Series2Series3Series4Series5Series6

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

Returns ADF test(t-statistic) Phillips-Perron test

None Constant Constant& Trend None Constant Constant& Trend

R(SPO) -36.723 -36.744 -36.745 -53.285 -53.300 -53.296R(FPB) -37.955 -37.975 -37.973 -53.205 -53.220 -53.215R(SPB) -35.645 -35.668 -35.664 -51.098 -51.115 -51.107R(FPO)

R(FPW)

R(SPW)

MGARCH MODELING IN CRUDE OIL PRICE RISK…….. •

MGARCH MODELING IN CRUDE OIL PRICE RISK…….. •

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

•

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

•

MGARCH MODELING IN CRUDE OIL PRICE RISK…….. • EMPIRICAL RESULTS

• An important task is to model the conditional mean and conditional variances of the return series.

• Therefore, univariate ARMA-GARCH models are estimated with the approriated univariated conditional volatility models given as ARMA(1,1) and GARCH(1,1).

• All estimations are done using Ox Metrics 6.3 version and DCC and VARMA-AGARCH are estimated

VARMA-AGARCH MODELING IN CRUDE OIL PRICE RISK……..

STATISTIC

BRENT WTI OPEC

SP FP SP FP SP FP

C 1.43(2.087) 1.23(2.786) 1.01(3.512) 1.14(3.987) 1.45(2.432) 1.23(3.435)

AR -0.86(-8.76) -0.43(-23.6) -0.06(-0.39) -0.17(-18.6) -0.43(-21.3) -0.43(-8.32)

MA 0.86(11.76) 0.43(22.66) 1.43(0.007) 0.105(9.71) 0.32(12.34) 1.23(4.56)

ώ 3.54(0.432) 6.98(2.87) 1.76(4.65) 1.09(8.96) 1.32(3.24) 4.23(3.23)

α 0.08(5.67) -0.07(-5.76) 0.32(22.5) 1.98(0.24) 0.54(3.43) 0.45(3.12)

α -0.04(-3.43) 0.21(7.98) -0.12(-23.6) 0.08(12.9) 0.43(5.6) 0.78(9.87)

β 0.51(4.32) 0.21(2.98) 0.35(11.54) 0.05(1.23) 0.04(3.45) 0.43(3.65)

β 0.83(5.34) 0.78(9.65) 0.63(15.98) 0.03(1.38) 0.45(2.34) 0.65(5.43)

α +β 0.605 0.136 0.657 0.12 0.686 0.886

CCC 0.87(143.2) 0.943( 0.789(32.7)

L-L 17435.458 18765.087 12435.76

AIC -15.986 -12.876 -11.987

DCC MODELING IN CRUDE OIL PRICE RISK……..

STATISTIC BRENT WTI OPEC

SP FP SP FP SP FP

C 1.23(2.087) 1.23(3.435) 1.45(2.432) 1.14(3.987) 1.01(3.512) 1.23(2.786)

AR -0.88(-8.76) -0.43(-8.32) 0.32(12.34) 0.105(9.71) 1.43(0.007) -0.43(-23.6)

MA 0.86(16.76) 1.23(4.56) 1.32(3.24) 1.09(8.96) 1.76(4.65) 0.43(22.66)

ώ 4.77(0.432) 4.23(3.23) 0.54(3.43) 1.98(0.24) 0.32(22.5) 6.98(2.87)

α -0.04(-3.43) 0.45(3.12) 0.43(5.6) 0.08(12.9) -0.12(-23.6) -0.07(-5.76)

β 0.51(4.32) 0.78(9.87) 0.04(3.45) 0.05(1.23) 0.35(11.54) 0.21(7.98)

θ1 0.07(18.70 0.43(3.65) 0.45(2.34) 0.03(1.38) 0.63(15.98) 0.21(2.98)

θ2 0.916(18.8) 0.65(5.43) 0.686 0.12 0.657 0.78(9.65)

α+β 0.47 0.886 0.47 0.789(32.7) 0.943( 0.136

L-L 16423.54 12435.76 1234.874

AIC -10.435 -11.987 -12.765

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

OPTIMAL PORTFOLIO AVERAGE OHR

MODELS BRENT WTI OPEC BRENT WTI OPEC

VARMA-A 0.377 0.382 0.398 0.840 0.955 0.989

DCC 0.366 0.478 0.765 0.827 0.922 0.811

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

HEDGE EFFECTIVENESS(%)

MODELS BRENT WTI OPEC

VARMA-AGARCH 56.724 80.857 76.765

DCC 57.045 80.942 77.654

MGARCH MODELING IN CRUDE OIL PRICE RISK……..

• CONCLUSION• The empirical results foer daily data from 30 Oct

2002 to 7 Feb 2013 showed that for the Brent market, the OPW of all multivariate volatility model suggested holding futures in larger proportion than spot.

• On the contrary, for the WTI and OPEC markets, the DCC recommended holding futures to spot but the VARMA-AGARCH suggested holding spot to futures.

• The calculated OHRs from each MGARCH recommended short position in crude oil futures with a high proportion of one dollar long in crude oil spot.

• The HE indicated that DCC(VARMA-GARCH) is the best(worst) model for OHR in terms variance of portfolio.