1. 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

2. MGARCH MODELING IN CRUDE OIL PRICE RISK…….. PAPER’S OUTLINE INTRODUCTION & RESEARCH MOTIVATION RECEIVED KNOWLEDGE ECONOMETRIC TOOLS EMPLOYED & THE ESTIMATION TECHNIQUES RESULTS & DISCUSSION CONCLUSION

3. 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.

4. 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.

5. 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.

6. 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.

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

11. Data Description MeanMinMaxSDCVSkewKurtJB RFO-0.0196.597-7.1281.078-0.0170.0827.7482448.53 RSO-0.0204.508-5.2610.926-0.0210.1735.539712.56 RFB-0.0215.674-7.1261.053-0.0200.0027.3022008.15 RSB-0.0227.310-7.8730.970-0.0230.0377.9072613.03 RFW-0.0204.965-5.5500.969-0.0200.1405.650770.57 RSW-0.0196.597-7.1281.078-0.0170.0827.7482448.53

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

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

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19. 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

20. VARMA-AGARCH MODELING IN CRUDE OIL PRICE RISK…….. STATIST IC BRENTWTIOPEC SPFPSPFPSPFP 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) ώ3.54(0.432)6.98(2.87)1.76(4.65)1.09(8.96)1.32(3.24)4.23(3.23) α0.08(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) β0.51(4.32)0.21(2.98)0.35(11.54)0.05(1.23)0.04(3.45)0.43(3.65) β0.83(5.34)0.78(9.65)0.63(15.98)0.03(1.38)0.45(2.34)0.65(5.43) α +β0.6050.1360.6570.120.6860.886 CCC 0.87(143.2)0.943(0.789(32.7) L-L 17435.45818765.08712435.76 AIC -15.986-12.876-11.987

21. DCC MODELING IN CRUDE OIL PRICE RISK…….. STATISTICBRENTWTIOPEC SPFPSPFPSPFP 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) θ1θ10.07(18.70 0.43(3.65)0.45(2.34)0.03(1.38)0.63(15.98)0.21(2.98) θ2θ20.916(18.8) 0.65(5.43)0.6860.120.6570.78(9.65) α+βα+β0.47 0.8860.470.789(32.7)0.943(0.136 L-L16423.54 12435.76 1234.874 AIC-10.435 -11.987 -12.765

22. MGARCH MODELING IN CRUDE OIL PRICE RISK…….. OPTIMAL PORTFOLIOAVERAGE OHR MODELSBRENTWTIOPECBRENTWTIOPEC VARMA-A0.3770.3820.3980.8400.9550.989 DCC0.3660.4780.7650.8270.9220.811

23. MGARCH MODELING IN CRUDE OIL PRICE RISK…….. HEDGE EFFECTIVENESS(%) MODELSBRENTWTIOPEC VARMA-AGARCH56.72480.85776.765 DCC57.04580.94277.654

24. 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.