The effects of skewness on hedging decisions: an application of the skew-normal distribution in WTI and Brent futures

Figures & data

Figure 1. The number of literature related to crude oil hedging.

Source: Wind database.

Figure 2. Prices of Brent and WTI crude oil.

Source: Wind database.

Figure 3. Returns of Brent and WTI crude oil.

Source: Wind database.

Table 1. Descriptive statistics of spot and futures.

	WTI Spot Return	WTI Futures Return	Brent Spot Return	Brent Futures Return
Mean	0.000686	−0.004224	0.000283	0.000284
Min	−0.341410	−3.059700	−0.268700	−0.244040
Max	0.497090	0.376620	0.176810	0.210190
Var	0.001443	0.015949	0.000888	0.000912
Std	0.037992	0.126290	0.029791	0.030193
Skew	0.931990	−19.948500	−1.081700	−0.619280
Kurt	58.991800	465.965500	22.603300	19.764100
Corr	0.588760		0.937320

Source: Wind database.

Figure 4. Q-Q plots of Brent and WTI crude oil returns.

Source: Wind database.

Table 2. Results of JBtest.

	H	P	JBSTAT	CV
WTI Return of Spot	1	1.0000e-03	99256.9485	5.9048
WTI Return of Futures	1	1.0000e-03	6828750.2962	5.9048
Brent Return of Spot	1	1.0000e-03	12301.2150	5.9048
Brent Return of Futures	1	1.0000e-03	8936.2103	5.9048

Source: Wind database.

Figure 5. Skewness of the crude oil hedged portfolio returns.

Source: Wind database.

Figure 6. The effects of the hedge ratio on the distribution parameters.

Source: Wind database.

Figure 7. CVaR of Brent crude oil hedged portfolio with different positions.

Source: Wind database.

Figure 8. CVaR of WTI crude oil hedged portfolio with different positions.

Source: Wind database.

Table 3. variance and VaR of the hedged portfolio with Brent oil futures.

$\alpha$	Unhedged variance	Normal variance	Normal efficiency	skew-normal variance	skew-normal efficiency
0.01	0.00106804	0.00014093	0.8680	0.00013873	0.8701
0.025	0.00106804	0.00014132	0.8677	0.00013935	0.8695
0.05	0.00106804	0.00014097	0.8680	0.00013964	0.8693
$\alpha$	Unhedged VaR	Normal VaR	normal efficiency	skew-normal VaR	skew-normal efficiency
0.01	0.08310697	0.03545438	0.5734	0.03249129	0.6090
0.025	0.06158675	0.02236547	0.6368	0.02221084	0.6394
0.05	0.04033000	0.01452311	0.6399	0.01448651	0.6408

Source: Wind database.

Table 4. variance and VaR of the hedged portfolio with WTI oil futures.

$\alpha$	Unhedged variance	Normal variance	Normal efficiency	skew-normal variance	skew-normal efficiency
0.01	0.00180836	0.01325607	−6.3304	0.00823415	−3.5534
0.025	0.00180836	0.01352966	−6.4817	0.00845996	−3.6783
0.05	0.00180836	0.01356996	−6.5040	0.00845907	−3.6778
$\alpha$	Unhedged VaR	Norma VaR	normal efficiency	skew-normal VaR	skew-normal efficiency
0.01	0.10969608	0.08227521	0.0489	0.04887263	0.5545
0.025	0.06889837	0.03658715	0.0315	0.03151173	0.5426
0.05	0.04634164	0.01898693	0.0235	0.02348099	0.4933

Source: Wind database.

Figure 9. variance of Brent crude oil hedged portfolio.

Source: Wind database.

Figure 10. VaR of Brent crude oil hedged portfolio.

Source: Wind database.

Figure 11. CVaR of Brent crude oil hedged portfolio.

Source: Wind database.