Question

Suppose you are producing crude oil in the Permian basin which is lighter than the benchmark WTI, which is the underlying for the futures contract. Recenlty the standard deviation of daily changes in the WTI spot price has been about 1.30. You expect that this new, lighter crude will have a little more price uncertainty, perhaps 1.34 daily standard deviation. The correlation between these spot price changes is about 0.98.

You will produce 450,000 barrels of this crude next month. How many WTI contracts do you want to enter into to get the best hedge for the sales price? Do you go long or short these contracts?  

One WTI futures contract is for 1,000 barrels.

Answer 1

Given

WTI ( Benchmark) Standard Deviation = 1.30

Future Lighter Crude Oil Standard Deviation = 1.34

Co relation between WTI and Lighter Crude Oil is 0.98

Total Number of Barrels = 450,000

1 Contract = 1000 Barrels

So, you have to hedge for = 450,000/1000 = 450 Contracts.

CROSS HEDGING : It means hedging risk using two products or assets which have co orelation between them.

Formula for optimal hedging = Co relation * (Standard deviation of Spot WTI / Standard Deviation of Future Lighter rude Oil)

= 0.98 * (1.30 / 1.34)

= 0.98 * 0.9701

= 0.9507

Number of Contracts that Can be hedged are = 0.9507 * 450 = 427.8 Contracts = Approximatley 428 Contracts.

The company has to take Short Position Since, it is going to sell its product after one month. Short Position means taking the position of seller sicne it will produce 450,000 barrels of Oil next month.