The current spot price of 1 barrel of crude oil is $120, the 1.75-year spot rate

Question

The current spot price of 1 barrel of crude oil is $120, the 1.75-year spot rate is 5% (c.c.), the (continuous flow of) storage costs of crude oil is 1% per year. In absence of arbitrage, what should be the forward price to trade crude oil in 1.75 years if crude oil was an investment asset? Assume crude oil is a consumption asset. Is there an arbitrage if the forward price to trade 1 barrel of crude oil in 1.75 years is $140? If so, describe an arbitrage strategy. What is the convenience yield if the true forward price to trade 1 barrel of crude oil in 1.75 years is $110?

Explanation / Answer

A.) Forward price should be more than 132.6 as computed in the process above, if same is not achieved it should be postponed for sale by the company.

B.) If crude oil is consumption asset, that is it is used for consumtion on the date as specified price is $140, then arbitrage exist and it benefits @ 140-132.6 = 7.4, so consumption of the asset should be reduced to a minimum level and should sell up maximum oil at this time and purchase from open market should also be reduced so oil reserves created by the company should be used to maximum with more concentration on selling the asset.

C.) 110*e4%*1.75

This formula needs to be applied when convenience yield is calculated taking true forward price and multiplying the same with exponential taking power as maturity time of 1.75 year's, interest rate of 5% and storage cost 1%. As Convenience yield will be taken out as the formula is applied as Forward price*Exponential power of interest - storage cost*holding period this, will come out to be 117.98.

Spot price Amount after compounding Storage cost Spot price after 1.75 years 120 130.9730717 2.1 132.6

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