Question

The spot price of oil is $54 per barrel and the the storage costs per barrel are a constant proportion, 2%, of the spot price. The risk-free interest rate is 5% per annum continuously compounded. If the one year futures price of oil is $55, estimate the convenience yield associated with holding oil.

Current price of oil ($/bbl) $54.00

Storage costs (%/year) 2%

Risk free rate (per annum) 5%

time to maturity of contract (months) 12

Futures Price of oil ($/bbl) $55.00

Answer 1

Spot price is the price at which you buy an asset (that pays no dividends or interests) today and Futures price is the pre determined price on the same asset on a predetermined future date and this futures price should guarantee risk free return. Hence according to the time value of money for continuous compounding we should be getting the following relationship,

where F(t) is the futures price

S is the spot price of asset

r is the risk free interest rate

t is the time to maturity in years

But few assets generates cash payments or convinence yield() such as interest rates or dividends and also incurs storage costs which is indicated as percentage of spot price (), then the above equation becomes,

The storage costs is positive opportunity cost which increases the value of asset as the interest rate and Convenience yield is the additional value gained by holding the asset rather than having a futures contract on the asset. Substituting the values given in the question

So convience yield associated with holding oil is $2.718