Question

Suppose that the spot price of oil is US$19,

The quoted 1-year futures price of oil is us$16

The 1-year US$ interest rate is 5% per annum

The storage cost of oil are %2 per annum

is there an arbitrage opportunity? is yes, please explain how you can observe this opportunity.

Answer 1

The spot price of oil: $19

Quoted 1-year futures price: $16

The 1-year US$ interest rate: 5% per annum

The storage cost of oil: 2% per annum

Hence, Storage cost: $ 19 *2% = $0.38 per unit per annum

Fair Future Price of oil: Spot price (1+ interest rate)ⁿ + storage cost

[Note: It is assumed that storage cost is incurred at the end of the year.]

Fair Future Price of oil: $19 (1+ 0.05)¹ + $0.38

Fair Future Price of oil: $ 20.33

Hence, there is an arbitrage opportunity because the Fair future price as per our calculation is $ 20.33 but the actual future price in the market is $ 16.

It means the current future price is undervalued by $4.33 ($20.33-$16.33).

We should take a long position (buy) in the future contract and sell in the cash market and earn the interest on that cash proceed received in the cash market.

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