It is December now. A March futures contract on 10,000 MMBtu of natural gas sett

Question

It is December now. A March futures contract on 10,000 MMBtu of natural gas settled for $3.95 per MMBtu. Assume that the contract has exactly 3 months (0.25 years) to maturity. The spot price is $3.78. Present value of three months’ worth of storage costs is $.05 per MMBtu. The interest rate is 3% annually. Assume convenience yield to be zero. Use continuous compounding. a. Using the formula for commodity futures parity, F = {S + PV(c)}*erT, establish that an arbitrage opportunity exists. b. Design the arbitrage strategy. Show profit for 10,000 MMBtu, i.e. per one futures contract.

Explanation / Answer

Solution:

Spot price = $3.78, time to maturity = 3 months = 0.25 years

Present value of storage cost = $0.05 , Interest rate = 3%

Given that March future contract settled at $3.95 per MMBtu

Now we can calculate theoretical future price using the formula

F = {S + PV(c)}*erT

F = {3.78 + 0.05)}*e(0.25*3%) = 3.83 * e(0.0075) = 3.83* 1.007528 = 3.858833

Part A ) There is an arbitrage opportunity as calculated future price is 3.858833, while future price in actual is 3.95 per MMBtu. This difference in price creates arbitrage oppportunity

Part B ) Arbitrage Strategy: We sell the asset that have higher price and buy the lower price assets.

Sell: We will sell the future contract of 10000 MMBtu at $3.95

Buy: We will buy the 10000 MMBtu of gas at current price of $3.78 and we will incur the storage cost on it as well as the interest cost. So total effective cost will be $3.858833

Profit per unit of MMBtu = 3.95 - 3.858833 = 0.091167

Profit per 10,000 unit or one future contract = 10000 * 0.091167 = 911.6701

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