Question

Suppose that there are no storage costs for crude oil and the interest rate for borrowing or lending is 2.25% per annum (continuously compounded). Consider the transactions that would allow you to make an arbitrage profit in March by trading in May and December forward contracts. Use the forward prices provided in the table below (Crude oil contracts are for 1,000 barrels, quoted in $ per barrel.) Month Settlement Price Change Volume May 51.51 2.76 9,315 December 55.23 2.19 7,055 Consider the following strategy. In March, enter a long position in a May forward contract and a short position in a December forward contract. In May, borrow at the interest rate and buy oil from the May forward contract. Store the crude oil till December. In December, sell oil to the December forward contract and repay the loan. What is the prot per barrel from the this strategy?

Answer 1

In this strategy, you can make a profit of $3.28 per barrel by entering a long position in a May forward contract and a short position in a December forward contract, and borrowing at the interest rate in May to buy oil, storing it until December, and then selling it.

Step-by-step explanation:

In this strategy, you enter a long position in a May forward contract and a short position in a December forward contract in March. In May, you borrow at the interest rate and buy oil from the May forward contract. Then, you store the crude oil until December. Finally, in December, you sell the oil to the December forward contract and repay the loan.

The profit per barrel from this strategy can be calculated by taking the difference between the selling price in December and the buying price in May, and subtracting the interest cost of borrowing the money. Let's calculate:

Selling Price in December = $55.23 per barrel

Buying Price in May = $51.51 per barrel

Difference = $55.23 - $51.51 = $3.72 per barrel

Interest Cost = $51.51 * e^(2.25% * (7/12)) - $51.51 = $0.44 per barrel (where e is the base of the natural logarithm)

Profit per Barrel = Difference - Interest Cost = $3.72 - $0.44 = $3.28 per barrel

Answer 2

The profit per barrel from the given trading strategy is -$42.11.

Step-by-step explanation:

To calculate the profit per barrel from the given strategy, we need to determine the net cost of buying and storing oil from May to December. Here's how:

Calculate the cost of buying oil in May by multiplying the May forward contract price (51.51) by the number of barrels (9,315): 51.51 * 9315 = 480,176.65

Calculate the cost of storing oil from May to December by multiplying the number of barrels by the interest rate (2.25%) for the holding period (7/12 years): 9315 * 0.0225 * (7/12) = 433.27

Calculate the revenue from selling oil in December by multiplying the December forward contract price (55.23) by the number of barrels (7,055): 55.23 * 7055 = 389,262.65

Calculate the cost of repaying the loan by multiplying the initial loan amount (480,176.65) by the interest rate (2.25%) for 9 months: 480,176.65 * 0.0225 * (9/12) = 9,102.47

Finally, calculate the profit per barrel by subtracting the total cost from the total revenue and dividing by the number of barrels: (389,262.65 - 480,176.65 - 433.27 - 9,102.47) / 7055 = -42.11

The profit per barrel from this strategy is -$42.11.