Question

PROBLEM 1. Spot price of gold is $1,407-40/oz. The total interest rate on three-month loans and deposits is 0.75% (i.e. $100 borrowed today would require a payment of $100.75 in three months). a. Assuming no storage cost and no transaction cost, determine the no-arbitrage price for a gold futures contract maturing three months from now. b. Suppose that the three-month gold futures contract is actually traded at $1,420.20/oz. Determine if an arbitrage opportunity is present. If so, describe a trading strategy that takes advantage of this arbitrage opportunity and calculate the profit of the strategy per contract. Make sure to clearly identify what position should be taken in the futures contract, whether the asset should be bought or sold, and how much cash will have to be borrowed or invested. The contract size is 100 oz. Note. Round all results to four decimal places.

Answer 1

a Calculation of No arbitrage price for gold futures contract maturing in 3 months from now.

As there are no storage costs and no transaction cost, the no arbitrage futures price is :-

Futures Price = Spot Price + Interest Cost

                      = Spot Price + Spot Price*Risk Free Interest Rate for 3 months

                      = 1407.40 + 1407.40*0.75%

                      = 1407.40 + 10.5555

Futures Price = $ 1417.9555/oz

Thus, the no arbitrage price for gold futures maturing in 3 months is $ 1417.9555/oz.

b. The no arbitrage price for gold futures maturing in 3 months is $ 1417.9555/oz and the futures contract are actually trading at $ 1420.20/oz. The futures are overvalued and so we sell futures.

We take a opposite position in cash market compared to futures market. Thus, we sell gold futures and buy gold in spot market. To buy gold in spot market, we need to borrow funds at risk free rate equal to the spot price of gold.

Each futures contract is for 100 oz, so we :-

1. sell 1 future contract maturing in 3 months

2. Buy 100 oz gold in spot market at spot price

3. Borrow amount equal to spot price of gold at risk free rate for 3 months.

Thus, cash flow today is as follows :-

Particulars	Amount
Sell 1 gold future contract	-
Purchase Gold Asset ($1407.40*100)	(1,40,740.00)
Borrow spot price at risk free rate	1,40,740.00
Net Cash Flow	-

After 3 months, the spot price of gold will be equal to no arbitrage price of gold futures i.e, $ 1417.9555/oz.

At expiry of futures contract the spot price and futures price are same.

Profit on futures = Sale Price of futures - Futures price on expiry

                          = (1420.20*100) - ( 1417.9555*100)

                          = 142020 - 141795.55

Profit on futures contract = $ 224.45 per futures contract.

Repayment of money borrowed = Amount Borrowed * (1+Interest Rate)

                                                 = 140,740 * (1 + 0.0075)

Repayment of money borrowed = 141,795.55.

Thus, after 3 months, on expiry date of futures, the cash flows will be as follows :-

Particulars	Amount
Profit on futures	224.4500
Repay amount borrowed	(1,41,795.5500)
Sell gold at spot rate	1,41,795.5500
Net Cash Flow	224.4500

Thus, the profit from arbitrage opportunity is $ 224.45 per gold futures contract.