Question

Assume that the only cost (or opportunity cost) associated with gold is the “interest on the money” if you own gold. There are no storage costs and the convenience yield is zero. Suppose you can borrow or lend money at 10 percent per annum (continuous compounding) if you buy / sell gold. Today's price of gold is $1,320 per ounce, and there are also gold futures contracts available. The 6-month gold futures is trading at $1,370 and the 12-month gold futures is at $1,458.83 (rounded from $1,458.8256). These contracts mature in exactly 6 and 12 months respectively. One futures contract is on one ounce of gold. Note: You are able to buy gold or short sell gold if required. You can also long or short the gold futures contracts at the traded prices (Note: Ignore any margin requirements associated with these contracts). Required: Suggest TWO different strategies you might use to make an arbitrage profit. Also calculate the arbitrage profit with reference to one futures contract only at the expiration date of your arbitrage strategy (being either 6 or 12 months hence). Use continuously compounded (c.c.) interest rates in all your calculations. Assume that the 10 percent interest rate (c.c.) will not change after 6 months.

Strategy One: Arbitrage profit at the end of 6 months

Strategy Two: Arbitrage profit at the end of 12 months

Answer 1

ARBITRAGE PROFIT AT THE END OF 6 MONTHS:-

Sell 1 ounce of gold @ $1,320

Deposit $1,320 for 6 months @ 10% p.a continuously compound

Buy(LONG) the 6 months gold future @ $1,370

PROFIT INCURRED:- 1,320×e(0.15×0.5) -1,320

= $52.807(approx).

ARBITRAGE PROFIT AT THE END OF 12 MONTHS:-

Sell 1 ounce of gold @ $1,320

Deposit $1,320 for 12 months @ 10% p.a continuously compound

But(LONG) the 12 months gold future @ $1458.83

PROFIT INCURRED:- 1,320×e(0.15×1) -1458. 83

= $74.791(approx).