Question

The current gold price for immediate delivery (i.e., gold spot price) is $1440 (bid) and $1450 (ask) per ounce. A one-year forward contract of gold trades at a forward price of $1500 (bid) and $1510 (ask) per ounce. In a long forward contract you will receive delivery of one ounce of gold in one year and you will need to pay $1510 at the time of delivery. Alternatively, in a short forward position you will need to deliver one ounce of gold in one year and you will receive $1500 at the time of delivery. Your one-year lending interest rate is 1% and your one-year borrowing interest rate is 3%. Assume that gold has no delivery costs, no storage costs, and no short-selling costs. You expect that the gold price is going to increase to around $1600 over the next year. Are there any arbitrage opportunities here? If yes, explain which transactions you need to perform and quantify the profits you make from this arbitrage. If not, explain why an arbitrage does not exist.

Answer 1

Given Gold Spot Price (Bid) Gold Spot Price (Ask) Gold Forward Price (Bid) Gold Forward Price (Ask) $1,440 $1,450 $1,500 $1,510 1% one-year lending rate one-year borrowing rate 3% Solution Abritrage profit are the profit when there is no uncertainity in the price of a underlying asset of the contract. Hence, price are expected to rise to $1600 is irrelavent for arbitrage profit transaction. Here, for Abitrage profit we shall buy gold in spot market at rate $1450, and Sell gold in future market at rate $1500. Summary and effect of Transaction CASHFLOW PARTICULARS At Beginning Buy Gold in Spot Market Borrow Enter in contract to Sell Gold in Forward Market -$1,450.00 $1,450.00 $0.00 At End (After 1 year) Gold Sold as per Forward Contract Borrowing Interest repayment = 1450 X 3% = Borrowing repayment $1,500.00 -$43.50 -$1,450.00 Sum of all Cashflow (Arbitrage Profit) $6.50 Hence, there is arbitrage profit of $6.5 from above transaction