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The one-year futures price of gold is $1,213 per oz. (i.e., the futures price on a...

The one-year futures price of gold is $1,213 per oz. (i.e., the futures price on a contract that expires in one year). The spot price is $1,152 per oz. and the continuous risk-free rate is 2.17% per annum. The storage costs for gold are $2 per oz. payable in arrears and we assume gold provides no income. What is the arbitrage profit per 100 oz. of gold? Ignore transactions costs.

Expert Solution

Theoretical Futures Price = Spot Price*e^[risk free rate*t]+Storage Cost Payable in Arrears

Where e = constant (2.71828), t = years to expiry

Applying the above formula,

Spot Price = 1152, Risk Free Rate = 0.0217, t = 1

Therefore, Theoretical Futures Price(according to cost & carry) = 1152*e^0.0217 = 1152*1.0219(from table) = $1177.23+2 = $1179.23

Actual Futures Price is $1213 i.e Greater than Theoretical Futures Price

Therefore, Future is Overvalued.

Therefore, to make an Arbitrage Gain, Buy Spot & Sell under Futures Contract i.e (Cash and Carry).

Steps to Arbitrage:

Now,

(1) Borrow 1152*100 = $115200 for 1 year @ Risk Free Rate

(2) Buy 100 oz of gold @ current price i.e. $1152

(3) Sell Futures contacts for 100 oz, expiring in 1 year

After 1 year,

(4) Sell 100 ounces of gold under Futures Contract and receive 1213*100 = $121300

(5) Repay loan with interest 115200*1.0219(value from table, same as above) = $117722.88

(6) Pay Storage Costs = 100*2 = $200

Arbitrage Gain = Realized from sale-Repaid the loan-Storage Costs = 121300-117722.88-200 = $3377.12

jeff jeffy answered 1 year ago

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