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.

Solutions

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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