Question

It is now January. The current interest rate is 3.8%. The June futures price for gold is $1490.60, while the December futures price is $1,500. Assume the June contract expires in exactly 6 months and the December contract expires in exactly 12 months.
a. Calculate the appropriate price for December futures using the parity relationship? (Do not round intermediate calculations. Round your answer to 2 decimal place.)
Price for December futures $
b. Is there an arbitrage opportunity here?
No
Yes

Answer 1

Answer:

a. $4,322.74

b. Yes

Explanation:

a. The computation of December futures is shown below:-

December futures = June futures × (1 + 1.9%)

= $1490.60 × (1 + 1.9%)

= $1490.60 × 2.9 %

= $4,322.74

Since the current interest rate is 3.8% and the contract is expired in 6 months so we half the interest rate i.e 1.9%

b. Yes, there is an arbitration opportunity here due to the difference between the future price of December. The real futures price for December is $1,500 and the potential price for December's parity relationship is $4,322.74