There are two futures contracts currently available for gold. One contract expires 6 months from today and the other expires 12 months from today. The spot price for gold is$1,850 per ounce and the 6-month and 12-monthspot rates are 1.35% and 1.90% respectively (both quoted as APRs with semi-annual compounding). Gold storage costs are$12.00 per 6-monthper ounce, paid at the end of the storage period (i.e. at the end of each6-month period). Short selling of physical gold is not possible.

a) The current 12-month futures price is$1,920.00. Is there an arbitrage trade? If so, describe the strategy and calculate the arbitrage profits.

b) The current 6-month futures price is$1,850.00. Is there an arbitrage trade? If so, describe the strategy and calculate the arbitrage profits.

c) If the term structure of interest rates remain constant over the next 6month and the spot price is the same as the theoretical futures price of the 6-month contract, how would the value of a 12-month futures contract evolve over the next 6-months?