a) (10 points). You are a junior trader at ALZ Investments Corp, responsible for trading gold futures contracts. The price of one ounce of gold is $1,800. For simplicity, suppose the interest rate is 0%. The annual storage cost of gold is $20 per ounce per year. Consider two gold futures contracts, expiring 1 year from now (2022) and 2 years from now (2023), respectively. What are the fair prices of these 2 contracts?

b) (10 points). Suppose, next year in 2022, the price of gold rises to $2,000. The interest rate remains at 0%, and the storage cost remains at $20 per year. What will the fair price of the 2023 contract be, in 2022?

c) (10 points). We are back in the present, in 2021. Suppose you think that interest rates will stay the same, but gold storage costs are likely to decline: you think the cost of storing gold will be $10 from 2022 onwards. However, you have a brokerage account, but no storage space for gold, so you can't actually buy any physical gold. How can you use gold futures contracts to make a bet on gold storage costs declining, without holding any exposure to the risk that gold prices change, and also without holding any physical gold at any point? Formally, construct a portfolio which profits from gold storage costs declining, but whose value is unaffected by changes in the level of gold prices, and which does not require ever buying and storing (or selling) any physical gold.

d) (10 points). You have made substantial profits speculating on storage costs using gold futures contracts, so you have been promoted to run the firm's wheat futures desk. For simplicity, assume interest rates are 0%. We are in March 2021 (month 3), and the price of wheat is currently $5 per bushel. Consider two wheat futures contracts, expiring in June 2021 (month 6) and September 2021 (month 9). Wheat can be stored for $1 per bushel per month. Wheat can also be planted in March. The total cost of buying a bushel of wheat seeds, planting the seeds, and growing the seeds into a bushel of wheat is $3. However, wheat takes six months to grow (i.e. if planted now, it can be harvested in September). For simplicity, suppose that one bushel can be harvested in September for each bushel planted in March. What are the fair prices of the June and September wheat futures contracts?