Midterm-Review

# Answer trader a makes a profit of s t ӎ 1000 and

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Answer: Trader A makes a profit of S T Ӎ 1,000 and Trader B makes a profit of max( S T Ӎ 1,000, 0) – 100 where S T is the spot price of gold in one year. Trader A does better if S T is above \$900 as indicated in Figure S1.3. Figure1.3 : Profit to Trader A and Trader B in Problem 1.24 2. Assume that the spot price for gold is \$1,200 per ounce and the gold futures contract for one year delivery is trading at \$1,270. The risk-free interest rate is 5% per year. Can you arbitrage? How? Answer: Theoretical futures price F = 1,200*e (0.05*1) = \$1,261.53 Since the actual futures price in the market is \$1,270 > \$1,261.53, it is overpriced so you can arbitrage Today: (1) Borrow \$120,000 at 5% for one year to buy 100 ounces of gold at \$1,200 (2) Sell a futures contract on gold at \$1,270 per ounce (one year delivery) In one year: (1) Make the delivery and collect \$127,000 (2) Repay the loan (principle plus interest) \$126,153 = 120,000*e (0.05*1) (3) Take risk-free profit = \$847

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