1. Your firm is a market maker in FX forwards. A customer wants a 6-month forward contract to sell 25 million Euro for dollars. The head of trading needs to quote a forward exchange rate to bid for the contract and she wants you to figure out a number that will produce an arbitrage profit for the firm worth $10,000 in today's dollars, i.e., in present value terms.

Current market data:

Current spot exchange rate: 0.9100 dollars per euro

US 6-month interest rates: 3.100% borrowing rate

2.900% lending rate

Euro-zone 6-month interest: 4.400% borrowing rate

4.200% lending rate

At what exchange rate do you recommend that she should commit the firm to buy 25 million euro in 6 months?

2. Your firm is a metals dealer. A customer wants a contract to sell you 50,000 ounces of gold in 4 months. The head of trading needs to quote a price to bid for the contract and she wants you to figure out a number that will produce an arbitrage profit for the firm worth $10,000 in today's dollars, i.e., in present value terms.

Current market data:

Current spot price for gold: 340.00 dollars per ounce

US 4-month interest rates: 3.100% borrowing rate

2.900% lending rate

Gold lease rate: 2.000% annual rate

At what price do you recommend that she should commit the firm to buy 50,000 ounces of gold 4 months from now?

3. Suppose the S&P 500 index is at 900, its dividend yield is 3% annually, and the futures contract expiring in 2 months is at 902. What is the implied riskless interest rate, i.e., what rate of interest would make 902 the cost of carry price? If you can borrow at 8.00% or lend money at 6.00%, exactly what would you do in this situation, assuming there were no costs or practical problems with doing arbitrage in this market? What would your excess profit be?

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4. You are trying to set up a 1 week hedge for a position of $60 million in PDQ stock. You have the following data computed from the recent prices for PDQ, the S&P 500 spot index and the nearby S&P futures contract.

R_PDQ = 2.41 + 1.23 R_SPCASH

R_PDQ = 1.51 + 1.15 R_SPFUT

PDQ S&P Index March S&P Future

Current level 50 1000.00 1012.50

Mean return 18.00% 15.20% 8.70%

Standard dev 22.00% 15.00% 15.50%

Correlations: PDQ vs S&P Index: 0.83

PDQ vs S&P Future: 0.81

Riskless rate 5.00%

a. With these data, what is the estimate of PDQ's beta relative to the cash index?

b. What hedge ratio should you use to achieve a minimum risk hedge for PDQ?

c. How many March S&P futures contracts would you trade to achieve the minimum risk hedge? (Contract size = $250 times the index.)

d. What will be the standard deviation of the return on the minimum risk hedge?

e. Suppose you only wanted to reduce the exposure to market risk, but not eliminate it entirely. What if you wanted the overall beta of the position to be 0.40. How many futures contracts should you trade? (Assume the beta of the futures is 1.00.)

f. What would be the expected return and standard deviation of the .40 hedged position?

5. Suppose your bank owns $25 million face value of a 6.50 percent coupon 30 year Treasury bond, currently priced at 103 that you are going to hedge with Tbond futures. The futures price is 97. Your research department reports the following results from a regression of past price changes for the bond (DB) regressed on the futures price changes (DF) over the past two years.

DB = 0.050 + 0.951 DF

a) How many futures contracts should you trade if you wanted to minimize the risk in your hedged position?

b) Suppose you trade 185 contracts instead. One month later, the bond price is 107 and the futures price is 99. What was the profit (in dollars) on your cash position, your futures position, and the hedged position? (Don't forget accrued coupon interest. Assume you will accrue 1/12 of the annual coupon.)

c) The chief financial officer would like a report from you on how the hedge (with 185 contracts) worked out. Please give an overall evaluation of the performance of this hedge.