derivatives

1. Suppose you short a one year forward on one share of Dell Stock at $13.65. One year later the spot price of Dell stock is $12.
a. What is the payoff of the forward to you?
b. What is the payoff to your counter party?

2. A two-year forward contract on ABC stock is available. The risk free interest rate is 2% and the spot price of the stock is $100. The stock does not pay any dividends. The forward is priced at $104.24.
a. Examine whether an arbitrage opportunity exists.
b. If there is an arbitrage opportunity, show the arbitrage strategy and calculate the arbitrage profit for each forward contract involved.

3. Sara has longed a forward contract. Her forward contract was initiated one year ago and still has one year to go. The forward price is $100. The underlying spot price right now is $104. The interest rate is 2%. To understand the value of her forward contract Sara forms a mimicking portfolio: she longs one unit of the underlying asset and takes out a loan. Assume the mimicking portfolio is correctly constructed, calculate the amount that she has borrowed (the loan size).

4. Calculate the profit from longing the futures contract. Each contract covers 10 units of underlying assets.
Trading Day Settlement Price ($) Opening Balance ($) Mark to Market Gain/Loss ($) Deposits or Withdrawals ($) Closing Balance ($) Margin Call? Can Withdraw Money?
0 550 0 0 200 200 No No
1 555 200 -50 0 150 No No
2 562 150 -70 0 80 Yes No
3 559 80 30 120 230 No Yes
4 565 230 -60 -30 140 No No
5 570 140 -50 0 90 Yes No
6 573 90 -30 110 170 No No

5. For each of the following situations, determine whether a long or short hedge is appropriate. Justify your answers.
a. A firm anticipates issuing stock in three months.
b. An investor plans to buy a bond in 30 days.
c. A firm plans to sell some foreign currency denominated assets and convert the proceeds to domestic currency.

6. On June 17 of a particular year, an American watch dealer decided to import 100,000 Swiss watches. Each watch costs SF225. The dealer would like to hedge against a change in the dollar/Swiss franc exchange rate. The forward rate was $0.3881. Determine the outcome from the hedge if it was closed on August 16, when the spot rate was $0.4434.

7. On January 2 of a particular year, an American firm decided to close out its account at a Canadian bank on February 28. The firm is expected to have 5 million Canadian dollars in the account at the time of the withdrawal. It would convert the funds to U.S. dollars and transfer them to a New York bank. The relevant spot foreign exchange rate was $0.7564. The March Canadian dollar futures contract was priced at $0.7541. Determine the outcome of a futures hedge if on February 28 the spot rate was $0.7207 and the futures rate was $0.7220. All prices are in U.S. dollars per Canadian dollar. The Canadian dollar futures contract covers CD 100,000.

8. You are the manager of a bond portfolio of $10 million face value of bonds worth $9,448,456. The portfolio has a yield of 12.25% and a duration of 8.33. You plan to liquidate the portfolio in six months and are concerned about an increase in interest rates that would produce a loss on the portfolio. You would like to lower its duration to 5 years. A T-bond futures contract with the appropriate expiration is priced at 72 3/32 with a face value of $100,000, an implied yield of 12%, and an implied duration of 8.43 years.

a. Should you buy or sell futures? How many contracts should you use?
b. In six months, the portfolio has fallen in value to $8,952,597. The futures price is 68 16/32. Determine the profit from the transaction.

9. (Structure and Use of a Typical FRA) Suppose you long a 90-day LIBOR-based FRA with notional amount of $50 million. At expiration, LIBOR is 4 % and the forward rate is 3%. Assuming a 360-day year, what is the dollar profit or loss on this FRA? How would your answer change if you were short? (Textbook ed.10 chap. 12 #6 / ed.9 Chap.13 #6)

10. (Structure and Use of a Typical FRA) Suppose you are long a 180-day LIBOR-based FRA with notional amount of $50 million. At expiration, LIBOR is 4% and the forward rate is 3%. Assuming a 360-day year, what is the dollar profit or loss on this FRA? (Textbook ed.10 chap. 12 #7 / ed. 9 Chap 13 #7)

11. (Quotation of a FRA) The following term structure of LIBOR is given. (Textbook ed.10 chap. 12 #10/ ed.9 chap 13. #10)
Term (days) Rate (%)
90 6
180 6.2
270 6.3
360 6.35

a. Find the rate on a new 6×9 FRA.
b. Consider an FRA that was established previously at a rate of 5.2% with a notional amount of $30 million. The FRA expires in 180 days, and the underlying is 180-day LIBOR. Find the value of the FRA for the long.