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Chapter 5 Financial Forwards and Futures Multiple Choice 1. KMW, Inc. plans to pay a dividend of $0.50 per share both 3 and 6 months from today. KMW’s share price today is $36.00 and the continuously compounded quarterly interest rate is 1.5%. What is the price of a 6-month prepaid forward contract, which expires immediately after the second dividend? (a) $35.00 (b) $35.02 (c) $36.98 (d) $37.00 Answer: B 2. The S&P 500 Index is priced at $950.46. The annualized dividend yield on the index is 1.40%. What is the price of a 6-month prepaid forward contract on the S & P 500 Index? (a) $943.83 (b) $950.00 (c) $964.26 (d) $984.21 Answer: A 3. HAW, Inc. plans to pay a $1.10 dividend per share in 3 months and a $1.15 dividend in 6 months. HAW’s share price today is $45.60 and the continuously compounded quarterly interest rate is 2.1%. What is the price of a forward contract, which expires immediately after the second dividend? (a) $45.28 (b) $45.96 (c) $45.60 (d) $46.24 Answer: A 4. The S&P 500 Index is priced at $950.46. The annualized dividend yield on the index is 1.40%. The continuously compounded annual interest rate is 8.40%. What is the price of a forward contract that expires 9 months from today? (a) $937.48 (b) $942.66 (c) $984.36 (d) $1001.69 Answer: D 18 McDonald • Derivatives Markets, Second Edition 5. Which of the following statements does NOT accurately reflect the relationship between securities and synthetic forward contracts? (a) Forward stock – zero coupon bond (b) Zero coupon bond stock – forward (c) Prepaid forward forward – zero coupon bond (d) Stock forward zero coupon bond Answer: C 6. The annualized dividend yield on the S&P 500 Index is 1.40%. The continuously compounded interest rate is 6.4%. If the 9-month forward price is $925.28 and the index is priced at $950.46, what is the profit/loss from a cash-and-carry strategy? (a) $25.18 loss (b) $25.18 gain (c) $61.50 loss (d) $61.50 gain Answer: C 7. The price of an S&P 500 Index futures contract is $988.26 when you decide to enter a long position. When the position is closed the futures price is $930.32. If there are no settlement requirements, what is your dollar gain or loss? (Ignore opportunity costs.) (a) $14,485 loss (b) $14,485 gain (c) $57.94 loss (d) $57.94 gain Answer: A 8. The price of an S&P 500 Index futures contract is $988.26 when you decide to enter a long position. When the position is closed the futures price is $930.32. If there are no settlement requirements, what is your percentage gain or loss under a 15.0% margin requirement? (Ignore opportunity costs.) (a) 39% gain (b) 39% loss (c) 43% gain (d) 43% loss Answer: B 9. Consider an investment in five S&P 500 Index futures contracts at a price of $924.80. The initial margin requirement is 15.0% and the maintenance margin is 10.0%. If the continuously compounded interest rate is 5.0% what will the futures price need to be for a margin call to occur 10 days from now? Assume no settlement within the 10 days. (a) $852.64 (b) $872.79 (c) $898.63 (d) $905.25 Answer: B Chapter 5 Financial Forwards and Futures 19 10. The S&P 500 Index price is $925.28 and its annualized dividend yield is 1.40%. LIBOR is 4.2%. How many futures contracts will you need to hedge a $25 million portfolio with a beta of 0.9 for one year? (a) 105 (b) 120 (c) 80 (d) 95 Answer: D 11. Interest rates on the U.S. dollar are 5.4% and euro rates are 4.6%. Given a dollar per euro spot rate of 0.918, what is the 6-month forward rate ($/E)? (a) 0.912 (b) 0.917 (c) 0.922 (d) 0.934 Answer: C 12. Interest rates on the U.S. dollar are 6.5% and euro rates are 5.5%. The dollar per euro spot rate is 0.950. What is the arbitrage profit on a required $1 million Euro payment if the forward rate is 0.980 dollars per Euro and the exchange occurs in one year? (a) $10,000 (b) $21,000 (c) $28,000 (d) $34,000 Answer: B 13. An investor wants to hold 200 euro two years from today. The spot exchange rate is $1.31 per euro. If the euro denominated annual interest rate is 3.0% what is the price of a currency prepaid forward? (a) $200 (b) $206 (c) $231 (d) $247 Answer: D 14. The manager of a blue chip growth stock mutual fund is trying to fully hedge the $650 million portfolio position during the last two months of the calendar year. The current price of the S&P 500 Index futures contract is 1200. If the mutual fund has a beta of 1.24, how many contracts will be needed to hedge the fund? (a) 1,083 (b) 3,033 (c) 242,963 (d) 541,666 Answer: B 20 McDonald • Derivatives Markets, Second Edition 15. The current currency spot rate is $1.31 per euro. If dollar denominated interest rates are 3.0% and euro denominated interest rates are 4.0%, what is the likely dollar per euro exchange rate for a 2 year forward contract? (a) $1.28 (b) $1.30 (c) $1.31 (d) $1.33 Answer: A Short Answer Essay Questions 1. Explain the impact transaction costs have on the ability to make arbitrage profits in forward and futures markets. Answer: The existence of bid-ask spreads, commissions, and taxes take away from profits. The existence of security mispricing and implementation of arbitrage strategies, therefore, may not produce profits if these costs exceed the potential profit. 2. Name some advantages that futures contracts have over forward contracts. Answer: Futures are more liquid and positions are easily closed. Futures eliminate counter party credit risk. Since futures are standardized, opening a position is easier and less expensive. 3. What is the process involved in creating a cash-and-carry strategy? Answer: Buy a tailed position in a security and sell it at time T. Borrow the amount necessary to enter the tailed position and repay the loan at time T. Short a forward contract and close the transaction at time T. 4. What are some uses for index futures contracts? Answer: In no particular order, the most common uses are index arbitrage, asset allocation, cross- hedging, risk management, and controlling transaction costs. Futures can also speed up the investment process as well as provide quick short-term vehicles. 5. Explain the steps necessary to take advantage of an arbitrage opportunity, which may exist between the dollar and yen, when a future yen payment is required. Answer: Rather than lock in the cost of a future yen payment with a forward or futures contract, calculate the PV of the yen payment using yen rates. Convert this figure to dollars at the spot rate. Borrow at the dollar rate, thus locking in your dollar cost. Exchange those funds and place in a yen time deposit account until needed. Class Discussion Question 1. Throughout the chapter the topic of arbitrage is mentioned. Ask the class to explain arbitrage. Follow-up the answers by asking what role arbitrage plays in futures and forward markets. Finish up the Q & A with a group discussion of why arbitrage exists, given the limited opportunity for arbitrage profits. Guide students towards an understanding of the necessity of the arbitrage function, despite the limited opportunity for profit.