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principles corporate finance

Questions and Answers of Principles Corporate Finance

18.22. Use the DerivaGem software to value a European swap option that gives you the right in two years to enter into a 5-year swap in which you pay a fixed rate of 6% and receive floating. Cash
18.21. Use the DerivaGem software to value a five-year collar that guarantees that the maximum and minimum interest rates on a LIBOR-based loan (with quarterly resets) are 5% and 7%, respectively.
18.20. Suppose that the LIBOR yield curve is flat at 8% with annual compounding. A swaption gives the holder the right to receive 7.6% in a five-year swap starting in four years. Payments are made
18.19. Calculate the price of a cap on the three-month LIBOR rate in nine months' time for a principal amount of $1,000. Use Black's model and the following information: Quoted nine-month Eurodollar
18.16. Explain why there is an arbitrage opportunity if the implied Black (flat) volatility for a cap is different from that for a floor. Do the broker quotes in Table 18.2 present an arbitrage
18.15. Show that V1 + f = V2 where V is the value of a swap option to pay a fixed rate of Rx and receive LIBOR between times T1 and T2, f is the value of a forward swap to receive a fixed rate of Rx
18.14. Suppose that the 1-year, 2-year, 3-year, 4-year and 5-year zero rates are 6%, 6.4%, 6.7%, 6.9%, and 7%. The price of a 5-year semiannual cap with a principal of $100 at a cap rate of 8% is $3.
18.13. What other instrument is the same as a five-year zero-cost collar in which the strike price of the cap equals the strike price of the floor? What does the common strike price equal?
18.12. Explain carefully how you would use (a) spot volatilities and (b) flat volatilities to value a five-year cap.
18.11. A corporation knows that in three months it will have $5 million to invest for 90 days at LIBOR minus 50 basis points and wishes to ensure that the rate obtained will be at least 6.5%. What
18.8. A bank uses Black's model to price European bond options. Suppose that an implied price volatility for a 5-year option on a bond maturing in 10 years is used to price a 9-year option on the
18.7. What are the advantages of yield curve models over the Black's model for valuing interest rate derivatives?
18.5. Suppose that the LIBOR yield curve is flat at 8% with annual compounding. A swaption gives the holder the right to receive 7.6% in a five-year swap starting in four years. Payments are made
18.4. Use Black's model to value a 1-year European put option on a 10-year bond. Assume that the current value of the bond is $125, the strike price is $110, the 1-year interest rate is 10% per
18.3. Explain why a swaption can be regarded as a type of bond option.
18.2. Explain the features of (a) callable and (b) puttable bonds.
17.14. How would you use the binomial tree approach to value an American option on a stock index when the dividend yield on the index is a function of time?
17.13. How would you use the control variate approach to improve the estimate of the delta of an American option when the binomial tree approach is used?
17.7. Explain why Monte Carlo simulation cannot be used to value American options.
17.3. Explain how the control variate technique is implemented.
16.24. Suppose that in Problem 16.23 the price of silver at the close of trading yesterday was $8, its volatility was estimated as 1.5% per day, and its correlation with gold was estimated as 0.8.
16.23. Suppose that the price of gold at close of trading yesterday was $300, and its volatility was estimated as 1.3% per day. The price at the close of trading today is $298. Update the volatility
16.19. Suppose that in Problem 16.18 the correlation between the S&P 500 Index (measured in dollars) and the FT-SE 100 Index (measured in sterling) is 0.7, the correlation between the S&P 500 index
16.18. Suppose that the daily volatility of the FT-SE 100 stock index (measured in pounds sterling) is 1.8% and the daily volatility of the dollar/sterling exchange rate is 0.9%. Suppose further that
16.14. Suppose that the 5-year rate is 6%, the 7-year rate is 7% (both expressed with annual compounding), the daily volatility of a 5-year zero-coupon bond is 0.5%, and the daily volatility of a
16.13. Verify that the 0.3-year zero-coupon bond in the cash-flow mapping example in the end- of-chapter Appendix is mapped in a $37,397 position in a three-month bond and a $11,793 position in a
16.12. Explain why the linear model can provide only approximate estimates of VaR for a portfolio containing options.
16.11. Explain how an interest rate swap is mapped into a portfolio of zero-coupon bonds with standard maturities for the purposes of a VaR calculation.
16.10. The volatility of a certain market variable is 30% per annum. Calculate a 99% confidence interval for the size of the percentage daily change in the variable.
16.8. Explain the difference between value at risk and conditional value at risk.
16.6. Suppose you know that the gamma of the portfolio in the previous quiz question is 16.0. How does this change your estimate of the relationship between the change in the portfolio value and the
16.4. A company uses an EWMA model for forecasting volatility. It decides to change the parameter from 0.95 to 0.85. Explain the likely impact on the forecasts.
16.3. Consider a position consisting of a $300,000 investment in asset A and a $500,000 investment in asset B. Assume that the daily volatilities of the assets are 1.8% and 1.2%, respectively, and
16.1. Explain the exponentially weighted moving average (EWMA) model for estimating volatility from historical data.
15.24. Consider again the situation in Problem 15.23. Suppose that a second traded option with a delta of 0.1, a gamma of 0.5, and a vega of 0.6 is available. How could the portfolio be made delta,
15.20. Does a forward contract on a stock index have the same delta as the corresponding futures contract? Explain your answer.
15.18. Show by substituting for the various terms in equation (15.7) that the equation is true for:a. A single European call option on a non-dividend-paying stockb. A single European put option on a
15.17. Repeat Problem 15.16 on the assumption that the portfolio has a beta of 1.5. Assume that the dividend yield on the portfolio is 4% per annum.
15.15. Under what circumstances is it possible to make a European option on a stock index both gamma neutral and vega neutral by adding a position in one other European option?
15.13. Repeat Problem 15.12 for a financial institution with a portfolio of short positions in put and call options for a currency.
15.11. In Problem 15.10, what initial position in nine-month silver futures is necessary for delta hedging? If silver itself is used, what is the initial position? If one-year silver futures are
15.8. The Black-Scholes price of an out-of-the-money call option with an exercise price of $40 is $4. A trader who has written the option plans to use a stop-loss strategy. The trader's plan is to
15.7. Why did portfolio insurance not work well on October 19, 1987?
15.5. What is meant by the gamma of an option position? What are the risks in the situation where the gamma of a position is large and negative and the delta is zero?
15.2. What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 options be made delta neutral when the delta of each option is 0.7?
15.1. Explain how a stop-loss hedging scheme can be implemented for the writer of an out-of- the-money call option. Why does it provide a relatively poor hedge?
2.1. Distinguish between the terms open interest and trading volume.
2.2. What is the difference between a local and a commission broker.
2.3. Suppose that you enter into a short futures contract to sell July silver for $5.20 per ounce on the New York Commodity Exchange. The size of the contract is 5,000 ounces. The initial margin is
2.4. Suppose that in September 2000 you take a long position in a contract on May 2001 crude oil futures. You close out your position in March 2001. The futures price (per barrel) is $18.30 when you
2.5. What does a stop order to sell at $2 mean? When might it be used? What does a limit order to sell at $2 mean? When might it be used?
2.9. What are the most important aspects of the design of a new futures contract?
2.10. Explain how margins protect investors against the possibility of default.
2.11. An investor enters into two long futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial
2.12. Show that if the futures price of a commodity is greater than the spot price during the delivery period there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures
2.13. Explain the difference between a market-if-touched order and a stop order.
2.14. Explain what a stop-limit order to sell at 20.30 with a limit of 20.10 means.
2.16. On July 1, 2001, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2002. On September 1, 2001, it enters into a forward contract to sell 10 million Japanese
2.17. The forward price on the Swiss franc for delivery in 45 days is quoted as 1.8204. The futures price for a contract that will be delivered in 45 days is 0.5479. Explain these two quotes. Which
2.18. Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.
2.19. "Speculation in futures markets is pure gambling. It is not in the public interest to allow speculators to trade on a futures exchange." Discuss this viewpoint.
2.20. Identify the contracts with the highest open interest in Table 2.2. Consider each of the following sections separately: grains and oilseeds, livestock and meat, food and fiber, and metals and
2.21. What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?
2.22. "When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one." Explain this statement.
2.23. Suppose that on October 24, 2001, you take a short position in an April 2002 live-cattle futures contract. You close out your position on January 21, 2002. The futures price (per pound) is
2.25. Suppose that on March 15, 2001, speculators tended to be short Sugar-World futures and hedgers tended to be long Sugar-World futures. What does the Keynes and Hicks argument imply about the
2.26. Suppose that corn can be stored for 20 cents per bushel per year and the risk-free interest rate is 5% per year. How could you make money in the corn market on March 15, 2001, by trading the
2.27. "A long forward contract is equivalent to a long position in a call option and a short position in a put option." Explain this statement.
3.2. Explain what happens when an investor shorts a certain share.
3.3. Suppose that you enter into a six-month forward contract on a non-dividend-paying stock when the stock price is $30 and the risk-free interest rate (with continuous compounding) is 12% per
3.9. What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding?
3.10. A deposit account pays 12% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?
3.13. Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and
3.15. Estimate the difference between short-term interest rates in Mexico and the United States on March 15, 2001, from the information in Table 3.8.
3.16. The two-month interest rates in Switzerland and the United States are 3% and 8% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is $0.6500. The futures
3.17. The current price of silver is $9 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities,
3.18. Suppose that F1 and F2 are two futures contracts on the same commodity with times to maturity t and t, where t > t. Prove thatwhere r is the interest rate (assumed constant) and there are no
3.19. When a known future cash outflow in a foreign currency is hedged by a company using a forward contract, there is no foreign exchange risk. When it is hedged using futures contracts, the
3.20. It is sometimes argued that a forward exchange rate is an unbiased predictor of future exchange rates. Under what circumstances is this so?
3.21. Show that the growth rate in an index futures price equals the excess return of the index over the risk-free rate. Assume that the risk-free interest rate and the dividend yield are constant.
3.22. Show that equation (3.7) is true by considering an investment in the asset combined with a short position in a futures contract. Assume that all income from the asset is reinvested in the
3.26. A foreign exchange trader working for a bank enters into a long forward contract to buy 1 million pounds sterling at an exchange rate of 1.6000 in three months. At the same time, another trader
3.27. A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $250 per ounce and sell gold for $249 per ounce. The trader can borrow funds at 6% per year and
4.1. Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
4.2. Explain what is meant by basis risk when futures contracts are used for hedging.
4.4. Under what circumstances does a minimum variance hedge portfolio lead to no hedging at all?
4.5. Give three reasons that the treasurer of a company might not hedge the company's exposure to a particular risk.
4.7. A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on the S&P 500 to hedge its risk. The index is currently standing at 1080, and each contract is
4.12. Suppose that in Table 4.5 the company decides to use a hedge ratio of 0.8. How does the decision affect the way in which the hedge is implemented and the result?
4.14. "If there is no basis risk, the minimum variance hedge ratio is always 1.0." Is this statement true? Explain your answer.
4.15. "When the convenience yield is high, long hedges are likely to be particularly attractive." Explain this statement. Illustrate it with an example.
4.18. On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and
4.19. Suppose that in Table 4.9 the company decides to use a hedge ratio of 1.5. How does the decision affect the way the hedge is implemented and the result?
4.20. A U.S. company is interested in using the futures contracts traded on the CME to hedge its Australian dollar exposure. Definer as the interest rate (all maturities) on the U.S. dollar and ry as
4.21. The following table gives data on monthly changes in the spot price and the futures price for a certain commodity. Use the data to calculate a minimum variance hedge ratio. Spot price change
4.23. It is now October 2001. A company anticipates that it will purchase 1 million pounds of copper in each of February 2002, August 2002, February 2003, and August 2003. The company has decided to
4.24. A fund manager has a portfolio worth $50 million with a beta of 0.87. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures
5.1. It is January 9, 2001. The price of a Treasury bond with a 12% coupon that matures on October 12, 2009, is quoted as 102-07. What is the cash price?
5.3. The term structure is upward sloping. Put the following in order of magnitude:a. The five-year zero rateb. The yield on a five-year coupon-bearing bondc. The forward rate corresponding to the
5.4. The six-month and one-year zero rates are both 10% per annum. For a bond that lasts 18 months and pays a coupon of 8% per annum (with a coupon payment having just been made), the yield is 10.4%

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