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Questions and Answers of
Corporate Finance
Give three reasons why the treasurer of a company might not hedge the company's exposure to a particular risk.
Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the
A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on a stock index to hedge its risk. The index futures is currently standing at 1080, and each contract
In the corn futures contract, the following delivery months are available: March, May, July, September, and December. State the contract that should be used for hedging when the expiration of the
A bank quotes you an interest rate of 7% per annum with quarterly compounding. What is the equivalent rate with(a) Continuous compounding(b) Annual compounding?
A deposit account pays 4% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are, respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding. Estimate the cash price of a bond
Explain how LIBOR is determined
A five-year bond with a yield of 7% (continuously compounded) pays an 8% coupon at the end of each year.a) What is the bond's price?b) What is the bond's duration?c) Use the duration to calculate the
"An interest rate swap where six-month LIBOR is exchanged for a fixed rate 5% on a principal of $100 million for five years is a portfolio of nine FRAs." Explain this statement.
Suppose that 3-month, 6-month, 12-months, 2-year, and 3-year OIS rates are 2.0%, 2.5%, 3.2%, 4.5%, and 5%, respectively. The 3-month, 6-month and 12-month OISs involve a single exchange at maturity;
The six-month and one-year zero rates are both 5% per annum. For a bond that has a life of 18 months and pays a coupon of 4% per annum (with semiannual payments and one having just been made), the
Suppose that risk-free rates are as in Problem 4.30. What is the value of an FRA where the holder pays LIBOR and receives 7% (semiannually compounded for a six-month period beginning in 18 months.
Verify that DerivaGem agrees with the price of the bond in Section 4.6. Test how well DV01 predicts the effect of a one-basis point increase in all rates. Estimate the duration of the bond from DV01.
An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum witha) Annual compounding,b) Semiannual compounding,c) Monthly
Suppose that zero interest rates with continuous compounding are as follows: Maturity (months) Rate (% per
Assuming that risk-free rates are as in Problem 4.5, what is the value of an FRA where the holder will pay LIBOR and receive 4.5% (quarterly compounded) for a three-month period starting in one year
What does duration tell you about the sensitivity of a bond portfolio to interest rates? What are the limitations of the duration measure?
Explain what happens when an investor shorts a certain share.
The risk-free rate of interest is 7% per annum with continuous compounding, and the dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What is the six-month
Assume that the risk-free interest rate is 4% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and November,
Suppose that the risk-free interest rate is 6% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price
The two-month interest rates in Switzerland and the United States are, respectively, 1% and 2% per annum with continuous compounding. The spot price of the Swiss franc is $1.0500. The futures price
The spot price of silver is $25 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 5% per annum for all maturities, calculate the
A U.S. company is interested in using the futures contracts traded by the CME Group to hedge its Australian dollar exposure. Define r as the interest rate (all maturities) on the U.S. dollar and rf
An index is 1,200. The three-month risk-free rate is 3% per annum and the dividend yield over the next three months is 1.2% per annum. The six-month risk-free rate is 3.5% per annum and the dividend
Suppose the current USD/euro exchange rate is 1.2000 dollar per euro. The six month forward exchange rate is 1.1950. The six month USD interest rate is 1% per annum continuously compounded?
The spot price of oil is $50 per barrel and the cost of storing a barrel of oil for one year is $3, payable at the end of the year. The risk-free interest rate is 5% per annum, continuously
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 5% per annum. What
A stock index currently stands at 350. The risk-free interest rate is 4% per annum (with continuous compounding) and the dividend yield on the index is 3% per annum. What should the futures price for
Explain carefully why the futures price of gold can be calculated from its spot price and other observable variables whereas the futures price of copper cannot.
Explain carefully the meaning of the terms convenience yield and cost of carry. What is the relationship between futures price, spot price, convenience yield, and cost of carry?
Explain why a foreign currency can be treated as an asset providing a known yield.
A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 5% per annum with continuous compounding.a) What are
A U.S. Treasury bond pays a 7% coupon on January 7 and July 7. How much interest accrues per $100 of principal to the bond holder between July 7, 2017 and August 8, 2017? How would your answer be
It is July 30, 2018. The cheapest-to-deliver bond in a September 2018 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2018. Coupon payments
Suppose that the 300-day LIBOR zero rate is 4% and Eurodollar quotes for contracts maturing in 300, 398 and 489 days are 95.83, 95.62, and 95.48. Calculate 398-day and 489-day LIBOR zero rates.
Between October 30, 2018, and November 1, 2018, you have a choice between owning a U.S. government bond paying a 12% coupon and a U.S. corporate bond paying a 12% coupon. Consider carefully the day
It is January 9, 2018. The price of a Treasury bond with a 6% coupon that matures on October 12, 2030, is quoted as 102-07. What is the cash price?
It is April 7, 2017. The quoted price of a U.S. government bond with a 6% per annum coupon (paid semiannually) is 120-00. The bond matures on July 27, 2033. What is the cash price? How does your
A Eurodollar futures quote for the period between 5.1 and 5.35 year in the future is 97.1. The standard deviation of the change in the short-term interest rate in one year is 1.4%. Estimate the
It is March 10, 2017. The cheapest-to-deliver bond in a December 2017 Treasury bond futures contract is an 8% coupon bond, and delivery is expected to be made on December 31, 2017. Coupon payments on
A Canadian company wishes to create a Canadian LIBOR futures contract from a U.S. Eurodollar futures contract and forward contracts on foreign exchange. Using an example, explain how the company
How is the conversion factor of a bond calculated by the CME Group? How is it used?
On June 25, 2017, the futures price for the June 2017 bond futures contract is 118-23.a) Calculate the conversion factor for a bond maturing on January 1, 2033, paying a coupon of 10%.b) Calculate
A Eurodollar futures price changes from 96.76 to 96.82. What is the gain or loss to an trader who is long two contracts?
What is the purpose of the convexity adjustment made to Eurodollar futures rates? Why is the convexity adjustment necessary?
It is January 30. You are managing a bond portfolio worth $6 million. The duration of the portfolio in six months will be 8.2 years. The September Treasury bond futures price is currently 108-15, and
It is May 5, 2017. The quoted price of a government bond with a 12% coupon that matures on July 27, 2034, is 110-17. What is the cash price?
A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 4% per annum and pays six-month LIBOR on a principal of $10 million for five
"Nonfinancial companies with high credit risks are the ones that cannot access fixed-rate markets directly. They are the companies that are most likely to be paying fixed and receiving floating in an
Six-month LIBOR is 5%. LIBOR forward rates for the 6- to 12-month period and for the 12- to 18-month period are both 5.5%. Swap rates for 2- and 3-year semiannual pay swaps are 5.4% and 5.6%,
A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, six-month LIBOR is exchanged for 4% per annum (compounded semiannually). Six-month LIBOR forward
Explain what a seven-year swap rate is.
A currency swap has a remaining life of 15 months. It involves exchanging interest at 10% on £20 million for interest at 6% on $30 million once a year. The term structure of risk-free interest rates
Explain the difference between the credit risk and the market risk in a financial contract.
A corporate treasurer tells you that he has just negotiated a five-year loan at a competitive fixed rate of interest of 5.2%. The treasurer explains that he achieved the 5.2% rate by borrowing at
A bank enters into an interest rate swap with a nonfinancial counterparty using bilateral clearing where it is paying a fixed rate of 3% and receiving LIBOR. No collateral is posted and no other
What was the role of GNMA (Ginnie Mae) in the mortgage-backed securities market of the 1970s?
Explain what is meant by a) an ABS and b) an ABS CDO.
What is a mezzanine tranche?
What is the waterfall in a securitization?
What are the numbers in Table 8.1 for a loss rate of a) 12% and b) 15%?
Why do you think the increase in house prices during the 2000 to 2007 period is referred to as a bubble?
Why did mortgage lenders frequently not check on information provided by potential borrowers on mortgage application forms during the 2000 to 2007 period?
Explain what CVA and DVA measure?
Explain how the "cure period" is used in the calculation of CVA.
A company is trying to decide between issuing debt and equity to fulfill a funding need. What in theory should happen to the return required by equity holders if it chooses (a) debt and (b) equity.
Explain the meaning of "netting." Suppose no collateral is posted. Why does a netting agreement usually reduce credit risks to both sides. Under what circumstances does netting have no effect on
The average funding cost for a company is 5% per annum when the risk-free rate is 3%. The company is currently undertaking projects worth $9 million. It plans to increase its size by undertaking $1
Suppose that, for a particular three-year derivative entered into by a bank, two outcomes, A and B, are equally likely. Under outcome A, the values of the derivative at the mid-point of the first,
If the market considers that the default probability for a bank has increased, what happens to its DVA? What happens to the income it reports?
"The impact of DVA on earnings volatility is generally greater than that of CVA." Explain this statement.
Explain what MVA and FVA measure.
Explain the difference between the views of financial economists and most practitioners on how MVA and FVA should be calculated.
Explain what KVA measures.
Explain the difference between the views of financial economists and most practitioners on how KVA should be calculated.
Explain why FVA can be calculated for a transaction without considering the portfolio to which the transaction belongs, but that the same is not true of MVA.
Suppose that a bank buys an option from a client. The option is uncollateralized and there are no other transactions outstanding with the client. The expected values of the option at the mid-point of
An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the
An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the
Options on General Motors stock are on a March, June, September, and December cycle. What options trade on (a) March 1, (b) June 30, (c) August 5?
An investor sells a European call option with strike price of K and maturity T and buys a put with the same strike price and maturity. Describe the investor's position.
Explain why margin accounts are required when clients write options but not when they buy options.
A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b) May 30?
A company declares a 2-for-1 stock split. Explain how the terms change for a call option with a strike price of $60.
"Employee stock options issued by a company are different from regular exchange-traded call options on the company's stock because they can affect the capital structure of the company." Explain this
List the six factors affecting stock option prices.
What is a lower bound for the price of a four-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?
What is the impact (if any) of negative interest rates on: a) The put-call parity result for European options b) The result that American call options on non-dividend-paying stocks should never be
What is a lower bound for the price of a one-month European put option on a non-dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per
Consider a put option on a non-dividend-paying stock when the stock price is $40, the strike price is $42, the risk-free rate of interest is 2%, the volatility is 25% per annum, and the time to
Give two reasons that the early exercise of an American call option on a non-dividend-paying stock is not optimal. The first reason should involve the time value of money. The second reason should
"The early exercise of an American put is a trade-off between the time value of money and the insurance value of a put." Explain this statement.
The price of a non-dividend paying stock is $19 and the price of a three-month European call option on the stock with a strike price of $20 is $1. The risk-free rate is 4% per annum. What is the
What is meant by a protective put? What position in call options is equivalent to a protective put?
Explain two ways in which a bear spread can be created.
Explain the statement at the end of Section 12.1 that, when dividends are zero, the principal protected note cannot be profitable for the bank no matter how long it lasts.
A trader creates a bear spread by selling a six-month put option with a $25 strike price for $2.15 and buying a six-month put option with a $29 strike price for $4.75. What is the initial
A trader sells a strangle by selling a call option with a strike price of $50 for $3 and selling a put option with a strike price of $40 for $4. For what range of prices of the underlying asset
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