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Questions and Answers of
Corporate Finance
A trader buys a call option with a strike price of $30 for $3. Does the trader ever exercise the option and lose money on the trade. Explain.
A trader sells a put option with a strike price of $40 for $5. What is the trader’s maximum gain and maximum loss? How does your answer change if it is a call option?
Trader A enters into a forward contract to buy an asset for $1000 an ounce in one year. Trader B buys a call option to buy the asset for $1000 in one year. The cost of the option is $100. What is the
On June 25, 2012, as indicated in Table 1.2, the spot offer price of Google stock is $561.51 and the offer price of a call option with a strike price of $560 and a maturity date of September is
What is arbitrage? Explain the arbitrage opportunity when the price of a dually listed mining company stock is $50 on the New York Stock Exchange and $52 CAD on the Toronto Stock Exchange. Assume
The price of gold is currently $1,800 per ounce. Forward contracts are available to buy or sell gold at $2,000 per ounce for delivery in one year. An arbitrageur can borrow money at 5% per annum.
In March, a US investor instructs a broker to sell one July put option contract on a stock. The stock price is $42 and the strike price is $40. The option price is $3. Explain what the investor has
Discuss how foreign currency options can be used for hedging in the situation described in Example 1.1 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.5800, (b)
The current price of a stock is $94, and three-month call options with a strike price of $95 currently sell for $4.70. An investor who feels that the price of the stock will increase is trying to
A trader buys a European call option and sells a European put option. The options have the same underlying asset, strike price and maturity. Describe the trader’s position. Under what
On June 25, 2012, an investor owns 100 Google shares. As indicated in Table 1.3, the bid share price is $561.32 and a December put option with a strike price $520 costs $26.10. The investor is
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next four months?
A stock when it is first issued provides funds for a company. Is the same true of an exchange-traded stock option? Discuss.
One orange juice future contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2013 a company sells a March 2015 orange juice futures contract for 120 cents per pound. In
Explain how margin protect investors against the possibility of default.
A trader buys two July 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 margin is $6,000 per
Show that, if the futures price of a commodity is greater than the spot price during the delivery period, then there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures
Explain the difference between a market-if-touched order and a stop order.
Explain what a stop-limit order to sell at 20.30 with a limit of 20.10 means.
At the end of one day a clearing house member is long 100 contracts, and the settlement price is $50,000 per contract. The original margin is $2,000 per contract. On the following day the member
On July 1, 2013, a Japanese company enters into a forward contract to buy $1 million with yen on January 1, 2014. On September 1, 2013, it enters into a forward contract to sell $1 million on January
The forward price on the Swiss franc for delivery in 45 days is quoted as 1.1000. The futures price for a contract that will be delivered in 45 days is 0.9000. Explain these two quotes. Which is more
Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.
“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.
A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead
Explain the difference between bilateral and central clearing for OTC derivatives.
What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?
“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.
Suppose that on October 24, 2013, a company sells one April 2014 live-cattle futures contract. It closes out its position on January 21, 2014. The futures price (per pound) is 91.20 cents when it
Explain how CCPs work. What are the advantages to the financial system of requiring all standardized derivatives transactions to be cleared through CCPs?
Trader A enters into futures contracts to buy 1 million euros for 1.4 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange (dollars per euro)
Explain what is meant by open interest. Why does the open interest usually decline during the month preceding the delivery month? On a particular day, there were 2,000 trades in a particular futures
Suppose that there are no storage costs for crude oil and the interest rate for borrowing or lending is 5% per annum. How could you make money if the June and December futures contracts for a
A company has derivatives transactions with Banks A, B, and C which are worth +$20 million, −$15 million, and −$25 million, respectively to the company. How much margin or collateral does the
A bank’s derivatives transactions with a counterparty are worth +$10 million to the bank and are cleared bilaterally. The counterparty has posted $10 million of cash collateral. What credit
The author’s Web page (www.rotman.utoronto.ca/~hull/data) contains daily closing prices for crude oil futures contract and gold futures contract. You are required to download the data and answer
A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the
Explain why a short hedger’s position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.
Imagine you are the treasurer of a Japanese company exporting electronic equipment to the United States. Discuss how you would design a foreign exchange hedging strategy and the arguments you would
Suppose that in Example 3.4 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?
“If the minimum-variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true? Explain your answer.
“If there is no basis risk, the minimum variance hedge ratio is always 1.0." Is this statement true? Explain your answer.
“For an asset where futures prices are usually less than spot prices, long hedges are likely to be particularly attractive." Explain this statement.
The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest
A corn farmer argues “I do not use futures contracts for hedging. My real risk is not the price of corn. It is that my whole crop gets wiped out by the weather.”Discuss this viewpoint. Should the
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 decides
Suppose that in Table 3.5 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?
A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the last year the risk-free rate was 5% and equities performed very badly providing a return of −30%. The
A futures contract is used for hedging. Explain why the daily settlement of the contract can give rise to cash flow problems.
The expected return on the S&P 500 is 12% and the risk-free rate is 5%. What is the expected return on the investment with a beta of (a) 0.2, (b) 0.5, (c) 1.4?
It is now June. A company knows that it will sell 5,000 barrels of crude oil in September. It uses the October CME Group futures contract to hedge the price it will receive. Each contract is on 1,000
Sixty futures contracts are used to hedge an exposure to the price of silver. Each futures contract is on 5,000 ounces of silver. At the time the hedge is closed out, the basis is $0.20 per ounce.
It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the CME December futures contract on the S&P 500 to change the
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.
It is now October 2013. A company anticipates that it will purchase 1 million pounds of copper in each of February 2014, August 2014, February 2015, and August 2015. The company has decided to use
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
A trader owns 55,000 units of a particular asset and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot
In the Chicago Board of Trade’s corn futures contract, the following delivery months are available: March, May, July, September, and December. State the contract that should be used for hedging
Does a perfect hedge always succeed in locking in the current spot price of an asset for a future transaction? Explain your answer.
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?
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the cash price of a bond
A three-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond’s yield?
Suppose that the 6-month, 12-month, 18-month, and 24-month zero rates are 5%, 6%, 6.5%, and 7% respectively. What is the two-year par yield?
Suppose that zero interest rates with continuous compounding are as follows: Maturity( years) Rate (% per annum) 1 ……………………………………. 2.0 2
Use the rates in Problem 4.14 to value an FRA where you will pay 5% for the third year on $1 million. In problem 4.14 Maturity( years) Rate (% per annum) 1
A 10-year, 8% coupon bond currently sells for $90. A 10-year, 4% coupon bond currently sells for $80. What is the 10-year zero rate? (Hint: Consider taking a long position in two of the 4% coupon
Explain carefully why liquidity preference theory is consistent with the observation that the term structure of interest rates tends to be upward sloping more often than it is downward sloping.
“When the zero curve is upward sloping, the zero rate for a particular maturity is greater than the par yield for that maturity. When the zero curve is downward sloping the reverse is true.”
Why are U.S. Treasury rates significantly lower than other rates that are close to risk free?
A bank can borrow or lend at LIBOR. The two-month LIBOR rate is 0.28% per annum with continuous compounding. Assuming that interest rates cannot be negative, what is the arbitrage opportunity if the
Why does a loan in the repo market involve very little credit risk?
Explain why an FRA is equivalent to the exchange of a floating rate of interest for a fixed rate of interest?
Explain how a repo agreement works and why it involves very little risk for the lender.
When compounded annually an interest rate is 11%. What is the rate when expressed with (a) Semiannual compounding, (b) Quarterly compounding, (c) Monthly compounding, (d) Weekly compounding, (e)
The following table gives Treasury zero rates and cash flows on a Treasury bond:Zero rates are continuously compounded (a) What is the bonds theoretical price? (b) What is the
A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that can be locked in for the period between six months and nine months using an FRA
An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with? (a) Annual compounding, (b) Monthly compounding, (c) Continuous compounding.
The 6-month, 12-month. 18-month and 24-month zero rates are 4%, 4.5%, 4.75%, and 5% with semiannual compounding. a) What are the rates with continuous compounding? b) What is the forward rate for the
What is the two-year par yield when the zero rates are as in Problem 4.30? What is the yield on a two-year bond that pays a coupon equal to the par yield?
The following table gives the prices of bonds*Half the stated coupon is paid every six monthsa) Calculate zero rates for maturities of 6 months, 12 months, 18 months, and 24 months. b) What are the
The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay
What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding?
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 November,
Suppose that the risk-free interest rate is 10% 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
Estimate the difference between short-term interest rates in Japan and the United States on July 13, 2012 from the information in Table 5.4.
The two-month interest rates in Switzerland and the United States are 2% and 5% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is $0.8000. The futures price
The current price of silver is $30 per ounce. The storage costs are $0.48 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate
Suppose that F1 and F2 are two futures prices on the same commodity where the times to maturity of the contracts are t1 and t2 with t2 > t1. Prove that
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 daily
It is sometimes argued that a forward exchange rate is an unbiased predictor of future exchange rates. Under what circumstances is this so?
Show that the growth rate in an index futures price equals the excess return of the portfolio underlying the index over the risk-free rate. Assume that the risk-free interest rate and the dividend
A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all
Show that equation (5.3) is true by considering an investment in the asset combined with a short position in a futures contract. Assume that all income from the asset is reinvested in the asset. Use
Explain carefully what is meant by the expected price of a commodity on a particular future date. Suppose that the futures price of crude oil declines with the maturity of the contract at the rate of
The Value Line Index is designed to reflect changes in the value of a portfolio of over 1,600 equally weighted stocks. Prior to March 9, 1988, the change in the index from one day to the next was
What is meant by (a) An investment asset (b) A consumption asset. Why is the distinction between investment and consumption assets important in the determination of forward and futures prices?
What is the cost of carry for (a) A non-dividend-paying stock, (b) A stock index, (c) A commodity with storage costs, (d) A foreign currency?
In early 2012, the spot exchange rate between the Swiss Franc and U.S. dollar was 1.0404 ($ per franc). Interest rates in the U.S. and Switzerland were 0.25% and 0% per annum, respectively, with
A bank offers a corporate client a choice between borrowing cash at 11% per annum and borrowing gold at 2% per annum. (If gold is borrowed, interest must be repaid in gold. Thus, 100 ounces borrowed
A company that is uncertain about the exact date when it will pay or receive a foreign currency may try to negotiate with its bank a forward contract that specifies a period during which delivery can
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