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business
options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

Explain why an FRA is equivalent to the exchange of a floating rate of interest for a fixed rate of interest.
Why does a loan in the repo market involve very little credit risk?
Why are US Treasury rates significantly lower than other rates that are close to risk-free?
"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." Explain
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.
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 bonds
Use the rates in Problem 4.14 to value an FRA where you will pay 5% (compounded anually) for the third year on $1 million.
Suppose that zero interest rates with continuous compounding are as follows:Maturity,(years) Rate (% per annum)1 2.0 2 3.0 3.7 4.2 A L11-IXUJ 4.5 A A Calculate forward interest rates for the second,
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 2-year par yield? F
A 3-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond’s yield? T T
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
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?
What rate of interest with continuous compounding is equivalent to 15% perannum with monthly compounding? A -
What does duration tell you about the sensitivity of a bond portfolio to interest rates.What are the limitations of the duration measure? 5
The term structure of interest rates is upward:-sloping. Put the following in order of magnitude: - - -(a) The 5-year zero rate , 2 ,(b) The yield on a 5-year coupon-bearing bond(c) The forward rate
Assuming that zero rates are as in Problem 4.5, what is the value of an FRA that enables the holder to earn 9.5% for a 3-month period starting in 1 year on a principal of$1,000,000? The interest rate
Suppose that zero interest rates with continuous compounding are as follows:Maturity (months) (Rate (% per annum), 3 8.0 6 8.2 9 8.4 12 8.5 15 8.6. 18 . 8.7 . .Calculate forward interest rates for
An investor receives ‘$1,100 in one year in return for an investment of $1,000 now.Calculate the percentage return per annum with:(a) Annual compounding(b) Semiannual compounding
The 6-month and 1-year zero rates are both 10% per annum. For a bond that has a life of 18 months and pays a coupon of 8% per annum (with semiannual payments and one having just been made), the yield
What is meant by LIBOR and LIBID. Which is higher?
A bank quotes an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?
It is now October 2010. A company anticipates that it will purchase 1 million pounds of copper in each of February 2011, August 2011, February 2012, and August 2012. The company has decided to use
A fund manager has a portfolio worth $50 million with a beta of0.87. The manager is concerned about the performance of the market over the next 2 months and plans to use 3-month futures contracts on
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.QM I M i I M iI I M. M i i
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 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
The expected return on the S&P 500 is 12% and the risk-free rate is 5%. What is the expected return on an investment with a beta of (a) 0.2, (b) 0.5, and (c) 1.4?
Suppose that the 1-year gold lease rate is 1.5% and the 1-year risk-free rate is 5.0%. Both rates are compounded annually. Use the discussion in Business Snapshot 3.1 to calculate the maximum 1-year
An airline executive has argued: "There is no point in our using oil futures. There is just as much chance that the price of oil in the future will be less than the futures price as there is that it
A futures contract is used for hedging. Explain why the daily settlement of the contract can give rise to cash-flow problems.
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?
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
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
The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It
The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound)
"For an asset where futures prices are usually less than spot prices, long hedges are likely to be particularly attractive." Explain this statement.
"If there is no basis risk, the minimum variance hedge ratio is always 1.0." Is this statement true? Explain your answer.
"If the minimum variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true? Explain your answer.
How does the decision affect the way in which the hedge is implemented and the result?
Suppose that in Example 3.2 of Section 3.3 the company decides to use a hedge ratio of
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
Explain why a short hedger's position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.
Does a perfect hedge always succeed in locking in the current spot price of an asset for a future transaction? Explain your answer.
In the corn futures contract traded on an exchange, the following delivery months are available: March, May, July, September, and December. Which of the available contracts should be used for hedging
It would like to use futures contracts on the S&P 500 to hedge its risk. The index futures price is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the
A company has a $20 million portfolio with a beta of
What is the optimal hedge ratio for a 3-month contract? What does it mean?
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
Give three reasons why the treasurer of a company might not hedge the company's exposure to a particular risk.
Under what circumstances does a minimum variance hedge portfolio lead to no hedging at all?
Explain what is meant by a perfect hedge. Does a perfect hedge always lead to a better outcome than an imperfect hedge? Explain your answer.
Explain what is meant by basis risk when futures contracts are used for hedging.
Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
The author’s website (www.rotman.utoronto.ca/~hu11/data) contains daily closing prices for crude oil and gold futures contracts. You are required to download the data and answer the following:(a)
What position is equivalent to a long forward contract to buy an asset at K on a certain date and a put option to sell it for K on that date.
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 on May 26, 2010, by trading July 2010 and December 2010
A company enters into a short futures contract to sell 5,000 bushels of wheat for 450 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead
One orange juice futures contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2011 a company sells a March 2013 orange juice futures contract for 120 cents per pound. In
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 tradesin a particular futures
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 rate (dollars per
It is July 2011. A mining company has just discovered a small deposit of gold. It will take 6 months to construct the mine. The gold will then be extracted on a more or less continuous basis for 1
A cattle farmer expects to have 120,000 pounds of live cattle to sell in 3 months. The live cattle futures contract traded, by the CME Group is for the delivery of 40,000 pounds of cattle. How can
Suppose that, on October 24, 2012, a company sells one April 2013 live cattle futures contract. It closes out its position on January 21, 2013. The futures price (per pound) is 91.20 cents when it
"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.
What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?
Live cattle futures trade with June, August, October, December, February, and April maturities. Why do you think the open interest for the June contract is less than that for the August contract in
"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.
Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.
The forward price of 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
On July 1, 2012, a Japanese company enters into a forward contract to buy $1 million with yen on January 1, 2013. On September 1, 2012, it enters into a forward contract to sell $1 million on January
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
Explain what a stop-limit order to sell at 20.30 with a limit of 20.10 means.
Explain the difference between a market-if-touched order and a stop order.
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
A trader buys two July futures contracts on 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
Explain how margins protect investors against the possibility of default.
What are the most important aspects of the design of a new futures contract?
The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on.
What differences exist in the way prices are quoted in the foreign exchange futures market, the foreign exchange spot market, and the foreign exchange forward market?
What is the difference between the operation of the margin accounts administered by a clearing house and those administered by a broker?
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?
Suppose that in September 2012 a company takes a long position in a contract on May 2013 crude oil futures. It closes out its position in March 2013. The futures price (per barrel) is $68.30 when it
Suppose that you enter into a short futures contract to sell July silver for $17.20 per ounce. The size of the contract is 5,000 ounces. The initial margin is $4,000, and the maintenance margin is
What is the difference between a local and a futures commission merchant?
Distinguish between the terms open interest and trading volume.
(Appendixes A) Explain how the Federal Reserve Bank affects the money supply in the United States. How do the Fed’s actions, including setting reserve requirements and controlling discount rates,
(Appendixes A) AGING RECEIVABLES AND UNCOLLECTIBLE ACCOUNT EXPENSE. Perkinson Corporation sells paper products to a large number of retailers. Perkinson’s accountant has prepared the following
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
Describe how foreign currency options can be used for hedging in the situation considered in Section 1.7 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.4600, and (b)
Suppose that in the situation of Table 1.1 a corporate treasurer said: “I will have£1 million to sell in 6 months. If the exchange rate is less than 1.41, I want you to give me 1.41. Ifit is
A bond issued by Standard Oil some time ago worked as follows. The holder received no interest. At the bond’s maturity the company promised to pay $1,000 plus an additional amount based on the
On July 15, 2010, an investor owns 100 Google shares. As indicated in Table 1.3, the share price is about $497 and a December put option with a strike price of $460 costs $27.30. The investor is
The current price of a stock is $94, and 3-month European 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
The price of gold is currently $1,000 per ounce. The forward price for delivery in 1 year is $1,200. An arbitrageur can borrow money at 10% per annum. What should the arbi- trageur do? Assume that
A stock price is $29. An investor buys one call option contract on the stock with a strike price of $30 and sells a call option contract on the stock with a strike price of $32.50. The market prices
A US company knows it will have to pay 3 million euros in three months. The current exchange rate is 1.4500 dollars per euro. Discuss how forward and options contracts can be used by the company to
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
Trader A enters into a forward contract to buy gold for $1,000 an ounce in one year. Trader B buys a call option to buy gold for $1,000 an ounce in one year. The cost of the option is $100 an ounce.
What opportunities are open to an arbitrageur in the following situations? '(a) A 180-day European call option to buy £1 for $1.42 costs 2 cents.(b) A 90-day European put option to sell £1 for

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