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business
options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

At the end of one day a clearinghouse 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, 2006, a US company enters into a forward contract to buy 10 million GBP on January 1, 2007. On September 1, 2006, it enters into a forward contract to sell 10 million GBP on January 1,
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 is more
Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.AppendixLO1
"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.AppendixLO1
Identify the contracts with the highest open interest in Table 2.2. Consider each of the following sections separately: grains and oilseeds, livestock, food and fiber, metals, and
What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?AppendixLO1
"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.AppendixLO1
Suppose that on October 24, 2006, you take a short position in an April 2007 live cattle futures contract. You close out your position on January 21, 2007. The futures price (per pound) is 61.20
A cattle farmer expects to have 120,000 pounds of live cattle to sell in 3 months. The live cattle futures contract on the Chicago Mercantile Exchange is for the delivery of 40,000 pounds of cattle.
It is now July 2005. 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
Suppose that there are no storage costs for corn and the interest rate for borrowing or lending is 5% per annum. How could you make money on February 4, 2004, by trading March 2004 and May 2004
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.AppendixLO1
The author's Web page (www.rotman.utoronto.ca/~hull/data) contains daily closing prices for the December 2001 crude oil futures contract and the December 2001 gold futures contract. (Both contracts
Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?AppendixLO1
Explain what is meant by basis risk when futures contracts are used for hedging.AppendixLO1
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.AppendixLO1
Under what circumstances does a minimum variance hedge portfolio lead to no hedging at all?AppendixLO1
Give three reasons that the treasurer of a company might not hedge the company's exposure to a particular risk.AppendixLO1
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 the S&P 500 to hedge its risk. The index is currently standing at 1080, and each contract is for
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 when
Does a perfect hedge always succeed in locking in the current spot price of an asset for a future transaction? Explain your answer.AppendixLO1
Explain why a short hedger's position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.AppendixLO1
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 3.2 of Section 3.3 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?AppendixLO1
"If the minimum variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true? Explain your answer.AppendixLO1
"If there is no basis risk, the minimum variance hedge ratio is always 1.0." Is this statement true? Explain your answer.AppendixLO1
"For an asset where futures prices are usually less than spot prices, long hedges are likely to be particularly attractive." Explain this statement.AppendixLO1
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
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?AppendixLO1
A futures contract is used for hedging. Explain why the marking to market of the contract can give rise to cash flow problems.AppendixLO1
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
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
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 +0.50
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
It is now October 2004. A company anticipates that it will purchase 1 million pounds of copper in each of February 2005, August 2005, February 2006, and August 2006. 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 2 months and plans to use 3-month futures contracts on
A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?AppendixLO1
What is meant by LIBOR and LIBID. Which is higher?AppendixLO1
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
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 (c) Monthly
Suppose that zero interest rates with continuous compounding are as follows: Rate Maturity (months) (% per annum) 3 8.0 6 8.2 9 8.4 12 8.5 8.6 8.7 15 18 Calculate forward interest rates for the
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
The term structure of interest rates is upward-sloping. Put the following in order of magnitude: (a) The 5-year zero rate (b) The yield on a 5-year coupon-bearing bond (c) The forward rate
What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding?AppendixLO1
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?AppendixLO1
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 compound- ing. Estimate the cash price of a
A 3-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond's yield?AppendixLO1
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?AppendixLO1
Suppose that zero interest rates with continuous compounding are as follows:Maturity (years) Rate (% per annum) 1 2.0 2 3.0 3 3.7 4.2 4.5 4 5 Calculate forward interest rates for the second, third,
Use the rates in Problem 4.14 to value an FRA where you will pay 5% for the third year on $1 million.AppendixLO1
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
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
"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
Why are US Treasury rates significantly lower that other rates that are close to risk-free?AppendixLO1
Why does a loan in the repo market involve very little credit risk?AppendixLO1
Explain why an FRA is equivalent to the exchange of a floating rate of interest for a fixed rate of interest.AppendixLO1
The cash prices of 6-month and 1-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every 6 months currently sells for $94.84. A 2-year bond that will pay coupons of
An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) con- tinuous compounding.AppendixLO1
The 6-month, 12-month, 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5%, with semiannual compounding. (a) What are the rates with continuous compounding? (b) What is the forward rate for
What is the 2-year par yield when the zero rates are as in Problem 4.25? What is the yield on a 2-year bond that pays a coupon equal to the par yield?AppendixLO1
The following table gives the prices of bonds: Bond principal Time to maturity ($) (years) 0.50 Annual coupon* ($) 0.0 Bond price ($) 98 TTTI 100 100 1.00 100 100 1.50 2.00 95 0.0 6.2 101 8.0 104
Portfolio A consists of a 1-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a
Explain what happens when an investor shorts a certain share.AppendixLO1
What is the difference between the forward price and the value of a forward contract?AppendixLO1
Suppose that you enter into a 6-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 annum. What
A stock index currently stands at 350. The risk-free interest rate is 8% per annum (with continuous compounding) and the dividend yield on the index is 4% 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.AppendixLO1
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?AppendixLO1
Explain why a foreign currency can be treated as an asset providing a known yield.AppendixLO1
Is the futures price of a stock index greater than or less than the expected future value of the index? Explain your answer.AppendixLO1
A 1-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 10% per annum with continuous compounding. (a) What are
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 6-month
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 Mexico and the United States on February 4, 2004, from the information in Table 5.4.AppendixLO1
The 2-month interest rates in Switzerland and the United States are, respectively, 3% and 8% per annum with continuous compounding. The spot price of the Swiss franc is $0.6500. The futures price for
The spot 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, calculate the
Suppose that F1 and F2 are two futures contracts on the same commodity with times to maturity, and 2, where t> 11. Prove thatwhere is the interest rate (assumed constant) and there are no storage
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
It is sometimes argued that a forward exchange rate is an unbiased predictor of future exchange rates. Under what circumstances is this so?AppendixLO1
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
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 on February 4, 2004, speculators tended to be short crude oil futures and hedgers tended
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
A US 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 US dollar and ry as the
A stock is expected to pay a dividend of $1 per share in 2 months and in 5 months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all
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
A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $450 per ounce and sell it for $449 per ounce. The trader can borrow funds at 6% per year and invest funds
A company enters into a forward contract with a bank to sell a foreign currency for K at time T. The exchange rate at time T proves to be S (> K). The company asks the bank if it can roll the

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