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principles of finance

Questions and Answers of Principles Of Finance

15.6. Calculate the value of a three-month at-the-money European call option on a stock index when the index is at 250, the risk-free interest rate is 10% per annum, the volatility of the index is
15.5. Explain how corporations can use range forward contracts to hedge their foreign exchange risk when they are due to receive a certain amount of a foreign currency in the future.
15.4. A currency is currently worth $0.80. Over each of the next two months it is expected to increase or decrease in value by 2%. The domestic and foreign risk-free interest rates are 6% and 8%,
15.3. A stock index is currently 300, the dividend yield on the index is 3% per annum, and the risk-free interest rate is 8% per annum. What is a lower bound for the price of a six-month European
15.2. “Once we know how to value options on a stock paying a dividend yield, we know how to value options on stock indices and currencies.” Explain this statement.
15.1. A portfolio is currently worth $10 million and has a beta of 1.0. An index is currently standing at 800. Explain how a put option on the index with a strike price of 700 can be used to provide
12.28. Calculate the value of nine-month American call option to buy 1 million units of a foreign currency using a three-step binomial tree. The current exchange rate is 0.79 and the strike price is
12.27. A stock index is currently 990, the risk-free rate is 5%, and the dividend yield on the index is 2%. Use a three-step tree to value an 18-month American put option with a strike price of 1,000
12.26. Repeat Problem 12.25 for an American put option on a futures contract. The strike price and the futures price are $50, the risk-free rate is 10%, the time to maturity is six months, and the
12.25. Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and
12.24. A stock price is currently $30. During each two-month period for the next four months it will increase by 8% or decrease by 10%. The risk-free interest rate is 5%. Use a twostep tree to
12.23. Using a “trial-and-error” approach, estimate how high the strike price has to be in Problem 12.22 for it to be optimal to exercise the put option immediately.
12.22. A stock price is currently $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous
12.21. A stock price is currently $50. It is known that at the end of six months it will be either$60 or $42. The risk-free rate of interest with continuous compounding is 12% per annum.Calculate the
12.20. In Problem 12.19, suppose a trader sells 10,000 European call options and a two-step tree describes the behavior of the stock. How many shares of the stock are needed to hedge the six-month
12.19. The current price of a non-dividend-paying biotech stock is $140 with a volatility of 25%.The risk-free rate is 4%. For a three-month time step:(a) What is the percentage up movement?(b) What
12.18. The futures price of a commodity is $90. Use a three-step tree to value (a) a nine-month American call option with strike price $93 and (b) a nine-month American put option with strike price
12.17. A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum(continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate
12.16. The volatility of a non-dividend-paying stock whose price is $78, is 30%. The risk-free rate is 3% per annum (continuously compounded) for all maturities. Calculate values for u,d, and p when
12.15. Calculate u,d, and p when a binomial tree is constructed to value an option on a foreign currency. The tree step size is one month, the domestic interest rate is 5% per annum, the foreign
12.14. A stock price is currently $25. It is known that at the end of two months it will be either$23 or $27. The risk-free interest rate is 10% per annum with continuous compounding.Suppose ST is
12.13. For the situation considered in Problem 12.12, what is the value of a six-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy
12.12. A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous
12.11. A stock price is currently $40. It is known that at the end of three months it will be either$45 or $35. The risk-free rate of interest with quarterly compounding is 8% per annum.Calculate the
12.10. A stock price is currently $80. It is known that at the end of four months it will be either$75 or $85. The risk-free interest rate is 5% per annum with continuous compounding.What is the
12.9. A stock price is currently $50. It is known that at the end of two months it will be either$53 or $48. The risk-free interest rate is 10% per annum with continuous compounding.What is the value
12.8. Consider the situation in which stock price movements during the life of a European option are governed by a two-step binomial tree. Explain why it is not possible to set up a position in the
12.7. What are the formulas for u and d in terms of volatility?
12.6. For the situation considered in Problem 12.5, what is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy
12.5. A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous
12.4. A stock price is currently $50. It is known that at the end of six months it will be either$45 or $55. The risk-free interest rate is 10% per annum with continuous compounding.What is the value
12.3. What is meant by the delta of a stock option?
12.2. Explain the no-arbitrage and risk-neutral valuation approaches to valuing a European option using a one-step binomial tree.
12.1. A stock price is currently $40. It is known that at the end of one month it will be either$42 or $38. The risk-free interest rate is 8% per annum with continuous compounding.What is the value
11.28. A bank decides to create a five-year principal-protected note on a non-dividend-paying stock by offering investors a zero-coupon bond plus a bull spread created from calls. The risk-free rate
11.27. Describe the trading position created in which a call option is bought with strike price K2 and a put option is sold with strike price K1 when both have the same time to maturity and K2 > K1.
11.26. What trading position is created from a long strangle and a short straddle when both have the same time to maturity? Assume that the strike price in the straddle is halfway between the two
11.25. Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the risk-free rate for all maturities is 5% per annum. Use DerivaGem to calculate the cost of setting
11.24. Draw a diagram showing the variation of an investor’s profit and loss with the terminal stock price for a portfolio consisting of:(a) One share and a short position in one call option(b) Two
11.23. A diagonal spread is created by buying a call with strike price K2 and exercise date T2 and selling a call with strike price K1 and exercise date T1 (T2 > T1). Draw a diagram showing the
11.22. Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65. The market prices are $3, $5, and $8, respectively. Explain how a butterfly spread can be
11.21. A trader sells a strangle by selling a European call option with a strike price of $50 for$3 and selling a European put option with a strike price of $40 for $4. For what range of prices of
11.20. 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
11.19. An index provides a dividend yield of 1% and has a volatility of 20%. The risk-free interest rate is 4%. How long does a principal-protected note, created as in Example 11.1, have to last for
11.18. A foreign currency is currently worth $0.64. A one-year butterfly spread is set up using European call options with strike prices of $0.60, $0.65, and $0.70. The risk-free interest rates in
11.17. What is the result if the strike price of the put is higher than the strike price of the call in a strangle?
11.16. “A box spread comprises four options. Two can be combined to create a long forward position and two can be combined to create a short forward position.” Explain this statement.
11.15. How can a forward contract on a stock with a particular delivery price and delivery date be created from options?
11.14. An investor believes that there will be a big jump in a stock price, but is uncertain as to the direction. Identify six different strategies the investor can follow and explain the differences
11.13. Construct a table showing the payoff from a bull spread when puts with strike prices K1 and K2 are used (K2 > K1).
11.12. A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4. Construct a table that shows the profit from a straddle. For what range of stock
11.11. Use put–call parity to show that the cost of a butterfly spread created from European puts is identical to the cost of a butterfly spread created from European calls.
11.10. Suppose that put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively.How can the options be used to create (a) a bull spread and (b) a bear spread?Construct a table
11.9. Explain how an aggressive bear spread can be created using put options.
11.8. Use put–call parity to relate the initial investment for a bull spread created using calls to the initial investment for a bull spread created using puts.
11.7. A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Explain how a strangle can be created from these two options. What is the pattern of profits
11.6. What is the difference between a strangle and a straddle?
11.5. What trading strategy creates a reverse calendar spread?
11.4. Call options on a stock are available with strike prices of $15, 1 2 $17 , and $20 and expiration dates in three months. Their prices are $4, $2, and 1 2 $ , respectively. Explain how the
11.3. When is it appropriate for an investor to purchase a butterfly spread?
11.2. Explain two ways in which a bear spread can be created.
11.1. What is meant by a protective put? What position in call options is equivalent to a protective put?
“If a company does not do better than its competitors but the stock market goes up, executives do very well from their stock options. This makes no sense.” Discuss this viewpoint. Can you think
A trader has a put option contract to sell 100 shares of a stock for a strike price of $60.What is the effect on the terms of the contract of:(a) A $2 dividend being declared(b) A $2 dividend being
Calculate the intrinsic value and time value from the mid-market (average of bid and offer)prices for the September 2015 call options in Table 1.2. Do the same for the September 2015 put options in
A U.S. investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?
Options on General Motors stock are on a March, June, September, and December cycle.What options trade on (a) March 1, (b) June 30, and (c) August 5?
Consider an exchange-traded call option contract to buy 500 shares with a strike price of$40 and maturity in four months. Explain how the terms of the option contract change when there is: (a) a 10%
Explain carefully the difference between (a) hedging, (b) speculation, and (c) arbitrage.
What is the difference between (a) entering into a long futures contract when the futures price is $50 and (b) taking a long position in a call option with a strike price of $50?
Suppose that you write a put contract with a strike price of $40 and an expiration date in three months. The current stock price is $41 and one put option contract is on 100 shares.What have you
What is the difference between the over-the-counter and the exchange-traded market?What are the bid and offer quotes of a market maker in the over-the-counter market?
It is May and a trader writes a September call option with a strike price of $20. The stock price is $18 and the option price is $2. Describe the trader’s cash flows if the option is held until
An investor writes a December put option with a strike price of $30. The price of the option is $4. Under what circumstances does the investor make a gain?
The CME Group offers a futures contract on long-term Treasury bonds. Characterize the traders likely to use this contract.
A company in the United States expects to have to pay 1 million Canadian dollars in six months. Explain how the exchange rate risk can be hedged using (a) a forward contract;(b) an option.
Trader A enters into a forward contract to buy an asset for $1,000 in one year. Trader B buys a call option to buy the asset for $1,000 in one year. The cost of the option is $100.What is the
On May 13, 2015, as indicated in Table 1.2, the spot offer price of Google stock is $532.34 and the offer price of a call option with a strike price of $525 and a maturity date of September is
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 1.5900, and (b)
On May 13, 2015, an investor owns 100 Google shares. As indicated in Table 1.3, the bid share price is $532.20 and a December put option with a strike price of $500 costs $22.10.The investor is
The author’s website (www-2.rotman.utoronto.ca/~hull/data) contains daily closing prices for the crude oil futures contract and the gold futures contract. You are required to download the data for
3.28. The following table gives data on monthly changes in the spot price of a commodity and the futures price of a contract used to hedge it. Use the data to calculate a minimum variance hedge
3.29. It is now October 2016. A company anticipates that it will purchase 1 million pounds of copper in each of February 2017, August 2017, February 2018, and August 2018. The company has decided to
Suppose that risk-free zero interest rates with continuous compounding are as follows:Calculate forward interest rates for the second, third, fourth, fifth, and sixth quarters. Maturity (months) Rate
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates continuously compounded are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum, respectively. Estimate the cash price of a bond with
Suppose that risk-free zero interest rates with continuous compounding are as follows:Calculate forward interest rates for the second, third, fourth, and fifth years. Maturity (years) Rate (% per
Use the risk-free rates in Problem 4.14 to value an FRA where you will pay 5% (compounded annually) and receive LIBOR for the third year on $1 million. The forward LIBOR rate (annually compounded)
A 10-year 8% coupon Treasury bond currently sells for $90. A 10-year 4% coupon-Treasury bond currently sells for $80. What is the 10-year zero rate? (Hint: Consider taking a long position in two of
Suppose that 3-month, 6-month, 12-month, 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;
Suppose that risk-free rates are as in Problem 4.28. 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?
The following table gives the prices of Treasury bonds:(a) Calculate zero rates for maturities of 6 months, 12 months, 18 months, and 24 months.(b) What are the forward rates for the periods: 6
What is the difference between the forward price and the value of a forward contract?
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
Estimate the difference between short-term interest rates in Japan and the United States on May 13, 2015, from the information in Table 5.4.
The two-month interest rates in Switzerland and the United States are 1% and 2% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is$1.0600. The futures price
Suppose that F1 and F2 are two futures contracts on the same commodity with times to maturity, t1 and t2, where t2 > t1. Prove thatwhere r is the interest rate (assumed constant) and there are no
Show that equation (5.3) is true by considering an investment in the asset combined with a short position in a futures contract. Assume that all income from the asset is reinvested in the asset. Use
What is the cost of carry for (a) a non-dividend-paying stock, (b) a stock index, (c) a commodity with storage costs, and (d) a foreign currency?
In early 2012, the spot exchange rate between the Swiss Franc and U.S. dollar was 1.0404($ per franc). Interest rates in the United States and Switzerland were 0.25% and 0% per annum, respectively,
Companies A and B have been offered the following rates per annum on a $20 million five-year loan:Company A requires a floating-rate loan; Company B requires a fixed-rate loan. Design a swap that

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