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principles of risk management

Questions and Answers of Principles Of Risk Management

25. Explain why the Black option on futures pricing model is simply a pricing mode! for options on instruments with a zero cost of carry.
24. On September 26 the spot price of wheat was $3.5225 per bushel and the price of a December wheat futures was $3.64 per bushel. How do you interpret the futures price if there is no risk premium
23. What is a contango market? How do we interpret the cost of carry in a contango market? What is a backwardation market? How do we explain the cost of carry in a backwardation market?
22. Describe two problems in using the Black option on futures pricing model for pric- ing options on Eurodollar futures.
21. Explain why American call options on futures could be exercised early when call options on the spot are not. Assume that there are no dividends.
20. If futures prices are less than spot prices, the explanation usually given is the con- venience yield. Explain what the convenience yield is. Then identify certain assets on which convenience
19. Identify and provide a brief explanation of the factors that affect the spot price of a storable asset.
18. (Concept Problem) Suppose that there is a futures contract on a portfolio of stocks that currently are worth $100. The futures has a life of 90 days, and during that time the stocks will pay
16. The put-call parity rule can be expressed as CP = (f(T)-X) (1+r)-T. Con- sider the following data: f,(T) = 102, X = 100, r = 0.1, T = 0.25, C = 4, and P = 1.75. A few calculations will show that
14. Using the information in problem 13, calculate the price of the put described in problem 6, using the Black model for pricing puts. 15. Suppose you observe a one-year futures price of $100, the
13. Assume a standard deviation of 8 percent, and use the Black model to determine if the call option in problem 6 is correctly priced. If not, suggest a riskless hedge strategy.
12. (Concept Problem) Suppose that a futures margin account pays interest but at a rate that is less than the risk-free rate. Consider a trader who buys the asset and sells a futures to form a
10. Consider the wheat example in problem 24. The interest forgone on money tied up in a bushel until expiration is 0.03, and the cost of storing the wheat is 0.0875 per bushel. The risk premium is
7. On September 12, a stock index futures contract was at 423.70. The December 400 call was at 26.25, and the put was at 3.25. The index was at 420.55. The futures and options expire on December 21.
5. Why is the value of a futures or forward contract at the time it is purchased equal to zero? Contrast this with the value of the corresponding spot commodity.
2. On a particular day the S&P 500 futures settlement price was 899.30. You buy one contract at around the close of the market at the settlement price. The next day, the contract opens at 899.70 and
1. Assume that there is a forward market for a commodity. The forward price of the commodity is $45. The contract expires in one year. The risk-free rate is 10 per- cent. Now, six months later, the
2. In November you buy a futures contract on a commodity at a price of $10,000. At the end of the year, the futures price is $10,500. You hold your position open until January 20, at which time the
1. On October 1, you purchase one March stock index futures contract at the open- ing price of 410.50. The contract multiplier is $500, so the price of 410.30 is really $500 (410.30) = $205,150. You
22. Explain how the clearinghouse operates to protect the futures market.
20. How do options on futures differ from options on the asset underlying the futures?
19. The open interest in a futures contract changes from day to day. Suppose that in- vestors holding long positions are divided into two groups: A is an individual investor and OL represents other
18. What factors distinguish a forward contract from a futures contract? What do for- ward and futures contracts have in common? What advantages does each have over the other?
17. Explain the difference between a forward contract and an option.
16. Explain the basic differences between open-outcry and electronic trading systems.
15. List and briefly explain the important contributions provided by futures exchanges.
14. How do locals differ from commission brokers? How do the latter differ from futures commission merchants?
13. What factors would determine whether a particular strategy is a hedge or a specu- lative strategy?
12. How are spread and arbitrage strategies forms of speculation? How can they be interpreted as hedges?
11. What is the objective of an industry self-regulatory organization?
10. What are the objectives of federal regulation of future markets?
9. Compare and contrast three types of futures trading costs.
8. Explain the differences among the three means of terminating a futures contract: an offsetting trade, cash settlement, and delivery. How is a forward contract terminated?
6. What are daily price limits, and why are they used?
4. Compare and contrast cash settlement with physical settlement.
3. Suppose that you buy a stock index futures contract at the opening price of 452.25 on July 1. The multiplier on the contract is 500, so the price is $500 (452.25) == $226,125. You hold the
24. Explain why a straddle is not necessarily a good strategy when the underlying event is well known to everyone.
23. Suppose that an option trader has a call bull spread. The stock price has risen sub- stantially, and the trader is considering closing the position early. What factors should the trader consider
22. Explain why option traders often use spreads instead of simple long or short options and combined positions of options and stock.
21. (Concept Problem) Another variation of the straddle is called a strangle. A strangle is the purchase of a call with a higher exercise price and a put with a lower exer- cise price. Evaluate the
20. (Concept Problem) Many option traders use a combination of a money spread and a calendar spread called a diagonal spread. This transaction involves the pur- chase of a call with a lower exercise
19. Complete the following table with the correct formula related to various spread strategies.
18. Complete the following table with the correct formula related to various spread strategies.
17. Analyze the August 160/170 box spread. Determine whether a profit opportunity exists and, if so, how one should exploit it.
14. Repeat problem 13, but close the positions on September 20. Use the spreadsheet to find the profits for the possible stock prices on September 20. Generate a graph and use it to identify the
5. The chapter showed how analyzing a box spread is like a capital budgeting prob- lem using the net present value approach. Consider the internal rate of return method of examining capital budgeting
4. Explain the process by which the profit of a short straddle closed out prior to expiration is influenced by the time values of the put and call.
2. Explain how a short call added to a protective put forms a collar and how it changes the payoff and up-front cost.
1. Suppose that you are following the stock of a firm that has been experiencing severe problems. Failure is imminent unless the firm is granted government- guaranteed loans. If the firm fails, its
25. (Concept Problem) Another consideration in evaluating option strategies is the effect of transaction costs. Suppose that purchases and sales of an option incur a brokerage commission of 1 percent
24. Explain the advantages and disadvantages to a covered call writer of closing out the position prior to expiration.
23. Discuss and compare the two bullish strategies of buying a call and writing a put. Why would one strategy.be preferable to the other? 24. Explain the advantages and disadvantages to a covered
22. Why is choosing an exercise price on a protective put like deciding which de- ductible to take on an insurance policy?
21. Suppose that one is considering buying a call at a particular exercise price. What reasons could be given for the alternative of buying a call at a higher exercise price? At a lower exercise
18. Use the information in problem 16 to construct a euro covered call. Assume that the spot rate at the start is $0.9825.
17. A euro put with an exercise price of $1.00 is priced at $0.0435. Construct a simple long position in the put.
15. The Black-Scholes-Merton option pricing model assumes the stock price changes are lognormally distributed. Show graphically how this distribution changes when an investor is long the stock and
14. The Black-Scholes-Merton option pricing model assumes the stock price changes are lognormally distributed. Show graphically how this distribution changes when an investor is long the stock and
12. Explain how a protective put is like purchasing insurance on a stock.
11. Explain the advantages and disadvantages to a call buyer of closing out a position prior to expiration rather than holding it all the way until expiration.
10. Buy 100 shares of stock and buy one August 165 put contract. Hold the position until expiration. Determine the profits and graph the results. Determine the breakeven stock price at expiration,
9. Repeat problem 8, but close the position on September 1. Use the spreadsheet to find the profits for the possible stock prices on September 1. Generate a graph and use it to approximate the
6. Repeat problem 5, but close the position on August 1. Use the spreadsheet to find the profits for the possible stock prices on August 1. Generate a graph and use it to identify the approximate
5. Buy one August 165 call contract. Hold it until the options expire. Determine the profits and graph the results. Then identify the breakeven stock price at expira- tion. What is the maximum
4. Explain the considerations facing a covered call writer regarding the choice of exercise prices. The following option prices were observed for a stock for July 6 of a particular year. Use this
25. (Concept Problem) Suppose that a stock is priced at 80 and has a volatility of 0.35. You buy a call option with an exercise price of 80 that expires in 3 months. The risk-free rate is 5 percent.
24. A stock is selling for $100 with a volatility of 40 percent. Consider a call option on the stock with an exercise price of 100 and an expiration of one year. The risk-free rate is 4.5 percent.
22. Compare the variables in the binomial model with those in the Black-Scholes Merton model. Note any differences and explain.
20. Using BSMbin7e.xls or BSMbwin7e.exe, compute the call and put prices for a stock option, where the current stock price is $100, the exercise price is $100, the risk-free interest rate is 5
19. What is the most critical variable in the Black-Scholes-Merton model? Explain.
18. Explain what we mean when we say that the binomial model is a discrete time model and the Black-Scholes Merton model is a continuous time model.
17. A financial institution offers a new over-the-counter option that pays off 150% of the payoff of a standard European option. Demonstrate, using BSMbin 7e.xls or BSMbwin7e.exe (or by hand), that
16. (Concept Problem) Show how a delta hedge using a position in the stock and a long position in a put would be set up.
15. Explain the difference between a normal and a lognormal distribution as it pertains to stock prices.
14. Repeat problem 13 using the approximation for an at-the-money call. Compare your answer with the one you obtained in problem 13. Is the approximation a good one?
13. Estimate the implied volatility of the August 165 call. Compare your answer with that obtained in problem 12. Use trial and error. Stop when your answer is within 0.01 of the true implied
12. Following is the sequence of daily prices on the stock for the preceding month of June:Date Price Date Price 6/1 159.88 6/16 162.00 6/2 157.25 6/17 161.38 6/3 160.25 6/18 160.88 6/4 161.38 6/19
11. On December 9, a Swiss franc call option expiring on January 13 had an exercise price of $0.46. The spot exchange rate was $0.4728. The U.S. risk-free rate was 7.1 percent, and the Swiss
10. Suppose on July 7 the stock will go ex-dividend with a dividend of $2. Assuming that the options are American, determine whether the July 160 call would be exercised.
9. On July 6, the dividend yield on the stock is 2.7 percent. Rework part a of problem 6 using the yield-based dividend adjustment procedure. Calculate this answer by hand and then recalculate it
8. Suppose the stock pays a $1.10 dividend with an ex-dividend date of September 10. Rework part a of problem 6 using an appropriate dividend-adjusted procedure. Calculate this answer by hand and
7. Use the Black-Scholes-Merton European put option pricing formula for the Octo- ber 165 put option. Repeat partsa, b, and cof question 6 with respect to the put.
6. Let the standard deviation of the continuously compounded return on the stock be 21 percent. Ignore dividends. Answer the following:a. What is the theoretical fair value of the October 165 call?
5. Which assumption in the Black-Scholes-Merton model did we drop somewhere in the chapter? What did we do in removing that assumption to make the model give the correct option price? The following
3. A stock is priced at $50 with a volatility of 35 percent. A call option with an exer- cise price of $50 has an expiration in one year. The risk-free rate is 5 percent. Construct a table for stock
1. Suppose that you subscribe to a service that gives you estimates of the theoretically correct volatilities of stocks. You note that the implied volatility of a particular option is substantially
20. Describe the three primary ways of incorporating dividends into the binomial model.
19. Explain the differences between a recombining and non-recombining tree. Why is the former more desirable?
17. What is the principal benefit of a binomial option pricing model? 18. How is the volatility of the underlying stock reflected in the binomial model?
16. Discuss how a binomial model accommodates the possibility of early exercise of an option.
15. If the binomial model produces a call option price that is higher than the price at which the option is trading in the market, what strategy is suggested?
14. Describe the components of a hedge portfolio in the binomial option pricing model where the instrument being hedged is, first, a call, and second, a put.
12. Explain the similarities and differences between pricing an option by its boundary conditions and using an exact option pricing formula.
11. Use the binomial model and two time periods to determine the price of the DCRB June 130 American put. Use the appropriate parameters from the information given in the chapter, which was
9. (Concept Problem) The binomial model can be used to price unusual features of options. Consider the following scenario. A stock priced at $75 can go up by 20 percent or down by 10 percent per
8. Construct a table containing the up and down factors for a one-year option with a stock volatility of 55 percent and a risk-free rate of 7 percent for n = 1, 5, 10, 50, and 100 where n is the
7. Consider a European call with an exercise price of 50 on a stock priced at 60. The stock can go up by 15 percent or down by 20 percent each of two binomial peri- ods. The risk-free rate is 10
6. (Concept Problem) In this chapter, we obtained the binomial option pricing for- mula by hedging a short position in the call option with a long position in stock. An alternative way to do this is
5. Use the Excel spreadsheet BSMbin7e.xls and determine the value of a call option on a stock currently priced at 165.13, where the risk-free rate is 5.875 percent (annually compounded), the exercise
4. Use the Excel spreadsheet BSMbin7e.xls and determine the value of a call option and a put option on a stock currently priced at 100, where the risk-free rate is 5 percent (annually compounded),

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