An executive compensation scheme might provide a manager a bonus of $1,000 for every dollar by which the company’s stock price exceeds some cutoff level. In what way is this arrangement equivalent to issuing the manager call options on the firm’s stock?
> Suppose that the spot price of the euro is currently $1.10. The 1-year futures price is $1.15. Is the interest rate higher in the United States or the euro zone?
> a. A single-stock futures contract on a non-dividend-paying stock with current price $150 has a maturity of 1 year. If the T-bill rate is 3%, what should the futures price be? b. What should the futures price be if the maturity of the contract is 3 years
> What is the difference in cash flow between short-selling an asset and entering a short futures position?
> Why might individuals purchase futures contracts rather than the underlying asset?
> Consider this arbitrage strategy to derive the parity relationship for spreads: (1) enter a long futures position with maturity date T1 and futures price F(T1); (2) enter a short position with maturity T2 and futures price F(T2); (3) at T1, when the firs
> The Excel Application box in the chapter (available in Connect; link to Chapter 22 material) shows how to use the spot-futures parity relationship to find a “term structure of futures prices,” that is, futures prices for various maturity dates. a. Suppos
> Noah Kramer, a fixed-income portfolio manager based in the country of Sevista, is considering the purchase of a Sevista government bond. Kramer decides to evaluate two strategies for implementing his investment in Sevista bonds. Table 16A gives the detai
> The S&P portfolio pays a dividend yield of 1% annually. Its current value is 2,000. The T-bill rate is 4%. Suppose the S&P futures price for delivery in 1 year is 2,050. Construct an arbitrage strategy to exploit the mispricing and show that your profits
> OneChicago has just introduced a single-stock futures contract on Brandex stock, a company that currently pays no dividends. Each contract calls for delivery of 1,000 shares of stock in 1 year. The T-bill rate is 6% per year. a. If Brandex stock now sell
> Consider a stock that pays no dividends on which a futures contract, a call option, and a put option trade. The maturity date for all three contracts is T, the exercise price of both the put and the call is X, and the futures price is F. Show that if X =
> Why is there no futures market in cement?
> Show that Black-Scholes call option hedge ratios increase as the stock price increases. Consider a 1-year option with exercise price $50, on a stock with annual standard deviation 20%. The T bill rate is 3% per year. Find N(d1) for stock prices (a) $45,
> Reconsider the determination of the hedge ratio in the two-state model (see Section 21.2), where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for the following exercise prices: (a) 120, (b) 110, (c) 100, (
> Use the put-call parity relationship to demonstrate that an at-the-money European call option on a non-dividend-paying stock must cost more than an at-the-money put option. Show that the prices of the put and call will be equal if X = S0(1 + r)T.
> You build a binomial model with one period and assert that over the course of a year, the stock price will either rise by a factor of 1.5 or fall by a factor of 2/3. What is your implicit assumption about the volatility of the stock’s rate of return over
> All else equal, will a call option with a high exercise price have a higher or lower hedge ratio than one with a low exercise price?
> Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = .40. What would be the appropriate values for u and d if your binomial model is set up using: a. 1 period of 1 year. b.
> A company’s current ratio is 2.0. Suppose the company uses cash to retire notes payable due within one year. What would be the effect on the current ratio and asset turnover ratio?
> What will happen to the delta of a convertible bond as the stock price becomes very large?
> All else equal, is a call option on a stock with a lot of firm-specific risk worth more than one on a stock with little firm-specific risk? The betas of the two stocks are equal.
> Let p(S, T, X) denote the value of a European put on a stock selling at S dollars, with time to maturity T, and with exercise price X, and let P(S, T, X) be the value of an American put. a. Evaluate p(0, T, X). b. Evaluate P(0, T, X). c. Evaluate p(S, T,
> These three put options are all written on the same stock. One has a delta of −.9, one a delta of −.5, and one a delta of −.1. Assign deltas to the three puts by filling in this table.
> Is a put option on a high-beta stock worth more than one on a low-beta stock? The stocks have identical firm-specific risk.
> The hedge ratio of an at-the-money call option on IBM is .4. The hedge ratio of an at-the-money put option is −.6. What is the hedge ratio of an at-the-money straddle position on IBM?
> According to the Black-Scholes formula, what will be the hedge ratio (delta) of a put option for a very small exercise price?
> According to the Black-Scholes formula, what will be the hedge ratio (delta) of a call option as the stock price becomes infinitely large? Explain briefly.
> If the time to expiration falls and the put price rises, then what has happened to the put option’s implied volatility?
> If the stock price falls and the call price rises, then what has happened to the call option’s implied volatility?
> A firm has net sales of $3,000, cash expenses (including taxes) of $1,400, and depreciation of $500. If accounts receivable increase over the period by $400, what would be cash flow from operations?
> Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would experience a slight downturn and suggested delta-hedging the BIC portfolio. U.S. equity markets did indeed fall, but BIC’s portfolio perf
> Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would experience a slight downturn and suggested delta-hedging the BIC portfolio. U.S. equity markets did indeed fall, but BIC’s portfolio perf
> Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would experience a slight downturn and suggested delta-hedging the BIC portfolio. U.S. equity markets did indeed fall, but BIC’s portfolio perf
> Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would experience a slight downturn and suggested delta-hedging the BIC portfolio. U.S. equity markets did indeed fall, but BIC’s portfolio perf
> Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would experience a slight downturn and suggested delta-hedging the BIC portfolio. U.S. equity markets did indeed fall, but BIC’s portfolio perf
> A call option with X = $50 on a stock priced at S = $55 sells for $10. Using a volatility estimate of σ = .30, you find that N(d1) = .6 and N(d2) = .5. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less
> Recalculate the value of the call option in Problem 11, successively substituting one of the changes below while keeping the other parameters as in Problem 11: a. Time to expiration = 3 months. b. Standard deviation = 25% per year. c. Exercise price = $5
> Find the Black-Scholes value of a put option on the stock in Problem 11 with the same exercise price and expiration as the call option. Data from problem 11: Time to expiration……………………………………6 months Standard deviation……………………………..50% per year Exercise p
> Use the Black-Scholes formula to find the value of a call option on the following stock: Time to expiration……………………………6 months Standard deviation………………………50% per year Exercise price………………………………………….$50 Stock price……………………………………………...$50 Annual interest r
> The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. T
> A 2-year investment of $2,000 results in a cash flow of $150 at the end of the first year and another cash flow of $150 at the end of the second year, in addition to the return of the original investment. What is the dollar-weighted (internal) rate of re
> Suppose you think AppX stock is going to appreciate substantially in value in the next year. Say the stock’s current price, S0, is $100, and a call option expiring in one year has an exercise price, X, of $100 and is selling at a price,
> Turn back to Figure 20.1, which lists prices of various Microsoft options. Use the data in the figure to calculate the payoff and the profits for investments in each of the following January 18 expiration options, assuming that the stock price on the exp
> Demonstrate that an at-the-money call option on a given stock must cost more than an at themoney put option on that stock with the same expiration. The stock will pay no dividends until after the expiration date. (Hint: Use put-call parity.)
> Netflux is selling for $100 a share. A Netflux call option with one month until expiration and an exercise price of $105 sells for $2 while a put with the same strike and expiration sells for $6.94. What must be the market price of a zero-coupon bond wit
> Joe Finance has just purchased a stock index fund, currently selling at $2,400 per share. To protect against losses, Joe also purchased an at-the-money European put option on the fund for $120, with exercise price $2,400, and 3-month time to expiration.
> You buy a share of stock, write a 1-year call option with X = $10, and buy a 1-year put option with X = $10. Your net outlay to establish the entire portfolio is $9.50. (a) What is the payoff of your portfolio? (b) What must be the risk-free interest rat
> Assume a stock has a value of $100. The stock is expected to pay a dividend of $2 per share at year-end. An at-the-money European-style put option with one-year expiration sells for $7. If the annual interest rate is 5%, what must be the price of a 1-yea
> A FinCorp put option with strike price 60 trading on the Acme options exchange sells for $2. To your amazement, a FinCorp put with the same expiration selling on the Apex options exchange but with strike price 62 also sells for $2. If you plan to hold th
> Consider the following portfolio. You write a put option with exercise price 90 and buy a put option on the same stock with the same expiration date with exercise price 95. a. Plot the value of the portfolio at the expiration date of the options. b. On t
> A portfolio of stocks generates a −9% return in 2018, a 23% return in 2019, and a 17% return in 2020. What was the annualized return (geometric mean) for the entire period?
> Use the spreadsheet from the Excel Application box on spreads and straddles (available in Connect or through your course instructor; link to Chapter 20 material) to answer these questions. a. Plot the payoff and profit diagrams to a straddle position wit
> A bearish spread is the purchase of a call with exercise price X2 and the sale of a call with exercise price X1, with X2 greater than X1. Graph the payoff to this strategy and compare it to Figure 20.10.
> a. A butterfly spread is the purchase of one call at exercise price X1, the sale of two calls at exercise price X2, and the purchase of one call at exercise price X3. X1 is less than X2, and X2 is less than X3 by equal amounts, and all calls have the sam
> Imagine that you are holding 5,000 shares of stock, currently selling at $40 per share. You are ready to sell the shares but would prefer to put off the sale until next year for tax reasons. If you continue to hold the shares until January, however, you
> An investor purchases a stock for $38 and a put for $.50 with a strike price of $35. The investor sells a call for $.50 with a strike price of $40. What is the maximum profit and loss for this position? Draw the profit and loss diagram for this strategy
> Recently, Galaxy Corporation lowered its allowance for doubtful accounts by reducing bad debt expense from 2% of sales to 1% of sales. Ignoring taxes, what are the immediate effects on (a) operating income and (b) operating cash flow?
> Use the DuPont system and the following data to find return on equity. Leverage ratio (assets/equity) ……………………………. 2.2 Total asset turnover…………………………………………….2.0 Net profit margin…………………………………………………5.5% Dividend payout ratio…………………………………………..31.8%
> Firm A and Firm B have the same ROA, yet Firm A’s ROE is higher. How can you explain this?
> The ABC Corporation has a profit margin on sales below the industry average, yet its ROA is above the industry average. What does this imply about its asset turnover?
> The Crusty Pie Co., which specializes in apple turnovers, has a return on sales higher than the industry average, yet its ROA is the same as the industry average. How can you explain this?
> a. If the exchange rate for the British pound goes from U.S.$1.55 to U.S.$1.35, then the pound has: i. Appreciated and the British will find U.S. goods cheaper. ii. Appreciated and the British will find U.S. goods more expensive. iii. Depreciated and the
> Use the following cash flow data for Rocket Transport to find Rocket’s a. Net cash provided by or used in investing activities. b. Net cash provided by or used in financing activities. c. Net increase or decrease in cash for the year. Cash dividend………………
> A firm has a tax burden ratio of .75, a leverage ratio of 1.25, an interest burden of .6, and a return on sales of 10%. The firm generates $2.40 in sales per dollar of assets. What is the firm’s ROE?
> Michelle Industries issued a Swiss franc–denominated 5-year discount note for SFr200 million. The proceeds were converted to U.S. dollars to purchase capital equipment in the United States. The company wants to hedge this currency exposure and is conside
> Joan Tam, CFA, believes she has identified an arbitrage opportunity for a commodity as indicated by the following information: Spot price for commodity……………………………………………..$120 Futures price for commodity expiring in 1 year……………….$125 Interest rate for 1 y
> Sandra Kapple asks Maria VanHusen about using futures contracts to protect the value of the Star Hospital Pension Plan’s bond portfolio if interest rates rise. VanHusen states: a. “Selling a bond futures contract will generate positive cash flow in a ris
> A firm has an ROE of 3%, a debt-to-equity ratio of .5, and a tax rate of 21% and pays an interest rate of 6% on its debt. What is its operating ROA?
> Maria VanHusen, CFA, suggests that using forward contracts on fixed-income securities can be used to protect the value of the Star Hospital Pension Plan’s bond portfolio against the possibility of rising interest rates. VanHusen prepares the following ex
> How can a perpetuity, which has an infinite maturity, have a duration as short as 10 or 20 years?
> In what circumstances would you choose to use a dividend discount model rather than a free cash flow model to value a firm?
> Consider an increase in the volatility of the stock in the previous problem. Suppose that if the stock increases in price, it will increase to $130, and that if it falls, it will fall to $70. Show that the value of the call option is now higher than the
> You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $120 and a 50% chance of decreasi
> Suppose that the risk-free interest rate is zero. Would an American put option ever be exercised early? Explain
> Return to Example 21.1. Use the binomial model to value a 1-year European put option with exercise price $110 on the stock in that example. Confirm that your solution for the put price satisfies put-call parity.
> You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of $100 at year-end. XYZ currently sells for $100. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bil
> You are very bullish (optimistic) on stock EFG, much more so than the rest of the market. In each question, choose the portfolio strategy that will give you the biggest dollar profit if your bullish forecast turns out to be correct. Explain your answer.
> A collar is established by buying a share of stock for $50, buying a 6-month put option with exercise price $45, and writing a 6-month call option with exercise price $55. On the basis of the volatility of the stock, you calculate that for a strike price
> Hatfield Industries is a large manufacturing conglomerate based in the United States with annual sales in excess of $300 million. Hatfield is currently under investigation by the Securities and Exchange Commission (SEC) for accounting irregularities and
> Consider a 6-month expiration European call option with exercise price $105. The underlying stock sells for $100 a share and pays no dividends. The risk-free rate is 5%. What is the implied volatility of the option if the option currently sells for $8? U
> Should the rate of return of a call option on a long-term Treasury bond be more or less sensitive to changes in interest rates than is the rate of return of the underlying bond?
> Would you expect a $1 increase in a call option’s exercise price to lead to a decrease in the option’s value of more or less than $1?
> Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would experience a slight downturn and suggested delta-hedging the BIC portfolio. U.S. equity markets did indeed fall, but BIC’s portfolio perf
> What would be the Excel formula in Spreadsheet 21.1 for the Black-Scholes value of a straddle position?
> a. Calculate the value of a call option on the stock in Problem 9 with an exercise price of 110. b. Verify that the put-call parity theorem is satisfied by your answers to Problem 9 and part (a). (Do not use continuous compounding to calculate the presen
> We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity theorem as well as a numerical example to prove your answer.
> You are a portfolio manager who uses options positions to customize the risk profile of your clients. In each case, what strategy is best given your client’s objective? a. ∙ Performance to date: Up 16%. ∙ Client objective: Earn at least 15%. ∙ Your for
> The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $50 per share for months, and you believe it is going to stay in that range for the next three months. The price of a 3-month put option with an exercise price of $50
> Why do you think the most actively traded options tend to be the ones that are near the money?
> Hatfield Industries is a large manufacturing conglomerate based in the United States with annual sales in excess of $300 million. Hatfield is currently under investigation by the Securities and Exchange Commission (SEC) for accounting irregularities and
> What are the trade-offs facing an investor who is considering writing a call option on an existing portfolio?
> You think there is great upward potential in the stock market and would like to participate in the upward move if it materializes. However, you are not able to afford substantial stock market losses and so cannot run the risk of a stock market collapse,
> Devise a portfolio using only call options and shares of stock with the following value (payoff) at the option expiration date. If the stock price is currently $55, what kind of bet is the investor making?
> You write a call option with X = 50 and buy a call with X = 60. The options are on the same stock and have the same expiration date. One of the calls sells for $3; the other sells for $9. a. Draw the payoff graph for this strategy at the option expiratio
> You write a put option with X = 100 and buy a put with X = 110. The puts are on the same stock and have the same expiration date. a. Draw the payoff graph for this strategy. b. Draw the profit graph for this strategy. c. If the underlying stock has posit
> Consider the following options portfolio. You write a February 8 expiration call option on Microsoft with exercise price $100. You write a February 8 put option with exercise price $95. a. Graph the payoff of this portfolio at option expiration as a func
> What are the trade-offs facing an investor who is considering buying a put option on an existing portfolio?
> In what ways is owning a corporate bond similar to writing a put option? A call option?
> Some agricultural price support systems have guaranteed farmers a minimum price for their output. Describe the program provisions as an option. What is the asset? The exercise price?
> Jane Joseph, a manager at Computer Science, Inc. (CSI), received 10,000 shares of company stock as part of her compensation package. The stock currently sells at $40 a share. She would like to defer selling the stock until the next tax year. In January,
> Hatfield Industries is a large manufacturing conglomerate based in the United States with annual sales in excess of $300 million. Hatfield is currently under investigation by the Securities and Exchange Commission (SEC) for accounting irregularities and
