Concept explainers
A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is $48, and the stock price is $45 on the exercise date, the investor can sell the stock for $48 and then immediately buy it back (that is, cover his position) for $45, making $3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)
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Chapter 11 Solutions
Practical Management Science
- A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.arrow_forwardIn the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?arrow_forwardIf you own a stock, buying a put option on the stock will greatly reduce your risk. This is the idea behind portfolio insurance. To illustrate, consider a stock that currently sells for 56 and has an annual volatility of 30%. Assume the risk-free rate is 8%, and you estimate that the stocks annual growth rate is 12%. a. Suppose you own 100 shares of this stock. Use simulation to estimate the probability distribution of the percentage return earned on this stock during a one-year period. b. Now suppose you also buy a put option (for 238) on the stock. The option has an exercise price of 50 and an exercise date one year from now. Use simulation to estimate the probability distribution of the percentage return on your portfolio over a one-year period. Can you see why this strategy is called a portfolio insurance strategy? c. Use simulation to show that the put option should, indeed, sell for about 238.arrow_forward
- Amanda has 30 years to save for her retirement. At the beginning of each year, she puts 5000 into her retirement account. At any point in time, all of Amandas retirement funds are tied up in the stock market. Suppose the annual return on stocks follows a normal distribution with mean 12% and standard deviation 25%. What is the probability that at the end of 30 years, Amanda will have reached her goal of having 1,000,000 for retirement? Assume that if Amanda reaches her goal before 30 years, she will stop investing. (Hint: Each year you should keep track of Amandas beginning cash positionfor year 1, this is 5000and Amandas ending cash position. Of course, Amandas ending cash position for a given year is a function of her beginning cash position and the return on stocks for that year. To estimate the probability that Amanda meets her goal, use an IF statement that returns 1 if she meets her goal and 0 otherwise.)arrow_forwardIt is January 1 of year 0, and Merck is trying to determine whether to continue development of a new drug. The following information is relevant. You can assume that all cash flows occur at the ends of the respective years. Clinical trials (the trials where the drug is tested on humans) are equally likely to be completed in year 1 or 2. There is an 80% chance that clinical trials will succeed. If these trials fail, the FDA will not allow the drug to be marketed. The cost of clinical trials is assumed to follow a triangular distribution with best case 100 million, most likely case 150 million, and worst case 250 million. Clinical trial costs are incurred at the end of the year clinical trials are completed. If clinical trials succeed, the drug will be sold for five years, earning a profit of 6 per unit sold. If clinical trials succeed, a plant will be built during the same year trials are completed. The cost of the plant is assumed to follow a triangular distribution with best case 1 billion, most likely case 1.5 billion, and worst case 2.5 billion. The plant cost will be depreciated on a straight-line basis during the five years of sales. Sales begin the year after successful clinical trials. Of course, if the clinical trials fail, there are no sales. During the first year of sales, Merck believe sales will be between 100 million and 200 million units. Sales of 140 million units are assumed to be three times as likely as sales of 120 million units, and sales of 160 million units are assumed to be twice as likely as sales of 120 million units. Merck assumes that for years 2 to 5 that the drug is on the market, the growth rate will be the same each year. The annual growth in sales will be between 5% and 15%. There is a 25% chance that the annual growth will be 7% or less, a 50% chance that it will be 9% or less, and a 75% chance that it will be 12% or less. Cash flows are discounted 15% per year, and the tax rate is 40%. Use simulation to model Mercks situation. Based on the simulation output, would you recommend that Merck continue developing? Explain your reasoning. What are the three key drivers of the projects NPV? (Hint: The way the uncertainty about the first year sales is stated suggests using the General distribution, implemented with the RISKGENERAL function. Similarly, the way the uncertainty about the annual growth rate is stated suggests using the Cumul distribution, implemented with the RISKCUMUL function. Look these functions up in @RISKs online help.)arrow_forwardAssume that at the beginning of the year, you purchase an investment for $5,480 that pays $138 annual income. Also assume the investment’s value has decreased to $5,080 by the end of the year. What is the rate of return for this investment?arrow_forward
- A 10% coupon $1,000 par value bond with four years to maturity is currently selling for $900. The bond pays coupon payments on a semiannual basis. If interest rates move in the corporation's favor, the bond will be called for $1,050. What is the bond's yield to maturity? 13.30% 11.65% 10.00% 8.48%arrow_forwardThe owner of a copper mine gets together with all the other copper mine owners and agrees to enter a trust with them. The board of “trustees” for this copper trust then sets the price of copper much higher than they were selling it for before. Is this a vertical integration or a horizontal integration?arrow_forwardEllen is a leading comedian in the USA. A movie producing company and a TV network both want exclusive rights to her latest comedy series. The TV network is willing to pay a single lump sum, but if she signed with the movie company, the sum she receives will depend on how the market responds to her series. The network is willing to pay a flat $900,000-00. The movie company is prepared to pay $200,000-00, $1,001, 000-00, and $3,000,000-00 for a ‘Minimal Hit’, ‘Average Hit’, and ‘Massive Hit’, respectively. The statisticians are forecasting a 30% probability of a minimal hit, 60% for an average hit, and a 10% for massive hit. Required: a) Construct a decision tree of the above situation clearly identifying the decision and chance nodes. b) What are the expected payoffs for each decision and what would be your recommendation to Ellen? c) If Ellen had the relevant information on all the possibilities, what would be her expected payoff? d) What price would you recommend she pays to acquire…arrow_forward
- An annuity pays $25,000 semiannually (every 6 months) for 12 years. An alternative investment’s APR is 10% with quarterly compounding. What is the value of this annuity?arrow_forwardWhich of the following statement is true? O For any type of derivatives, the payoffs will never be negative For any type of derivatives, the profit will never be negative There is no derivative that offers non-negative payoffs There is no derivative that offers non-negative profit All of the statements above are wrongarrow_forwardIf all the individual land parcels in a new housing development are sold for $300,000 each, the developer projects total revenue from land sales will be $120 million. If the land lender requires that their $60 million land loan be completely paid off by the time that 75% of the individual land parcels have been sold, what would be the lender’s minimum release price for each parcel? a. $150,000 b. $200,000 c. $250,000 d.$300,000arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,