Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 11.3, Problem 23P
Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are $42.76, $81.33, and, $58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and
- a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%?
- b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Suppose an investor has the opportunity to buy the followingcontract, a stock call option, on March 1. Thecontract allows him to buy 100 shares of ABC stock atthe end of March, April, or May at a guaranteed priceof $50 per share. He can exercise this option at mostonce. For example, if he purchases the stock at the endof March, he can’t purchase more in April or May atthe guaranteed price. The current price of the stock is$50. Each month, assume that the stock price eithergoes up by a dollar (with probability 0.55) or goesdown by a dollar (with probability 0.45). If the investorbuys the contract, he is hoping that the stock price willgo up. The reasoning is that if he buys the contract, theprice goes up to $51, and he buys the stock (that is, heexercises his option) for $50, he can then sell the stockfor $51 and make a profit of $1 per share. On the otherhand, if the stock price goes down, he doesn’t haveto exercise his option; he can just throw the contractaway.a. Use a decision tree…
We are going to invest $1,000 for a period of 6 months.Two potential investments are available: T-bills and gold. Ifthe $1,000 is invested in T-bills, we are certain to end the6-month period with $1,296. If we invest in gold, there is a34chance that we will end the 6-month period with $400 anda 14chance that we will end the 6-month period with $10,000.If we end up with x dollars, our utility function is given byu(x) x1/2. Should we invest in gold or T-bills?
Company A's stock sells for $142 a share and has a 3-year average annual return of $27 per share. The beta value, a measure of risk, is 0.38. Company B sells for $149 a share and has a 3-year average annual return of $61 a share. The beta value is 1.23. Tori wants to spend no more than $12000 investing in these two stocks, but she wants to obtain at least $3000 in annual revenue. Tori also wants to minimize the risk, that is, the beta value. Determine how many shares of each stock Tori should buy.
Chapter 11 Solutions
Practical Management Science
Ch. 11.2 - If the number of competitors in Example 11.1...Ch. 11.2 - In Example 11.1, the possible profits vary from...Ch. 11.2 - Referring to Example 11.1, if the average bid for...Ch. 11.2 - See how sensitive the results in Example 11.2 are...Ch. 11.2 - In Example 11.2, the gamma distribution was used...Ch. 11.2 - Prob. 6PCh. 11.2 - In Example 11.3, suppose you want to run five...Ch. 11.2 - In Example 11.3, if a batch fails to pass...Ch. 11.3 - Rerun the new car simulation from Example 11.4,...Ch. 11.3 - Rerun the new car simulation from Example 11.4,...
Ch. 11.3 - In the cash balance model from Example 11.5, the...Ch. 11.3 - Prob. 12PCh. 11.3 - Prob. 13PCh. 11.3 - The simulation output from Example 11.6 indicates...Ch. 11.3 - Prob. 15PCh. 11.3 - Referring to the retirement example in Example...Ch. 11.3 - A European put option allows an investor to sell a...Ch. 11.3 - Prob. 18PCh. 11.3 - Prob. 19PCh. 11.3 - Based on Kelly (1956). You currently have 100....Ch. 11.3 - Amanda has 30 years to save for her retirement. At...Ch. 11.3 - In the financial world, there are many types of...Ch. 11.3 - Suppose you currently have a portfolio of three...Ch. 11.3 - If you own a stock, buying a put option on the...Ch. 11.3 - Prob. 25PCh. 11.3 - Prob. 26PCh. 11.3 - Prob. 27PCh. 11.3 - Prob. 28PCh. 11.4 - Prob. 29PCh. 11.4 - Seas Beginning sells clothing by mail order. An...Ch. 11.4 - Based on Babich (1992). Suppose that each week...Ch. 11.4 - The customer loyalty model in Example 11.9 assumes...Ch. 11.4 - Prob. 33PCh. 11.4 - Suppose that GLC earns a 2000 profit each time a...Ch. 11.4 - Prob. 35PCh. 11.5 - A martingale betting strategy works as follows....Ch. 11.5 - The game of Chuck-a-Luck is played as follows: You...Ch. 11.5 - You have 5 and your opponent has 10. You flip a...Ch. 11.5 - Assume a very good NBA team has a 70% chance of...Ch. 11.5 - Consider the following card game. The player and...Ch. 11.5 - Prob. 42PCh. 11 - You now have 5000. You will toss a fair coin four...Ch. 11 - You now have 10,000, all of which is invested in a...Ch. 11 - Suppose you have invested 25% of your portfolio in...Ch. 11 - Prob. 47PCh. 11 - Based on Marcus (1990). The Balboa mutual fund has...Ch. 11 - Prob. 50PCh. 11 - Prob. 52PCh. 11 - The annual demand for Prizdol, a prescription drug...Ch. 11 - Prob. 54PCh. 11 - The DC Cisco office is trying to predict the...Ch. 11 - A common decision is whether a company should buy...Ch. 11 - Suppose you begin year 1 with 5000. At the...Ch. 11 - You are considering a 10-year investment project....Ch. 11 - Play Things is developing a new Lady Gaga doll....Ch. 11 - An automobile manufacturer is considering whether...Ch. 11 - It costs a pharmaceutical company 75,000 to...Ch. 11 - Prob. 65PCh. 11 - Rework the previous problem for a case in which...Ch. 11 - Prob. 68PCh. 11 - The Tinkan Company produces one-pound cans for the...Ch. 11 - Prob. 70PCh. 11 - In this version of dice blackjack, you toss a...Ch. 11 - Prob. 76PCh. 11 - It is January 1 of year 0, and Merck is trying to...Ch. 11 - Suppose you are an HR (human resources) manager at...Ch. 11 - You are an avid basketball fan, and you would like...Ch. 11 - Suppose you are a financial analyst and your...Ch. 11 - Software development is an inherently risky and...Ch. 11 - Health care is continually in the news. Can (or...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?arrow_forwardA 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.)arrow_forwardBased on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low level of effort, or (3) put forth a high level of effort. Suppose for simplicity that each salesperson will sell 0, 5000, or 50,000 worth of brushes. The probability of each sales amount depends on the effort level as described in the file P07_71.xlsx. If a salesperson is paid w dollars, he or she regards this as a benefit of w1/2 units. In addition, low effort costs the salesperson 0 benefit units, whereas high effort costs 50 benefit units. If a salesperson were to quit Fuller and work elsewhere, he or she could earn a benefit of 20 units. Fuller wants all salespeople to put forth a high level of effort. The question is how to minimize the cost of encouraging them to do so. The company cannot observe the level of effort put forth by a salesperson, but it can observe the size of his or her sales. Thus, the wage paid to the salesperson is completely determined by the size of the sale. This means that Fuller must determine w0, the wage paid for sales of 0; w5000, the wage paid for sales of 5000; and w50,000, the wage paid for sales of 50,000. These wages must be set so that the salespeople value the expected benefit from high effort more than quitting and more than low effort. Determine how to minimize the expected cost of ensuring that all salespeople put forth high effort. (This problem is an example of agency theory.)arrow_forward
- In 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_forwardIn August of the current year, a car dealer is trying to determine how many cars of the next model year to order. Each car ordered in August costs 20,000. The demand for the dealers next year models has the probability distribution shown in the file P10_12.xlsx. Each car sells for 25,000. If demand for next years cars exceeds the number of cars ordered in August, the dealer must reorder at a cost of 22,000 per car. Excess cars can be disposed of at 17,000 per car. Use simulation to determine how many cars to order in August. For your optimal order quantity, find a 95% confidence interval for the expected profit.arrow_forwardReferring to the retirement example in Example 11.6, rerun the model for a planning horizon of 10 years; 15 years; 25 years. For each, which set of investment weights maximizes the VAR 5% (the 5th percentile) of final cash in todays dollars? Does it appear that a portfolio heavy in stocks is better for long horizons but not for shorter horizons?arrow_forward
- An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors: The fixed cost of developing the Racer is triangularly distributed with parameters 3, 4, and 5, all in billions. Year 1 sales are normally distributed with mean 200,000 and standard deviation 50,000. Year 2 sales are normally distributed with mean equal to actual year 1 sales and standard deviation 50,000. Year 3 sales are normally distributed with mean equal to actual year 2 sales and standard deviation 50,000. The selling price in year 1 is 25,000. The year 2 selling price will be 1.05[year 1 price + 50 (% diff1)] where % diff1 is the number of percentage points by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the year 1 sales figure is 180,000, which is 10 percentage points below the expected year 1 sales, then the year 2 price will be 1.05[25,000 + 50( 10)] = 25,725. Similarly, the year 3 price will be 1.05[year 2 price + 50(% diff2)] where % diff2 is the percentage by which actual year 2 sales differ from expected year 2 sales. The variable cost in year 1 is triangularly distributed with parameters 10,000, 12,000, and 15,000, and it is assumed to increase by 5% each year. Your goal is to estimate the NPV of the new car during its first three years. Assume that the company is able to produce exactly as many cars as it can sell. Also, assume that cash flows are discounted at 10%. Simulate 1000 trials to estimate the mean and standard deviation of the NPV for the first three years of sales. Also, determine an interval such that you are 95% certain that the NPV of the Racer during its first three years of operation will be within this interval.arrow_forwardThe stocks in Example 7.9 are all positively correlated. What happens when they are negatively correlated? Answer for each of the following scenarios. In each case, two of the three correlations are the negatives of their original values. Discuss the differences between the optimal portfolios in these three scenarios. a. Change the signs of the correlations between stocks 1 and 2 and between stocks 1 and 3. (Here, stock 1 tends to go in a different direction from stocks 2 and 3.) b. Change the signs of the correlations between stocks 1 and 2 and between stocks 2 and 3. (Here, stock 2 tends to go in a different direction from stocks 1 and 3.) c. Change the signs of the correlations between stocks 1 and 3 and between stocks 2 and 3. (Here, stock 3 tends to go in a different direction from stocks 1 and 2.) EXAMPLE 7.9 PORTFOLIO SELECTION AT PERLMAN BROTHERS Perlman Brothers, an investment company, intends to invest a given amount of money in three stocks. From past data, the means and standard deviations of annual returns have been estimated as shown in Table 7.2. The correlations among the annual returns on the stocks are listed in Table 7.3. The company wants to find a minimum-variance portfolio that yields a mean annual return of at least 0.12.arrow_forwardIt is surprising (but true) that if 23 people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that if 30 people are in the same room, at least two of them will have the same birthday. You can proceed as follows. a. Generate random birthdays for 30 different people. Ignoring the possibility of a leap year, each person has a 1/365 chance of having a given birthday (label the days of the year 1 to 365). You can use the RANDBETWEEN function to generate birthdays. b. Once you have generated 30 peoples birthdays, how can you tell whether at least two people have the same birthday? One way is to use Excels RANK function. (You can learn how to use this function in Excels online help.) This function returns the rank of a number relative to a given group of numbers. In the case of a tie, two numbers are given the same rank. For example, if the set of numbers is 4, 3, 2, 5, the RANK function returns 2, 3, 4, 1. (By default, RANK gives 1 to the largest number.) If the set of numbers is 4, 3, 2, 4, the RANK function returns 1, 3, 4, 1. c. After using the RANK function, you should be able to determine whether at least two of the 30 people have the same birthday. What is the (estimated) probability that this occurs?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Single Exponential Smoothing & Weighted Moving Average Time Series Forecasting; Author: Matt Macarty;https://www.youtube.com/watch?v=IjETktmL4Kg;License: Standard YouTube License, CC-BY
Introduction to Forecasting - with Examples; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=98K7AG32qv8;License: Standard Youtube License