Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 8

Eva is risk-averse. Currently she has \(\$ 50,000\) to invest. She faces the following choice: she can invest in the stock of a dot-com company, or she can invest in IBM stock. If she invests in the dot-com company, then with probability 0.5 she will lose \(\$ 30,000\), but with probability 0.5 she will gain \(\$ 50,000\). If she invests in IBM stock, then with probability 0.5 she will lose only \(\$ 10,000,\) but with probability 0.5 she will gain only $\$ 30,000$. Can you tell which investment she will prefer to make?

Short Answer

Expert verified
Answer: Eva is more likely to choose the IBM investment due to its lower potential loss of $10,000 compared to the dot-com investment's potential loss of $30,000, even though both investments have the same expected value of $10,000.

Step by step solution

01

Calculate the expected value of each investment

To calculate the expected value of each investment, multiply the gain/loss amount of each outcome by their respective probabilities, and then add them together. For the dot-com investment: Expected Value = (0.5 * (-\(30,000)) + (0.5 * \)50,000) For the IBM investment: Expected Value = (0.5 * (-\$10,000)) + (0.5 * \$30,000)
02

Computations

Now let's perform the calculations for each investment: Dot-com investment Expected Value: = (-\$15,000) + (\$25,000) = \$10,000 IBM investment Expected Value: = (-\$5,000) + (\$15,000) = \$10,000
03

Comparing the expected values

Both the dot-com and IBM investments have the same expected value of \$10,000. However, the dot-com investment has a higher potential loss of \$30,000, while the IBM investment has a smaller potential loss of only \$10,000.
04

Conclusion

Since Eva is risk-averse, she will prioritize minimizing potential losses over potential gains with the same expected value. Therefore, she will likely prefer investing in the IBM stock as it has a lower potential loss when compared to the dot-com investment.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

From 1990 to 2013,1 in approximately every 277 cars produced in the United States was stolen. Beth owns a car worth \(\$ 20,000\) and is considering purchasing an insurance policy to protect herself from car theft. For the following questions, assume that the chance of car theft is the same in all regions and across all car models. a. What should the premium for a fair insurance policy have been in 2013 for a policy that replaces Beth's car if it is stolen? b. Suppose an insurance company charges \(0.6 \%\) of the car's value for a policy that pays for replacing a stolen car. How much will the policy cost Beth? c. Will Beth purchase the insurance in part b if she is risk-neutral? d. Discuss a possible moral hazard problem facing Beth's insurance company if she purchases the insurance.

You have \(\$ 1,000\) that you can invest. If you buy General Motors stock, then, in one year's time: with a probability of 0.4 you will get \(\$ 1,600\); with a probability of 0.4 you will get \(\$ 1,100\); and with a probability of 0.2 you will get \(\$ 800\). If you put the money into the bank, in one year's time you will get \(\$ 1,100\) for certain. a. What is the expected value of your earnings from investing in General Motors stock? b. Suppose you prefer putting your money into the bank to investing it in General Motors stock. What does that tell us about your attitude to risk?

For each of the following situations, do the following: first describe whether it is a situation of moral hazard or of adverse selection. Then explain what inefficiency can arise from this situation and explain how the proposed solution reduces the inefficiency. a. When you buy a second-hand car, you do not know whether it is a lemon (low quality) or a plum (high quality), but the seller knows. A solution is for sellers to offer a warranty with the car that pays for repair costs. b. Some people are prone to see doctors unnecessarily for minor complaints like headaches, and health maintenance organizations do not know how urgently you need a doctor. A solution is for insurees to have to make a co-payment of a certain dollar amount (for example, \(\$ 10\) ) each time they visit a health care provider. All insurees are risk-averse. c. When airlines sell tickets, they do not know whether a buyer is a business traveler (who is willing to pay a lot for a seat) or a leisure traveler (who has a low willingness to pay). A solution for a profit-maximizing airline is to offer an expensive ticket that is very flexible (it allows date and route changes) and a cheap ticket that is very inflexible (it has to be booked in advance and cannot be changed). d. A company does not know whether workers on an assembly line work hard or whether they slack off. A solution is to pay the workers "piece rates," that is, pay them according to how much they have produced each day. All workers are risk-averse, but the company is not risk-neutral. e. When making a decision about hiring you, prospective employers do not know whether you are a productive or unproductive worker. A solution is for productive workers to provide potential employers with references from previous employers.

Suppose you have \(\$ 1,000\) that you can invest in Ted and Larry's Ice Cream Parlor and/or Ethel's House of Cocoa. The price of a share of stock in either company is \(\$ 100\). The fortunes of each company are closely linked to the weather. When it is warm, the value of Ted and Larry's stock rises to \(\$ 150\) but the value of Ethel's stock falls to \$60. When it is cold, the value of Ethel's stock rises to \(\$ 150\) but the value of Ted and Larry's stock falls to \(\$ 60\). There is an equal chance of the weather being warm or cold. a. If you invest all your money in Ted and Larry's, what is your expected stock value? What if you invest all your money in Ethel's? b. Suppose you diversify and invest half of your \(\$ 1,000\) in each company. How much will your total stock be worth if the weather is warm? What if it is cold? c. Suppose you are risk-averse. Would you prefer to put all your money in Ted and Larry's, as in part a? Or would you prefer to diversify, as in part b? Explain your reasoning.

For each of the following situations, calculate the expected value. a. Tanisha owns one share of IBM stock, which is currently trading at $\$ 80 .\( There is a \)50 \%\( chance that the share price will rise to \)\$ 100$ and a \(50 \%\) chance that it will fall to \(\$ 70\). What is the expected value of the future share price? b. Sharon buys a ticket in a small lottery. There is a probability of 0.7 that she will win nothing, of 0.2 that she will win \(\$ 10,\) and of 0.1 that she will win \(\$ 50 .\) What is the expected value of Sharon's winnings? c. Aaron is a farmer whose rice crop depends on the weather. If the weather is favorable, he will make a profit of \(\$ 100\). If the weather is unfavorable, he will make a profit of \(-\$ 20\) (that is, he will lose money). The weather forecast reports that the probability of weather being favorable is 0.9 and the probability of weather being unfavorable is \(0.1 .\) What is the expected value of Aaron's profit?
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free