Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 4

You have \(\$ 1,000\) that you can invest. If you buy Ford stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.2 you will get \(\$ 1,500\); with a probability of 0.4 you will get \(\$ 1,100\); and with a probability of 0.4 you will get \(\$ 900 .\) 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 Ford stock? b. Suppose you are risk-averse. Can we say for sure whether you will invest in Ford stock or put your money into the bank?

Short Answer

Expert verified
Answer: For a risk-averse individual, they will prefer to put their money in the bank rather than investing in Ford stock. This is because the bank option provides a certain outcome of $1,100 while the investment has potential outcomes ranging from $900 to $1,500, despite the equal expected values for both options.

Step by step solution

01

Calculate the expected value of the earnings from investing in Ford stock

To calculate the expected value, multiply the potential outcomes by their corresponding probabilities and sum the results. The expected value of the earnings from investing in Ford stock is: $$ E(Ford)=0.2(\$1,500)+0.4(\$1,100)+0.4(\$900) $$
02

Solve for the expected value

Calculate the expected value: $$ E(Ford)=0.2(\$1,500)+0.4(\$1,100)+0.4(\$900)=\$300+\$440+\$360=\$1,100 $$ So, the expected value of investing in Ford stock for one year is \(\$1,100\).
03

Compare the options

The expected value of investing in Ford stock (\$1,100) is the same as the certain outcome of putting the money in the bank (\$1,100). However, given risk aversion, an individual will generally prefer the option with a certain outcome over the one with uncertainty, even if expected values are equal.
04

Conclusion

For a risk-averse individual, we can say for sure that they will prefer to put their money in the bank rather than investing in Ford stock, because the bank option provides a certain outcome of \$1,100 while the expected value of investing in Ford stock is also \$1,100 but with potential outcomes ranging from \$900 to \$1,500.

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

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?

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.

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?

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?

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.
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