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Chapter 20: Problem 9

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.

Short Answer

Expert verified
Answer: A risk-averse investor would prefer to diversify the investment by investing half of the money in Ted and Larry's and half in Ethel's. This strategy provides a more predictable outcome with the same total stock value in both warm and cold weather conditions, making it more suitable for those who are risk-averse.

Step by step solution

01

a. Expected Stock Value for Ted and Larry's

To calculate the expected stock value when investing all the money in Ted and Larry's, we first need to find out how many shares we can buy. Since each share costs \(100 and we have \)1,000 to invest, we can buy 10 shares. Once we know the number of shares, we can calculate the stock value in warm and cold weather conditions: - Warm weather: Ted and Larry's stock value rises to \(150. The total stock value in warm weather is \)150 * 10 = $1,500. - Cold weather: Ted and Larry's stock value falls to \(60. The total stock value in cold weather is \)60 * 10 = $600. There is an equal chance of the weather being warm or cold. Therefore, the expected stock value for investing all the money in Ted and Larry's is: Expected value = (probability of warm weather * stock value in warm weather) + (probability of cold weather * stock value in cold weather) Expected value = (0.5 * \(1,500) + (0.5 * \)600) = $1,050.
02

a. Expected Stock Value for Ethel's

Following the same steps as for Ted and Larry's, we calculate the stock value in warm and cold weather conditions for investing all the money in Ethel's: - Warm weather: Ethel's stock value falls to \(60. The total stock value in warm weather is \)60 * 10 = $600. - Cold weather: Ethel's stock value rises to \(150. The total stock value in cold weather is \)150 * 10 = $1,500. The expected stock value for investing all the money in Ethel's is: Expected value = (0.5 * \(600) + (0.5 * \)1,500) = $1,050.
03

b. Diversifying Investment - Warm and Cold Weather Stock Value

To diversify the investment, we invest half of our money (\(500) in each company. With \)500, we can buy 5 shares of each company. Let's calculate the total stock value for both warm and cold weather conditions: - Warm weather: Ted and Larry's stock value = \(150 * 5 = \)750; Ethel's stock value = \(60 * 5 = \)300. Total stock value = \(750 + \)300 = $1,050. - Cold weather: Ted and Larry's stock value = \(60 * 5 = \)300; Ethel's stock value = \(150 * 5 = \)750. Total stock value = \(300 + \)750 = $1,050.
04

c. Risk-averse Investor Preference

A risk-averse investor prefers investments that have lower risk and more predictable outcomes. In this case, both investing all the money in one company and diversifying the investment have the same expected stock value of $1,050. However, diversifying the investment leads to the same total stock value of $1,050 in both warm and cold weather conditions. This reduces the uncertainty and risk associated with investing in only one company, whose stock value greatly depends on the weather. Therefore, a risk-averse investor would prefer to diversify the investment, as described in part b. This provides a more predictable outcome, which is more suitable for those who are risk-averse.

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Most popular questions from this chapter

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, 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 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?

Kory owns a house that is worth \(\$ 300,000 .\) If the house burns down, she loses all \(\$ 300,000\). If the house does not burn down, she loses nothing. Her house burns down with a probability of 0.02 . Kory is risk-averse. a. What would a fair insurance policy cost? b. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of \(\$ 1,500\). Can you say for sure whether Kory will or will not take the insurance? c. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of \(\$ 6,000\). Can you say for sure whether Kory will or will not take the insurance? d. Suppose that an insurance company offers to insure her fully against the loss from the house burning down, at a premium of \(\$ 9,000\). Can you say for sure whether Kory will or will not take the insurance?

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.
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