# Demand

### Contents

#### Practice Problems

Problem : Company A and Company B are both selling stock at \$1 a share. If risk-neutral Kenny wants to buy stock in either Company A or Company B, and he thinks that the possible future values for Company A's stock are \$0, \$1, \$5, and \$20, with respective probabilities of 20%, 50%, 20%, and 10%, and that the possible future values of B's stock are \$0, \$1, \$10, and \$100, with respective probabilities of 50%, 30%, 15%, and 5%, which stock will he pick?

Kenny will pick Company B, whose stock has a higher expected value:

Company A:
EV = (0.20)(0) + (0.50)(1) + (0.20)(5) + (0.10)(20) = \$3.50/share

Company B:
EV = (0.50)(0) + (0.30)(1) + (0.15)(10) + (0.05)(100) = \$6.80/share

Problem : Which of the following are high risk investments, and which are low risk?

Gold
Stocks in new companies
IRA's
Savings bonds
Lottery tickets

High risk: socks in new companies, lottery tickets
Low risk: gold, IRA's, savings bonds

Problem : What is the expected value of a stock whose possible future values are \$0, \$1, \$10, and \$60 with respective probabilities of 25%, 50%, 20%, and 5%?

EV = (0.25)(0) + (0.50)(1) + (0.20)(10) + (0.05)(60) = \$5.50 a share

Problem : If the current price of a stock is \$7 a share, will risk-neutral Andy buy any stock if he believes that the possible future values are \$0, \$2, \$5, \$10, and \$50, with respective probabilities of 10%, 15%, 50%, 20%, and 5%?

Yes, because the expected value is higher than the present price.

EV = (0.10)(0) + (0.15)(2) + (0.50)(5) + (0.20)(10) + (0.05)(50)
EV = \$7.30/share

Problem : What is the maximum price that risk-neutral Tamara will be willing to pay for a stock which she believes has possible future values of \$0, \$5, \$10, and \$200, with respective probabilities of 50%, 25%, 24%, and 1%?

EV = (0.50)(0) + (0.25)(5) + (0.24)(10) + (0.01)(200)
EV = \$5.65 a share

Tamara believes that the stock is worth about \$5.65 a share, she will not be willing to pay more than that for a share of stock. If she pays \$5.65 a share, she will have an expected return of 0. If the price is lower than that, she will have positive expected returns.