Question

2. An investor has to invest for a period of one year. She must decide whether to invest the money in a stock her broker recommends or in an insured bond fund. If she invests in the fund, she will collect $1,100 (her original $1000 + a profit of $100). If she invests in the stock and there is a merger, she will realize $1800) (her original $1,000 + a profit of $800). If she invests in the stock and there is no merger, she will receive only $900 (a loss of $100). The probability that there will be a merger is 0.40. Assume that units of utility can be correlated with dollars (no other utilities are involved in this decision).

a. What is the probability that no merger will occur?

b. What is the expected utility of investing in the bond fund?

c. What is the expected utility of investing in the stock?

d. What decision rule should the investor use?

e. What is the rational decision in this case?

Answer 1

a. What is the probability that no merger will occur

Probability = 1- 0.4 = 0.6

b. What is the expected utility of investing in the bond fund

Expecetd utility = profit

= 100

c. What is the expected utility of investing in the stock

= 0.4 * 800 + 0.6 *(-100)

= 320 - 60 = 260

d. What decision rule should the investor use

Invester should invest in stock

e. What is the rational decision in this case

As we can see utility for stock is greater than bond.

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