Question

1. You have gotten your dream job, which comes with the benefit of a 401(k) plan. You are trying to figure out how to make your investments. While the stock market has been very strong lately, you are afraid it is overdue for a correction. On the other hand, you also want to continue gaining if the stock market keep climbing. You have done a fair bit of analysis and come up with the following payoff table, for the gain or loss on your investment of $5,000 after the next year.

Decisions

State of economy

Weak Economy Moderate Economy Strong Economy

Buy Bond Funds $200 $200 $175

Buy Stock Funds -$1000 $300 $500

a. What are the states of nature in this situation?

b. What are the decisions?

c. Which of decisions or states of nature do you have control over?

d. Suppose you are a conservative decision-maker. What criterion would you use in that case to make your decision?

e. Use your criterion in d. to decide which action to take. Show your work to justify your answer.

f. Suppose you are an optimistic decision-maker. What criterion would you use in that case to make your decision?

g. Use your criterion in f. to decide which action to take. Show your work to justify your answer.

h. Draw the decision tree corresponding to the payout table (pay attention to the correct order and node symbols). Assume that the chance of a weak economy is 0.15 and of a moderate economy is 0.7.

i. Calculate the EV for the possible decisions.

 

j. Which decision would you make if you were to use a probability method? Why?

k. What is the expected value WITHOUT perfect information?

l. What is the expected value WITH perfect information?

m. What is the expected value OF perfect information (EVPI)?

Answer 1

a. The states of nature are weak economy, moderate economy and strong economy.

b. The decisions are to buy bond funds or stock funds.

c. We have control over the decisions to buy stock or bond.

d,e). If I am conservative decision maker I would choose the criteria in which I can minimize my maximum loss or maximize the minimum profit (minimax criteria). From the decisions we see that in bonds minimum profit is 175 and in stocks it is a loss of 1000. So we will choose to buy bonds.

f,g). If I am an optimist decision maker I will choose the criteria which maximizes the profit ie maximax critera. From bonds maximum profit is 200 and in stocks maximum profit is 500, so buying stocks will be the decision here.