Question

One of Mabel Smith’s investments is going to mature, and he wants to determine how to invest the proceeds of $30,000. Mabel is considering two new investments: a stock mutual fund and a one-year certificate of deposit (CD). The CD is guaranteed to pay an 8% return. Mabel estimates the return on the stock mutual fund as 16%, 9%, or 22%, depending on whether market conditions are good, average, or poor, respectively. Mabel estimates the probability of a good, average, and poor market to be 0.1, 0.85, and 0.05, respectively.

a. What decision should be made according to the EMV decision rule?

b. What decision should be made according to the EOL decision rule?

c. How much should Mabel be willing to pay to obtain a market forecast that is 100% accurate?

Answer 1

We calculate Value for each state of nature as shown below:

CD:

8% * 30000 = $2400 for all states of nature

Stock Mutual Fund:

16% * 30000 = 4800

9% * 30000 = 2700

22% * 30000 = 6600

We prepare a payoff table as shown below and find EMV:

The above table in the form of formulas is shown below for better understanding and reference:

As seen from above, the EMV is higher for Stock Mutual funds. Hence, according to the EMV decision rule, Stock Mutual Fund is the best alternative

b) We prepare the opportunity loss matrix as shown below:

The above table in the form of formulas is shown below for better understanding and reference:

As seen from above, the minimum opportunity loss is for Stock Mutual funds. Hence, according to the EOL decision rule, Stock Mutual Fund is the best alternative.

c) To find the value of perfect information:

Step - 1: The best outcome for the state of nature “Good" market is “Stock Mutual funds” with a payoff of 4800. The best outcome for the state of nature “Average” market is “Stock Mutual funds” with a payoff of $2700. The best outcome for the state of nature “Poor” market is “Stock Mutual funds” with a payoff of $6600.

Expected value with perfect information = (4800)(0.1) + (2700)(0.85) + (6600)(0.05) = $3105.

Step-2:

The maximum EMV is $3105 for Stock Mutual funds, which is the expected outcome without perfect information.
Thus:

Expected Value of perfect information EVPI = EVwPI - Maximum EMV
= 3105 - 3105 = $0

Mabel should be willing to pay $0 to obtain a market forecast that is 100% accurate

-----------------------------------------------------------------------------------------------------------------------

In case of any doubt, please ask through the comment section before Upvote/downvote.