Question

Mickey Johnson is considering investing some money that he inherited. The following payoff table gives the               profits that would be realized during the next year for each of three investment alternatives Mickey is               considering (You should calculate the results to support your conclusions to get the credit): (10 points)

	State of Nature
Decision Alternative	Good Economy	Poor Economy
Stock market	50,000	-20,000
Bonds	30,000	15,000
CDs	20,000	20,000
Probability	0.8	0.2

1. What decision would maximize expected profits? (4 points)

2. What is the maximum amount that should be paid for a perfect forecast of the economy? (3 points)

3. Develop an opportunity loss table for the investment problem that Mickey Lawson faces. What decision would minimize the expected opportunity loss? What is the minimum EOL? (3 points)

Answer 1

a) Based on the given data, we find the Expected Monetary Value for each alternative as shown below:

As seen from above, the decision of Stock Market would maximize the expected profits.

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

b) We find the expected value of perfect information as:

The best outcome for the state of nature "Good Economy" is “Stock Market” with a payoff of 50000. The best outcome for the state of nature “Poor Economy” is “CDs” with a payoff of $20000.

Expected value with perfect information = 50000*0.8 + 20000*0.2 = 44000

Hence, the maximum amount that should be paid for a perfect forecast of the economy = Expected value with perfect information - Maximum EMV = 44000 - 36000 = $8000

c) We prepare an opportunity loss table as shown below:

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

Hence, the decision that would minimize the expected opportunity loss = Bonds. The minimum EOL = $20000

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