Mickey Lawson is considering investing some money that he inherited. The followi
ID: 3240852 • Letter: M
Question
Mickey Lawson 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:
State of Nature
Decision Alternative
Good Economy
Poor Economy
Stock Market
80000
-20000
Bonds
40000
21000
CDs
25000
25000
Probability
.5
.5
(a) What decision would maximize expected profits?
(b) What is the maximum amount that should be paid for a perfect forecast of the economy?
(c) Develop an opportunity loss table for the investment problem that Mickey Lawson faces.
(d) What decision would minimize the expected opportunity loss?
(e) What is the minimum EOL?
State of Nature
Decision Alternative
Good Economy
Poor Economy
Stock Market
80000
-20000
Bonds
40000
21000
CDs
25000
25000
Probability
.5
.5
Explanation / Answer
a) The expected profits for each decision are as follows:
E (Stock Market) = 80,000*0.5 - 20000*0.5 = 40,000 - (10,000) = 30,000
E (Bonds) = 40,000*0.5 – 21,000*0.5 = 20,000 – 10,500 = 9,500
E (CDs) = 25,000*0.5 – 25,000*0.5 = 12,500 – 12,500 = 0
The maximum expected profit is from decision Stock Market with a maximum expected profit of $30,000, hence, EMV = $30,000
b)
The expected value for perfect information,
EVPI = Expected profit with perfect info – EMV.
The expected profit with perfect information can be determined by choosing the optimal course of action for each states of nature, multiplying its conditional value by the probability and then summing the products.
EPPI = 80,000 * 0.5 + 40,000 * 0.5 + 25,000 * 0.5 = 40,000 + 20,000 + 12,500 = $72,500
the amount that should be paid for perfect forecast of the economy is
EVPI = EPPI – EMV = $72,500 - $30,000 = $42,500
c),d),e)
Total expected opportunity loss-
State of Nature
Decision Alternative Good Economy Poor Economy Maximum in a Row
Stock Market 80000 - 80000 23000 – (-20000) $43,000
Bonds 80000 - 40000 23000 - 21000 $40,000
CDs 80000 - 25000 23000 – 25000 $53,000
Probability .5 .5
Smallest expected opportunity loss based on probability for each state of nature:
Stock Market: $43,000 * .5 = $21,500
Bonds: $40,000 * .5 = $20,000
CDs: $53,000 * .5 = $26,500
With the information above, the best decision would be to invest his monies in Bonds