Question

2.Felix Kamuche has always been proud of his personal investment strategies and has done very well over the last several years. He invests primarily in the stock market. Over the last several months, however, Felix has become very concerned about the stock market as a good investment. In some cases, it would have been better for Felix to have his money in a bank than in stock market. During the next six months, Felix must decide whether to invest $20,000 in the stock market or in a six-month certificate of deposit (CD) at an interest rate of 10%. If the market is good, Felix believes that he could get a 15% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get no return at all in other words; the return would be 0%. Felix estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2. (a) Develop a decision table for this problem. (b) What is the best decision using EMV? (c) Construct an opportunity loss table (d) Determine EOL and the best strategy. (e) What is the expected value of perfect information? (fWhat is the maximin decision?

Answer 1

A.

Decision Table:

		State of nature
		Good	Fair	Bad
Alternative	Stocks	3000	1600	0
	Bank	2000	2000	2000
	Probability	0.4	0.4	0.2

B.

EMV(Stocks) = 0.4*3000 + 0.4*1600 + 0.2*0

= 1840

EMV(Bank) = 0.4*2000 + 0.4*2000 + 0.2*2000

= 2000

Best decision using EMV = Bank

C.

Opportunity Loss Table is created by subtracting payoff of each state of nature from the best payoff of that state. e.g. for stock and good it is calculated by 3000 - 3000 = 0 and for bank and good it is calculated by 3000-2000 = 1000 and so on.

Opportunity Loss Table:

		State of nature
		Good	Fair	Bad	Expected Regret
Alternative	Stocks	0	400	2000	560
	Bank	1000	0	0	400
	Probability	0.4	0.4	0.2

D.

EOL will be calculated in the same way as EMV was calculated and is given in the above table.

Best Decision = Bank (As the regret is less)

E.

Expected Value of Perfect Information (EVPI) Calculation of EVPI • EVPL = ERPI - EREV Where, EREV: Expected Return of the EV approach ERPI: Expected Return with Perfect Information - Expected Return with Perfect Information ERPI= (best payoff for first state of nature) < (probability of first state of nature) + (best payoff for second state of nature) x (probability of second state of nature) + ... + (best payoff for last state of nature)x (probability of last state of nature

ERPI = 3000*0.4 + 2000*0.4 + 2000*0.2

= 2400

EREV = Largest EMV

= 2000

ERPI = 2400- 2000

= 400

F.

Maximin Approach = maximizes the minimum payoff

Table:

		State of nature
		Good	Fair	Bad	Minimum in a row
Alternative	Stocks	3000	1600	0	0
	Bank	2000	2000	2000	2000

Thus Optimal decision is Bank as the minima is maximized.

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