An investor has the opportunity to buy one of four different stocks. Each stock
ID: 2773296 • Letter: A
Question
An investor has the opportunity to buy one of four different stocks. Each stock is currently selling for $50 per share, and the investor will purchase 20 shares of one of the stocks and sell them one year later. If there is a recession (state 1) the selling prices will be $40, $52, $58, and $45. If there is no recession, the selling prices will be $53, $56, $54, and $60. Complete the payoff table and opportunity loss table below.
Payoff Table
Alternatives
State 1
State 2
Stock 1
Stock 2
Stock 3
Stock 4
Opportunity Loss Table
Alternatives
State 1
State 2
Stock 1
Stock 2
Stock 3
Stock 4
Given the information above,
Are any of the stocks clearly inferior choices? (Explain. You can eliminate any inferior choice(s) from the rest of the analysis).
What is the alternative chosen using the optimistic (maximax) criterion?
What is the alternative chosen using the pessimistic (minimax) criterion?
What is the alternative chosen using the minimax regret criterion?
Over the past 40 years, the probability of any given year being a recessionary year is 0.1. Given this information,
Calculate the expected monetary value (EMV) for each stock. Which stock would an EMV maximizer choose?
Calculate the EVPI (that is, how much the investor should be willing to pay an economist (or a psychic) to tell him, with certainty, next year’s state of nature).
Payoff Table
Alternatives
State 1
State 2
Stock 1
Stock 2
Stock 3
Stock 4
Explanation / Answer
As per the rule, I can answer first four parts only:
Alternatives
State 1
State 2
Stock 1
40
53
Stock 2
52
56
Stock 3
58
54
Stock 4
45
60
2.Opportunity loss table: this table will show amount of profit under the states of economy:
Alternatives
State 1
State 2
Stock 1
40-50 = -10
53-50 =3
Stock 2
52-50 = 2
56-50 =6
Stock 3
58-50 =8
54-50=4
Stock 4
45-50 =-5
60-50 = 10
3.Inferior choice: stock A is the inferior choice as it has the lowest value in the opportunity loss table. So this should be eliminated.
4.Under maximax criterion, we chose maximum of maximum:
Alternatives
State 1
State 2
Maximum
Stock 1
-10
3
3
Stock 2
2
6
6
Stock 3
8
4
8
Stock 4
-5
10
10
Maximum value is 10 for stock 4. Therefore stock 4 should be chosen under maximax criterion.
Alternatives
State 1
State 2
Stock 1
40
53
Stock 2
52
56
Stock 3
58
54
Stock 4
45
60
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