An investor has the opportunity to buy one of four different stocks. Each stock

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,

A.Are any of the stocks clearly inferior choices? (Explain. You can eliminate any inferior choice(s) from the rest of the analysis).

B. What is the alternative chosen using the optimistic (maximax) criterion?

C. What is the alternative chosen using the pessimistic (minimax) criterion?

D. 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,

E. Calculate the expected monetary value (EMV) for each stock. Which stock would an EMV maximizer choose?

F. 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 years state of nature).

Payoff Table

Alternatives

State 1

State 2

Stock 1

Stock 2

Stock 3

Stock 4

Explanation / Answer

Payoff Table Alternatives State 1 State 2 Stock 1 800 1060 Stock 2 1040 1120 Stock 3 1160 1080 Stock 4 900 1200 Opportunity Loss Alternatives State 1 State 2 Stock 1 360 140 Stock 2 120 80 Stock 3 0 120 Stock 4 260 0 What is the alternative chosen using the optimistic (maximax) criterion? Stock4 1200 What is the alternative chosen using the pessimistic (minimax) criterion Stock 3 1160 What is the alternative chosen using the minimax regret criterion? Stock 3 120 expected monetary value (EMV) for each stock Alternatives State 1 State 2 State 1 .1 State 2 .90 EMV Stock 1 800 1060 80 954 1034 Stock 2 1040 1120 104 1008 1112 Stock 3 1160 1080 116 972 1088 Stock 4 900 1200 90 1080 1170 Which stock would an EMV maximizer choose? Stock 4 Stock 3 1160 0.1 116 Stock 4 1200 0.9 1080 Expected Value Under Certainty 1196

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