(18 points) An investor has the opportunity to buy one of four different stocks.
ID: 3260492 • Letter: #
Question
(18 points) 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
Solution:
Payoff table = Number of shares x (Selling price - Purchase price)
Opportunity loss = Highest payoff in a state of nature - Actual payoff
A) Stock 1 is clearly inferior choice. Becasue state 2 return for this stock is positive 60 which is lowest while state 1 return is highest negative.
B) Under Maximax selction will be based on highest yielding stock accordingly stock 4 should be selcted.
C) Pessimistic Minmax: Using opportunity loss table minimum regert is for stock 2 accordingly stock 2 will be selected.
D) Minimax criterion: Using opportunity loss table :
Maximum loss under state 1 = Stock 4
Maximum loss stock under state 2 = Stock 3
Minimum of these 2 = Stock 3.
Accordingly stock 3 will be selected.
E) EMV = State 1 return*Probability + State2 return * Probability
Stock 2 return = 40*.9 + 120*.1 = 48
Stock 3 return = 160*.9 + 80*.1 = 152
Stock 4 return = -100*.9 + 200*.1 = -70
Stock 3 has highest EMV.
F) EVPI = EMV of best market situation - Maximum value of stock's EMV
EMV of best market situation = 160*.9 + 200*.10 = 164
EMV of stock is calculated under part (E) and stock 3 has highest value.
EVPI = 164 - 152
EVPI = 12
Alternatives State 1 State 2 Stock 1 (40-50) x 20 = -200 (53-50)x20=60 Stock 2 (52-50)x20 =40 (56-50)x20=120 Stock 3 (58-50)x20=160 (54-50)x20=80 Stock 4 (45-50)x20=-100 (60-50)x20=200Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.