You have available five different investment strategies and their respective payoffs for various states-of-nature as shown in the chart below. Which investment would you make under the different decision criteria?
States of Nature
Sever
Decline Moderate Decline Stable Moderate Advance Strong Advance
T-Bills 3.50 3.50 3.50 3.50 3.50
Paragon (22.50) (2.00) 20.00 35.00 50.00
Luster 28.00 14.70 0.00 (10.00) (20.00)
Apex 10.00 5.00 7.00 45.00 30.00
Market (13.00) 5.00 22.00 38.00 Portfolio 47.00
Probability 0.05 0.35 0.30 0.20 0.10
Note: For the following questions, ¡§Investment¡¨ is the name of the strategy not the number, i.e., Luster, Apex, etc.
a)Maximin criteria
Answer: Investment
b)Maximax criteria
Answer:Investment
c)Equally Likely criteria
Answer:Investment
d)Criterion of realism (assume Ą = 0.6)
Answer:Investment
e)Minimax regret criteria
Answer:Investment
f)Criterion of maximum expected value
Answer:Investment
To determine which investment would be made under different decision criteria, we need to understand the decision rules for each criterion and evaluate the payoffs for each investment strategy. Here's how you can find the answer for each criterion:
a) Maximin criteria:
The maximin criteria seeks to maximize the minimum payoff. To find the maximum minimum payoff for each investment strategy, look at the smallest payoff for each strategy and then choose the one with the highest value.
b) Maximax criteria:
The maximax criteria seeks to maximize the maximum payoff. To find the maximum payoff for each investment strategy, look at the highest payoff for each strategy and then choose the one with the highest value.
c) Equally Likely criteria:
The equally likely criteria assumes that each state-of-nature is equally likely to occur. To determine the expected payoff for each investment strategy, multiply each payoff by the probability of its corresponding state-of-nature and then choose the one with the highest expected value.
d) Criterion of realism (assume Ą = 0.6):
The criterion of realism considers a decision maker's level of optimism or pessimism. Multiply each payoff by the probability of its corresponding state-of-nature and then choose the one with the highest weighted average payoff. In this case, assume Ą = 0.6 (the weight for optimism) and 1 - Ą = 0.4 (the weight for pessimism).
e) Minimax regret criteria:
The minimax regret criteria seeks to minimize the maximum regret. Regret is the difference between the highest payoff for a state-of-nature and the payoff for a particular strategy. Calculate the regret for each state-of-nature and then choose the strategy with the smallest maximum regret.
f) Criterion of maximum expected value:
The criterion of maximum expected value simply seeks to maximize the expected payoff. Calculate the expected payoff for each investment strategy by multiplying each payoff by the probability of its corresponding state-of-nature. Then, choose the one with the highest expected value.
By using the decision rules and evaluating the payoffs for each investment strategy, you can determine the investment strategy that would be chosen under each of the given decision criteria.