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
what are the shortcoming of minimax
To determine which investment to make under different decision criteria, we need to understand the various decision criteria and how they are applied.
a) Maximin criteria:
Under the maximin criteria, we select the investment that maximizes the minimum payoffs across all states of nature. To find the maximum of the minimum payoffs, we compare the minimum payoffs of each investment across different states of nature and select the investment with the highest minimum payoff.
b) Maximax criteria:
Under the maximax criteria, we select the investment that maximizes the maximum payoffs across all states of nature. To find the maximum of the maximum payoffs, we compare the maximum payoffs of each investment across different states of nature and select the investment with the highest maximum payoff.
c) Equally Likely criteria:
Under the equally likely criteria, we assign equal probabilities to each state of nature and calculate the expected payoff for each investment. The investment with the highest expected payoff is selected.
d) Criterion of realism:
The criterion of realism introduces the concept of risk aversion using a risk-aversion factor, denoted as Ą. The expected payoff for each investment is multiplied by (1-Ą) and then added to the minimum payoff for each investment, multiplied by Ą. The investment with the highest adjusted expected payoff is selected.
e) Minimax regret criteria:
Under the minimax regret criteria, we calculate the regret for each investment by finding the difference between the maximum payoff in each state of nature and the payoff of each investment in that state. The investment with the minimum maximum regret is selected.
f) Criterion of maximum expected value:
Under the criterion of maximum expected value, we calculate the expected payoff for each investment by multiplying the payoff in each state of nature by its respective probability and summing them up. The investment with the highest expected payoff is selected.
To determine the answer for each criteria, we need to compute the results for each investment using the given data and formulas. Unfortunately, the provided data is incomplete as the portfolio payoff is missing. Can you please provide the portfolio payoff value for each state of nature?