Model Answer
0 min readIntroduction
Investment decisions often involve uncertainty regarding future returns. Decision-making under uncertainty necessitates employing various criteria to evaluate potential investments. These criteria help investors navigate risk and select the most suitable option based on their risk appetite and beliefs about future outcomes. The Maximin, Equal Likelihood, and Hurwitz criteria are commonly used techniques for making such decisions. This answer will demonstrate how to apply these criteria to determine the best investment option, assuming a hypothetical payoff scenario. The absence of a provided payoff table necessitates its construction for the purpose of illustration.
Understanding the Decision Criteria
Before applying the criteria, let's define each one:
- Maximin Criterion (Pessimistic): This criterion assumes the worst possible outcome for each investment option and then selects the option with the highest of these worst-case scenarios. It prioritizes minimizing potential losses.
- Equal Likelihood Criterion (Optimistic): This criterion assumes that all possible outcomes are equally likely. It calculates the expected value for each investment option and selects the option with the highest expected value.
- Hurwitz Criterion (Coefficient of Optimism): This criterion combines the Maximin and Maximax (most optimistic) criteria using a coefficient of optimism (α). It represents a weighted average of the worst-case and best-case scenarios, where α reflects the investor's degree of optimism.
Hypothetical Payoff Table
Since the question does not provide a payoff table, we will assume the following for three investment options (A, B, and C) under three possible states of the economy (Boom, Normal, Recession):
| Investment Option | Boom (State 1) | Normal (State 2) | Recession (State 3) |
|---|---|---|---|
| A | 50 | 30 | 10 |
| B | 40 | 40 | 20 |
| C | 30 | 50 | 30 |
Applying the Criteria
(i) Maximin Criterion
First, identify the minimum payoff for each investment option:
- Option A: Minimum payoff = 10
- Option B: Minimum payoff = 20
- Option C: Minimum payoff = 30
The Maximin criterion selects the option with the highest minimum payoff, which is Option C (30).
(ii) Equal Likelihood Criterion
Calculate the expected value for each investment option, assuming each state has a probability of 1/3:
- Option A: Expected Value = (50 + 30 + 10) / 3 = 30
- Option B: Expected Value = (40 + 40 + 20) / 3 = 33.33
- Option C: Expected Value = (30 + 50 + 30) / 3 = 36.67
The Equal Likelihood criterion selects the option with the highest expected value, which is Option C (36.67).
(iii) Hurwitz Criterion (α = 0.3)
The Hurwitz criterion uses the formula: Hurwitz Value = α * (Maximum Payoff) + (1 - α) * (Minimum Payoff)
Calculate the Hurwitz value for each option:
- Option A: Hurwitz Value = 0.3 * 50 + 0.7 * 10 = 15 + 7 = 22
- Option B: Hurwitz Value = 0.3 * 40 + 0.7 * 20 = 12 + 14 = 26
- Option C: Hurwitz Value = 0.3 * 50 + 0.7 * 30 = 15 + 21 = 36
The Hurwitz criterion selects the option with the highest Hurwitz value, which is Option C (36).
In this example, all three criteria point to Option C as the best investment option. However, this is not always the case, and the chosen option will depend on the investor's risk tolerance and beliefs about the future.
Conclusion
In conclusion, applying the Maximin, Equal Likelihood, and Hurwitz criteria to the hypothetical payoff table demonstrates how different decision-making approaches can lead to the same or different investment choices. The Maximin criterion prioritizes safety, the Equal Likelihood criterion focuses on average returns, and the Hurwitz criterion offers a balance between optimism and pessimism. The choice of criterion should align with the investor’s risk profile and expectations. Further analysis, including sensitivity analysis and consideration of other factors, is crucial for making informed investment decisions.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.