Financial Risk Manager Part 1
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The resulting probability matrix displays the amount of returns of two income-generating sections of bank: Loans and Stock Market
Loans Returns (X₁) – Marginal Probabilities
| Loans Return (X₁) | -20% | 0% | 20% |
|---|---|---|---|
| Probability | 30% | 55% | 15% |
Stock Market Returns (X₂) – Marginal Probabilities
| Stock Market Return (X₂) | -5% | 0% | 9% |
|---|---|---|---|
| Probability | 40% | 31% | 29% |
Assuming that the two income-generating avenues are independent of each other, what is the joint probability distribution (matrix)?
Other
Community
NNikitesh
A
| Stock Market Returns (X₂) | Loan Return (X₁): -20% | Loan Return (X₁): 0% | Loan Return (X₁): 20% |
|---|---|---|---|
| -5% | 12% | 22% | 6% |
| 0% | 9.3% | 17.05% | 4.65% |
| 9% | 8.7% | 15.95% | 4.35% |
B
| Stock Market Returns (X₂) | Loan Return (X₁): -20% | Loan Return (X₁): 0% | Loan Return (X₁): 20% |
|---|---|---|---|
| -5% | 12% | 12% | 7% |
| 0% | 10.3% | 17.05% | 4.65% |
| 9% | 8.7% | 15.95% | 4.35% |
C
| Stock Market Returns (X₂) | Loan Return (X₁): -20% | Loan Return (X₁): 0% | Loan Return (X₁): 20% |
|---|---|---|---|
| -5% | 12% | 12% | 6% |
| 0% | 9.3% | 27.05% | 5.65% |
| 9% | 8.7% | 25.95% | 4.35% |
D
| Stock Market Returns (X₂) | Loan Return (X₁): -20% | Loan Return (X₁): 0% | Loan Return (X₁): 20% |
|---|---|---|---|
| -5% | 12% | 22% | 6% |
| 0% | 9.3% | 14.05% | 4.65% |
| 9% | 7.7% | 55.95% | 4.35% |
Explanation:
The correct answer is A because the question tests understanding of independence between marginal distributions. When two random variables are independent, their joint probability distribution equals the product of their marginal distributions. The explanation provided states that if two marginal distributions are independent, then f_{(X₁, X₂)}(x₁, x₂) = f_{(X₁)}(x₁)f_{(X₂)}(x₂). The example given shows that the joint probability of loan return being -20% and stock return being -5% is calculated as 30% × 40% = 12%, which matches the value in the table. This demonstrates that Table A correctly represents the joint distribution when the marginal distributions are independent.
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