Financial Risk Manager Part 1
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Recall that if two marginal distributions are independent then:
f₍ₓ₁,ₓ₂₎(x₁, x₂) = f₍ₓ₁₎(x₁) f₍ₓ₂₎(x₂)
We are given the marginal distributions so that the joint distributions are given by multiplying their corresponding PMFs. For example, the joint probability that loan return is -20%, and the stock return is -5% is 30% × 40% = 12.
The other joint distributions are given in the table below:
| Loan | Return (X₁) | |
|---|---|---|
| –20% | 0% | |
| Stock | –5% | 12% |
| Market | 0% | 9.3% |
| Returns(X₂) | 9% | 7.7% |
A. Table A
B. Table B
C. Table C
D. Table D
Explanation:
The correct answer is A because when two marginal distributions are independent, the joint probability distribution is obtained by multiplying the corresponding marginal probabilities.
Explanation:
- For independent random variables X₁ and X₂, the joint probability f₍ₓ₁,ₓ₂₎(x₁, x₂) equals the product of the marginal probabilities f₍ₓ₁₎(x₁) × f₍ₓ₂₎(x₂)
- The example given shows: joint probability for loan return -20% and stock return -5% = 30% × 40% = 12%
- This demonstrates the multiplication principle for independent distributions
- Table A correctly represents the joint distribution calculated by multiplying the marginal probabilities
This concept is fundamental in probability theory and quantitative analysis, particularly when dealing with independent random variables in financial modeling.