Financial Risk Manager Part 1

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Explanation:

The two income-generating avenues (Loans and Stock Market) are independent, so the joint probability for any combination of returns is simply the product of their individual (marginal) probabilities.

Marginal Probabilities (from the given tables):

Loans Return (X₁):

-20%: 30% = 0.30
0%: 55% = 0.55
20%: 15% = 0.15

Stock Market Return (X₂):

-5%: 40% = 0.40
0%: 31% = 0.31
9%: 29% = 0.29

Joint Probability Calculation (P(X₁, X₂) = P(X₁) × P(X₂)):

Now calculate each cell:

For Stock -5% row:

P(-20%, -5%) = 0.30 × 0.40 = 0.12 → 12%
P(0%, -5%) = 0.55 × 0.40 = 0.22 → 22%
P(20%, -5%) = 0.15 × 0.40 = 0.06 → 6%

For Stock 0% row:

P(-20%, 0%) = 0.30 × 0.31 = 0.093 → 9.3%
P(0%, 0%) = 0.55 × 0.31 = 0.1705 → 17.05%
P(20%, 0%) = 0.15 × 0.31 = 0.0465 → 4.65%

For Stock 9% row:

P(-20%, 9%) = 0.30 × 0.29 = 0.087 → 8.7%
P(0%, 9%) = 0.55 × 0.29 = 0.1595 → 15.95%
P(20%, 9%) = 0.15 × 0.29 = 0.0435 → 4.35%

Correct Joint Probability Matrix:

This exactly matches option A:

	Loan Return (X₁)
Stock Market (X₂)	-20%	0%	20%
-5%	12%	22%	6%
0%	9.3%	17.05%	4.65%
9%	8.7%	15.95%	4.35%

Answer: A

Explanation:

The two income-generating avenues (Loans and Stock Market) are independent, so the joint probability for any combination of returns is simply the product of their individual (marginal) probabilities.

Marginal Probabilities (from the given tables):

Loans Return (X₁):

-20%: 30% = 0.30
0%: 55% = 0.55
20%: 15% = 0.15

Stock Market Return (X₂):

-5%: 40% = 0.40
0%: 31% = 0.31
9%: 29% = 0.29

Joint Probability Calculation (P(X₁, X₂) = P(X₁) × P(X₂)):

Now calculate each cell:

For Stock -5% row:

P(-20%, -5%) = 0.30 × 0.40 = 0.12 → 12%
P(0%, -5%) = 0.55 × 0.40 = 0.22 → 22%
P(20%, -5%) = 0.15 × 0.40 = 0.06 → 6%

For Stock 0% row:

P(-20%, 0%) = 0.30 × 0.31 = 0.093 → 9.3%
P(0%, 0%) = 0.55 × 0.31 = 0.1705 → 17.05%
P(20%, 0%) = 0.15 × 0.31 = 0.0465 → 4.65%

For Stock 9% row:

P(-20%, 9%) = 0.30 × 0.29 = 0.087 → 8.7%
P(0%, 9%) = 0.55 × 0.29 = 0.1595 → 15.95%
P(20%, 9%) = 0.15 × 0.29 = 0.0435 → 4.35%

Correct Joint Probability Matrix:

This exactly matches option A:

	Loan Return (X₁)
Stock Market (X₂)	-20%	0%	20%
-5%	12%	22%	6%
0%	9.3%	17.05%	4.65%
9%	8.7%	15.95%	4.35%

Answer: A

Comments (1)

Yash ParwaniApr 13, 2026 6:00 AM

The question is framed incorrectly

LeetQuiz .Apr 13, 2026 7:08 PM

Hi Yash, Sorry for the broken question. We've reviewed the question and corrected the question. Thanks for pointing out !

Q.3750 The resulting probability matrix displays the amount of returns of two income-generating sections of bank: Loans and Stock Market

Loans Return Returns(X₁) -20% 0% 20%
Probability 30% 55% 15%

Stock Market Returns Returns(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)?

Loans Return	Returns(X₁)	-20%	0%	20%
	Probability	30%	55%	15%

Stock Market Returns	Returns(X₂)	-5%	0%	9%
	Probability	40%	31%	29%

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TTanishq

Last updated: April 13, 2026 at 19:07

	Loan Return (X₁)
Stock Market (X₂)	-20%	0%	20%
-5%	12%	22%	6%
0%	9.3%	17.05%	4.65%
9%	8.7%	15.95%	4.35%

42.9%

	Loan Return (X₁)
Stock Market (X₂)	-20%	0%	20%
-5%	12%	12%	7%
0%	10.3%	17.05%	4.65%
9%	8.7%	15.95%	4.35%