Financial Risk Manager Part 1

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Explanation:

Explanation

For independent events, the joint probability is calculated by multiplying the individual probabilities:

Given probabilities:

Loans: P(-20%) = 30% = 0.30, P(0%) = 55% = 0.55, P(20%) = 15% = 0.15
Stock Market: P(-5%) = 40% = 0.40, P(0%) = 31% = 0.31, P(9%) = 29% = 0.29

Joint probability calculations:

P(-20%, -5%) = 0.30 × 0.40 = 0.12
P(-20%, 0%) = 0.30 × 0.31 = 0.093
P(-20%, 9%) = 0.30 × 0.29 = 0.087
P(0%, -5%) = 0.55 × 0.40 = 0.22
P(0%, 0%) = 0.55 × 0.31 = 0.1705
P(0%, 9%) = 0.55 × 0.29 = 0.1595
P(20%, -5%) = 0.15 × 0.40 = 0.06
P(20%, 0%) = 0.15 × 0.31 = 0.0465
P(20%, 9%) = 0.15 × 0.29 = 0.0435

Option E correctly shows these joint probabilities in decimal form, which is the standard representation for probability distributions.

Explanation:

Explanation

For independent events, the joint probability is calculated by multiplying the individual probabilities:

Given probabilities:

Loans: P(-20%) = 30% = 0.30, P(0%) = 55% = 0.55, P(20%) = 15% = 0.15
Stock Market: P(-5%) = 40% = 0.40, P(0%) = 31% = 0.31, P(9%) = 29% = 0.29

Joint probability calculations:

P(-20%, -5%) = 0.30 × 0.40 = 0.12
P(-20%, 0%) = 0.30 × 0.31 = 0.093
P(-20%, 9%) = 0.30 × 0.29 = 0.087
P(0%, -5%) = 0.55 × 0.40 = 0.22
P(0%, 0%) = 0.55 × 0.31 = 0.1705
P(0%, 9%) = 0.55 × 0.29 = 0.1595
P(20%, -5%) = 0.15 × 0.40 = 0.06
P(20%, 0%) = 0.15 × 0.31 = 0.0465
P(20%, 9%) = 0.15 × 0.29 = 0.0435

Option E correctly shows these joint probabilities in decimal form, which is the standard representation for probability distributions.

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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 Return Returns(X₁) Probability –20% 0% 20%
30% 55% 15%
Stock Market Returns Returns(X₂) Probability –5% 0% 9%
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) Probability	–20%	0%	20%
		30%	55%	15%
Stock Market Returns	Returns(X₂) Probability	–5%	0%	9%
		40%	31%	29%

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TTanishq

Joint probability matrix with probabilities: (-20%, -5%) = 12%, (-20%, 0%) = 9.3%, (-20%, 9%) = 8.7%, (0%, -5%) = 22%, (0%, 0%) = 17.05%, (0%, 9%) = 15.95%, (20%, -5%) = 6%, (20%, 0%) = 4.65%, (20%, 9%) = 4.35%

38.5%

Joint probability matrix with probabilities: (-20%, -5%) = 30%, (-20%, 0%) = 30%, (-20%, 9%) = 30%, (0%, -5%) = 55%, (0%, 0%) = 55%, (0%, 9%) = 55%, (20%, -5%) = 15%, (20%, 0%) = 15%, (20%, 9%) = 15%

15.4%

Joint probability matrix with probabilities: (-20%, -5%) = 70%, (-20%, 0%) = 86%, (-20%, 9%) = 44%, (0%, -5%) = 95%, (0%, 0%) = 86%, (0%, 9%) = 44%, (20%, -5%) = 70%, (20%, 0%) = 86%, (20%, 9%) = 44%

Joint probability matrix with probabilities: (-20%, -5%) = 0.12, (-20%, 0%) = 0.093, (-20%, 9%) = 0.087, (0%, -5%) = 0.22, (0%, 0%) = 0.1705, (0%, 9%) = 0.1595, (20%, -5%) = 0.06, (20%, 0%) = 0.0465, (20%, 9%) = 0.0435

23.1%

Joint probability matrix with probabilities: (-20%, -5%) = 0.3, (-20%, 0%) = 0.31, (-20%, 9%) = 0.29, (0%, -5%) = 0.55, (0%, 0%) = 0.55, (0%, 9%) = 0.55, (20%, -5%) = 0.15, (20%, 0%) = 0.15, (20%, 9%) = 0.15