Financial Risk Manager Part 1

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Q.3744 The yearly profits of the two firms A and B can be summarized in the following probability matrix.

Company A Profits (X₁)	-1 Million	0 Million	2 Million	4 Million
-50 Million	0.0197	0.0395	0.010	0.002
0 Million	0.0390	0.230	0.124	0.0298
10 Million	0.011	0.127	0.144	0.0662
100 Million	0	0.0309	0.0656	0.0618

What is the marginal distribution of company B?

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Company B(X₂) Profits	-50 Million	0 Million	10 Million	100 Million
P(X₂ = x₂)	0.1325	0.4244	0.3599	0.0832

Company B(X₂) Profits	-50 Million	0 Million	10 Million	100 Million
P(X₂ = x₂)	0.0235	0.4856	0.3254	0.1655

Company B(X₂) Profits	-50 Million	0 Million	10 Million	100 Million
P(X₂ = x₂)	0.0712	0.4228	0.3482	0.1583

Company B(X₂) Profits	-50 Million	0 Million	10 Million	100 Million
P(X₂ = x₂)	0.0633	0.4423	0.3658	0.1286

Explanation:

Explanation

To find the marginal distribution of Company B, we need to sum the probabilities across each row (for each value of Company B's profits).

For Company B = -50 Million: 0.0197 + 0.0395 + 0.010 + 0.002 = 0.0712

For Company B = 0 Million: 0.0390 + 0.230 + 0.124 + 0.0298 = 0.4228

For Company B = 10 Million: 0.011 + 0.127 + 0.144 + 0.0662 = 0.3482

For Company B = 100 Million: 0 + 0.0309 + 0.0656 + 0.0618 = 0.1583

Total probability should sum to 1: 0.0712 + 0.4228 + 0.3482 + 0.1583 = 1.0005 (rounding error due to decimal precision)

Therefore, the correct marginal distribution for Company B is:

Company B(X₂) Profits	-50 Million	0 Million	10 Million	100 Million
P(X₂ = x₂)	0.0712	0.4228	0.3482	0.1583

This matches Option C.

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