Financial Risk Manager Part 1
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An analyst covers two companies – Xela Ltd. and Yena Inc. Yena Inc. is a subsidiary of Xela. The probability that the return on equity (ROE) of Xela exceeds 20% this year is 0.10, while the probability that the ROE of Yena exceeds 30% is 0.05 for the same time period. If the probability that the ROE of Xela exceeds 20% and the ROE of Yena exceeds 30% is 0.02, then the probability that the ROE of Yena exceeds 30% given that the ROE of Xela has already exceeded 20% is closest to:
Other
Community
NNikitesh
A
0.2
B
0.1
C
0.05
D
0.025
Explanation:
Explanation
This is a conditional probability problem. We are asked to find P(B|A) - the probability that Yena's ROE exceeds 30% given that Xela's ROE has already exceeded 20%.
Given:
- P(A) = Probability that Xela's ROE > 20% = 0.10
- P(B) = Probability that Yena's ROE > 30% = 0.05
- P(A ∩ B) = Probability that both events occur = 0.02
Using the conditional probability formula:
Calculation:
Interpretation:
- The result 0.20 means that if we know Xela's ROE has exceeded 20%, there's a 20% chance that Yena's ROE will also exceed 30%.
- This is higher than the unconditional probability of Yena's ROE exceeding 30% (which is 0.05), suggesting some positive correlation between the performance of the parent company and its subsidiary.
Why other options are incorrect:
- B (0.1): This is simply P(A) = 0.10, not the conditional probability.
- C (0.05): This is P(B) = 0.05, the unconditional probability of Yena's ROE exceeding 30%.
- D (0.025): This would be P(A) × P(B) = 0.10 × 0.05 = 0.005 if the events were independent, but the actual joint probability is higher (0.02), indicating dependence.
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