Answer-first summary for fast verification
Answer: 7.89%
The correct answer to the question is C, which is 7.89%. This is determined by using Bayes' theorem to calculate the conditional probability that the longevity bond defaults given that the market returns decrease by 20%. Bayes' theorem is expressed as: \[ P[A|B] = \frac{P[A \cap B]}{P[B]} \] In this context: - \( A \) represents the event of the bond defaulting. - \( B \) represents the event of a 20% decrease in market returns. From the table provided: - \( P[A \cap B] \) is the probability of both the bond defaulting and the market decreasing by 20%, which is 3%. - \( P[B] \) is the total probability of the market decreasing by 20%, which is the sum of the probabilities of the market decreasing when the bond defaults (3%) and does not default (35%), totaling 38%. Plugging these values into Bayes' theorem gives: \[ P[A|B] = \frac{0.03}{0.38} \approx 0.0789 \text{ or } 7.89\% \] This calculation shows that if the market decreases by 20%, the probability that the longevity bond defaults in one year is approximately 7.89%.
Author: LeetQuiz Editorial Team
Ultimate access to all questions.
A fund manager is analyzing the correlation between the 1-year default risk of a longevity bond from an insurance company and the stock market's performance. To aid this, the manager has created a probability matrix derived from initial research data showing the 1-year probabilities for different scenarios:
| Longevity bond | Market returns | Probability |
|---|---|---|
| No default | 20% increase | 61% |
| Default | 20% increase | 1% |
| No default | 20% decrease | 35% |
| Default | 20% decrease | 3% |
Using this probability matrix, calculate the probability that the longevity bond will default within a year, given that the market experiences a 20% decline in that year.
A
3.00%
B
4.00%
C
7.89%
D
10.53%
No comments yet.