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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.