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Answer: $2.3 million
## Explanation To calculate the one-month 99.0% CVaR for this three-bond portfolio, we need to: ### Step 1: Convert annual default probability to monthly - Annual cumulative default probability = 4.0% = 0.04 - Monthly default probability = 1 - (1 - 0.04)^(1/12) ≈ 0.0034 or 0.34% ### Step 2: Calculate default probabilities for the portfolio Since the bonds are independent, we can model this as a binomial distribution: - Probability of 0 defaults: (1 - 0.0034)^3 ≈ 0.9898 - Probability of 1 default: 3 × 0.0034 × (1 - 0.0034)^2 ≈ 0.0102 - Probability of 2 defaults: 3 × (0.0034)^2 × (1 - 0.0034) ≈ 0.0000347 - Probability of 3 defaults: (0.0034)^3 ≈ 0.000000039 ### Step 3: Determine the 99.0% confidence level We need to find the loss level that corresponds to the 99th percentile: - Cumulative probability of 0 defaults: 98.98% - Cumulative probability of 1 default: 98.98% + 1.02% = 100.00% Since 99.0% confidence falls between 0 defaults (98.98%) and 1 default (100.00%), the unexpected loss at 99.0% confidence corresponds to 2 defaults. ### Step 4: Calculate the CVaR - With zero recovery rate, each default results in a loss of $1.0 million - 2 defaults = $2.0 million loss - The nearest option to $2.0 million is **$2.3 million** Therefore, the one-month 99.0% CVaR is approximately $2.3 million.
Author: LeetQuiz .
Becky the Risk Analyst is trying to estimate the credit value at risk (CVaR) of a three-bond portfolio, where the CVaR is defined as the maximum unexpected loss at 99.0% confidence over a one-month horizon. The bonds are independent (i.e., no default correlation) and identical with a one-month forward value of $1.0 million each, a one-year cumulative default probability of 4.0%, and an assumed zero recovery rate. Which is nearest to the one-month 99.0% CVaR?
A
$989,812
B
$1.0 million
C
$1.7 million
D
$2.3 million
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