NO.PZ2024042601000038
问题如下：
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?
选项：
A.$989,812
B.$1.0 million
C.$1.7 million
D.$2.3 million
解释：
The one-month PD = 1 - (100% - 4%)(1/12) = 0.3396%.
Expected loss = 98.9846% × 0 + 1.0119% × $1.0 million + 0.0034% × $2.0 million + 0% × $3.0 million = $10,188
The probability of zero defaults = (1 - 0.3396%)3 = 98.98464%.
Therefore, the 99.0% WCL is one default or $1.0 million, and
the 99.0% CVaR = $1.0 million - $10,188 = $989,812.
Expected loss = 98.9846% × 0 + 1.0119% × $1.0 million + 0.0034% × $2.0 million + 0% × $3.0 million = $10,188
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