NO.PZ2020011303000127
问题如下:
A USD 1million loan has a probability of 0.5% of defaulting in a year. The recoveryrate is estimated to be 40%.
The expected loss in USD is 0.003. This is USD 3,000.
The variance of the loss is 0.001791. The standard deviation is the square root of this, or USD 0.04232 million. This is USD 42,320.
Suppose that there are three USD 1 million loans. The correlation between any pair of the loans is 0.2. What is the mean and standard deviation of the portfolio credit loss?
解释:
The expected loss on the three loans is three times the expected loss on one loan
3 × 0.001791+ 6 × 0.001791 × 0.2 = 0.007522
The standard deviation of the portfolio loss is the square root of this or USD
题目问:假设有三个1m的贷款,每个贷款的一年的违约概率是0.5%,recover rate是40%,任意两个贷款之间的相关系数是0.2,求这个贷款组合的EL和损失的标准差。
EL=n*PD*EAD*LGD=3*0.5%*1m*(1-40%)=0.009
$形式9000
组合方差=3*单个方差+6*ρ*单个方差=3 ×0.001791+ 6 × 0.001791 × 0.2 = 0.007522
标准差=0.007522^0.5=0.086731
dollar形式USD 86,731
解答里3个同样loan的方差公式了解即可。就是3*单个方差+6*ρ*单个方差,开方就得到标准差了。是为啥