shihong · 2021年11月01日
NO.PZ2020011303000127
问题如下：
Suppose that there are three USD 1 million loans like the one in the previous question. 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
NO.PZ2020011303000127问题如下 A US1million loha probability of 0.5% of faulting in a year. The recoveryrate is estimateto 40%. The expecteloss in USis 0.003. This is US3,000. The varianof the loss is 0.001791. The stanrviation is the square root of this, or US0.04232 million. This is US42,320. Suppose ththere are three US1 million loans. The correlation between any pair of the loans is 0.2. Whis the meanstanrviation of the portfolio cret loss? The expecteloss on the three loans is three times the expecteloss on one loor US9,000. The varianof the portfolio loss is3 × 0.001791+ 6 × 0.001791 × 0.2 = 0.007522The stanrviation of the portfolio loss is the square root of this or US0.086731. This is US86,731. (Note ththe stanrviation is less ththree times the stanrviation calculatefor one lobecause there are some versification benefits.)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*PEALG3*0.5%*1m*(1-40%)=0.009$形式9000组合方差=3*单个方差+6*ρ*单个方差=3 ×0.001791+ 6 × 0.001791 × 0.2 = 0.007522标准差=0.007522^0.5=0.086731llar形式US86,731 1、老师，只要题目问到“stanrviation of the portfolio cret loss”究竟是不是等于资产组合的“UL”？2、EL是cret loss的均值？
NO.PZ2020011303000127问题如下 A US1million loha probability of 0.5% of faulting in a year. The recoveryrate is estimateto 40%. The expecteloss in USis 0.003. This is US3,000. The varianof the loss is 0.001791. The stanrviation is the square root of this, or US0.04232 million. This is US42,320. Suppose ththere are three US1 million loans. The correlation between any pair of the loans is 0.2. Whis the meanstanrviation of the portfolio cret loss? The expecteloss on the three loans is three times the expecteloss on one loor US9,000. The varianof the portfolio loss is3 × 0.001791+ 6 × 0.001791 × 0.2 = 0.007522The stanrviation of the portfolio loss is the square root of this or US0.086731. This is US86,731. (Note ththe stanrviation is less ththree times the stanrviation calculatefor one lobecause there are some versification benefits.)题目问假设有三个1m的贷款，每个贷款的一年的违约概率是0.5%，recover rate是40%，任意两个贷款之间的相关系数是0.2，求这个贷款组合的EL和损失的标准差。EL=n*PEALG3*0.5%*1m*(1-40%)=0.009$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=0.086731llar形式US86,731 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
NO.PZ2020011303000127 问题如下 A US1million loha probability of 0.5% of faulting in a year. The recoveryrate is estimateto 40%. The expecteloss in USis 0.003. This is US3,000. The varianof the loss is 0.001791. The stanrviation is the square root of this, or US0.04232 million. This is US42,320. Suppose ththere are three US1 million loans. The correlation between any pair of the loans is 0.2. Whis the meanstanrviation of the portfolio cret loss? The expecteloss on the three loans is three times the expecteloss on one loor US9,000. The varianof the portfolio loss is3 × 0.001791+ 6 × 0.001791 × 0.2 = 0.007522The stanrviation of the portfolio loss is the square root of this or US0.086731. This is US86,731. (Note ththe stanrviation is less ththree times the stanrviation calculatefor one lobecause there are some versification benefits.)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*PEALG3*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=0.086731llar形式US86,731 请问组合标准差求出后为何只乘以100万呢，应该乘以300万吧。否则如果直接用LL形式的话，结果应该不同。谢谢
NO.PZ2020011303000127问题如下 A US1million loha probability of 0.5% of faulting in a year. The recoveryrate is estimateto 40%. The expecteloss in USis 0.003. This is US3,000. The varianof the loss is 0.001791. The stanrviation is the square root of this, or US0.04232 million. This is US42,320. Suppose ththere are three US1 million loans. The correlation between any pair of the loans is 0.2. Whis the meanstanrviation of the portfolio cret loss? The expecteloss on the three loans is three times the expecteloss on one loor US9,000. The varianof the portfolio loss is3 × 0.001791+ 6 × 0.001791 × 0.2 = 0.007522The stanrviation of the portfolio loss is the square root of this or US0.086731. This is US86,731. (Note ththe stanrviation is less ththree times the stanrviation calculatefor one lobecause there are some versification benefits.)三个一样的组合的话，公式前一半不是w²σ²×3嘛，每个的w都是三分之一，那就算出来和答案差了九分之一了，这是为什么咧
