三个的组合

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为什么最后方差0.86731乘的不是3million？