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Petrichor · 2024年04月21日

这道题的解析有问题吧?

NO.PZ2023091701000134

问题如下:

A risk analyst at a bank is estimating the distribution of credit losses for a portfolio of 30 identical loan exposures. The analyst assumes that the credit losses follow a binomial distribution. Each loan has the following characteristics:

• Amount: SGD 500,000

• Probability of default: 4%

• Recovery rate: 30%

• Average pairwise default correlation: 0.4

What is the standard deviation of losses on the loan portfolio expressed as a percentage of the size of the portfolio?

选项:

A.3.8%

B.5.8%

C.7.8%

D.8.9%

解释:

The standard deviation of losses for each individual loan is:

where p represents probability of default, Li represents exposure at default (amount borrowed), and Ri represents recovery rate.

The standard deviation of losses on the portfolio of n loans as a percentage of its size is then calculated as:


视屏中解析求组合的标准差应该是:



梦梦 · 2024年11月12日

老师,是不是漏了一个系数2啊,V(X+Y)=V(X)+V(Y)+2Cov,应该是n(n-1)/2再乘以2吧?

2 个答案

pzqa39 · 2024年11月12日

嗨,从没放弃的小努力你好:


我们讨论的是协方差的数量,对于n个资产组合,有n(n-1)/2个协方差。你说的这个公式是在计算组合方差时,由于每对协方差项会出现两次,因此会在组合方差公式中乘以2,但这与协方差数量的计算无关,不是一回事。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

梦梦 · 2024年11月12日

哦,谢谢

pzqa39 · 2024年04月21日

嗨,从没放弃的小努力你好:


N个资产的组合里有N个方差,N*(N-1)个协方差,N*(N-1)/2个 distinct 的covariance。这些结论可以直接记忆。

题目中求的是协方差 也就是说 cov(x1,x2) 和 cov(x2,x1) 虽然相同,但都计入,所以是N*(N-1)

N*(N-1)/2求出来的是完全不同的协方差 ,也就是说cov(x1,x2) 和 cov(x2,x1) 这两个只算一个,这样算是错误的

请记住结论:N个资产的组合里有N个方差,N*(N-1)个协方差


具体解析如下:

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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