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梦梦 · 2024年07月30日

关于信用损失的方差

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2023090401000003

问题如下：

Question A risk manager at a bank is speaking to a group of analysts about estimating credit losses in loan portfolios. The manager presents a scenario with a portfolio consisting of two loans and provides information about the loans as given below:


Assuming portfolio losses are binomially distributed, what is the estimate of the standard deviation of losses on the portfolio?

选项：

A.

CNY 1.38 million

B.

CNY 1.59 million

C.

CNY 3.03 million

D.

CNY 3.36 million

解释：

C is correct. The standard deviation of losses (si) for each individual loan is:


where, pi represents probability of default (p1 = 2%, p2 = 2%), Li represents exposure at default (amount borrowed) (L1 = CNY 15 million, L2 = CNY 20 million), and Ri represents recovery rate (R1 = 40%, R2 = 25%)).

Therefore, the standard deviations for loan 1 and loan 2 are:


The variance of losses on the portfolio can then be calculated as:


The standard deviation is therefore √9.1728 = 3.0287.

A is incorrect. This uses the incorrect formula for standard deviation of losses of the individual loans

B is incorrect. This incorrectly assumes portfolio standard deviation of losses to be ρ1,2σ1σ2

D is incorrect. This incorrectly assumes portfolio standard deviation of losses to be the sum of the individual loans’ standard deviations of losses.

Section: Valuation and Risk Models

Learning Objective:

Estimate the mean and standard deviation of credit losses assuming a binomial distribution.

Reference: Global Association of Risk Professionals. Valuation and Risk Models. New York, NY: Pearson, 2022. Chapter 6. Measuring Credit Risk

1、老师好，这么解答哪里不对呢？

2、答案解析给的公式不明白原理

是红色圈1推的？具体咋推导的啊？能给个过程吗？

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已采纳答案

pzqa27 · 2024年08月01日

嗨，从没放弃的小努力你好：


UL是WCL-EL，如果是算组合的UL，那么则可以用那个类似组合标准差的公式。可问题你这个算的也不是UL，你算的PD*LGD*EAD，这个是EL的公式，所以你的算法是不对的，请严格按照何老师的讲解进行计算。

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梦梦 · 2024年08月01日

好的，谢谢

pzqa27 · 2024年07月31日

嗨，从没放弃的小努力你好：


1、老师好，这么解答哪里不对呢？

题目要算的是组合的波动率，不是unexpected loss。所以不能这么算。


2、答案解析给的公式不明白原理是红色圈1推的？具体咋推导的啊？能给个过程吗？

这个题是个比较经典的题目，很多地方都讲过这个题，比如经典题的这个视频的这个位置，有何老师详细的讲解，其中包括了公式的推导，同学可以参考下这个视频的这个位置。如果对过程仍有疑问，我们可以进一步讨论。


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加油吧，让我们一起遇见更好的自己！

梦梦 · 2024年07月31日

老师好，看了一遍经典题，解题过程是明白了，但是，我在NO.PZ2020011303000127的题目下问了一个问题即“关于EL和UL的概念”，只要题目问到'“standard deviation of theportfolio credit loss"究竟是不是等于资产组合的“UL”？老师在下面的回答是“是的，UL 可以理解为 loss 的标准差，UL =根号下Var (loss)”。那么这道题问的是“standard deviation of losses on the portfolio?”这种只问losses的方式就不是UL，而是资产组合损失的标准差？就看有没有credit？

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