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皓皓心 · 2024年10月02日

这个计算EL方差的公式在讲义里面哪里出现过吗

  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

这个计算EL方差的公式在讲义里面哪里出现过吗

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1 个答案

pzqa27 · 2024年10月08日

嗨，努力学习的PZer你好：



这个是用的原版书教材里面的公式：

红框公式1是单个loan的Loss的标准差，红框公式2是组合的方差。


首先用公式1计算出Loan1和Loan2各自的σ。 σ1 = 根号(2%-2%^2) * [15 * (1-40%)]，σ2 = 根号(2%-2%^2) * [20 * (1-25%)]，

再用公式2求出组合的σ^2。组合的σ^2就类似于把两只股票组合起来求方差一样，σp^2 = σ1^2 + σ2^2 + 2*ρ*σ1*σ2.

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