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徐威廉 · 2024年03月24日

这题怎么算的

NO.PZ2023090501000092

问题如下:

A risk manager at a small bank is using Euler's theorem to calculate the contributions of individual loans to the VaR of a loan portfolio. The portfolio VaR isGBP 20,300. Information on the 3 loans in the portfolio is shown below:


Which of the following is closest to the contribution of Loan 3 to the portfolio VaR?

选项:

A.

GBP 6,015

B.

GBP 6,320

C.

GBP 7,013

D.

GBP 7,930

解释:

Explanation

D is correct. In its application to credit risk, Euler's theorem states that:


and that (in the limit, as △xi goes to zero):


where F is a (homogeneous) risk measure for a portfolio, xi is the same risk measure calculated for one component position in the portfolio, △xi is a small change in this risk measure, and △Fi is the resultant change in the portfolio's risk measure.

Therefore, using the information given:


A is incorrect. This is the proportion of portfolio VaR equivalent to the proportion of Loan 3's amount to the total amount of all of the loans:

B is incorrect.

C is incorrect. This is the proportion of portfolio VaR equivalent to the proportion of

Loan 3's individual VaR to the sum of the individual loan VaRs:

20,300*9,500/(10,000 + 8,000 + 9,500)= 7,012.73

Section Valuation and Risk Models

Learning Objective Describe and use Euler's theorem to determine the contribution of a loan to the overall risk of a portfolio.

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

完全不懂

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已采纳答案

李坏_品职助教 · 2024年03月25日

嗨,从没放弃的小努力你好:


根据讲义里面的Euler定理:

投资组合总风险(也就是公式里的F)=每一个部分的风险(Q)之和。题目里给的Loan 1的increase in portfolio var if loan var increase by 1%是58.1, 这说明loan 1的风险变化1%给组合带来的影响是58.1,也就是△F1=58.1,那么Q1 = △F1 / 1% = 5810.

同理,Q2 = △F2 / 1% = 6560.


组合的VaR=20300,这个也就是讲义里面的F。

F = Q1 + Q2 + Q3 = 5810 + 6560 + Q3 = 20300, 所以Q3 = 7930.

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努力的时光都是限量版,加油!

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2024-07-30 21:53 1 · 回答