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.
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