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
给了一堆算EL的数据，怎么算标准差？
