这是个什么公式？

问题如下：

A risk analyst at a bank is estimating the distribution of credit losses for a portfolio of 30 identical loan exposures. The analyst assumes that the credit losses follow a binomial distribution. Each loan has the following characteristics:

• Amount: SGD 500,000

• Probability of default: 4%

• Recovery rate: 30%

• Average pairwise default correlation: 0.4

What is the standard deviation of losses on the loan portfolio expressed as a percentage of the size of the portfolio?

选项：

A.

3.8%

B.

5.8%

C.

7.8%

D.

8.9%

解释：

Explanation

D is correct. The standard deviation of losses for each individual loan is:

where p represents probability of default, Li represents exposure at default (amount borrowed), and Ri represents recovery rate.

The standard deviation of losses on the portfolio of n loans as a percentage of its size is then calculated as:

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

B is incorrect. This uses the incorrect formula for standard deviation of losses on the portfolio

C is incorrect. This uses the incorrect formula for standard deviation of losses on

the portfolio

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.