按照答案的意思

问题如下：

A risk manager at a retail bank is conducting a training session for newly hired risk analysts about the concept of unexpected loss (UL). To illustrate the calculation of UL, the manager provides the following data on a hypothetical loan portfolio:

• Principal amount of loan portfolio: SGD 120 million

• Portfolio default rate: 2.5%

• Recovery rate: 30%

• 1-year 99% VaR: SGD 9.6 million

• 1-year 99% ES: SGD 14.8 million

What is the 1-year UL of the loan portfolio at the 99% confidence level?

选项：

A.

SGD 7.5 million

B.

SGD 11.7 million

C.

SGD 12.7 million

D.

SGD 16.9 million

解释：

Explanation

A is correct. Using the terminology of value-at-risk (VaR), the 1-year 99% unexpected loss of a portfolio is equal to its expected loss subtracted from its VaR with a 1-year time horizon and a 99% confidence level. The expected loss equals portfolio default rate * (1 - recovery rate) * exposure at default = 0.025 * (1 - 0.3) * 120 = SGD 2.1 million. Therefore, the UL of this loa n portfolio is 9.6 - 2.1 = SGD 7.5 million.

B is incorrect. This is the 1-year, 99% ES minus the expected loss.

C is incorrect. This is the 1-year, 99% VaR plus the expected loss.

D is incorrect. This is the 1-year, 99% ES plus the expected loss.

Section Valuation and Risk Models

Learning Objective Define and explain unexpected loss (UL). Define and calculate expected loss (EL).

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