Interest rate = Expected loss + Margin for profit and OpEx + Fun

问题如下：

A small bank sets the interest rates it charges on loans to its business clients at a level equal to the sum of the loans’ expected loss, the bank’s funding cost, and a margin for the bank’s profit and operating expenses. A risk analyst at the bank compiles the following information related to the loan portfolio:

Interest rate: 8.18%

Margin for profit and operating expense: 2.10%

Funding cost: 4.85%

Recovery rate: 45%

Given this information, what is the estimated average probability of default for the loans in the portfolio?

选项：

A.0.68% B.1.23% C.2.24% D.2.73%

解释：

Explanation: C is correct. The bank’s formula for setting the interest rate on loans is given as:

Interest rate = Expected loss + Margin for profit and OpEx + Funding cost

Using this formula and the information given:

Expected loss = 8.18% − 2.10% − 4.85% = 1.23%

Because

Expected loss = Probability of default * Loss given default

therefore

Probability of default = 1.23% / (1 − 45%) = 2.2364%

A is incorrect. This multiplies the expected loss by the loss given default instead of dividing.

B is incorrect. This is the expected loss (Interest rate − Margin for OpEx − Funding cost).

D is incorrect. This divides the expected loss by the recovery rate instead of the loss given default.

Learning Objective: Define and calculate expected loss (EL).

Reference: Global Association of Risk Professionals, Valuation and Risk Models (New York, NY: Pearson, 2023). Chapter 6. Measuring Credit Risk [VRM–6]