Explanation:
The bank's formula for setting the interest rate on loans is:
Interest rate = Expected loss + Margin for profit and OpEx + Funding cost
Using the given values:
We can calculate the expected loss:
Expected loss = 8.18% - 2.10% - 4.85% = 1.23%
The expected loss formula is:
Expected loss = Probability of default × Loss given default
Where:
Therefore:
Probability of default = Expected loss ÷ Loss given default
Probability of default = 1.23% ÷ 55% = 2.2364% ≈ 2.24%
This matches option C.
Ultimate access to all questions.
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:
| Average recovery rate of loans | 45% |
|---|---|
| Margin for profit and operating expenses | 2.10% |
| Average funding cost | 4.85% |
| Average interest rate on loans | 8.18% |
Given this information, what is the estimated average probability of default for the loans in the portfolio?
A
0.68%
B
1.23%
C
2.24%
D
2.73%
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