Module: | MODULE B: RISK MANAGEMENT
Q416: A commercial bank has recorded the following Gross Income figures over the last three financial years:
* Year 1: 100 Crore
* Year 2: Negative 20 Crore (loss)
* Year 3: 160 Crore
The regulatory Alpha factor prescribed under the Basel guidelines is 15 percent. Calculate the operational risk capital charge for this bank under the Basic Indicator Approach (BIA).
* Year 2: Negative 20 Crore (loss)
* Year 3: 160 Crore
The regulatory Alpha factor prescribed under the Basel guidelines is 15 percent. Calculate the operational risk capital charge for this bank under the Basic Indicator Approach (BIA).
✅ Correct Answer: B
The correct answer is B.
Step-by-step breakdown of the Basic Indicator Approach (BIA) formula:
The BIA capital charge is calculated as 15 percent (Alpha factor) of the average positive annual gross income over the previous three years.
Crucial Regulatory Rule: Any year with a negative or zero gross income must be strictly excluded from both the numerator (the sum) and the denominator (the number of years averaged).
Year 1 Gross Income = 100 Crore (Positive, include)
Year 2 Gross Income = -20 Crore (Negative, exclude entirely)
Year 3 Gross Income = 160 Crore (Positive, include)
Step 1: Sum the positive years = 100 + 160 = 260 Crore.
Step 2: Calculate the average.
Since only 2 years were positive, divide by 2 (not 3).
Average Gross Income = 260 / 2 = 130 Crore.
Step 3: Apply the regulatory Alpha factor of 15 percent.
Capital Charge = 130 Crore * 0.15 = 19.5 Crore.
Option A is incorrect (Calculated using incorrect beta or misapplied logic).
Option C is incorrect (Result of dividing by 3 despite the negative year: 260/3 * 0.15).
Option D is incorrect (Result of subtracting the loss and dividing by 3: 240/3 * 0.15).
Option B represents the correct and exact mathematical application of the BIA rule.
Step-by-step breakdown of the Basic Indicator Approach (BIA) formula:
The BIA capital charge is calculated as 15 percent (Alpha factor) of the average positive annual gross income over the previous three years.
Crucial Regulatory Rule: Any year with a negative or zero gross income must be strictly excluded from both the numerator (the sum) and the denominator (the number of years averaged).
Year 1 Gross Income = 100 Crore (Positive, include)
Year 2 Gross Income = -20 Crore (Negative, exclude entirely)
Year 3 Gross Income = 160 Crore (Positive, include)
Step 1: Sum the positive years = 100 + 160 = 260 Crore.
Step 2: Calculate the average.
Since only 2 years were positive, divide by 2 (not 3).
Average Gross Income = 260 / 2 = 130 Crore.
Step 3: Apply the regulatory Alpha factor of 15 percent.
Capital Charge = 130 Crore * 0.15 = 19.5 Crore.
Option A is incorrect (Calculated using incorrect beta or misapplied logic).
Option C is incorrect (Result of dividing by 3 despite the negative year: 260/3 * 0.15).
Option D is incorrect (Result of subtracting the loss and dividing by 3: 240/3 * 0.15).
Option B represents the correct and exact mathematical application of the BIA rule.