Explanation

Under the Basic Indicator Approach (BIA) for operational risk capital calculation:

Key Formula: Capital Charge = α × [Σ(GI₁...ₙ) ÷ n]

Where:

• α = 15% (fixed percentage)
• GI = Gross Income for each year (positive values only)
• n = number of years with positive gross income

Given Data:

• Year T-3: +$130 million (positive)
• Year T-2: -$60 million (negative - exclude from calculation)
• Year T-1: +$230 million (positive)

Calculation Steps:

1. Only include years with positive gross income: T-3 and T-1
2. Sum of positive gross income = $130 million + $230 million = $360 million
3. Number of years with positive income = 2
4. Average gross income = $360 million ÷ 2 = $180 million
5. Capital charge = 15% × $180 million = $27 million

Why other options are incorrect:

• $15.0 million: This would result from using all 3 years including the negative year
• $18.0 million: This doesn't match the proper BIA calculation
• $34.5 million: This would be 15% of $230 million only, ignoring the other positive year

The correct answer is $27.0 million.