FRM Exam Part I · Operational Risk

Operational Risk Capital: Basel Approaches Explained

Updated 11 October 2026 · Fact-checked

Basel sets bank capital for operational risk using several approaches. The basic indicator approach charges 15% of average positive gross income. The standardized approach applies 12% to 18% to business lines. The AMA uses internal models. The newer Standardized Measurement Approach (SMA) combines a business indicator with loss history.

Understand Operational Risk Capital: Basel Approaches

Operational risk is the risk of loss from failed processes, people, systems or external events. Banks must hold capital against it. Basel rules offer different ways to measure that capital, and they get more risk-sensitive as you move up.

The basic indicator approach (BIA) is the simplest. Capital is a fixed percentage, alpha = 15%, of the bank's average annual positive gross income over the previous three years. Years with zero or negative gross income are left out of both the sum and the count.

The standardized approach (TSA) splits gross income into eight business lines. Each line has its own beta factor: 12%, 15% or 18%. Capital is the three-year average of the yearly sum of beta times gross income. In the Basel II version, a negative result in one business line can offset positive results in others within a year, but the yearly total is floored at zero.

The advanced measurement approach (AMA) let banks use their own internal models, usually built on loss data, scenario analysis, business environment factors and internal controls. The capital target was a 99.9% confidence level over one year. It needed supervisory approval. It was criticized because results varied widely between banks, so models were hard to compare.

The Standardized Measurement Approach (SMA) replaces BIA, TSA and AMA in the revised Basel framework. It has two parts: the Business Indicator Component (BIC), based on a financial-statement indicator that grows with size using marginal coefficients, and the Internal Loss Multiplier (ILM), which raises or lowers capital based on the bank's own historical losses relative to the BIC. Capital is BIC times ILM.

Key formulas to remember

Basic indicator approach: K(BIA) = α × [Σ(GI₁…ₙ) ÷ n], α = 15%; GI is annual gross income. Include only years where GI is positive; n is the number of those years, out of the previous three.
Standardized approach: K(TSA) = {Σ over years 1–3 of max[Σ(GI × β), 0]} ÷ 3; β = 12%, 15% or 18% depending on the business line. Yearly total floored at zero in Basel II.
Beta factors by business line: 18%: corporate finance, trading and sales, payment and settlement; 15%: commercial banking, agency services; 12%: retail banking, asset management, retail brokerage; Eight business lines in total. Learn the 18% group first.
SMA capital: K(SMA) = BIC × ILM; For banks in the larger size bucket. BIC comes from the business indicator with increasing marginal coefficients. ILM reflects average historical loss relative to BIC.
Risk-weighted assets equivalent: RWA = 12.5 × operational risk capital; Capital is converted to RWA by multiplying by 12.5 (1 ÷ 8%).

How to solve Operational Risk Capital: Basel Approaches questions

Most questions either ask for a number under BIA or TSA, or test which approach has which feature. Use this routine.

1Identify the approach named: BIA, TSA, AMA or SMA.
2For BIA, list gross income for the last three years and drop any year that is zero or negative.
3Average the remaining positive years, dividing by the count of positive years, not by three.
4Multiply by 15% for BIA. For TSA, multiply each business line's gross income by its beta, sum within each year, floor each year at zero, then average over three years.
5For SMA, remember capital equals BIC times ILM, and that a bank with lower historical losses gets an ILM below one.
6Convert to RWA with 12.5 if the question asks for risk-weighted assets.
7Sanity check: TSA betas are 12% to 18%, so TSA capital can be above or below BIA depending on income mix.

Quickest way: Positive-year average shortcut

When to use it: Use for BIA numerical questions with a mix of positive and negative years.

Cross out every year with gross income at or below zero.
Add the remaining years and divide by how many are left.
Multiply by 0.15 and check the units.

Common mistakes in Operational Risk Capital: Basel Approaches

Dividing by three when one year has negative gross income under BIA.
Students remember 'three-year average' and stop reading.
Fix: Exclude non-positive years from both numerator and denominator.
Using 15% for every business line under the standardized approach.
15% is the BIA alpha and is also the middle beta.
Fix: Look up each line's beta: 12%, 15% or 18%.
Thinking AMA is still the current approach.
Older texts describe AMA as the advanced option.
Fix: Know that the revised Basel framework replaces BIA, TSA and AMA with the SMA.
Thinking SMA uses internal models.
SMA includes internal loss data, which sounds model-based.
Fix: SMA is a standardized formula: BIC times ILM. Loss data only feeds the multiplier.
Forgetting that BIA and TSA use gross income as a proxy.
Students focus on rates and skip the idea behind them.
Fix: Remember that gross income is a size proxy and is not directly linked to operational loss experience, a key criticism.

Worked examples

Example 1

A bank has gross income of USD 400 million, USD 500 million and -USD 100 million over the last three years. Using the basic indicator approach, what is the operational risk capital?

Show the solution

Drop the negative year, leaving 400 and 500.
Average = (400 + 500) ÷ 2 = 450.
Capital = 15% × 450 = 67.5.

Answer: USD 67.5 million

Example 2

Under the standardized approach, a bank has in one year gross income of USD 200 million in trading and sales (β = 18%) and USD 300 million in retail banking (β = 12%). Assume the same figures in each of the three years. What is the operational risk capital?

Show the solution

Trading and sales: 18% × 200 = 36.
Retail banking: 12% × 300 = 36.
Yearly total = 72, which is positive so no floor applies.
Three-year average of 72, 72, 72 = 72.

Answer: USD 72 million

Exam tips

Expect a calculation for BIA or TSA and a conceptual question on SMA or AMA.
Watch for negative gross income years; they are a favourite trap.
Know the direction of change: SMA was introduced to improve comparability and simplicity versus AMA.
Memorize which business lines carry 18%, 15% and 12% betas.
If asked for RWA, multiply capital by 12.5.

Practice questions from Operational Risk

Operational Risk Capital: Basel Approaches in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Operational Risk Capital: Basel Approaches: frequently asked questions

What is the difference between the basic indicator and standardized approaches?

The basic indicator approach applies one 15% factor to total gross income. The standardized approach splits income into eight business lines and applies 12%, 15% or 18% depending on the line. TSA is therefore more sensitive to the business mix.

Is the advanced measurement approach still used?

Under the revised Basel framework the SMA replaces the AMA, along with BIA and TSA. You still need to understand AMA for the exam, including why it was criticized for inconsistent results.

What does the SMA use as inputs?

It uses a business indicator, which gives the business indicator component, and the bank's historical operational losses, which feed the internal loss multiplier. Capital is the product of the two.

How do I calculate operational risk capital under the basic indicator approach?

Take the average of positive annual gross income over the last three years, counting only positive years, and multiply by 15%.