Skip to content

FRM Exam Part II · Introduction to Operational Risk and Resilience

Regulatory Capital for Operational Risk: BIA, TSA and SMA

Updated 11 October 2026 · Fact-checked

Operational risk capital is the minimum capital Basel rules require against losses from failed processes, people, systems or external events. Basel II offered the basic indicator, standardised and advanced measurement approaches. Basel III replaced them with one standardised approach: capital = business indicator component × internal loss multiplier.

Understand Regulatory Capital for Operational Risk

Operational risk is the risk of loss from inadequate or failed internal processes, people and systems, or from external events. Basel's definition includes legal risk but excludes strategic and reputational risk. Banks must hold regulatory capital against it, because these losses can be large and cannot be hedged away with market positions.

Basel II gave three approaches. The Basic Indicator Approach (BIA) takes a flat 15% of average positive gross income over three years. The Standardised Approach (TSA) splits gross income into eight business lines, each with its own beta factor of 12%, 15% or 18%. The Advanced Measurement Approach (AMA) let banks use internal models, typically a one-year, 99.9% confidence loss estimate. After the crisis, supervisors found AMA results too varied and too complex to compare. Gross income also proved a weak guide to risk.

The Basel III reforms removed all three and introduced the Standardised Measurement Approach (SMA). It has two parts. The first is the Business Indicator Component (BIC), which scales with the size of the bank's business. The second is the Internal Loss Multiplier (ILM), which adjusts the BIC up or down using the bank's own 10-year loss history. Capital = BIC × ILM.

The Business Indicator (BI) is built from three parts: the interest, leases and dividend component (ILDC), the services component (SC) and the financial component (FC). It is averaged over three years. Unlike gross income, it uses absolute values for the profit and loss items, so losses add to the indicator instead of reducing it. A bank pays marginal rates of 12%, 15% and 18% as BI grows across three buckets.

The loss component is 15 × the average annual operational losses over ten years. Compare it with the BIC. If a bank's loss history is worse than its BIC implies, ILM is above 1 and capital rises. If it is better, ILM is below 1. Operational risk RWA is capital × 12.5.

Key formulas to remember

Basic Indicator Approach (Basel II)
K(BIA) = 15% × average of annual gross income over the last 3 years, counting only years with positive gross income
Divide by the number of positive years, not by 3. Negative or zero years are left out of both numerator and denominator.
Standardised Approach, TSA (Basel II)
K(TSA) = average over 3 years of max[Σ(GI of line i × βi), 0]
Betas: corporate finance 18%, trading and sales 18%, payment and settlement 18%, commercial banking 15%, agency services 15%, retail banking 12%, asset management 12%, retail brokerage 12%. Negative lines can offset positive lines within a year, but the yearly total is floored at zero.
Business Indicator (BI)
BI = ILDC + SC + FC, each averaged over 3 years
BI is the average of the three annual figures and is measured in EUR.
Interest, leases and dividend component
ILDC = min[ |interest income − interest expense| , 2.25% × interest-earning assets ] + dividend income
The cap on net interest stops a large balance sheet from inflating the figure.
Services component
SC = max(other operating income, other operating expense) + max(fee income, fee expense)
Taking the larger side captures gross activity.
Financial component
FC = |net P&L trading book| + |net P&L banking book|
Absolute values: a trading loss still raises the indicator.
Business Indicator Component (BIC)
BI ≤ €1bn: BIC = 12% × BI | €1bn < BI ≤ €30bn: BIC = €120m + 15% × (BI − €1bn) | BI > €30bn: BIC = €4,470m + 18% × (BI − €30bn)
Marginal rates apply only to the part of BI inside each bucket. The 4,470m is 120m + 15% × 29,000m.
Loss component
LC = 15 × average annual operational risk losses over the previous 10 years
Uses net losses after recoveries, above the loss data threshold.
Internal Loss Multiplier
ILM = ln[ e − 1 + (LC ÷ BIC)^0.8 ]
If LC = BIC, ILM = 1. If LC > BIC, ILM > 1. If LC < BIC, ILM < 1. For banks in the lowest bucket (BI up to €1bn), ILM is set to 1.
SMA capital and RWA
Operational risk capital = BIC × ILM; RWA = 12.5 × capital
The 12.5 is the reciprocal of the 8% minimum ratio.

How to solve Regulatory Capital for Operational Risk questions

Identify which framework the question uses first. Then follow the data to the capital figure and interpret it.

  1. 1Name the approach: BIA, TSA, AMA or SMA. Check the wording for 'gross income', 'business line' or 'business indicator'.
  2. 2For BIA, list the three annual gross income figures, drop any zero or negative year, average the rest and multiply by 15%.
  3. 3For TSA, multiply each business line's income by its beta, sum the lines within each year, floor each yearly total at zero, then average over three years.
  4. 4For SMA, work out BI (or use the figure given) and place it in the correct bucket. Apply marginal rates only to the slice of BI in each bucket.
  5. 5Compute LC as 15 × average annual loss, compare it with BIC, and calculate ILM. Check direction: LC above BIC must give ILM above 1.
  6. 6Capital = BIC × ILM. Convert to RWA with × 12.5 if asked.
  7. 7Interpret: say what drives the answer, such as a poor loss history, a large fee business or a bucket boundary.

Quickest way: Bucket first, then loss ratio

When to use it: Use for SMA multiple-choice questions where BI and average losses are given.

  1. Find BIC from the bucket formula. For BI up to €30bn it is €120m + 15% × (BI − €1bn).
  2. Calculate LC ÷ BIC. If it is about 1, ILM is about 1 and capital is about BIC.
  3. If LC ÷ BIC is below 1, eliminate any option where capital exceeds BIC. If above 1, eliminate any option below BIC.
  4. Only then compute the exact ILM with the power 0.8 and the natural log.

Common mistakes in Regulatory Capital for Operational Risk

  • In BIA, dividing the sum of positive years by 3 instead of by the number of positive years.

    Students remember 'three-year average' and stop reading.

    Fix: Count only years with positive gross income in both the sum and the divisor. If all three are positive, divide by 3.

  • Applying 15% or 18% to the whole BI instead of only the slice in that bucket.

    Students treat the bucket rates like flat rates.

    Fix: Use marginal logic. For BI of €10bn the BIC is €120m + 15% × €9bn, not 15% × €10bn.

  • Using net or signed trading results in the financial component, so a loss reduces BI.

    Gross income under Basel II netted losses, and students carry that habit over.

    Fix: Take absolute values of trading book and banking book net P&L, and of net interest income.

  • Getting the ILM direction wrong, for instance lowering capital for a bank with heavy losses.

    Students mix up LC and BIC in the ratio.

    Fix: The ratio is LC ÷ BIC. Higher losses give a ratio above 1 and an ILM above 1. Run this sense check before and after calculating.

  • Forgetting that LC is 15 × the average annual loss, or using a 3-year average.

    BI uses 3 years and losses use 10, so the two are confused.

    Fix: BI averages 3 years. Loss data covers 10 years. Multiply the average annual loss by 15.

  • Stopping at capital when the question asks for RWA.

    Time pressure.

    Fix: Re-read the last line of the question. RWA = 12.5 × capital.

Worked examples

Example 1

A bank reports annual gross income of €600m, −€200m and €900m over the last three years. Under the Basel II Basic Indicator Approach, what is the operational risk capital charge?

Show the solution
  1. Drop the negative year (−€200m). Two positive years remain: €600m and €900m.
  2. Average over the number of positive years: (600 + 900) ÷ 2 = €750m.
  3. Apply 15%: 0.15 × 750 = €112.5m.

Answer: €112.5m

Example 2

Under the Basel III SMA, a bank has an average Business Indicator of €10bn and average annual operational losses of €60m over the last ten years. Find the operational risk capital and RWA (round ILM to three decimals).

Show the solution
  1. BI of €10bn lies in the €1bn to €30bn bucket.
  2. BIC = €120m + 15% × (10,000 − 1,000) = 120 + 1,350 = €1,470m.
  3. LC = 15 × 60 = €900m.
  4. LC ÷ BIC = 900 ÷ 1,470 = 0.6122. This is below 1, so ILM should be below 1.
  5. (0.6122)^0.8 = exp(0.8 × ln 0.6122) = exp(0.8 × −0.4906) = exp(−0.3925) = 0.6754.
  6. ILM = ln(1.7183 + 0.6754) = ln(2.3937) = 0.873.
  7. Capital = 1,470 × 0.873 ≈ €1,283m.
  8. RWA = 12.5 × 1,283 ≈ €16,040m.

Answer: Capital ≈ €1,283m (about €1.28bn), below the BIC of €1,470m because the loss history is favourable. RWA ≈ €16.0bn.

Exam tips

  • Know the chain: BI → bucket → BIC, then loss history → ILM, then capital = BIC × ILM. Questions often give a middle value and ask for the next step.
  • Use the sense check on ILM direction to remove wrong options quickly, even before you compute.
  • Recall the BIA, TSA and AMA features precisely: 15%, the 12/15/18% betas and the 99.9% one-year AMA measure. Questions on the evolution compare these.
  • Expect interpretation questions about why Basel replaced AMA: lack of comparability, complexity and weak risk sensitivity of gross income.
  • Read units and currency carefully. Basel thresholds are in EUR, and the answer may need RWA rather than capital.

Practice questions from Introduction to Operational Risk and Resilience

Regulatory Capital for Operational Risk in other exams

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

Regulatory Capital for Operational Risk: frequently asked questions

What is the difference between the basic indicator approach and the standardised approach?

The basic indicator approach applies one 15% rate to average positive gross income. The Basel II standardised approach splits income across eight business lines and applies betas of 12%, 15% or 18%. Both are replaced under Basel III by the SMA.

What is the business indicator in Basel III?

It is the sum of the interest, leases and dividend component, the services component and the financial component, averaged over three years. It uses absolute values for profit and loss items. It drives the business indicator component, which sets the base capital.

How does loss history affect operational risk capital under the SMA?

Loss history enters through the internal loss multiplier. A bank whose 10-year average loss, scaled by 15, exceeds its BIC gets an ILM above 1 and pays more capital. A bank with lower losses gets an ILM below 1. Banks in the lowest bucket have ILM set to 1.

Is the advanced measurement approach still allowed?

Under the finalised Basel III framework, the AMA, BIA and TSA are all replaced by the SMA. For the exam, know AMA as the Basel II internal model approach and know why supervisors withdrew it.