Risk Management in Banking and Insurance · Operational Risk and Off-Balance Sheet Risk

Operational Risk Capital Measurement Approaches: BIA, TSA, AMA and SMA

Updated 11 October 2026 · Fact-checked

Operational risk capital is the capital a bank holds against losses from failed processes, people, systems or external events. Basel II offered three approaches: Basic Indicator (15% of average positive gross income), Standardised (beta of 12% to 18% by business line) and Advanced Measurement (bank's own model). The newer Standardised Measurement Approach replaces them.

Understand Operational Risk Capital Measurement Approaches

Operational risk is the risk of loss from inadequate or failed internal processes, people and systems, or from external events. It includes legal risk but excludes strategic and reputational risk. Basel norms ask banks to hold capital against it, because fraud, system failure or a process error can wipe out earnings.

Basel II gave three ways to measure the capital charge, in rising order of sophistication. The Basic Indicator Approach (BIA) is the simplest. It takes a fixed percentage, called alpha, of the bank's average annual positive gross income over the previous three years. Alpha is 15%.

The Standardised Approach (TSA) splits gross income into eight business lines. Each line has its own beta factor: 18% for corporate finance, trading and sales, and payment and settlement; 15% for commercial banking and agency services; 12% for retail banking, asset management and retail brokerage. The capital charge is the three-year average of the yearly sum of beta × gross income, where a negative total in any year is set to zero.

Under the Advanced Measurement Approach (AMA), the bank uses its own internal model, built on internal loss data, external data, scenario analysis and business environment and internal control factors. It needs supervisory approval and strict qualifying standards. Results varied widely between banks, so they were hard to compare.

Because of this, the Basel Committee brought in the Standardised Measurement Approach (SMA) in its revised framework. It replaces BIA, TSA and AMA. It combines a Business Indicator Component (based on a business indicator, with marginal coefficients rising for larger banks) and an Internal Loss Multiplier (which uses the bank's own loss history). Larger loss history raises the multiplier and the capital charge. For the exam, know the three older formulas well and the SMA in concept.

Key rules to remember

Basic Indicator Approach: K(BIA) = [Σ(GI₁ … GIₙ) × α] ÷ n, with α = 15%; GI is annual gross income, only for the previous three years in which it was positive. n is the number of those years. Years with zero or negative income are left out of both numerator and denominator.
Standardised Approach: K(TSA) = {Σ years 1-3 max[Σ(GI₁₋₈ × β₁₋₈), 0]} ÷ 3; Eight business lines. In any year, negative capital in one line can offset positive capital in another, but a negative yearly total is set to zero (and still counted in the divisor of 3).
Beta factors (Basel II): 18%: corporate finance, trading and sales, payment and settlement | 15%: commercial banking, agency services | 12%: retail banking, asset management, retail brokerage; Learn the three groups. This is the most tested fact in numericals.
Gross income: Gross income = Net interest income + Net non-interest income; Taken gross of provisions and operating expenses, and excluding realised profits from sale of securities in the banking book and extraordinary or insurance income.
Capital in risk-weighted terms: Operational risk RWA = Capital charge × 12.5; 12.5 is the reciprocal of the 8% minimum capital ratio used in Basel II.

How to solve Operational Risk Capital Measurement Approaches questions

Use this sequence for any numerical on operational risk capital, whichever approach is asked.

1Identify the approach named in the question: BIA, TSA, AMA or SMA.
2List gross income for each of the previous three years, by business line if TSA is asked.
3Apply the exclusion rules: BIA ignores years with zero or negative income; TSA floors a negative yearly total at zero.
4Apply the factor: alpha of 15% for BIA, or the right beta for each business line under TSA.
5Average over the correct divisor: the number of positive years for BIA, always 3 for TSA.
6If asked for risk-weighted assets, multiply the capital charge by 12.5.
7State the result with units and add one line of comment, for example which approach gives a lower charge and why.

Quickest way: Three-line shortcut for BIA and TSA

When to use it: Use when a numerical gives three years of gross income and asks for the capital charge under BIA or TSA.

For BIA, strike out any non-positive year first, add the rest, divide by their count, then multiply by 15%.
For TSA, compute each year's weighted total in one pass (income × beta, summed), floor at zero, then divide the three totals by 3.
Write the data in a small table of years against lines so you do not miss a line or a year.
Check: the TSA charge usually lies between 12% and 18% of average income, so a result outside that range signals an error.

Common mistakes in Operational Risk Capital Measurement Approaches

Dividing by 3 under BIA even when one year has negative income.
Students carry the TSA divisor over to BIA.
Fix: Under BIA, drop non-positive years and divide by the number of positive years only.
Using the wrong beta for a business line, for example 15% for retail banking.
The betas are similar and easy to mix up.
Fix: Remember the groups: 18% for the three market and wholesale lines, 15% for commercial banking and agency, 12% for retail, asset management and retail brokerage.
Dropping a negative year under TSA instead of treating it as zero.
Students apply the BIA rule to TSA.
Fix: Under TSA, a negative yearly total is floored at zero but the year still counts in the divisor of 3.
Saying AMA is a fixed-percentage method.
Students blur the three approaches together.
Fix: AMA uses the bank's own model with approval from the supervisor. BIA and TSA use fixed factors.
Treating SMA as one of the three Basel II approaches.
The names sound alike.
Fix: SMA belongs to the revised Basel framework and replaces BIA, TSA and AMA. It uses a business indicator and an internal loss multiplier.
Forgetting that capital charge and risk-weighted assets are different.
The question asks for RWA but the student stops at the capital charge.
Fix: Read the last line of the question. Multiply the charge by 12.5 if RWA is asked.

Worked examples

Example 1

A bank's gross income for the last three years was ₹800 crore, ₹(−)100 crore and ₹1,000 crore. Compute the operational risk capital charge under the Basic Indicator Approach and the equivalent risk-weighted assets.

Show the solution

Exclude the negative year of ₹(−)100 crore. Positive years: ₹800 crore and ₹1,000 crore.
Sum of positive years = ₹1,800 crore. Number of positive years n = 2.
Average positive gross income = 1,800 ÷ 2 = ₹900 crore.
Capital charge = 15% × 900 = ₹135 crore.
Risk-weighted assets = 135 × 12.5 = ₹1,687.5 crore.

Answer: Capital charge = ₹135 crore; risk-weighted assets = ₹1,687.5 crore.

Example 2

A bank has the following gross income (₹ crore) for three years. Compute the capital charge under the Standardised Approach. Corporate finance (β 18%): 100, 120, 140. Retail banking (β 12%): 400, 450, 500. Commercial banking (β 15%): 200, 200, 300.

Show the solution

Year 1: 100 × 18% = 18; 400 × 12% = 48; 200 × 15% = 30. Total = 96.
Year 2: 120 × 18% = 21.6; 450 × 12% = 54; 200 × 15% = 30. Total = 105.6.
Year 3: 140 × 18% = 25.2; 500 × 12% = 60; 300 × 15% = 45. Total = 130.2.
All three yearly totals are positive, so no flooring is needed.
Sum = 96 + 105.6 + 130.2 = 331.8.
Capital charge = 331.8 ÷ 3 = ₹110.6 crore.

Answer: Operational risk capital charge under the Standardised Approach = ₹110.6 crore.

Exam tips

Numericals are usually BIA or TSA. Practise both until the steps are automatic, and learn the three beta groups by heart.
In theory answers, always compare the approaches on complexity, risk sensitivity, data needs and supervisory approval.
If a question mentions SMA, name its two parts: the business indicator component and the internal loss multiplier. Add that it replaces BIA, TSA and AMA.
Write the formula first and show each year's working. Step marks are given even if the final figure is wrong.
In MCQs, watch for traps such as the alpha figure (15%) and the 12.5 multiplier for RWA.

Practice questions from Operational Risk and Off-Balance Sheet Risk

Operational Risk Capital Measurement 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 Measurement Approaches: frequently asked questions

What is the alpha factor in the Basic Indicator Approach?

Alpha is 15%. The bank multiplies its average annual positive gross income over the previous three years by this figure to get the operational risk capital charge.

What is the difference between BIA, TSA and AMA?

BIA applies one fixed percentage to total gross income. TSA applies different beta factors to eight business lines. AMA lets the bank use its own internal model, subject to supervisory approval and strict qualifying standards.

Why was the Standardised Measurement Approach introduced?

AMA results differed widely between banks, and the older approaches were not sensitive to a bank's actual loss history. SMA replaces them with one standardised method that is simpler and more comparable. It combines a business indicator component with an internal loss multiplier.

How do I convert an operational risk capital charge into risk-weighted assets?

Multiply the capital charge by 12.5. This is the reciprocal of the 8% minimum capital ratio used in Basel II, and it lets operational risk be added to credit and market risk RWA.