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Contrast three ways of arriving at regulatory capital for operational risk: the advanced measurement approach, the standardized approach and the basic indicator approach.

FRM® Part I · Valuation and Risk Models · Operational Risk · FRM1.VR.7.b

The idea

Basel II offers three ways to set operational risk capital, in rising order of sophistication. The basic indicator approach sets capital at 15% of average annual gross income over the previous three years, counting only years in which gross income was positive. The standardized approach splits gross income into eight business lines and multiplies each by a beta between 12% and 18%, for example 18% for trading and sales and 12% for retail banking. Negative lines offset positive ones within a year, but a negative yearly total is set to zero and still counts in the three-year average. The advanced measurement approach lets a bank use its own model, built on internal and external loss data, scenario analysis and control factors, to estimate a 99.9% one-year loss, subject to supervisory approval. Only the AMA responds to the bank's own loss experience and controls. Exam traps are the zero floor in the standardized approach and the exclusion of negative years in the basic indicator approach.

Formulas

Basic indicator approach capital

capital = 0.15 × average positive annual gross income

average positive annual gross income
the mean gross income over the previous three years, counting only years in which it was positive

Drop negative years and divide by the number of positive years. Capital depends only on income, not on losses or controls.

Standardised approach charge for one year

annual charge = max(Σ βⱼ × GIⱼ, 0)

βⱼ
the beta for business line j, between 12 and 18 percent
GIⱼ
gross income of business line j in the year

Capital is the average of the three annual charges. Lines net within a year, and a negative year is floored at zero but still counts in the three-year average: that floor is the usual trap.

A practice question

From the question bank, with the reason each wrong option is wrong.

Under the basic indicator approach, operational risk capital is set at:

  1. Business-line betas of 12 to 18 percent applied to each line's gross incomeWhy not: This is the standardized approach, which differentiates by business line.
  2. 15 percent of average annual gross income over the previous three years, using only years with positive gross income - correct
  3. A 99.9 percent one-year loss from the bank's own loss modelWhy not: This is the advanced measurement approach, not the basic indicator approach.
  4. 8 percent of average annual gross income over the previous three yearsWhy not: Uses the 8 percent credit-risk capital ratio instead of the 15 percent alpha factor of the basic indicator approach.

The basic indicator approach is alpha x average positive annual gross income over three years, with alpha = 15 percent.

A harder one

A bank's gross income this year is EUR 100 million in corporate finance (beta 18 percent), EUR 500 million in retail banking (beta 12 percent) and EUR 200 million in asset management (beta 12 percent). Treating this as a single year, the standardized approach charge is closest to:

  1. EUR 120 millionWhy not: Applies the basic indicator 15 percent to total gross income of 800, ignoring the betas.
  2. EUR 144 millionWhy not: Applies the highest beta of 18 percent to all gross income instead of line by line.
  3. EUR 112 millionWhy not: Uses the simple average of the three betas instead of weighting each line's income by its own beta.
  4. EUR 102 million - correct

Charge = 0.18 x 100 + 0.12 x 500 + 0.12 x 200 = 18 + 60 + 24 = 102. Each business line has its own beta.

The hardest tier

A bank reports gross income of EUR 600 million, negative EUR 100 million and EUR 900 million over the last three years. Under the basic indicator approach, its capital is closest to:

  1. EUR 70.0 millionWhy not: Includes the negative year in the average, dividing the total of 1,400 by three.
  2. EUR 112.5 million - correct
  3. EUR 75.0 millionWhy not: Sets the negative year to zero but keeps it in the denominator; the BIA excludes it from both numerator and denominator.
  4. EUR 135.0 millionWhy not: Applies 15 percent to only the latest year's gross income instead of averaging the positive years.

Only positive years count: (600 + 900) / 2 = 750, and 15 percent of 750 = 112.5.

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