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Contrast how Basel II's basic indicator approach, standardized approach and AMA (advanced measurement approach) each produce a charge for operational risk.

FRM® Part II · Operational Risk and Resilience · Capital Regulation Before the Global Financial Crisis · FRM2.ORR.21.g

The idea

Basel II offers three operational risk methods. The basic indicator approach sets BIA = 15 percent × average annual gross income over the previous three years. Only years with positive gross income count, in both numerator and denominator. The standardized approach splits gross income across eight business lines, each with a beta of 12, 15 or 18 percent. Corporate finance, trading and sales, and payment and settlement take 18 percent. Commercial banking and agency services take 15 percent. Retail banking, asset management and retail brokerage take 12 percent. Each year the weighted amounts are summed, with negatives offsetting positives, and the year is floored at zero. Capital is the three-year average of these yearly totals. The advanced measurement approach (AMA) is the bank's own model, with a 99.9 percent one-year confidence level, using internal and external loss data, scenario analysis and business environment and control factors. AMA needs supervisory approval.

Formulas

Basic indicator approach for operational risk

BIA = 0.15 × ΣGI ÷ n

GI
annual gross income in each of the previous three years that had positive gross income
n
the number of those positive years

Years with zero or negative gross income are dropped from both the sum and the count, not entered as zero.

Standardised approach for operational risk

TSA = Σ max(Σ β × GI, 0) ÷ 3

β
the beta of each business line (12, 15 or 18 percent)
GI
the gross income of that business line in the year

Within a year negative lines offset positive ones and the total is floored at zero; capital averages the three yearly totals.

A practice question

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

Under the Basel II basic indicator approach, operational risk capital is based on which measure?

  1. 8 percent of average annual gross income over the previous three yearsWhy not: 8 percent is the minimum total capital ratio; the basic indicator percentage (alpha) is 15 percent.
  2. 15 percent of gross income in the most recent year onlyWhy not: Uses a single year; the approach averages the previous three years to smooth volatility.
  3. 15 percent of average annual positive gross income over the previous three years - correct
  4. A 99.9 percent one-year loss quantile from the bank's own loss dataWhy not: This describes the advanced measurement approach, not the basic indicator approach.

Basic indicator approach: capital = 15 percent x average of annual gross income for the previous three years, excluding years in which gross income was zero or negative.

A harder one

In each of the last three years a bank earned gross income of USD 600 million in retail brokerage (beta 12 percent), USD 250 million in commercial banking (beta 15 percent) and USD 150 million in corporate finance (beta 18 percent). Operational risk capital under the standardized approach is closest to:

  1. USD 150.0 millionWhy not: Applies the single 15 percent alpha of the basic indicator approach to total gross income.
  2. USD 136.5 million - correct
  3. USD 180.0 millionWhy not: Applies the highest beta of 18 percent to all gross income.
  4. USD 163.5 millionWhy not: Assigns the betas to the wrong business lines, swapping the highest and lowest.

Each year: 600 x 12% + 250 x 15% + 150 x 18% = 72 + 37.5 + 27 = 136.5. The three-year average is also 136.5.

The hardest tier

A bank's gross income by business line (USD million) over three years is: Year 1: corporate finance 100, trading and sales 200, retail banking 400. Year 2: corporate finance 50, trading and sales -300, retail banking 300. Year 3: corporate finance 120, trading and sales 150, retail banking 350. The betas are 18, 18 and 12 percent respectively. Capital under the standardized approach is closest to:

  1. USD 61.2 millionWhy not: Does not floor Year 2 at zero; the year's weighted total is negative, but it enters as zero, not as a negative.
  2. USD 96.3 millionWhy not: Divides by two positive years; the standardized approach always divides the sum by three.
  3. USD 64.2 million - correct
  4. USD 79.2 millionWhy not: Floors the negative trading line at zero before weighting, so losses in one line cannot offset gains in others within the year.

Weighted totals: Y1 = 102.0; Y2 = -9.0, floored to 0; Y3 = 90.6. Capital = (102.0 + 0 + 90.6)/3 = 64.2.

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