Describe the components of the new standardized method for operational risk capital, namely the loss component, the internal loss multiplier and the business indicator, and compute a bank's requirement with it.

FRM® Part II · Operational Risk and Resilience · Basel III: Finalising post-crisis reforms · FRM2.ORR.24.a

The idea

The Basel III standardized measurement approach (SMA) starts from the business indicator (BI), a three-year average of three components. Interest, leases and dividends is the interest margin, capped at 2.25 percent of interest-earning assets, plus dividends. Services is the larger of fee income and expense plus the larger of other operating income and expense. Financial is the absolute net trading book result plus the absolute net banking book result. The business indicator component, BIC, uses marginal rates of 12 percent up to EUR 1 billion, 15 percent from 1 to 30 billion and 18 percent above. The bank's own history enters through losses. The loss component is LC = 15 × average annual net losses over ten years. Dividing the loss component by the business indicator component gives the ratio of losses to size, Ratio = LC ÷ BIC. The internal loss multiplier equals 1 when LC equals BIC. It is ILM = ln(e − 1 + Ratio^0.8). Capital = BIC × ILM. RWA is 12.5 times capital. The usual slip is applying one flat rate to all of BI.

Formulas

Business indicator

BI = ILDC + SC + FC

ILDC: interest, leases and dividends: the interest margin capped at 2.25 percent of interest-earning assets, plus dividends
SC: services: larger of fee income and expense plus larger of other operating income and expense
FC: financial: absolute trading book result plus absolute banking book result

Each component is a three-year average. Forgetting the cap on the interest margin is a common slip.

Business indicator component for BI between EUR 1 and 30 billion

BIC = 0.12 × 1 + 0.15 × (BI − 1)

BI: the business indicator in EUR billion

The rates are marginal: 12 percent on the first billion, 15 percent up to 30 billion, 18 percent above. One flat rate is wrong.

Loss component

LC = 15 × L

L: the average annual net operational loss over the previous ten years

Losses are net of recoveries. Where the supervisor permits fewer years, average over the years actually used.

Internal loss multiplier

ILM = ln(e − 1 + (LC ÷ BIC)^(0.8))

LC: the Loss Component, 15 times average annual operational losses over ten years
BIC: the Business Indicator Component

Equals 1 when LC equals BIC; above 1 when losses are heavy relative to size.

SMA operational risk capital

ORC = BIC × ILM

BIC: the business indicator component
ILM: the internal loss multiplier

RWA is 12.5 times this figure. There is no internal model, diversification or insurance benefit.

A practice question

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

Under the Basel III standardized measurement approach, how is the loss component (LC) defined?

15 percent of the average of the previous three years of positive gross incomeWhy not: Describes the basic indicator approach charge, not the SMA loss component.
15 times the average annual net operational losses over the previous ten years - correct
15 times the single largest annual operational loss in the previous ten yearsWhy not: Uses the worst year rather than the average of annual losses.
The 99.9th percentile of the bank's modelled one-year aggregate loss distributionWhy not: Describes the advanced measurement approach, which the SMA does not use.

LC = 15 x average annual net operational losses over ten years (net of recoveries). The 15 percent of gross income is the old basic indicator approach, and a 99.9 percent modelled loss belongs to the AMA.

A harder one

A bank reports the following for the year, in EUR million: interest income 9,000, interest expense 6,500, interest-earning assets 150,000, dividend income 300, fee income 2,100, fee expense 2,500, other operating income 1,800, other operating expense 1,200, net trading book result -400 and net banking book result +150. Treating this as the bank's three-year average, which business indicator (BI) is closest to the SMA definition?

EUR 7,650 million - correct
EUR 3,550 millionWhy not: Nets income against expense in the services component (200 instead of the larger of each pair, 4,300).
EUR 7,350 millionWhy not: Nets the trading and banking book results (-250) instead of adding their absolute values.
EUR 10,950 millionWhy not: Adds all four fee and operating items in the services component instead of taking the larger of each income-expense pair.

ILDC = min(|9,000 - 6,500|, 2.25% x 150,000 = 3,375) + 300 = 2,800. SC = max(1,800, 1,200) + max(2,100, 2,500) = 4,300. FC = 400 + 150 = 550. BI = 2,800 + 4,300 + 550 = 7,650.

The hardest tier

A bank reports a three-year average of the following, in EUR million: interest income 16,000, interest expense 5,000, interest-earning assets 300,000, dividend income 1,200, fee income 3,000, fee expense 2,600, other operating income 4,500, other operating expense 3,900, absolute trading book result 1,200 and absolute banking book result 800. Applying the SMA marginal coefficients (12 percent to EUR 1,000 million, 15 percent from 1,000 to 30,000 million, 18 percent above), its business indicator component is closest to:

EUR 2,588 million - correct
EUR 3,225 millionWhy not: Ignores the 2.25 percent cap on interest-earning assets, using the full 11,000 interest margin in the interest component.
EUR 2,737 millionWhy not: Applies the 15 percent rate to all BI above zero and adds 120 million, omitting the EUR 1 billion deduction.
EUR 2,094 millionWhy not: Applies the 12 percent first-band rate to the entire business indicator.

ILDC = min(11,000, 2.25% x 300,000 = 6,750) + 1,200 = 7,950. SC = max(3,000, 2,600) + max(4,500, 3,900) = 7,500. FC = 2,000. BI = 17,450. BIC = 120 + 15% x (17,450 - 1,000) = 2,587.5. The cap on the net interest margin is what changes the answer.

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