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Explain why the Basel Committee introduced the standardized measurement approach and describe what it involves.

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

The idea

The Basel Committee replaced the basic indicator, standardized and advanced measurement approaches with the standardized measurement approach (SMA). The AMA gave complex capital figures that were hard to compare across banks and open to model manipulation. The older standardized approaches were not risk-sensitive, scaling only with gross income. The SMA keeps a simple, comparable base and adds the bank's own loss history. First compute the Business Indicator from interest, services and financial components. Then compute the Business Indicator Component (BIC) using marginal coefficients of 12 percent on the part up to EUR 1 billion, 15 percent on the part from 1 to 30 billion and 18 percent above 30 billion. The Internal Loss Multiplier is ILM = ln(e − 1 + (LC ÷ BIC)^0.8). The Loss Component LC is 15 times average annual operational losses over ten years. Capital = BIC × ILM. When LC equals BIC the ILM is exactly 1. The coefficients apply marginally, like a tax schedule.

Formulas

SMA operational risk capital

capital = BIC × ILM

BIC
the Business Indicator Component, from marginal coefficients of 12, 15 and 18 percent
ILM
the Internal Loss Multiplier

Apply the BIC coefficients marginally, like a tax schedule, not the top rate to the whole Business Indicator.

SMA 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

ILM is exactly 1 when LC equals BIC. Above that it rises less than proportionally, so doubling losses does not double capital.

A practice question

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

Why did the Basel Committee replace the advanced measurement approach and the earlier standardized approaches with the standardized measurement approach?

  1. Banks using the AMA were consistently holding too little capital for credit riskWhy not: The SMA concerns operational risk; credit risk capital is a separate framework.
  2. Regulators wanted to encourage each bank to build more elaborate internal modelsWhy not: The SMA does the opposite: it removes internal modelling for regulatory capital.
  3. Internal models gave widely differing, hard-to-compare capital results, and the old standardized approaches were not risk-sensitive - correct
  4. Gross income stopped being reported by supervisors after accounting changesWhy not: Not the reason; the concern was comparability and risk sensitivity, and the SMA still builds on financial statement data.

The AMA was complex and gave inconsistent results across banks, while the basic indicator and standardized approaches were driven only by gross income. The SMA is simple, comparable and includes loss history.

A harder one

A bank has a Business Indicator of EUR 5 billion. Using marginal coefficients of 12 percent up to EUR 1 billion, 15 percent from EUR 1 billion to EUR 30 billion and 18 percent above EUR 30 billion, its Business Indicator Component is closest to:

  1. EUR 720 million - correct
  2. EUR 900 millionWhy not: Applies the top 18 percent coefficient to the whole BI although BI is far below EUR 30 billion.
  3. EUR 750 millionWhy not: Applies 15 percent to the whole BI instead of charging the first EUR 1 billion at 12 percent.
  4. EUR 600 millionWhy not: Applies the lowest 12 percent to everything, ignoring the 15 percent on the part above EUR 1 billion.

Coefficients are marginal: 0.12 x 1,000 + 0.15 x 4,000 = 120 + 600 = 720 (EUR million).

The hardest tier

A bank has a BIC of EUR 1,000 million and a Loss Component equal to its BIC, so its ILM is 1. After a very large loss, the ten-year average rises so the Loss Component doubles to EUR 2,000 million, BIC unchanged. Using ILM = ln(exp(1) - 1 + (LC/BIC)^0.8), capital rises by approximately:

  1. 100 percentWhy not: Assumes capital is proportional to the Loss Component; the log and the 0.8 exponent make the response concave.
  2. 24 percent - correct
  3. 31 percentWhy not: Uses an exponent of 1 instead of 0.8 on LC/BIC.
  4. 246 percentWhy not: Omits the natural log and compares the inner terms, (e - 1 + 2^0.8) against 1.

ILM(1) = ln(e) = 1. ILM(2) = ln(1.718 + 2^0.8) = ln(1.718 + 1.741) = 1.241. Capital rises about 24 percent: doubling losses does not double capital.

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