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FRM Part II · FRM Exam Part II · Range of Practices and Issues in Economic Capital Frameworks

A bank's one-year economic capital at the 99.9% level is USD 900 million. The bank has three business units with stand-alone 99.9% economic capital of USD 500 million, USD 400 million and USD 300 million, totalling USD 1,200 million. A senior manager asks why the sum of stand-alone capital exceeds the bank-level figure. Which explanation is best, and what is the diversification benefit as a percentage of the stand-alone sum?

The gap reflects diversification from imperfectly correlated unit losses. The benefit is (1,200 − 900)/1,200 = 25% of stand-alone capital. Using the bank-level figure as base gives 33.3%, which is the wrong denominator.

  1. AImperfect correlation among unit losses; benefit is 25%Correct
  2. BImperfect correlation among unit losses; benefit is 33.3%
  3. CExpected losses being deducted; benefit is 25%
  4. DUse of a lower confidence level at bank level; benefit is 33.3%

Explanation

Diversification benefit = (1,200 - 900)/1,200 = 25%. It arises because unit tail losses are not perfectly correlated, so VaR-based capital is not additive. 33.3% wrongly uses 300/900 as the base. The confidence level is the same, and expected loss does not explain the gap.

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