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FRM Part II · FRM Exam Part II · Risk Capital Attribution and Risk-Adjusted Performance Measurement

A bank allocates economic capital to its business units. The head of risk wants an attribution in which the capital assigned to each unit sums exactly to the total portfolio capital, and each unit's share reflects its contribution to portfolio risk given its correlation with the rest of the bank. Which approach best meets this requirement?

Euler or marginal contribution allocation is best. For a homogeneous risk measure, each unit's weight times its marginal risk sums exactly to total capital and captures correlation with the rest of the bank, unlike stand-alone or incremental methods, which do not add up to the total.

  1. AStand-alone capital for each unit, computed as if it were an independent firm
  2. BIncremental capital, computed as total capital minus capital without the unit
  3. CEuler (marginal) contribution to risk, which allocates capital proportional to each unit's weight times its marginal riskCorrect
  4. DAllocation based on each unit's share of total book assets

Explanation

Euler (marginal) contributions use homogeneity of the risk measure so the weighted marginal contributions sum exactly to total portfolio capital, and they reflect correlations. Stand-alone capital ignores diversification and generally sums to more than total capital. Incremental capital typically does not sum to the total.

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