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

A bank holds 100 of total economic capital. Unit X has stand-alone capital of 60 and Unit Y of 70. Y is highly diversifying against X. Incremental capital (total less capital without the unit) is 45 for X and 35 for Y. Management allocates capital proportional to stand-alone capital. Which Unit X allocation and conclusion are correct?

Proportional allocation gives X 100 × 60/130, about 46.2. This is higher than X's incremental capital of 45, so X bears slightly more capital than its marginal contribution to total risk, while the diversification benefit is spread across both units.

  1. AAllocation 46.2; it exceeds X's incremental capital, so X is charged more than its marginal effect on total riskCorrect
  2. BAllocation 60; stand-alone is always the correct amount
  3. CAllocation 45; proportional allocation equals incremental capital
  4. DAllocation 53.8; it is lower than incremental capital so X is subsidized

Explanation

Proportional allocation = 100 × 60/130 = 46.15. This is above X's incremental capital of 45, so X is charged slightly more than its incremental effect. Distractor 60 ignores diversification, while 53.8 is Y's share of 70/130 applied to the wrong unit. Incremental capital does not generally equal the proportional share.

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