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

A firm has three units whose diversified (Euler) contributions to firm capital are 30, 45 and 25 million, and total firm capital is 100 million. Management compares this with marginal capital, measured as the drop in firm capital if each unit were removed: 22, 38 and 18 million. Which statement is correct?

Marginal capital sums to 78 million versus firm capital of 100 million, so it is not fully additive and needs scaling or a residual allocation. The Euler contributions sum to exactly 100 million, so they allocate all capital.

  1. AMarginal capital sums to 78 million, so it understates firm capital and cannot be used for full allocation without a scaling or residual stepCorrect
  2. BMarginal capital sums to 100 million, so it is fully additive
  3. CEuler contributions sum to 110 million, so they overstate firm capital
  4. DMarginal capital exceeds Euler contribution for every unit

Explanation

22+38+18=78, below 100, so marginal amounts are not additive; a residual must be allocated. Euler contributions sum to 30+45+25=100, fully additive. Marginal amounts are below Euler for each unit, not above.

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