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

A bank allocates capital to three desks using the Euler (marginal contribution) approach based on a portfolio VaR of 100 million. Desk contributions are computed as weight times partial derivative of VaR. Desk X's standalone VaR is 50 million, and its correlation with the rest of the portfolio is low, so its Euler contribution is 30 million. Desk Y has standalone VaR of 60 million and contribution of 45 million. What is Desk Z's contribution, and what property of the Euler method does this illustrate?

Desk Z's contribution is 25 million. Under Euler allocation, component contributions add up exactly to total portfolio VaR because VaR is homogeneous of degree one, so Z equals 100 less 30 and 45. This illustrates the full allocation property, with diversification already reflected.

  1. A25 million; contributions sum exactly to total portfolio VaR (full allocation)Correct
  2. B25 million; contributions sum to the sum of standalone VaRs
  3. C20 million; contributions sum to less than total VaR to reflect diversification
  4. D30 million; each desk receives an equal share of the remainder

Explanation

For VaR, which is homogeneous of degree one, Euler's theorem makes the component contributions sum exactly to total VaR. Z = 100 - 30 - 45 = 25 million. This is the full allocation property. The sum of standalone VaRs would exceed the total because of diversification.

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