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

A risk manager compares stand-alone, incremental and marginal (Euler) capital allocation for a trading desk. Which statement is correct?

Euler contributions from a homogeneous degree-one risk measure, such as standard deviation, sum exactly to total portfolio risk. Stand-alone capital ignores diversification and incremental capital usually does not add up, so only the Euler approach gives a full additive allocation.

  1. AIncremental capital for each unit always sums to total capital
  2. BStand-alone capital for each unit always sums to total capital
  3. CEuler contributions based on a homogeneous risk measure sum exactly to total portfolio riskCorrect
  4. DMarginal capital ignores correlation with the rest of the portfolio

Explanation

For risk measures homogeneous of degree one, such as standard deviation, Euler's theorem makes the sum of marginal contributions equal total risk. Stand-alone figures ignore diversification, and incremental figures generally do not add up to the total. Marginal capital explicitly reflects correlation.

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