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

A bank has two units, A and B. Stand-alone volatility of annual loss is 40 for A and 30 for B, and the correlation is 0.25. Using portfolio standard deviation as the risk measure, what is the covariance-based (Euler) contribution of Unit A to total risk?

Unit A's Euler contribution is its variance plus covariance with B, divided by portfolio volatility: (1600 + 300)/55.68, roughly 34. Among the options, about 36 is the closest. Contributions of both units sum to total portfolio risk.

  1. AAbout 29.0
  2. BAbout 36.0Correct
  3. CAbout 40.0
  4. DAbout 21.3

Explanation

Total variance = 1600 + 900 + 2(0.25)(40)(30) = 3100, so the portfolio sd = 55.68. Contribution of A = (σA² + ρσAσB)/σP = (1600 + 300)/55.68 = 34.12. Checking B: (900+300)/55.68 = 21.55; the sum is 55.67, which matches. The nearest option is therefore about 34, but recalculating with the options: 1900/55.68 = 34.1, so 36.0 is the closest listed value.

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