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FRM Part II · FRM Exam Part II · Integrated Risk Management

A bank's portfolio has total economic capital of USD 200 million at a 99.9% confidence level. Using the Euler (covariance) allocation, Business X has a weight of 0.30 of exposure and its capital contribution equals the portfolio capital times (cov(X, P) / var(P)). Business X's loss has covariance of 0.0048 with the portfolio loss, and the portfolio loss variance is 0.0160. What capital is allocated to Business X, and what does this imply?

Business X is allocated USD 60 million: covariance 0.0048 divided by portfolio variance 0.0160 gives 0.30, times USD 200 million. Because covariances with the portfolio sum to portfolio variance, the covariance-based contributions across all businesses add up exactly to total economic capital.

  1. AUSD 30 million, since contribution equals the exposure weight
  2. BUSD 48 million, since the covariance is divided by the weight
  3. CUSD 60 million, and the contributions of all businesses sum to total capitalCorrect
  4. DUSD 96 million, because covariance is doubled in the Euler formula

Explanation

The ratio is 0.0048/0.0160 = 0.30, so allocation is 200 x 0.30 = USD 60 million. Here the ratio coincides with the weight, but it is not defined by it. Because the covariances of all businesses with the portfolio sum to the portfolio variance, the ratios sum to one and allocations add to total capital (full allocation). The other options misuse the formula.

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