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FRM Part I · FRM Exam Part I · Enterprise Risk Management and Future Trends

A firm allocates economic capital to two business units using the marginal (incremental) approach. Unit A stand-alone capital is 40 and Unit B is 30, with correlation 0.30 between them. Total firm capital is sqrt(40^2 + 30^2 + 2*0.3*40*30) = sqrt(3220) = 56.75. Without Unit B, the firm's capital would be 40. Which is the incremental capital attributable to Unit B?

Incremental capital for Unit B is total firm capital of 56.75 minus the capital of 40 that would remain without B, giving 16.75. The stand-alone figure of 30 overstates B's contribution because it ignores diversification with Unit A.

  1. A30.00
  2. B16.75Correct
  3. C26.75
  4. D13.25

Explanation

Incremental capital for B is total capital minus capital without B: 56.75 - 40 = 16.75. The stand-alone figure of 30 ignores diversification. 13.25 is 30 minus 16.75, the diversification benefit, not the incremental capital.

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