December 3rd, 2009

A Survey of Capital Allocation Metrics: Covariance

Posted at 1:00 AM ET

Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
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Covariance is the expected value of the product of the deviations of two variables from their means. In each iteration, the difference between a segment’s value and its mean is multiplied by the difference between the total value and the total mean. The average of these products is the covariance. Capital is then allocated in proportion to the covariances. Figure 3 shows the covariances and allocated capital for the sample company.

capitalallocation3

The advantages to covariance as an allocation metric are:

  • It is fairly well understood, even outside actuarial circles.
  • It is easy to calculate.
  • It is coherent.
  • It reflects the correlations among segments and with the total.

The disadvantage is that it considers both favorable and adverse deviations from expectations, while capital allocation is usually focused on adverse deviations. Covariance is considered an improvement on standard deviation because of its coherence property and its recognition of correlations.

Previous articles in this series:

Part I: Introduction >>

Part II: Illustration >>

Part III: Standard Deviation >>

Click here to receive the rest of this series by e-mail >>

Click here to learn more about capital management >>

Guy Carpenter & Company, LLC provides this material for general information only. Guy Carpenter & Company, LLC makes no representations or warranties, express or implied. The information is not intended to be taken as advice with respect to any individual situation and cannot be relied upon as such.

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