Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
The shared asset method is a bit different from the other proportional approaches to capital allocation.1 The cost of capital is allocated to line rather than allocating capital itself. Capital is viewed as a shared asset to support all risks assumed by the insurer, and the company estimates the cost of replacing capital at different levels of loss. Figure 5 shows an illustration of these differing cost of capital levels, with the cost increasing as more capital is lost.
To allocate the cost of capital to segment, the amount of surplus lost in each iteration at the company level is first calculated. The cost of capital for that amount is calculated as the weighted average of the replacement costs in the table above. The weighted average cost of capital is then multiplied by the contribution of each segment to the loss of surplus to derive each segment’s cost in that iteration. The average cost of capital is then calculated across all iterations.
Figure 6 shows the relative amounts of profit required for each segment based on this approach.
If the replacement cost of capital is constant at all levels in the shared asset approach, it will produce the same profit requirements by segment as would be derived using the co-xTVaR approach with expected income as the threshold and the same cost of capital.2
The shared asset approach has similar advantages and disadvantages as co-xTVaR. Additional benefits to this approach are (1) its avoidance of directly allocating capital to line which recognizes that all surplus is available to all lines and (2) the ability for the user to specify greater preference for smaller surplus losses than larger ones.
- Mango, Donald F., “Insurance Capital as a Shared Asset,” ASTIN Bulletin International Actuarial, 2005: 35:2, 471-486, http://www.casact.org/library/astin/vol35no2/471.pdf.
- There is also a metric, weighted co-xTVaR, that will produce equivalent results to the shared asset approach with the same weights. As is inferred by its name, weighted co-xTVaR is a weighted average of the values that are given equal weights in an unweighted co-xTVaR calculation.
Previous articles in this series:
Part I: Introduction >>
Part II: Illustration >>
Part III: Standard Deviation >>
Part IV: Covariance >>
Part V: Co-xTVaR >>
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