A comparison of the percentages of capital or the cost of capital allocated to each line using each of the proportional methods is shown in Figure 7. As you can see, there are significant differences in allocation percentages among the different metrics.
The high correlation between property and total results leads to an increase in the allocation percentage for property when moving from standard deviation to covariance. Recall that covariance considers these correlations, whereas standard deviation does not.1
The use of the one-sided co-xTVaR metrics leads to very different allocations when compared to the two-sided covariance metric.2 When the threshold is expected income, smaller deviations from the mean are relatively more important and surplus is allocated fairly evenly among business segments. As the metric focuses on increasingly severe metrics, such as co-xTVaR with a zero income threshold and then the shared asset approach which gives even greater weight to adverse results, the allocation to property increases again as property cat losses (a segment of the property model) are the primary driver of severe adverse results for this company.
- Note that there is a not-very-commonly used metric, co-standard deviation — the square root of the covariance — that would produce coherent allocations.
- One-sided metrics that are not conditional on the overall result include semi-variance and semi-standard deviation. These metrics are calculated in the same manner as variance and standard deviation with the exception that only values less than the mean for the statistic being calculated (rather than for the total) are included.
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