Susan E. Witcraft, Managing Director
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Capital needs can be defined from a number of different perspectives:

• Regulatory: which focuses on the probability of insolvency;
• Rating agency: which focuses on both the probability of insolvency and the ability to continue with the current rating; and
• Going concern: which focuses on the ability to continue to implement current plans.

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Susan E. Witcraft, Managing Director
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In the 1980s many large general insurance companies investigated the use of dynamic financial analysis for corporate decision making. Only a small number of insurers and reinsurers, (1) many of which were European, were able to develop dynamic financial models that were adequate for use in decision making. The primary obstacles
to implementation were actuarial knowledge and computer technology. By the early 2000s, technology had improved, actuaries had developed techniques that allowed better quantification of insurance risks and dynamic financial analysis had evolved
into enterprise risk management (ERM) supported by economic capital models. With these improvements, regulators began to develop solvency rules that create incentives for insurers to implement economic capital models. Although the current impetus for economic capital models is regulatory, the original purpose of enhanced strategic decision making is still valid and companies that use their economic capital models for ERM will be industry leaders.

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Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
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Insurers have choices in evaluating how to allocate capital and its cost. The ultimate goal is to strike a balance between feasibility (based on management acceptance and effort) and capital optimization. Eventually, most companies are likely to migrate towards contribution methods, along the lines of co-xTVaR and the shared asset approach, with thresholds varying with the specific questions being reviewed and specific corporate risk tolerances.

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Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
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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.

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Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
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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.

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Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
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Co-xTVaR has almost the opposite advantages and disadvantages of standard deviation. It is calculated as the amount by which each risk is worse than its expectation in those situations in which the totality of risks being modeled exceeds its expectation. Co-xTVaR can be viewed as the amount by which a segment is “over budget” in those scenarios in which the company as a whole is “over budget.” In other words, co-xTVaR looks at the average amount by which each segment exceeds its mean in the scenarios in which the company result exceeds some threshold.

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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.

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Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
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Standard deviation has long been a common allocation basis in actuarial literature. There have been many papers published discussing the use of standard deviation as a basis for allocating capital for pricing either explicitly or implicitly — e.g., in calculating increased limits factors. With this approach, the standard deviation of each segment is calculated independently. Capital is allocated to each segment in the same proportion as its standard deviation bears to the sum of the standard deviations.

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Susan Witcraft, Managing Director, Financial Intelligence Team, Instrat
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To understand the differences in proportional capital allocation methods, it helps to have a reference point. Consider a simple hypothetical insurer that writes auto, general liability, workers’ compensation and property business. The loss distributions are a bit exaggerated to highlight some of the differences among metrics. A profile of the company’s business is shown in Figure 1.

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