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DFA Insurance Company Case Study, Part I: - page 23 / 40





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the higher end of the reasonable range2~. Our intent was to make it slightly more difficult to discard the current program in favor of the alternative aggregate coverage.

Finally, the required capital under the current and alternative reinsurance programs is roughly one-third of DFAIC's statutory surplus.22 Actual capital in excess of required capital was the only capital constraint that we imposed on the alternative reinsurance programs considered for DFAIC. We note that a capital-oriented approach, where alternative programs are judged by changes in the company's required capital, could have been employed to evaluate alternative reinsurance programs. Below we present one interesting reinsurance finding based on a capital-oriented approach, but we chose to define "efficiency" of the company's reinsurance program in terms of the stability of loss ratios and the shift in the company's efficient frontier for the remainder of the case study.

Risk Based Capital (RBC) was introduced by the NAIC in the 1990s to supplement the .then-existing solvency early warning tests. More recently, rating agencies including A.M. Best and S&P have introduced their own brand of capital adequacy ratio. The underlying tenet of these ratios is that the combined charges for various risk factors provide guidance as to the amount of capital required by an organization. The ratio of actual capital to capital required (as determined by the risk factor charges) is the "capital adequacy ratio". We can use these ratios to compare the expected performance of alternative reinsurance programs within the context of a DFA model.

Working with the NAIC RBC factors, we calculated the probability of DFAIC's actual capital falling below the required capital level at any time in:a five-year period under three scenarios: (1) no reinsurance; (2) current reinsurance; and (3) the alternative reinsurance program. The results are presented in the Table 6.

Table 6: Probability of Actual Capital Falling below the Required RBC Level



No Reinsurance


Current Reinsurance


Alternative Reinsurance


  • Cumulative probability over five years.

21The accident year aggregate cover provides approximately $375 million of coverage for approximately $94 million, a rate on line of roughly 25%. Considering the duration of the expected payments, we believe that this is a reasonably conservative price for the contract.

22Philbnck, Stephen and Robert Painter, "DFA Insurance Company Case Study, Part Ih Capital Adequacy and Capital Allocation," Casualty Actuarial Society Forum, Summer 2001. Arlington, VA: Casualty Actuarial Society.


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