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DFA Insurance Company Case Study, Part I: - page 24 / 40





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First, observe that these probabilities are very low. DFAIC is a strongly capitalized company with an RBC ratio of over 300%23. Second, it is not surprising that the alternative reinsurance program reduces the likelihood of "impairing" surplus because it results in a more stable distribution of net loss ratios (see Table 7 below). Finally, the interesting conclusion is that DFAIC actually increases its chance of impairing surplus by purchasing its existing reinsurance program!

This somewhat odd finding occurs because the company "trades dollars" with its reinsurer, not because reinsurance is over priced24. In other words, DFAIC reinsures losses that on average occur every year; they incur additional expenses (e.g., the reinsurer's profit) which increases their probability of failing the capital adequacy test. Capital testing, as in the RBC example above, can be used to choose between alternative reinsurance programs. However, we took a slightly different approach, by screening potential reinsurance programs based on loss ratio variability, then comparing selected programs based on economic risk/reward.

Note that we could just as easily have compared several alternative reinsurance programs based on the risk/reward analysis, using the economic value of surplus, statutory surplus, GAAP equity or some other metric, without reviewing loss ratio variability. In fact, screening reinsurance programs based on loss ratio variability arguably is not DFA because although the process includes the impact of the simulated economic conditions (i.e., inflation) on losses and premium, changes in asset values are ignored. Nonetheless, we have included it to emphasize that there are many ways to use DFA (in this case a single DFA model) to conduct such an analysis. Another, perhaps more important motivation for using the loss ratio analysis was that without a thorough understanding of the key drivers of our results, our analysis may be subject to criticism. As we will see the loss ratio analysis provides that understanding.

We screened several alternative reinsurance programs for possible use in the case study including two variants of DFAIC's existing program substituting $1 and $5 million retentions on the per occurrence contracts. We also considered and ultimately settled L~ponan accident year aggregate cover in place of all of the company's non-catastrophe coverage. To illustrate the process, the net loss ratios from accident year 2 and the corresponding standard deviations of net losses are summarized in Table 7.

23DFAIC's statutory surplus is more than three times the minimum surplus, according to the risk based capital formula. Under the more conservative assumptions underlying the rating agency capital adequacy ratios, this ratio drops to roughly two times the minimum.

24The ultimate ceded loss ratio modeled for the current program (including the catastrophe contract) was 80.6% versus 80.0% for the alternative program. The alternative program's ceded payments were much more volatile than under the current program but its duration was also

much longer. We assumed that the longer duration adequately compensated the reinsurer for the increased volatility.


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