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DFA Insurance Company Case Study, Part I: - page 22 / 40





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Line-oriented management of ceded reinsurance will likely lead to a program that guards against large individual claims even in years where actual losses (in total) are lower than originally anticipated and/or in reinsurance that fails to recognize the diversification benefits of writing multiple LOBs. But this is nothing new, and it certainly does not require a DFA model to recognize that diversification exists whenever a company writes two or more LOBs.18 We will show that the inefficiency goes beyond a missed opportunity (failing to recognize the diversification already present in their business), since for DFAIC their existing program actually impairs (slightly) certain capital adequacy measures.

We will demonstrate that Falcon's enterprise-level philosophy to managing risk with reinsurance is by far the most important element to building the efficient program that the company seeks. Given that DFAIC is large and well capitalized, by focusing on company-wide results rather than LOB results DFAIC could eliminate most of its current reinsurance programs without any significant increase in risk to the consolidated company loss ratio. We will also show that additional improvement can be achieved through new reinsurance structures that embrace enterprise-level rather than LOB-level reinsurance strategies. Thus, reinsurance in the "new" DFAIC will truly become a mechanism by which the enterprise forgoes part of its expected return~9, in exchange for protection from events that jeopardize overall stability.

Before we begin, a discussion of the modeling of the reinsurance program and the alternatives is required. Almost any reinsurance program can be made to look exceptionally good or bad within a DFA model by simply mis-pricing the coverage. We modeled DFAIC's existing reiqsurance program which has a large component of per occurrence excess of toss coverage attaching at $500,000 in combination with a per risk excess cover on commercial propertym and a property catastrophe cover attaching at $50 million. We created an alternative reinsurance structure wherein the per occurrence and per risk covers are replaced with an accident year aggregate stop loss contract covering 75% of 20 loss ratio points excess of 80.

In deriving the prices for the various reinsurance contracts, we erred on the side of conservatism specifically to avoid making the current program look bad or the alternative look good. That is, we priced the current program at a rate that we believe is slightly biased toward the low end of the reasonable range, thereby increasing overall ceded loss ratios. Likewise, we priced the aggregate contract in the alternative program toward

~8Unless the LOBs are perfectly positively correlated, some diversification will be achieved.

~9Throughout this case study we have assumed the company cannot achieve a gain by purchasing under-priced reinsurance.

2oWe assumed that DFAIC's $20 million excess $1 million per risk excess cover applied exclusively to property m its CMP program. In doing so, we implicitly assumed that there was no homeowner exposure above $1 million. If this were a "live" DFA study this assumption might deserve additional consideration. Further, we assumed that the $50 million occurrence aggregate had a minimal impact on the coverage.


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