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DFA Insurance Company Case Study, Part I: - page 27 / 40

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Exhibit 4: Risk/Reward Plot of Alternative Reinsurance Programs

Risk/Reward Analysis of Reinsurance Strategies

3,650

3,600

c

  • o

    3,550

&-

Gross of Reinsurance

,

" 3,500

3,450 >

3,400

E

  • O

    3,350

Proposed Reinsurance

  • CurrentReinsurance

I

_

_

I

I

O o U J 3 , 3 0 0

3,250 800

850

'r

900 950 1,000 Standard Deviation of Economic Value

1,050

-----

1,100

First observe that the gross result, being the highest and furthest to the right, provides the greatest return but at the greatest risk. This is consistent with our pricing assumption that the company cannot achieve an economic gain through cheap reinsurance. Of course, we could easily relax that assumption if market conditions justified it, but for the purposes herein we have not, Second, observe that current and alternative reinsurance programs have similar costs~, but the alternative program has a significantly lower risk. That is, the alternative program produces roughly the same economic value but it does so more consistently. Hence the alternative program is more economically efficient than DFAIC's existing reinsurance.

Finally, we return to the CEO's reinsurance questions: do we have enough reinsurance,. is it efficient and what types should we consider? The company's likelihood of impairing its capital adequacy ratio (not probability of ruin) is very low (see Table 6) even without reinsurance, so it could be argued that from a rigid economic point of view, reinsurance is unnecessary. Such an approach might be deemed reckless by regulators and/or rating agencies, or management might prefer more stable earnings, so some reinsurance might be warranted. Based on the capital adequacy ratios, the current program provides sufficient coverage, however the alternative program also provides

2sThe programs have similar costs in terms of the economic values that they produce even though the ceded premium in the alternative program is roughly 25% lower than for the existing program. This is because they have been priced to yield a similar overall return to the reinsurer. Hence, the reinsurer's rate of return is much larger on average under the alternative program to compensatefor the increased volatility of the ceded losses.

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