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3. Summary of Market Dynamics
Hypothetical Re's Clash Sales Department reports following:
 There are about 250 significant Clash programs bought in the U.S.A. right now. Hypothetic Re is involved in 150 of them.
Total limits purchased by reinsureds range between $4 and $400 Mn.; Hypothetic Re's share averages $5 Mn. but is never more than $10 Mn.
There are approximately 70 reinsurers, worldwide, and a further 20 syndicates at Lloyds who make a market in Clash. There are also several life reinsurers who write High Layer WC, but not Clash. Many reinsurers are capable and interested leads who now complete fiercely on price and terms.
Rates-on-line vary widely, depending on layer, original premiums, inuring protections and exposure, although generally are between 2% and 20%.
4. Corporate Risk and Capacity Analysis
The CFO maintains the following analysis:
The highest allowable annual probability of bunkruptcy is 0.2% (1 in 500 years).
Hypothetic Re has $200 Mn. in Surplus, which supports five Underwriting Departments:
- Clash/High Layer WC
- Property Cat
- Working Covers/Facultative
- Specialty Coverages
- Foreign
The CFO and actuary agree that each of these five products offerings poses different and statistically independent risks.
To maintain the 1-in-500 year ruin scenario, each of the five Underwriting Departments is allowed to expose Hypothetic Re's Surplus to no more than a 1% probability of a $100 Mn. underwriting loss in any one year.
The Clash Department could incur losses of $150 Mn. before it loses $100 Mn. That would be limits losses to at least 15 accounts.
At a 50% expected los ratio, and a 6-7% average rate-on-line, assuming that accounts are independent of each other, the Clash Department should expect 4 accounts per year to show losses, with a standard deviation of 2.0 accounts per year.
But there is statistical dependence between accounts, both in:
- Parameter risk, e.g., claim severity trends industrywide are higher than expected; and
- Process risk, e.g., wide-spread WC losses in an earthquake.
The Corporate Finance and Actuarial Departments agree that the annual standard deviation about the number of Clash accounts with claims is closer to 5.0.
The probability of 15 accounts with total losses is approximately the target probability of 1% per year.
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