2. Results of the analysis of the practical effect of reinsurance
2.1 Basic details of the model company
Selected key figures:
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Medium-sized European multi-line insurer (five lines of insurance, approximately 50/50 long-tail/short-tail) with annual earned premiums of €120m
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Investments of €142m (20% equities, 70% bonds, 10% property)
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Gross loss reserves of €120m
Reinsurance policy:
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Various working excess-of-loss treaties (XL), one quota share treaty, plus natural catastrophe cover (NatCat XL) for windstorm and flooding
2.2 Method of analysis
First, an economic balance sheet was prepared showing the investments and underwriting liabilities at market value. This balance sheet enables the eligible capital (available solvency margin) to be determined. The capital requirements in respect of underwriting, market risk on investments and reinsurer default risk were then calculated. The overall risk capital (solvency capital requirement) can then be obtained by adding the capital requirement for operational risk. The solvency ratio is the ratio of the available solvency margin to the solvency capital requirement.
Simplified economic balance sheet of the model company according to QIS 3
€156.7m
Market value Assets
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€52.2m
ASM
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Solvency Ratio = 130.6%
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€104.5m
Market value Liabilities
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Sensitivity analyses were carried out on the basis of the existing reinsurance structure. Single reinsurance covers were excluded in turn from the reinsurance programme as a whole, permitting the impact of both a working XL and a quota share treaty to be analysed. In the QIS 3 model, the impact of a NatCat XL can be calculated on the basis of the sum insured separately from and independently of the historical time series.
2.3 Results
An understanding of the effect of diversification in the standard approach is necessary to appreciate the results.
2.3.1 Effect of diversification at various levels
Sample calculation: exclusion of a working XL from the reinsurance programme
The table shows that the risk capital for the premium and reserve risks (SCR(pre/res)) rises by 2.1% when a working XL is excluded, though the solvency ratio is reduced by only 0.5%. Thus, the reinsurance treaty has a positive effect on solvency.
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Base case (Net)
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Example 1: Without WXL Line 1
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Difference
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SCR(pre/res)
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32,055 |
32,727 |
2.1% |
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SCR(overall)
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39,941 |
40,549 |
1.5% |
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Solvency ratio
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130.6%
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130.0%
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- 0.5%
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However, the impact of a working XL depends to a large extent on its parameters and a company's loss ratios over the last 15 years. The capital relief and risk reduction achieved at business-line level is only partially reflected in the solvency ratio ("dilution effect"). This is principally due to diversification, which affects the calculations at three levels: (1) the correlation between the business lines through the correlation matrix laid down in QIS 3, (2) the underwriting of NatCat risks and (3) the calculation of the SCR(overall) (overall solvency capital requirement) incorporating all risk categories.
The columns show the amount of capital consumption/relief resulting from diversification (in red).
If a quota share treaty is excluded, basically the same dilution effect can be seen as for a working XL treaty.
2.3.2 Historical experience of reinsurance protection and changes in reinsurance structure/conditions
Use of reinsurance cover during a 15-year time series also influences the solvency ratio. The effect of claims payments on the net loss ratios available should be examined, particularly where there have been claims events with return periods of more than 15 years, since distortions can occur (resulting from "random" losses).
Any transfer of historical net loss ratios to a changed reinsurance structure should be carefully scrutinised, as it can also distort the solvency ratio – the more recent the change, the greater the distortion. It would be possible to depict the effect of the changes approximately using "as if" calculations, though this involves a great deal of work and it is not yet clear whether and subject to what conditions the regulator will recognise such calculations.
Overarching covers (e.g. multi-line stop-loss treaties) can provide considerable risk relief for insurers for major losses. However, treaty structures of this type cannot be depicted, as business-line loss ratios are considered individually and cannot be linked.
2.3.3 NatCat XL
Capital requirements for natural hazards are considerable. In contrast to the business-line calculation methodology used for premiums and reserves, the German QIS 3 model uses a market loss curve for NatCat risks, with full recognition of the reinsurance limit. As a result, a NatCat XL provides substantial relief, with cover for a 200-year loss, of course, having the greatest impact on the solvency ratio.
2.4 Is it worth spreading the risk across several reinsurers (diversification)?
In a nutshell, ratings are more important than the number of reinsurers, as the examples below demonstrate.
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Example 1 (one reinsurer with AA rating)
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| Reinsurer M - Rating AA |
Cost of default = €30,000,000 |
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Example 2 (several reinsurers with AA rating)
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| Reinsurer X - Rating AA |
Cost of default = €10,000,000 |
| Reinsurer Y - Rating AA |
Cost of default = €10,000,000 |
| Reinsurer Z - Rating AA |
Cost of default = €10,000,000 |
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Example 3 (one reinsurer with lower rating)
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| Reinsurer X - Rating AA |
Cost of default = €10,000,000 |
| Reinsurer Y - Rating AA |
Cost of default = €10,000,000 |
| Reinsurer Z - Rating A |
Cost of default = €10,000,000 |
Conclusion:
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The SCR (default) depends on the rating and number of providers
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The number of reinsurers only provides diversification within a rating category
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Recourse to reinsurers with lower ratings increases the capital requirement
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The amount of capital relief obtainable is in any event small compared with other risk categories
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