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IMPACT OF REINSURANCE ON RISK CAPITALA practical example based on QIS5

AuthorsDr. Norbert KuschelEkaterina MamykinaRadek Pavlis

[email protected]

You can download the Knowledge Series at www.munichre.com

February 2011

Solvency II obliges companies to take a risk-based view of their opera-tions as a whole. Sample calculations for a specimen company using the standard formula and a partial model show that reinsurance remains the simplest and most flexible way for an insurer to manage its business on an economic basis.

The European Union’s modernisation of solvency requirements in the insurance industry poses a major challenge to all insurance companies. The proposed standard approaches to determining solvency are intended to result in a risk-based view of each insurer’s overall situation, with all risk drivers being taken into account in the calculations. But what does this mean for insurance companies in practice? What implications does the change from a rules-based calcu-lation of solvency to a principles-based determination of capital require-ments under Solvency II have for available risk capital and how can reinsurance be used to reduce risk capital?

Discussions of these issues based on models and methodology in the course of the debate surrounding the intro-duction of Solvency II has been very much theoretical, a key role being played by the “quantitative impact studies” (QISs). But what are the limitations of the standard model with its fixed factors and scenarios? Stochastic models may well help to determine the real impact of reinsur-ance on an insurance company’s risk situation, permitting a reduction in risk capital required.

To find the answers to these ques-tions, Munich Re’s Solvency Consult-ing Team set itself an ambitious objective as early as 2008 i.e. to create transparency. Taking the balance sheet of a specimen company, the experts calculated the risk capital required if reinsurance is used on the basis of actual figures – firstly with the standard formula and then with a partial (internal) model. Determined to research the implications thor-oughly, they analysed the complex correlations and strove to make them as transparent as possible.

The resultant portfolio data are being made publicly accessible on the PillarOne Solvency II portal (www.pillarone.org), initiated and sponsored by Munich Re, with a view to making a real, practice-based contribution to the discussion for the whole insurance industry.

Using these data, the calculations have now been performed for the current study (QIS5) and the differ-ences in methodology compared to the last study (QIS4) have been ana-lysed and documented. This analysis will focus on the effect of reinsurance on risk capital.

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The specimen company: a medium-sized property-casualty insurerIn modelling the specimen company, the Solvency II experts took account of the wide range of possible aspects, especially as regards the impact of reinsurance. Consequently, data from various lines of business with different run-off patterns were used for the modelling (see Fig. 1). To ensure com-parability with the QIS4 analyses, all of the specimen company’s portfolios were carried forward as they were.

Thus, the 2008 figures were trans-ferred to 2010, so that the calculation differences only result from changes in methodology and calibration and are not affected by any changes in investment and underwriting data.

Further assumptions: the company’s historical results are average for the insurance market as a whole and past large loss events were predom-inantly in property business. Natural catastrophes in the financial years 2002 (flooding) and 2007 (Hurricane Kyrill) played a major part. At 99.95%, the specimen company’s planned combined ratio for the 2010 financial year means that it just achieves an underwriting profit.

The large portion of the specimen company’s investments held in EU government bonds reflects its very conservative investment strategy. The percentage of total investments held in equities is 12.1%. Investments total €314m, with €56m in property, €9m in shareholdings and €249m in other investments, of which €38m is in equities, €204m in bonds and €7m in sundry investments.

The specimen company’s premium income shows the following split: €189m from motor liability, €97m from other motor business (motor own damage), €54m from general personal accident and €73m from homeowners’/householders’ com-prehensive insurance. This results in the balance sheet shown in Table 1:

Table 1: Specimen company’s German GAAP balance sheet

Assets €314m– Property €56m– Participations €9m– Other €249mEquity and liabilities €314m– Equity €112m– Liabilities €202m

According to the current Solvency I rules, these figures result in a sol-vency capital requirement of €70m and equity capital of €112m for the specimen company. Hence, its sol-vency ratio under Solvency I is 160%.

The standard formula

The guidelines and principles estab-lished by the European Commission and CEIOPS for the calculation of the solvency criteria under Solvency II place exacting demands on com-panies: the solvency criteria have to be precisely modelled and calibrated. The QISs provide an indication of whether the measurements are real-istic. At present, it can be assumed that several options will be available under Solvency II.

It is likely that many companies will use an (adjusted) standard formula, with the adjustment taking the form of a partial calibration with the com-pany’s own data. If part-modules are to be stochastically modelled, a par-tial model is required. Companies wishing to model all relevant risks will need to have an internal model certified by the supervisory authori-ties. In addition, companies will have to reckon with far-reaching require-ments for data storage, accounting and IT infrastructure.

18%3%

A: 65%

B: 12%

C: 2%

Investment structure

Other investments A: BondsB: EquitiesC: Other

PropertyParticipations

18%

13%

46%

Portfolio structure

23%

Motor liability (ML)Other motor business (MOD)Homeowners’/Householders’ comprehense (Prop.)Personal accident (PA)

Typical property-casualty insurer:Operates in a number of classes/busi-ness lines

Fig. 1: Investment and portfolio structure of the specimen company


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Model assumptions and risk measure

To calculate the solvency require-ments using the standard formula, an economic balance sheet first needs to be prepared to determine the available capital. The solvency capital requirement (SCR) is then calculated in order to arrive at the solvency measures for Solvency II.

Determining the solvency measure

Investments and liabilities are recog-nised at market value in the solvency balance sheet. The following steps are necessary to determine the sol-vency measure:

1. Value the portfolio actuarially: the associated cash flow is valued at market value on the basis of the risk-free interest-rate curve (as prescribed by the European Com-mission/CEIOPS). The outcome is the market-value balance sheet as per Fig. 2.

2. Determine the “market value mar-gin”: the item “market value mar-gin” in the market-value balance sheet enhances transparency with regard to the portfolio. Thus, for example, purely on the basis of this simple solvency measure from the balance sheet, it is possible to (roughly) estimate the “long-tail bias” of a company’s portfolio.

3. Calculate the available capital from the market-value balance sheet: the specimen company’s available capital rises by €77m.

4. Determine the SCR and solvency ratio according to QIS5: the SCR can be broken down further into various categories (see Fig. 3), with BSCR (basic solvency capital requirement) accounting for the main portion of financial and insur-ance risks. The BSCR can, in turn, be split into the subcategories “non-life”, “market”, “health”, “counterparty/default” and “life”. For the specimen company, all other types of risk except “life underwriting risk” have been modelled. The Solvency II balance sheet shows that underwriting is clearly the main driver of the dra-matic increase in the SCR com-pared to the Solvency I balance sheet. If the Solvency II regulations were already in force, this would result in the supervisory authority having to take action in respect of the specimen company.

Without reinsurance, the SCR rises to €198m if the standard formula according to QIS5 is used. With available capital of €189m, the sol-vency ratio is 95%.

As can be seen from the breakdown of the total capital requirement in Fig. 4, the predominant risks are in non-life, with catastrophes the major factor. The SCR can therefore only be reduced by a decrease in underwrit-ing risks. The individual components of the capital requirement for non-life risk are shown in Fig. 5.

Fig. 2: Statutory and solvency balance sheets compared (€m)

AssetsAvailable capital LiabilitiesSCR

Solvency I balance sheet

Assets0

50

100

150

200

250

300

350

Liabilities Solvency Icapital requirement

314

202

11270

189

Assets Available capitalMarket value margin (net)Best estimateSCR

QIS5 balance sheet

Assets0

50

100

150

200

250

300

350

Liabilities QIS5 capital requirement

342

142

206

12


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Fig. 3: Modular structure of QIS51 showing partial internal modelling

Fig. 4: Breakdown of the capital requirement by individual risk component (€m)

NL uw Health Market Default Op. risk Diversifi- SCRrisk uw risk risk risk cation

18320

26 012 35

206

QIS5 risk capital (SCR) without reinsurance

0

50

100

150

200

250

1 CEIOPS: QIS5 Technical Specifications, p. 90, online at https://www.ceiops.eu/fileadmin/tx_dam/files/consultations/QIS/QIS5/QIS5-technical_specifications_20100706.pdf

Adj.

Market Health Life Non-life Intang.

Equity

Currency

Property

Interest rate

Spread

Mortality

SLTHealthNon-SLT HealthCAT

Lapse

Expenses

Revision

Disability/Morbidity

Longevity

Lapse

Premium ReserveMortality

Lapse

DisabilityMorbidity

Longevity

SCR

BSCR

Default

Op.

Premium Reserve

Expenses

Revision = Included in the adjustment for the loss-absorbing capacity of technical provisions under the modular approach.

Concentration

LapseCAT

Illiquidity CAT


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Impact of reinsurance Munich Re prepares reinsurance pro-grammes for the specimen company that are individually tailored to its needs. The impact of the following four reinsurance programmes on the net solvency capital was calculated (cf. Fig. 6):

– Peak risk cover (Peak): Pure non-proportional cover with relatively high first loss retentions in all classes of business

– Pure non-proportional cover (NP): Pure non-proportional cover with very low first loss retentions in all classes of business; in addition, the reinsurance structure for the prop-erty class of business was changed from a CXL with a high annual aggregate limit to a frequency CXL with a low annual aggregate limit and a stop-loss treaty covering the retention (see Fig. 6).

– ML quota share and NP cover (ML50+NP): Cession of quota share in motor liability to improve diversification, and non-proportional cover for the retention with a low priority, as well as pure non-propor-tional cover with low priorities in the other classes of business (as per NP)

– Quota shares and NP cover (All50+ NP): Cession of quota share in all classes of business, and non-propor-tional cover for the retention with a low priority (as per NP)

Fig. 5: Breakdown of the capital requirement for non-life risk by individual risk component (€m)

Prem./res. risk Cat risk Diversification NL uw risk

90

139 45

183

Risk capital for non-life (NL uw risk) without reinsurance

0

50

100

150

200

250


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It is assumed that the company has data records going back ten years, that the reinsurance programme has remained constant over the last ten years (“as-if” calculations), and that all scenarios are based on the same initial situation and the same avail-able capital.

Determining the solvency ratio after reinsurance

1. Prepare the balance sheet: Table 2 shows the valuation of the assets and liabilities for the various insur-ance programmes. Under QIS5, the item “reinsurance” appears as an asset in the balance sheet and therefore has to be recognised at market value. The value of the rein-surance asset is highly dependent on the reinsurer’s rating.2

The liabilities in the QIS5 balance sheet are recognised at the present value of the best estimate (before reinsurance), whilst the market value margins (MVMs), which are calculated using the cost-of-capital approach, take reinsurance into account. Thus, for example, the MVM of the liabilities without rein-surance is €12m, whereas with the All50+NP programme the figure is only €6m. It is assumed for sim-plicity that all participating rein-surers have a rating of AA.

2. Calculate the risk capital require-ment under QIS5 for all pro-grammes: reinsurance has the effect of reducing the risk capital in every case. Fig. 7 shows that the reduction in the underwriting risk capital (SCRnon-life) is reflected in the overall SCR.

With the QIS4 methodology, reinsur-ance reduced risk capital essentially by affecting the volumes in each class of insurance, i.e. the premiums and reserves. However, it was diffi-cult to give appropriate recognition to the risk-mitigating effect of XL treaties using this methodology and the QIS4 analysis of the specimen company confirms this. Munich Re set up a working group to look at this issue in 2008. For QIS5, non-pro-portional reinsurance will now be depicted more appropriately by means of adjustment factors.3

Motor liability

Motor own damage

Personal accident

Property

MOD CXL10 xs 10

ML WXL95 xs 5

PA WXL1 xs 2

Prop. CXL170 xs 10

PA CXL10 xs 2

MOD CXL19.5 xs 0.5

ML WXL99 xs 1

PA WXL2.8 xs 0.2

Prop. WCXL14 xs 1

PA CXL1.4 xs 0.2

Prop. SL300% xs 100%

Motor liability

Motor own damage

Personal accident

Property

MOD CXL19.5 xs 0.5

ML WXL99 xs 1

PA WXL2.8 xs 0.2

Prop. WCXL14 xs 1

PA CXL1.4 xs 0.2

MOD CXL19.5 xs 0.5

ML WXL99 xs 1

PA WXL2.8 xs 0.2

Prop. 50%quota share

PA CXL1.4 xs 0.2


ML 50% quotashare cession

MOD 50%quota share

ML 50% quotashare cession

PA 50%quota share

Prop. WCXL14 xs 1


Peak (Peak risk cover) NP (Pure non-proportional cover)

ML50+NP (ML quota and NP cover) All50+NP (Quota share and NP cover)

Fig. 6: The specimen company’s reinsurance programmes (€m)

2 Cf. Munich Re 2010: Solvency II and reinsurer ratings. Online at http://www.munichre.com/publications/302-06232_de.pdf

3 CEIOPS: Annexes to QIS5 Technical Specifications, Annex N, p. 47 ff., online at https://www.ceiops.eu/fileadmin/tx_dam/files/consultations/QIS/QIS5/Annexes-to-QIS5-technical_specifications_20100706.pdf

The solvency capital is calculated based on four different reinsurance programmes.


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Table 2: Valuations of the assets and liabilities and solvency ratios for the various reinsurance programmes

Gross Peak NP ML50+NP All50+NPSolvency IAssets 314 314 313 308 306Liabilities 202 202 201 196 194Available capital 112 112 112 112 112Solvency capital 70 64 63 48 35Solvency ratio – Solvency I 160% 174% 178% 236% 319%QIS5 balance sheetAssets 342 342 341 338 336 Reinsurance 0 0.02 7 54 74 Investments 342 342 334 284 262Liabilities 153 153 153 149 147 Best estimate 142 142 142 142 142 Market value margin (net) 12 12 11 7 6Available capital 189 189 189 189 189SCR 206 129 126 107 83Solvency ratio – QIS5 91% 146% 150% 177% 227%

Fig. 7: Impact of reinsurance on underwriting risk capital (€m)

NL uw risk w/o NP-RINL uw risk

Gross Peak ML50+NPNP All50+NP

183 183

105 103 108100

82 78

56 52

200

150

100

50

0

Fig. 8: Impact of reinsurance on overall risk capital (€m)

SCR w/o NP-RISCR

Gross ML50+NPNPPeak All50+NP

206 206

131 129 133126

110 10787 83

200

150

100

50

0

Solvency capital requirement non-life

Overall solvency capital requirement (SCR)

Munich ReSolvency Consulting Knowledge SeriesWirkung von Rückversicherung auf das Risikokapital

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Fig. 8 shows the “model artefact” between the Peak and NP pro-grammes that continues to arise if the adjustment factors are not applied. Risk capital rises from €130m to €133m, i.e. despite the fact that more risk is ceded under the NP pro-gramme, the risk capital requirement is higher.

However, using the adjustment factors for the non-SLT health and non-life premium modules pro-duces a depic-tion of the non-proportional reinsur-ance that is more commensurate with the risk. It has only been possible to consider in our example the simplest standard products (quota share rein-surance and XL reinsurance). How-ever, the individual character of lines of insurance and their risk drivers generally makes it difficult to model underwriting, and especially reinsur-ance, satisfactorily.

Using the adjustment factors reduces overall risk capital (SCR) for all of the reinsurance programmes:

– Peak: from €131m to €129m– NP: from €133m to €126– ML50+NP: from €110m to €107m– All50+NP: from €87m to €83m

With reinsurance, the specimen company’s total capital requirement falls to only €83–129m, depending on the reinsurance programme.

A partial internal model

Underwriting risk is by some margin the main driver in the non-life seg-ment. This is evident from the QIS4 results published in November 20084 and is likely to be confirmed by QIS5. Particularly in the non-life segment, reinsurance plays a central role in capital management. Partial modelling can be used, for example, to determine the 99.5% quantile as a risk measure and the impact of rein-surance on the management of risk capital. The required stochastic model can be created and calibrated in the following way.

Calculating the risk capital require-ment for the underwriting risk

1. The higher the quality of the data, the more informative the result: a precondition is that risk manage-ment be deeply integrated in the company and that there be a broad understanding of the principles of the risk model.

2. Select and calibrate the modelling methods: it is necessary to define the risk factors, which may include new products, strong volatility, uncertainties in pricing or increas-ing claims costs.

3. Simulate the portfolio: the Pillar-One open-source platform (www.pillarone.org) was used to perform the calculations for the specimen company. This website also con-tains the detailed calibration for the classes of insurance and the reinsurance treaties. The Pillar-One.RiskAnalytics software was used to perform Monte Carlo sim-ulations (100,000 iterations).

4. Determine the distribution of aggregate losses: an important outcome of the simulation is the distribution of aggregate losses for the whole portfolio and for all modelled lines of business taking account of reinsurance. This enables an insurer’s actual risk situation to be quantified on the basis of the model.

5. Determine risk capital: a variety of approaches and methods are avail-able to calculate risk capital. In this example, the VaR (value at risk) approach was chosen, since this is the method also employed for the QIS studies. The loss distri-bution, the expected value and the 99.5% quantile are needed to cal-culate risk capital. In the VaR approach, the required risk capital is calculated as the difference between the 99.5% quantile and the expected value (Fig. 9).

Using the PillarOne.RiskAnalytics simulation software, the loss distri-butions for each class of insurance and the distribution of aggregate losses are modelled and the expected value and the 99.5% quantile calcu-lated (see Fig. 10).

4 CEIOPS’ Report on its Fourth Quantitative Impact Study (QIS4) for Solvency II, p. 174, online at https://www.ceiops.eu/fileadmin/tx_dam/files/consultations/QIS/CEIOPS-SEC-82-08%20QIS4%20Report.pdf


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Without reinsurance cover, the specimen company’s risk capital requirement for the overall under-writing risk in the current financial year amounts to €136m.

Impact of reinsurance

The specimen company’s risk capital requirement for each of the four reinsurance programmes (Peak, NP, ML50+NP und All50+NP) was then calculated. Fig. 10 shows the distribution of aggregate losses tak-ing account of the reinsurance pro-grammes.

With the partial internal modelling, the risk capital for the Peak reinsur-ance programme totals only €69m, equivalent to a reduction of €67m. The risk capital can be reduced still further – albeit to a very limited extent – by fixing lower first loss retentions. At €62m, the risk capital requirement for the NP programme is only €7m lower than for the peak risk cover.

A significant reduction in the risk capital requirement is only possible with proportional reinsurance. If, additionally, 50% of the motor liabil-ity business is reinsured using a quota share treaty, risk capital can be reduced with the ML50+NP pro-gramme by a further €14m to €48m.

If the four reinsurance programmes are compared, the risk capital require-ment is lowest for a quota share rein-surance with a retention of 50% with XL cover for the retention. The risk capital requirement for the All50+NP is only €31m, a reduction of €31m compared to the NP programme.

Fig. 9: Loss distribution with expected value, 99.5% quantile and risk capitalProbability (%)

The risk capital is the difference between the 99.5% quantile and the expected value.

Expected value 99.5% quantile

Loss

Risk capital

Fig. 10: Overall risk situation of the specimen company without reinsuranceProbability (%)

Loss (€m) 100 200 300 400 500

5

4

3

2

1

0

327 463

136

Gross aggregate loss distribution– Expected value €327m– 99.5% quantile €463m– Risk capital €136m = €(463 – 327)m

Fig. 11: Comparison of the risk situation for the specimen company’s four reinsurance programmes

Loss (€m) 100 200 300 400 500

Probability (%)

10

8

6

4

2

0

Risk capital Gross €136m Peak €69m NP €62m

ML50+NP €48m All50+NP €31m


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With reinsurance, the specimen company’s risk capital requirement amounts to between €31m and €69m, depending on the reinsur-ance programme used. The risk capital requirement for the overall underwriting risk can thus be reduced by up to €105m.

Comparison of standard model and partial internal model

To compare sample results of the standard model with the stochastic model, it was assumed that the bal-ance sheet corresponds to that shown in Table 2 and that the amount of the available capital remains the same, since the figures in the balance sheet are principally market values.

The non-life underwriting module is made up of the premium and reserve risk, the cat risk and the lapse risk. Since only the premium risk and the cat risk were simulated in the sto-chastic model, to meet QIS5 require-ments the reserve risk has to be modelled as well. As the lapse risk was not considered in the QIS5 analysis of the specimen company, it does not need to be taken into account in the partial model either. This produces a comparable figure for the calculation of the underwrit-ing risk (Fig. 12).

After this, the remaining types of risk are calculated according to the QIS5 methodology in order to arrive at the overall capital requirement for the specimen company. The SCR calcu-lated using the partial model is lower than with the standard formula in every case as can be seen in Fig. 13.

The solvency ratio, in turn, is obtained by comparing the solvency require-ment calculated with the available capital. The better results obtained by using a partial model, even before reinsurance, raise the solvency ratio to 108%, though this is still not a par-ticularly comfortable solvency posi-tion. Only by using the reinsurance programmes can the solvency ratio be increased substantially, as shown in Fig. 14.

Fig. 12: Modelling the underwriting risk capital (SCRnl) using a stochastic model (€m)

136

29 13152

0

50

100

150

200

250

New risks and existing portfolioReserve riskDiversificationNL uw risk

Fig. 13: Impact of reinsurance on overall SCR (€m)

Gross Peak NP ML50+NP All50+NP

Solvency capital requirement (SCR)

0

50

100

150

200

250

206

175

129112

126104 107

85 8371

Fig. 14: Impact of reinsurance on the solvency ratio

Gross Peak NP ML50+NP All50+NP

Solvency ratio

300%

250%

200%

150%

100%

50%

0%

91108

146168

150

181 177

223 227

267

QIS5 standard formulaQIS5 partial internal model

QIS5 standard formulaQIS5 partial internal model


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© 2011Münchener Rückversicherungs-GesellschaftKöniginstrasse 107, 80802 München, Germany

Order number 302-05823

Efficient balance sheet management with reinsuranceDespite its complexity, Solvency II ultimately provides companies with a transparent, holistic view of their risk situation that has not been available so far. However, the calculations based on the actual data of the speci-men company also show that the standard formula often fails to reflect underwriting properly because of the heterogeneity of insurance port folios. Yet particularly in property-casualty insurance, underwriting is frequently the main driver of risk and complexity. A partial model based on stochastic calculations may help maintain capi-tal requirements at an appropriate level and produce an acceptable sol-vency ratio.

Irrespective of whether the company decides to use the standard formula or a partial model, reinsurance will reduce the risk capital requirement. In other words, reinsurance remains the simplest and most flexible way of managing a balance sheet.

Solvency Consulting for your companyMunich Re assists its clients in all areas of Solvency II. Using practical examples, Solvency Consulting creates transparency and provides insurers with the knowledge base needed to find a systematic strategy and to plan appropriate measures. It is our primary objective in the con-text of Solvency II to design reinsur-ance programmes that are even more individually and holistically geared to clients’ requirements than before. Solvency Consulting already has a wealth of experience in the develop-ment and use of internal stochastic risk models and their linkage to value-based portfolio management. We also play an active role in indus-try committees looking at regulation and specialist issues and ensure that knowledge and expertise are trans-ferred and translated into practical recommendations for action on the ground. We are thus able to offer our clients practical and efficient help in preparing for Solvency II.

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