IMPACT OF REINSURANCE ON RISK CAPITAL

Transcription

1 IMPACT OF REINSURANCE ON RISK CAPITAL A practical example based on QIS5 Authors Dr. Norbert Kuschel Ekaterina Mamykina Radek Pavlis Contact solvency-solutions@munichre.com You can download the Knowledge Series at February 211 Solvency II obliges companies to take a risk-based view of their operations 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 calculation of solvency to a principles-based determination of capital requirements 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 introduction 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 reinsurance on an insurance company s risk situation, permitting a reduction in risk capital required. To find the answers to these questions, Munich Re s Solvency Consulting Team set itself an ambitious objective as early as 28 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 thoroughly, 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 differences in methodology compared to the last study (QIS4) have been analysed and documented. This analysis will focus on the effect of reinsurance on risk capital.

2 Page 2/11 The specimen company: a medium-sized propertycasualty insurer In 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 comparability with the QIS4 analyses, all of the specimen company s portfolios were carried forward as they were. Fig. 1: Investment and portfolio structure of the specimen company Investment structure C: 2% B: 12% 18% Other investments A: Bonds B: Equities C: Other Portfolio structure 18% 23% 13% 3% A: 65% Property Participations 46% Motor liability (ML) Other motor business (MOD) Homeowners /Householders comprehense (Prop.) Personal accident (PA) Typical property-casualty insurer: Operates in a number of classes/business lines Thus, the 28 figures were transferred to 21, 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 predominantly in property business. Natural catastrophes in the financial years 22 (flooding) and 27 (Hurricane Kyrill) played a major part. At 99.95%, the specimen company s planned combined ratio for the 21 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, 24m 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 comprehensive 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 249m Equity and liabilities 314m Equity 112m Liabilities 22m According to the current Solvency I rules, these figures result in a solvency capital requirement of 7m and equity capital of 112m for the specimen company. Hence, its solvency ratio under Solvency I is 16%. The standard formula The guidelines and principles established by the European Commission and CEIOPS for the calculation of the solvency criteria under Solvency II place exacting demands on companies: the solvency criteria have to be precisely modelled and calibrated. The QISs provide an indication of whether the measurements are realistic. 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 company s own data. If part-modules are to be stochastically modelled, a partial model is required. Companies wishing to model all relevant risks will need to have an internal model certified by the supervisory authorities. In addition, companies will have to reckon with far-reaching requirements for data storage, accounting and IT infrastructure.

3 Page 3/11 Model assumptions and risk measure To calculate the solvency requirements 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 recognised at market value in the solvency balance sheet. The following steps are necessary to determine the solvency 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 Commission/CEIOPS). The outcome is the market-value balance sheet as per Fig Determine the market value margin : the item market value margin 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 insurance 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 dramatic increase in the SCR compared 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 solvency 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 underwriting 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) Solvency I balance sheet QIS5 balance sheet Assets Liabilities Solvency I capital requirement Assets Liabilities QIS5 capital requirement Assets Available capital Liabilities SCR Assets Available capital Market value margin (net) Best estimate SCR

4 Page 4/11 Fig. 3: Modular structure of QIS5 1 showing partial internal modelling SCR Adj. BSCR Op. Market Health Default Life Non-life Intang. Interest rate SLT Health CAT Non-SLT Health Mortality Premium Reserve Equity Property Mortality Longevity Premium Reserve Lapse Longevity Disability Morbidity Lapse CAT Spread Currency Disability/ Morbidity Lapse Lapse Expenses Concentration Illiquidity Expenses Revision Revision CAT = Included in the adjustment for the loss-absorbing capacity of technical provisions under the modular approach. Fig. 4: Breakdown of the capital requirement by individual risk component ( m) NL uw Health Market Default Op. risk Diversifi- SCR risk uw risk risk risk cation QIS5 risk capital (SCR) without reinsurance 1 CEIOPS: QIS5 Technical Specifications, p. 9, online at QIS5/QIS5-technical_specifications_2176.pdf

5 Page 5/11 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 Risk capital for non-life (NL uw risk) without reinsurance Impact of reinsurance Munich Re prepares reinsurance programmes 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 nonproportional cover with relatively high first loss retentions in all classes of business ML quota share and NP cover (ML5+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-proportional cover with low priorities in the other classes of business (as per NP) Quota shares and NP cover (All5+ NP): Cession of quota share in all classes of business, and non-proportional cover for the retention with a low priority (as per NP) 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 property 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).

6 Page 6/11 Fig. 6: The specimen company s reinsurance programmes ( m) Peak (Peak risk cover) NP (Pure non-proportional cover) Motor liability ML WXL 95 xs 5 ML WXL 99 xs 1 Motor own damage MOD CXL 1 xs 1 MOD CXL 19.5 xs.5 Personal accident PA WXL 1 xs 2 PA CXL 1 xs 2 PA WXL 2.8 xs.2 PA CXL 1.4 xs.2 Property Prop. CXL 17 xs 1 Prop. WCXL 14 xs 1 Prop. SL 3% xs 1% ML5+NP (ML quota and NP cover) All5+NP (Quota share and NP cover) Motor liability ML 5% quota share cession ML WXL 99 xs 1 ML 5% quota share cession ML WXL 99 xs 1 Motor own damage MOD CXL 19.5 xs.5 MOD 5% quota share MOD CXL 19.5 xs.5 Personal accident PA WXL 2.8 xs.2 PA CXL 1.4 xs.2 PA 5% quota share PA WXL 2.8 xs.2 PA CXL 1.4 xs.2 Property Prop. WCXL 14 xs 1 Prop. SL 3% xs 1% The solvency capital is calculated based on four different reinsurance programmes. Prop. WCXL 14 xs 1 Prop. 5% quota share Prop. SL 3% xs 1% 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 available 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 insurance 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 reinsurance 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 reinsurance is 12m, whereas with the All5+NP programme the figure is only 6m. It is assumed for simplicity that all participating reinsurers have a rating of AA. 2. Calculate the risk capital requirement under QIS5 for all programmes: 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, reinsurance reduced risk capital essentially by affecting the volumes in each class of insurance, i.e. the premiums and reserves. However, it was difficult 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 28. For QIS5, non-proportional reinsurance will now be depicted more appropriately by means of adjustment factors. 3 2 Cf. Munich Re 21: Solvency II and reinsurer ratings. Online at publications/ _de.pdf 3 CEIOPS: Annexes to QIS5 Technical Specifications, Annex N, p. 47 ff., online at files/consultations/qis/qis5/annexes-to- QIS5-technical_specifications_2176.pdf

7 Seite 7/11 Table 2: Valuations of the assets and liabilities and solvency ratios for the various reinsurance programmes Gross Peak NP ML5+NP All5+NP Solvency I Assets Liabilities Available capital Solvency capital Solvency ratio Solvency I 16% 174% 178% 236% 319% QIS5 balance sheet Assets Reinsurance Investments Liabilities Best estimate Market value margin (net) Available capital SCR Solvency ratio QIS5 91% 146% 15% 177% 227% Fig. 7: Impact of reinsurance on underwriting risk capital ( m) Gross Peak NP ML5+NP All5+NP Solvency capital requirement non-life NL uw risk w/o NP-RI NL uw risk Fig. 8: Impact of reinsurance on overall risk capital ( m) Gross Peak NP ML5+NP All5+NP Overall solvency capital requirement (SCR) SCR w/o NP-RI SCR

8 Wirkung von Rückversicherung auf das Risikokapital Seite 8/11 Fig. 8 shows the model artefact between the Peak and NP programmes that continues to arise if the adjustment factors are not applied. Risk capital rises from 13m to 133m, i.e. despite the fact that more risk is ceded under the NP programme, the risk capital requirement is higher. However, using the adjustment factors for the non-slt health and non-life premium modules pro-duces a depiction of the non-proportional reinsurance that is more commensurate with the risk. It has only been possible to consider in our example the simplest standard products (quota share reinsurance and XL reinsurance). However, the individual character of lines of insurance and their risk drivers generally makes it difficult to model underwriting, and especially reinsurance, 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 ML5+NP: from 11m to 17m All5+NP: from 87m to 83m With reinsurance, the specimen company s total capital requirement falls to only m, depending on the reinsurance programme. A partial internal model Underwriting risk is by some margin the main driver in the non-life segment. This is evident from the QIS4 results published in November 28 4 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 reinsurance on the management of risk capital. The required stochastic model can be created and calibrated in the following way. Calculating the risk capital requirement for the underwriting risk 1. The higher the quality of the data, the more informative the result: a precondition is that risk management 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 increasing 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 contains the detailed calibration for the classes of insurance and the reinsurance treaties. The Pillar- One.RiskAnalytics software was used to perform Monte Carlo simulations (1, 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 available 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 distribution, the expected value and the 99.5% quantile are needed to calculate 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 distributions for each class of insurance and the distribution of aggregate losses are modelled and the expected value and the 99.5% quantile calculated (see Fig. 1). 4 CEIOPS Report on its Fourth Quantitative Impact Study (QIS4) for Solvency II, p. 174, online at dam/files/consultations/qis/ceiops- SEC-82-8%2QIS4%2Report.pdf

9 Page 9/11 Fig. 9: Loss distribution with expected value, 99.5% quantile and risk capital Probability (%) Expected value 99.5% quantile Risk capital Without reinsurance cover, the specimen company s risk capital requirement for the overall underwriting risk in the current financial year amounts to 136m. Impact of reinsurance The risk capital is the difference between the 99.5% quantile and the expected value. Fig. 1: Overall risk situation of the specimen company without reinsurance Probability (%) Gross aggregate loss distribution Expected value 327m 99.5% quantile 463m Risk capital 136m = ( )m Fig. 11: Comparison of the risk situation for the specimen company s four reinsurance programmes Probability (%) Loss Loss ( m) The specimen company s risk capital requirement for each of the four reinsurance programmes (Peak, NP, ML5+NP und All5+NP) was then calculated. Fig. 1 shows the distribution of aggregate losses taking account of the reinsurance programmes. With the partial internal modelling, the risk capital for the Peak reinsurance 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, 5% of the motor liability business is reinsured using a quota share treaty, risk capital can be reduced with the ML5+NP programme by a further 14m to 48m. If the four reinsurance programmes are compared, the risk capital requirement is lowest for a quota share reinsurance with a retention of 5% with XL cover for the retention. The risk capital requirement for the All5+NP is only 31m, a reduction of 31m compared to the NP programme. 4 2 Risk capital Gross 136m Peak 69m NP 62m ML5+NP 48m All5+NP 31m Loss ( m)

10 Page 1/11 With reinsurance, the specimen company s risk capital requirement amounts to between 31m and 69m, depending on the reinsurance programme used. The risk capital requirement for the overall underwriting risk can thus be reduced by up to 15m. 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 balance 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. Fig. 12: Modelling the underwriting risk capital (SCRnl) using a stochastic model ( m) New risks and existing portfolio Reserve risk Diversification NL uw risk 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 stochastic model, to meet QIS5 requirements 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 underwriting 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 calculated 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 requirement calculated with the available capital. The better results obtained by using a partial model, even before reinsurance, raise the solvency ratio to 18%, though this is still not a particularly comfortable solvency position. Only by using the reinsurance programmes can the solvency ratio be increased substantially, as shown in Fig. 14. Fig. 13: Impact of reinsurance on overall SCR ( m) Gross Peak NP ML5+NP All5+NP Solvency capital requirement (SCR) Fig. 14: Impact of reinsurance on the solvency ratio 3% 25% 2% 15% 1% 5% % 91 Solvency ratio Gross Peak NP ML5+NP All5+NP QIS5 standard formula QIS5 partial internal model 267 QIS5 standard formula QIS5 partial internal model

11 Page 11/11 Efficient balance sheet management with reinsurance Despite 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 specimen 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 capital requirements at an appropriate level and produce an acceptable solvency 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 company Munich 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 context of Solvency II to design reinsurance programmes that are even more individually and holistically geared to clients requirements than before. Solvency Consulting already has a wealth of experience in the development and use of internal stochastic risk models and their linkage to value-based portfolio management. We also play an active role in industry committees looking at regulation and specialist issues and ensure that knowledge and expertise are transferred 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. 211 Münchener Rückversicherungs-Gesellschaft Königinstrasse 17, 882 München, Germany Order number