From Solvency I to Solvency II: a new era for capital requirements in insurance?

Milan, 26 November 2015 From Solvency I to Solvency II: a new era for capital requirements in insurance? prof. Nino Savelli Full professor of Risk Theory Faculty of Banking, Financial and Insurance Sciences Catholic University of Sacred Hearth academic member of IRSG EIOPA Email: nino.savelli@unicatt.it

From the first studies to European Directives 2

Introduction The first Non-Life and Life directives of EU (published on July 24 th 1973 and on March 5 th 1979 respectively, at that time the European Economic Community (EEC)) marked the first steps toward the establishment of the free market in insurance within the European Community. In those directives new capital requirements are prescribed for insurance companies within the EEC in order to fulfil the solvency assessment. In the first Non-life directive (1973) it is a said that it is necessary that insurance undertakings should possess, over and above technical reserves of sufficient amount to meet their underwriting liabilities, a supplementary reserve, to be known as the solvency margin, and represented by free assets, in order to provide against business fluctuations. A similar statement was also made in the first Life directive (1979). The reports by Campagne (1961) contain the main analyses for these requirements in Life and Non-Life Insurance (Solvency 0). 3

Campagne Approach for Non-Life Insurance (1/3) 4 In the first Non-Life report of Campagne, the data used were taken from 10 insurance companies operating in Switzerland during years 1945-1954. The next breakdown for premiums net of reinsurance was assumed: - premium risk 46% - safety loading 12% - expenses 42% Combined Ratio distribution - Expense ratio was assumed constant = 42% - Loss ratio (net of reinsurance) to follow a Beta distribution, with parameters drawn up empirical data. - Level of confidence = 99.97% approx. - Time horizon: 1 year Accordingly the worst Loss ratio obtained was 83%, thus producing an extreme Combined ratio of 125% (125=83+42). On the basis of that empirical analysis, a risk capital measure of 25% of net premiums volume was then derived for a 1 year time horizon to meet that extreme event (25=125-100). Note that approach used already a VaR measure

Campagne Approach for Non-Life Insurance (2/3) Probability Loss Ratio VaR Mean Mean + safety loading 12% Measure in Directive S0 Campagne suggestion VAR(LR): calculated by assuming ruin probability = 0.33% Conf.level = 99.67% 16% 25% VAR(LR): calculated by assuming ruin probability = 0.03% Conf.level = 99.97% 46% 58% 74% 83% LR 5

Campagne Approach for Non-Life Insurance (3/3) - Subsequent studies carried on 8 European countries (years 1952-57) led Campagne to confirm a solvency margin of 25% of the retained premiums, roughly equal to the average of the empirical results for the eight countries as a whole. - To this end, it was suggested that 2.5% of the ceded reinsurance premiums should be added on to cover against the risk of reinsurance failure (i.e. a «credit risk factor»). - In the final formula of Solvency 0 a 16% risk coefficient was preferred 6

Campagne Approach for Life Insurance for Life Insurance (1/2) Campagne considered a minimum solvency margin as given by a percentage of the technical provisions. He took into consideration other ratios, e.g. the minimum solvency margin as a percentage of either sum insured or sum at risk. Campagne (1961) got the following table of characterization ratios from five European countries (years 1952-1957). The three ratios are the free assets (A) in relation to the technical provisions (A/tp), to the sum at risk (A/sr), and to the sum insured (A/si): Ratios France Germany Italy The Netherlands Sweden Mean A/tp=FR 32.4 3.5 46.1 11.5 13.6 21.4 A/sr 2.6 0.6 6.4 2.2 5.4 3.4 A/si 2.3 0.5 5.5 1.8 3.8 2.8 7

Campagne Approach for Life Insurance (2/2) A loss ratio (LR) is defined as the loss (L) in a year as a percentage of the technical provisions (tp), LR=L/tp. The LRs assumed to be random variables i.i.d for different years and companies. The free reserve ratio of technical previsions (FR= A/tp) must be such that: Prob( LR FR) This can be defined as the VaR of variable LR (VaR-LR), which is the smallest value satisfying Prob(LR>FR)=ε where LR is distributed according to a Pearson type IV distribution. The minimum solvency margins, as a percentage of the technical provisions, are given in the following table according time horizon and ruin probability: VaR-LR 1 year 2 year 3 year 5 year 10 year ε=0.001 9 10 10 12 14 ε=0.01 7 7 7.5 8 9 ε=0.05 3.5 4 4 4 3 ε=0.1 2.5 2.5 2 2 1 Campagne proposed 1-ε = 95% and therefore a necessary Minimum solvency margin = 4% * Technical Provisions 8

Some drawbacks of Solvency I Standard Formula (1/2) Non-Life Insurance: Percentages used for both formulae (premium and claims) are not linked to the risk profile of each single LoB (but GTPL). Furthermore, they don t seem adequate for the actual complexity of the insurance market; Mainly Premium Risk is regarded in the formula (see Campagne results) Diversification benefits are summarized in the Solvency I formula coefficients, but it is not flexible according to the portfolio mix Market risk is not considered at all and Reserve and CAT risk are not appropriately considered; Reinsurance treaties (QS or XL) and Reinsurer characteristics (e.g. commissions) are not considered. Life Insurance: Allocation of asset portfolio is not considered in market risk; Longevity risk is not considered; Mortality risk is proportional to capital sum at risk amount (no diversification effect); Reinsurance treaties and Reinsurer characteristics are not considered. 9

Some drawbacks of Solvency I Standard Formula (2/2) Required Solvency Margin is derived for a solo entity and takes into account mainly: premium risk for Non-Life Insurance; market, mortality and expenses risk for Life Insurance. It is not considered: - reserve risk (for Non-Life); - lapse and longevity risk (for Life); - market risk (for Non-Life and partially for Life too); - credit risk; - liquidity risk / ALM risk; - operational risk -... 10

EIOPA Risk Dashboard: EU Solvency I ratio 2010-2015 For both Life and Non Life business, the available solvency margin (Solvency I) is greater than the minimum required. For Life business the median of Solvency Ratio is around 200%; The median of the Solvency Ratio for Non Life companies is around 250-350% Solvency Ratio Life Solvency Ratio Non Life The graphs show the median and the interquartile range. The black lines are representing 10% and 90% percentile. Source: EIOPA Risk Dashboard, June 2015 11

Solvency II Capital Requirements 12

Why Solvency II? Higher Risk Sensitivity and updated calibration; Aggregation explicitely included by correlation matrix; Internal Models: ad hoc calculation of capital requirement (and USP approaches); Market disclosure; Market Consistent Valuation for Assets and Liabilities in order to properly reflect the real value of Free Assets; To insert macro-risks not fully taken into account in Solvency I: - Nonlife-Life-Health Underwriting risk - Market risk - Counterparty risk as in Basel II for banking sector - Operational risk 13

Three Pillars structure in Solvency II SCR Confidence Level = 99.5% Risk Measure = VaR (Value-at-Risk) Time horizon = 1 year 14

Solvency II Keywords Full Partial (under Supervisor approval) if Standard Formula not used New requirement: more risk sensitive SOLVENCY CAPITAL REQUIREMENT INTERNAL MODEL STANDARD FORMULA Market-Wide Approach (MW) Undertaking Specific Approach (USP) Own Risk and Solvency Assessment ORSA SOLVENCY II RISK AGGREGATION Use of a correlation matrix for diversification benefit Additional valuation for liabilities (CoC - Cost of Capital approach) in order to get a market consistent valuation RISK MARGIN MCV for A/L BEST ESTIMATE Insurance Liabilities: discounted and not conservative valuation 15

SCR Standard Formula Main Characteristics Based on a modular structure (modules and sub-modules) Aggregation based on linear? correlation (fixed correlation matrix) At least following risks (art. 103 of Solvency II Directive): Non-life underwriting risk Life underwriting risk Health underwriting risk Market risk Counterparty default risk Operational risk Each sub-module is based on a fixed methodology (scenario or factor based) with fixed parameters\shock. In some cases (e.g. premium and reserve risk) parameters could be calibrated by using internal data (USP approach) Simplified approaches or proxies available for small insurers 16

Risk Measure, Confidence Level and Time Horizon 17

Risk Measure Main Purpose: Derive the probability distribution of Total Losses (X) or Risk Capital (RC) at the end of the time horizon defined by Solvency II (i.e. 1 year) NB: Skewn.>0 Probability Distribution of Total Losses Mean Mean + Expected Profit Both standard deviation (or variability coefficient) and skewness of distribution assume great relevance. Value-at-Risk (confid.lev.=99,5%) Usually Skewness of Total Losses is greater than 0 (< 0 if look at RC distribution), leading to a greater capital requirement (with both VaR and TVaR) under the same mean and variance. Expected Losses Expected Profit SCR Capital Requirement 18

Normal vs Not-Normal Distributions Risk Measures: VaR vs TVaR Time Horizon: TH=1 year Confidence Level: 99.5/99.0% VaR TVaR min( x ~ P( X x) 1 ) E( X X VaR ) X Da cui segue: VaR Exp = 2,58*s VaR Exp 2,58 3,50*s 19

Risk Measures: VaR vs TVaR The example shows a comparison between the VaR at 99.5% (Solvency II) and the TVaR at 99% (Swiss Solvency Test) obtained from Normal and LogNormal distributions assuming two different coefficients of variability CoV(X)=σ(X)/E(X). Mean=3.500, CoV=0,5 Var VaR Tvar TVaR 0,95 0,99 0,995 0,95 0,99 0,995 Normale 6.378,49 7.571,11 8.007,70 7.108,14 8.158,37 8.551,14 LogNormale 6.808,61 9.394,39 10.569,40 8.428,23 11.127,10 12.349,48 Mean=3.500, CoV=2 Var VaR Tvar TVaR 0,95 0,99 0,995 0,95 0,99 0,995 Normale 15.013,98 19.784,44 21.530,81 17.932,57 22.133,48 23.704,56 LogNormale 12.613,47 29.944,13 41.092,86 24.563,00 49.999,36 65.433,31 As observed in the table above, in the case of a skewed distribution, the increase of the variability involves a TVaR capital requirement even larger in comparison with the SCR obtained with the VaR. Tvar TVaR 99% /VaR 99.5% 99,5% 102% 105% RBC(TVaR 99.0% )/RBC(VaR 99.5% ) Norm 103.3% LogNorm 107.9% Tvar TVaR 99% /VaR 99.5% 99,5% 103% 122% RBC(TVaR 99.0% )/RBC(VaR 99.5% ) Norm 103.3% LogNorm 123.7% 20

Some Comments The choice of a VaR measure is at the moment a good solution: - because of a wider comprehension - in using TVaR a larger accuracy is necessary to properly estimate the tail distribution, to be improved for such various risks in the future after some years of SII experience The choice of a TH=1 year: is very likely a good solution at the moment also if some concerns are in place for a potential short-term vision in the top management strategies. A double risk measurement? At this regard it may be useful to recall the IAA proposal in 2004 to regard a double measure, the first one calibrated at 1 year with a high level of confidence level (e.g. 99.5%) and the second one calibrated at 3 years at a lower level (e.g. 95.0%). Quantitative Models dictatorship? Some people are afraid that business strategies will be conducted only by models, my idea is that is not the case but quantitative models have to provide where the company is going under alternative strategies, providing the impact on the risk/return trade-off; 21

Risk Aggregation 22

SCR structure and risk aggregation SCR=BSCR+SCRop-Adj Adj Market Health SCR BSCR Default Life Op Non-life Intang Risks: Non life UW Risk Life UW Risk Health UW Risk Market Risk Default Risk Intangible asset Risk Operational Risk Interest rate SLT Health CAT Non-SLT Health Mortality Premium Reserve Equity Property Spread Mortality Longevity Disability Morbidity Premium Reserve Lapse Longevity Disability Morbidity Lapse Lapse CAT Currency Concentration Illiquidity Lapse Expenses Revision Expenses Revision CAT = included in the adjustment for the lossabsorbing capacity of technical provisions under the modular approach 23

BSCR (Basic Solvency Capital Requirement) BSCR is obtained by aggregation of the 5 components on the base of the fixed correlation matrix : For example, considering only SCR mkt and SCR life, we have: BSCR SCR SCR 2 0, 25 SCR 2 Life 2 mkt life SCR mkt 24

Aggregation Formula Some comments CEIOPS Consultation Paper n.74 (2009) shows that: The capital requirements that are aggregated in the standard formula are, from a mathematical point of view, not standard deviations but quantiles of probability distributions. it can be shown that for multivariate normal distributions (or more general: for elliptic distributions), the aggregation with correlation matrices produces a correct aggregate of quantiles. On the other hand, only for a restricted class of distributions the aggregation with linear correlation coefficients produces the correct result. Two main reasons can be identified for this aggregation problem: - The dependence between the distributions is not linear (e.g. tail dependencies are present ) - The shape of the marginal distributions is significantly different from the normal distribution (e.g. if distributions are skewed) In practice, although certain risks can be assumed to be independent, the selection of the correlation parameter is difficult. Often the shape of the underlying distribution is not known or it differs from undertaking to undertaking and over time. If such uncertainties exist it appears to be appropriate to choose a slightly positive correlation parameter, for example 0.25 in order to avoid a systematic underestimation of the combined risk. 25

26 Tail dependencies: by two different copula functions 0.04 0.03 0.02 Copula clayton To estimate dependency structure among different risks is one of the most challenging issues in the next future Copula Gumbel 0.01 0 1 0.5 u 0 0 v 0.5 1 0.04 0.03 0.02 0.01 0 1 0.5 0.5 1 u 0 0 v

An example of aggregation in Non-Life Underwriting Risk 450 Accident 450 MOD 700 Property 400 350 300 250 Mean: 146.3 mln CV: 7.34% Skew: 0.28 400 350 300 250 Mean: 115.1 mln CV: 7.33% Skew: 0.22 600 500 400 Mean: 274.6 mln CV: 6.58% Skew: 0.48 200 200 300 150 150 200 100 100 50 50 100 450 400 350 300 250 200 0 1 1.2 1.4 1.6 1.8 2 2.2 MTPL x 10 8 Mean: 1,390.2 mln CV: 4.14% Skew: 0.13 0 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1200 1000 800 600 GTPL x 10 8 Mean: 401.9 mln CV: 8.36% Skew: 0.70 600 500 400 300 0 2 2.5 3 3.5 4 4.5 5 Total Gaussian Copula. L ~ CY ~ ~ paid, PY ~ PY X t 1, h Et 1, h X t 1, h BEt 1, h h 1 x 10 8 Mean: 2,328 mln CV: 3.95% Skew: 0.22 150 400 200 100 50 200 100 0 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 x 10 9 0 2 3 4 5 6 7 8 9 10 11 x 10 8 0 1.8 2 2.2 2.4 2.6 2.8 3 3.2 x 10 9 27

Aggregate Distribution (Premium + Reserve Risk) SCR is derived by using a Gaussian copula (with the same r of SF). 4500 4000 3500 3000 2500 2000 1500 1000 500 Premium Risk: ~ Mean: 596.9 mln CV: 7.18% Skew: 0.17 0 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 ~ x 10 8 450 400 350 OMEGA - MTPL Gaussian Copula (r=0.5) Premium + Reserve Risk: 400 350 300 250 200 150 100 50 Reserve Risk: CY paid, PY PY X t 1, h Et 1, h X t 1, h BEt 1, h ~ ~ ~ CY paid, PY PY X t 1, h Et 1, h X t 1, h BEt 1, h ~ ~ Mean: 793.3 mln CV: 2.84% Skew: 0.14 0 7 7.5 8 8.5 9 9.5 ~ x 10 8 300 250 200 150 100 50 Mean: 1390.2 mln CV: 4.14% Skew: 0.13 0 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 x 10 9 28

SCR for NL&Health Underwriting Risk MOD Property MTPL GTPL OMEGA DELTA MOD Property MTPL GTPL 29

Final Comments 30

Comments Over/Under estimation of risks by a Standard Formula: a formula «one-sizefits- for-all» is obviously non perfect but it is necessary as a basic point (e.g. unique volatility factors or stress scenario independent by size and reference market). The calibration of the various parameters should be revised time by time but approved Internal Model and USP approaches are suitable solutions (when available) to reduce the risk to obtain an inappropriate capital requirement by using SF. At a certain level ORSA and FLAOR are also going in that direction. Higher volatility of Solvency II ratios compared to Solvency I ratios: mainly as a consequence of the MCV (market consistent valuation) of assets and liabilities affecting either Own Funds and SCR (in the last case by the change of volume measures as TP) To assure a satisfactory trade-off between solvency measures and RoE: as well known a larger capital requirement implies a lower return for shareholders Further research on many items: aggregation, financial and underwriting cycles, statistical analyses of collected data, tail calibration (extreme events) 31

THANK YOU FOR YOUR ATTENTION 32

BACK UP 33

Unique volatility factor (no factors diversified for macroregion) No size factor Over/Under calibration of capital requirements? Standard Formula USP Internal Model (to be extended?) Aggregation (implicit in SI): linear correlation, copula, tail dependencies Reinsurance: SI Prop retention preferred SII Non- Prop retention preferred (by favourable NPlob) Different Volatility factors by LoB (unique in SI) Premium Risk only included in SI 34

Relevance of Best Estimate Liabilities (for Non-Life in particular, both in SF e USP) High volatility of Solvency ratios under SII regime Time Horizon: 1 or 3 years? Too short-term vision? Risk Measure: VaR or TVaR? Hard estimation of the tails New strategies are possible today using different diversification effects: by LoBs and for different macro-risks Trade-off Risk and Performance The fear of a models dictatorship The CRO has not to overlay business management but cooperate 35

FUTURE CHALLENGES FOR SOLVENCY II To identify financial and underwriting cycles (re)calibration of SF on a larger scale (not limited to only few and not always significative countries) Fine tuning of operational risk (data collection need as for Basle II) and cyber risk Dependencies by linear correlation Risk tolerance Huge amount of data for Eiopa once SII will be in force (international university networks?) Higher harmonization between different supervisory approaches and practices 36

NEW STRATEGIES UNDER SII OPPORTUNITIES Reduction of Loss Reserve Volume by higher settlement speed Different Premium Volume mix according volatility factors or correlations 37