Sponsored by and Solvency II Risk Management Forecasting Presenter(s): Peter M. Phillips
Solvency II Risk Management Forecasting Peter M Phillips Equity Based Insurance Guarantees 2015 Nov 17, 2015 8:30 9:15 a.m. Prepared by PathWise Solutions Group
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Solvency II Overview Solvency II is the new regulatory framework for the European Insurance Industry Solvency II consists of three pillars: Pillar I: quantitative requirements Technical provisions Solvency Capital Requirement (SCR) Pillar II: qualitative requirements Defines the risk management and governance framework that is used to identify and manage risk--orsa Pillar III: reporting and disclosures Focus on market consistent valuation for both Assets and Liabilities Required capital is equal to the loss of a 1-in-200yrs event (VaR 99.5% ) over 12-month time horizon In this context dynamic investment or hedging strategies may help Insurance companies reduce their capital requirements and achieve better overall risk adjusted returns 3
Solvency II Balance Sheet Excess Capital Solvency Capital Requirement (SCR) Market Value of Assets (MVA) Risk Margin Best Estimate of Liabilities (BEL) Solvency II Ratio is equal to the ratio of Available Capital to the Solvency Capital Requirement (SCR) When Own Funds falls below the Solvency Capital Requirement (SCR), the insurance company is considered insolvent 4
European Insurers Challenges Poor Returns and Climbing Liabilities Realized General Account returns have been low while Liabilities have increased as rates have fallen Source: ESRB, June 2015 5
European Insurers Challenges Duration Gaps and Investment Spreads European life insurance companies have large net duration exposures with high guaranteed rates for inforce business Source: ESRB, June 2015 6
Solvency II Issues and Challenges Liabilities are to be calculated based on best estimate assumptions without provisions for adverse deviations Many of these Liabilities are uncertain and have very long durations Assets are to be valued on a marked-to-market basis Any changes in value of Assets will be directly reflected in Own Funds and Excess Capital Levels Stochastic-on-Stochastic simulations are required to correctly project future Assets and Liabilities in a market consistent manner This means dramatic increases in computation length and complexity Need for increased capital forecasting and visibility on drivers of the change in forecasted capital levels Incorporation of dynamic investing and/or hedging strategies make the simulations even that much more difficult 7
Solvency II Case Study A European annuity product with guaranteed rate Backtest SCR levels using historical economic data from 2003 to 2015 Project and forecast SCR 12-months into future using a stochastic-onstochastic economic scenario generator Project SCR and run off a policy until maturity along one sample real world path 3.47 Million paths 299 Million paths 3.47 Million paths
Product Features Product: Lifelong Annuity with Guaranteed Survivors Pension Maturity: Age 60 Guarantee Period: 20 years Payout Scheme: If the life dies before age 60, annuity payment starts at year of death for 20 years If the life dies after age 60 but before age 80, annuity payment continues for (20-x) years, x being the number of years that the annuity payments have been paid. (i.e. pays until age 80 as if the policyholder did not died) If the life dies after age 80, since 20 years of annuity benefit have been paid, the policy terminates at age 80, No surrender value Policyholder can stop the premium payment and consider the policy as paid-up, with reduced annuity and death benefit levels Premium is fixed over the lifetime of the policy At each time step, 3 states of a policyholder have to be modeled: an active, died, and paid-up state 9
Assets and Guarantee Return A portfolio of government bonds, corporate bonds, equities Assume an initial and constant allocation of Asset classes: 66.6% corporate bond fund 16.7% government bond fund 16.7% equity fund At each month end, the Asset portfolio automatically rebalances between these Asset classes to the initial fixed target allocation The guarantee rate for the policy premium is assumed to be 3.25%. The actual growth rate of the policy premium is max(r t, 3.25%) 10
Sample Policyholder Policy issued: 1988-01-31 Date of birth: 1968-01-15 Valuation Date: 2003-01-31 Issued at age: 20 Valuation age: 35 Gender: Male Guaranteed rate: 3.25% Monthly benefit paid out: $3000 Calculated monthly premium: $300 11
Historical Backtest with E.U. economic data (2003 ~2015) 12
Historical Backtest Stochastic-on-Historical Simulation Monthly projection based on a realized information set from Jan 2003 to July 2015. At each month, 1000 scenarios are simulated based on the historical information. For each path and step pair, 22 shocked and 1 base calculation are performed. Each inner loop path projects the policy until maturity (Age 60). Ran on 4 GPUs, and took 37 seconds to finish. Monthly time steps Historical economic scenario Projection based on the realized information set from j-th month historical economic scenario using 1000 scenarios Historical path 1 2 3 12.5 yrs The j-th month for SCR calculation # paths # time steps # Exp. Calc. 1 x 12.5 X12 x 23 X 1000 = 3.47 Million Unique Paths Ran on 4 GPUs, 37 seconds ~ 23500 paths per GPU per second 13
Excess Capital and SCR movement At each point on this graph, SCR levels and Excess Capital (XS Capital) levels changes as time passes and capital market conditions change. Financial Crisis European Debt Crisis Note: during the 2 crises, the excess capital for the company falls below zero, which would have rendered this company insolvent. Excess Capital is defined as Market value of Asset less market value of Liabilities less SCR: XS Capital = MVA MVL SCR. 14
Own Funds vs. SCR Plot When Own Funds are less than SCR, the Market Value of Assets (MVA) is not enough to cover the Liabilities plus solvency capital. For example regulatory intervention would have happened at the point circled in red. Own Funds is defined as the difference between market value of Asset and market value of Liabilities. Own Funds = MVA MVL 15
Spread During the financial crisis, the spread between the 30yr and 10yr bond yield became negative. The insurance company holds essentially a 10yr bond as an Asset, while the Liability duration was close to 30yrs. When this spread contracts, or becomes more negative, Asset levels fall and Liabilities increase. The insurance company in this case is long the basis. It benefits if the basis increases or goes up and suffers if it falls. 16
Account Value Performance w/o Product Cashflow σ Equity = 16.6% The equity return was very volatile over the past 12 years, while the bond price index increase was more steady. σ Total = 4.63% σ Bond = 4.54% 17
Solvency Margin Ratio The solvency margin ratio is defined to be the ratio of Own Funds to SCR. SMR = Own Funds SCR When SMR is less than 1.0, it means the Own Funds are not enough to cover the Solvency Capital Requirement (SCR) and extra capital is needed. 18
SOS Forecasting with E.U. economic projection (2015~2016) 19
Future SCR Forecasting with Stochastic-on-Stochastic Simulations Monthly projection based on projected paths from Aug 2015 to Aug 2016. 1000 Real world scenarios are use to project the future economic environments. At each month in the next 13 months, 1000 inner loop paths are simulated for the SCR calculations. Each inner loop path projects the policy until maturity (Age 60) with 22 shocked assumptions. Ran on 16 GPUs, and took 2 min 14 sec ~ which is about 140,000 paths per GPU per second. Inner Loop Paths (1000) Shocks (22) Real World Paths (1000) 0 1 2 3. 12 # paths # time steps # Exp. Calc. Time Steps (13) 1 000 x 13 x 23 x 1000 = 299 Million Unique Paths 20
Future SCR Projection (Stochastic on Stochastic) Simulated the Asset and Liability for 12 months into the future under a set of real world scenarios. For each month, simulate Asset and Liability under the same set of scenarios until the end of the policy. 1000 outer loop scenarios were used and 1000 inner loop scenarios for each month in the future. Status of the policy as of start of the simulation: Market Value of Asset: $ 579k Market Value of Liability: - $ 442k Solvency Capital Requirement: - $ 57k Excess capital: + $ 139k 21
SOS Projected SCR Distribution (EU 2015~2016) SCR levels tend to be low and asymmetric over the next 12months. The expected SCR level is stable over the next 12 months. But very high levels of SCR can also occur towards the end of the 12 months. 22
SOS Projected Excess Capital Distribution (E.U. 2015~2016) The excess capital levels are somewhat healthy over the next 12 months. However, there are some tail events with excess capital levels significantly under 0 23
One Path Policy Run Off (2015 ~ 2028) 24
One Sample Path Stochastic-on-Stochastic Simulation Monthly projection based on a projected path from Aug 2015 to maturity (Dec 2028). At each month, 1000 scenarios are simulated based on the given simulated information from the previous SOS forecast. For each path and step pair, 22 shocked and 1 base calculation are performed. Each inner loop path projects the policy until maturity (Age 60). Projected economic scenario Projection based on the projected real world information set at j-th month using 1000 scenarios 1 sample path Aug 2015 The j-th month for SCR calculation Dec 2028 # paths # time steps # Exp. Calc. 1 x 151 x 23 x 1000 = 3.47 Million Unique Paths 25
Excess Capital and SCR movement - 1 Path (75 th percentile XS Capital) Under this unfavourable scenario, the excess capital dips below 0 for sustained periods, which means the insurance company has become insolvent Excess Capital is defined as Market value of Asset less market value of Liabilities less SCR: XS Capital = MVA MVL SCR. 26
Key Solvency II Considerations Solvency II requires the modeling of Assets and Liabilities together under a complex framework. Total SCR is driven by the SCR market risk for products with guarantees which in this case are exposed to duration and spread risks. Market risk is driven by the returns and volatility of the Market Value of Assets (MVA) too. MVA can be very volatile. 27
Modeling Dynamic Investment Strategies 28
Dynamic Investment Strategies Dynamic investment portfolio strategies may have a role to play in improving risk adjusted MVA returns and SCR levels thereby helping companies with their Solvency II capital requirements In this setting asset allocation changes at each time step and is tailored to the risk tolerance of the company and the product designs of the company and can incorporate other things too: Realized Vol targets, returns, correlations Optimized movement amongst a portfolio of Assets not just cash and equities Data Selection time step, sample statistic, risk of product Optimization multi objective functions, inequality constraints, etc Such investment strategies can be designed to reduce the effective cost of financial guarantees embedded in life insurance products, and lower capital levels But it can quickly become fishing expedition and data dredging exercise so the use of out of sample testing, statistical significance testing and resampling methods is highly recommended 29
Investment Strategies: Own Funds Plot and SCR Plot A very different pattern of Own Funds and SCR Capital emerges during the back test. It is clear dynamic asset allocation can have an impact on SCR and Own Funds levels over the back test period. 30
Investment Strategies: Own Funds and SCR Plots Under two allocation strategies, the dynamic allocation produces a much higher level of Own Funds and lower amount of SCR, especially during the economic crises. 31
Dynamic Allocation vs. Fixed Allocation 300 250 200 150 100 Portfolio Index Level In this situation the portfolio with dynamic optimized asset allocation strategy outperforms the portfolio with a constant or fixed target weights allocation. 50 0 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Fixed Allocation Dynamic Allocation Monthly Log Returns and STD Of course past performance is no guarantee of future performance and insample results can be very different than outof-sample results! Mean STD Min Max Fixed Allocation 0.42% 1.34% -4.57% 4.46% Dynamic Allocation 0.62% 1.81% -3.90% 4.66% 32
SCR Comparison Dynamic Allocation Fixed allocation In this case the market risks of the Solvency II calculation were significantly reduced when using dynamic asset allocation strategy 33
Solvency II SCR Comparison Plot The differences between the fixed allocation and dynamic allocation for SCR interest risk and SCR spread risk are significant in this case. The dynamic allocation strategy reduces the absolute level of both risk components, in part due to initial conditions and in part due to lower projected absolute market risk levels. 34
SOS Forecasting SCR with Dynamic Asset Allocation Under the dynamic allocation, the future SCR levels are significantly lower than under the fixed allocation (slide 22). Furthermore, SCR decreases over time under this strategy whereas SCR stays constant under the fixed strategy. 35
SOS Forecasting Excess Capital with Dynamic Asset Allocation Under the dynamic allocation, future excess capital levels are significantly higher than under the fixed allocation (slide 23). Furthermore, the chances of excess capital falling below 0 over the next 12 months are also lower under this strategy. 36
Conclusion With Solvency II around the corner: Capital requirements for some life insurance companies may increase significantly. Asset portfolio risk and returns for equity-based/linked products have a key role to play in determining future capital requirements. Managing capital becomes even more important in a low return and low interest rate environment. Forecasting capital and understanding the reasons why forecasted capital changes means running more computationally intensive nested stochastic simulations. Dynamic Asset allocation strategies may help: Insurance Companies Reduce modeled capital requirements Lower the cost of existing financial guarantees embedded in life insurance products Help develop new products to help drive retirement market needs Policyholders Achieve better risk-adjusted returns and richer benefit designs 37
Appendix 38
Historical Data For the historical analysis, the Asset portfolio was constructed using the following weights: Europe 66.6% Corporate Bond: Barclays Euro Aggregate Corporate Total Return Index (LECPTREU Index) 16.7% Government Bond divided equally between the following three indices: Bloomberg/EFFAS Euro Government 1-5 years total return index (EU15TR Index) Bloomberg/EFFAS Euro Government 5-10 years total return index (EU50TR Index) Bloomberg/EFFAS Euro Government 10+ years total return index (EUG5TR Index) 16.7% Equity: Euro Stoxx 50 Net Return Index (SX5T Index) 39
Solvency II Standard Formula Methodology Project out 12 months into the future for capital valuation For each capital revaluation point, project each inforce policy to maturity Shocks are applied to the valuation assumptions at each capital valuation date. SCR Life Component shocks Mortality: 15% increase in mortality rates Longevity: 20% decrease in mortality rates Expense: 10% increase in future expense and 1% per annum inflation Lapse: Max of the three sub shocks Lapse down: 50% decrease in lapse rate Lapse up: 50% increase in lapse rate Mass lapse: immediate 30% lapse of inforce Catastrophe: 1.5 per thousand increase in 1 st year mortality since capital valuation date SCR Market Component shocks Interest rate shocks: prescribed shocks along 30 year term structure Equity shocks: 30% immediate shock Spread Shock: depends on the duration and rating of the bond, immediate shock applied to the bond value 40
Solvency II Shocks Specific to product 41
Solvency II Life Component Capital for mortality risk Capital for longevity risk Capital for lapse risk Capital for catastrophe risk Capital for expense risk SCR Life = shocks i,j Corr ij Cap i Cap j Correlation Matrix = 42
Solvency II Market Component Capital for interest rate risk (Mkt up) Capital for equity risk (Mkt up) Capital for spread risk (Mkt up) Capital for interest rate risk (Mkt down) Capital for equity risk (Mkt down) Capital for spread risk (Mkt down) Correlation Matrices: 43
Solvency II Risk Aggregation The Basic SCR is aggregated SCR sub categories using correlation matrix 44
Sample SCR Breakdown Report 45
Sample SCR Breakdown Report 46