Development of Risk and (Market) Valuation Models: From Measurement to Management

1. >> 18 September 2003 AFIR Colloquium 2003 Maastricht Development of Risk and (Market) Valuation Models: From Measurement to Management Farid Kabbaj Inge Zeilstra

2. Introduction • Development of Risk and (Market) Valuation Models • Farid Kabbaj, Inge Zeilstra • Introduce concepts using an example product. • Risk/ Return, Risk Based Capital, Multi Party Flow Analysis • Extensions to these concepts • Dynamic Management Decisions, Projected Realistic Balance Sheets • Analysing results • Sensitivities, Analysis of Change • Conclusions fkabbaj@bw-deloitte.com

3. Example Product Description • Regular Premium Endowment Product • Reserve = 800 mln. • Profit sharing = 80% (investment return – VRI – 0,5%) • Valuation Rate of Interest (VRI) = 4% • 5% Solvency Margin • Free Assets (including SM) = 45 mln. • New business not included

4. Risk/ Return Measures Classic ALM technique. The development of the average free assets is compared to the associated risk of ruin. Within the 5th percentile for risk of ruin, strategy 3 (5% equity) seems the preferred option (over a 20 year horizon) as this gives the highest average free assets. We are maximising equity exposure under a constraint (risk of ruin). example product Strategy 2 (2,5% equity) would be preferred when the objective is minimisation of risk.

5. Risk Based Capital Definition: Capital required to ensure that the company is not impaired, over a certain period of time (1 yr), to a certain level of probability (99%). Conceptually comparable to Value at Risk and Economic Capital illustrative “Locked-in Capital” – can’t be used to fund business growth

6. Risk Based Capital • 1 year time horizon, 99% confidence interval • RBC required to protect 100% solvency • No new business • New business strain can have a huge impact example product Based on this information alone, Strategy 1 seems optimal.

7. Multi Party Flow Analysis In the Multi Party Flow Analysis thevalue of the company is attributed to various stakeholders like a pie being sliced. A possible split of stakeholders: • Policyholders, paying a premium and receiving benefits. • Shareholders, providing capital injections/ receiving dividends. • Government, tax is paid by the shareholders and policyholders. • Expense receivers, costs are made to run the company like wages and rent. • etc. illustrative Which choice is best from a commercial point of view? • Might impact new business volumes, lapse rates, pricing decisions, etc These decisions have an impact on the cash inflow. The pie can get bigger!

8. Multi Party Flow Analysis • FV Liabilities ~ Policyholder Value + Expenses > Traditional Reserve • Margins in traditional valuation are not sufficient (in this example). For example, the best estimate expenses are bigger than the expense loadings. • Shareholder value is negative! (in this example) example product • Shareholder value decreases when the equity backing ratio increases • The greater volatility of equity causes the investment return to fall below the guarantee (the VRI = 4%) more often. • The dynamic effect on sales and lapses has not been taken into account (minor impact). • Value of expenses constant • Linked to inflation only

9. Dynamic Interactions • Investment strategy • For example Constant Proportion Portfolio Insurance (CPPI) illustrative • New business volumes, lapse rates • Based on assumptions regarding profit sharing rates relative to the market, financial strength, etc • Other – expenses, profit sharing strategy, pricing, indexation

10. Run Time Issues • Calculations previously very difficult due to run time issues • Previously, 50 simulations in 10 hours was considered acceptable • Standard run now very fast - 5,000 simulations in 1 hour • 1,000 liability segments (grouped) • 20 year projection period • 2.6 GHZ PC Pentium IV • Intel Compiler • Run time decreases linearly when using multiple PCs • Acceptable run times for large companies • For development work a smaller number of scenarios is used 250 Simulations in 3 minutes – a huge number of strategies can be investigated

11. Two Dimensional Matrix • Horizontal axis - from deterministic to dynamic stochastic modelling • Vertical axis - understanding and measurement of risk and return • No fixed categorisation • Gives good insight in the way models are heading

12. Projected Realistic Balance Sheets • FSA (UK regulator) – Realistic Balance Sheet • Companies to file a balance sheet on IFRS basis using a stochastic approach. • Projecting forward requires a combination of stochastic techniques with Black–Scholes and/ or interpolation formulae to place a fair value on embedded options. • PVK(NL regulator) – Continuïteitstoets(Long Term Solvency Test) • The PVK stated that a projected realistic balance sheet approach will be required but so far a discussion paper has not been released. • Solvency II

13. Analysis of Change AoC for Embedded Value AoC for Risk Based Capital illustrative illustrative Important tool for “Back Testing” results

14. Sensitivities Even more important in a stochastic model than in an EV model. • Greater complexity requires more sensitivities to get a grip on the results • Helps to capture the drivers of Risk Based Capital • 50+ sensitivities to the base run is not exceptional in the development stage • Run times are essential illustrative

15. Management Strategies and Solutionssome examples Traffic Light Approach • Different strategy for green/ amber/ red situations • Management actions tested before needed • Enhanced dynamic decisions Dynamic Asset Strategy (e.g. CPPI) • Risk exposure dependent on buffer available • Gives satisfying results but needs to followed in practice – strict guidelines We see many companies using stochastic techniques in product design.

16. Conclusions • Multiple risk measures are needed to get an understanding of the risk/ return profile of the company. • An integrated model is preferable • Consistency • Regulatory pressures – projected realistic balance sheets • Dynamic management decisions implemented in the model • Greater complexity increases the need for digging into results • Run times are essential

17. >> 18th September 2003 AFIR Colloquium 2003 Maastricht Development of Risk and (Market) Valuation Models: From Measurement to Management Farid Kabbaj Inge Zeilstra