1. 1 Using Stochastic Models in Risk and Capital Management in Life Assurance Tuesday 5 th April 2005 Craig Turnbull

2. 2 Agenda Introduction: Developments in the use of (internal) stochastic models in life assurance –Why now? Who wants it? –How does it work? –What questions is it used to answer? Assessing Risk-Based Capital for With-Profits Business –Quantifying risks and their interaction Using Models as a Capital Management Tool –Identifying and appraising candidate solutions Questions and Answers

3. 3 Introduction: Developments in the use of (internal) stochastic models in life assurance

4. 4 What Developments? Global life assurance industry developing large-scale internal stochastic asset-liability models –Sophisticated arbitrage-free multi-asset models –Complex liability models Dynamic management rules, 000s model points, etc Particularly in UK life industry and the top 20 multinational insurance groups

5. 5 Why Now? Regulatory compulsion (UK only) Greater appreciation of risks in guarantees in life & pensions business Less capital / risk appetite than 5 years ago Appreciation that life / pensions ALM falling behind banking industry Technology –Cheaper, faster

6. 6 Who Wants It? Regulators –FSA Market-consistent guarantee costs (RBS / Pillar 1) Risk-based capital assessment (ICA / Pillar 2) –Stochastic modelling approach required in US and Canada –Will other regulators follow FSA regime? Accountants –IAS, FRS 27 (FRS 17) –European Embedded Value Credit rating agencies –Risk-based capital adequacy –Calculation and communication Internal management –Economic capital allocation and performance measurement –Risk / capital management –Product design / pricing

7. 7 What can it deliver? Quantification of costs, risks and capital requirements –Relative size of drivers –Risk dynamics Diversification, interaction, non-linearity Identification and appraisal of candidate management solutions –Informing trade-offs

8. 8 How Does it Work? Office - Specific Liability Features, Management Strategies (Market – Consistent) Economic Scenario Generator Model Office Software Market-Consistent Balance Sheet / Capital Assessment / etc Market Prices / Best- Estimates

9. 9 Assessing Risk-Based Capital Requirements

10. 10 Approaches to measuring RBC What approaches can be taken to assessing risk-based capital requirements for insurance liabilities? –Run-Off Capital required to fund projected cashflow shortfalls with a specified level of confidence –Value-At-Risk Capital required to fund a future market-consistent liability value with a specified level of confidence –Funding the cost of transferring market risk to market

11. 11 With-Profit Implementation challenges Run-Off –Estimating long-term asset return tails Scarcity of relevant data –Projecting market-consistent balance sheet forward over multiple time horizons Important if m-c balance sheet is a driver of decision rules

12. 12 With-Profit Implementation challenges VaR –Estimating 1-year asset return extreme tails Conditional on recent market behaviour, option prices? –Nested simulations required (in theory!!) –Practical (approximate) implementation approaches

13. 13 Recent 1-yr FTSE 100 Option-Implied Volatilities

14. 14 Implied Equity Falls

15. 15 Individual Capital Assessment Predominantly VaR-style definitions used currently –Capital required to produce 99.5% confidence that realistic liabilities are funded after one year –Given the above difficulties, how is VaR being implemented for With-Profits? Unconditional asset modelling Broadly two implementation approaches for VaR –Univariate –Multivariate

16. 16 ICA for With-Profits – Univariate Approach Calculate 99.5 th percentile events for each risk factor, and obtain capital requirements for each risk factor Calculate total capital requirement by applying a correlation matrix to the capital requirements for each risk factor This assumes: –Risks are linear –Risks do not interact

17. 17 ICA for With-Profits Multivariate Approach 1.Estimate sensitivities of realistic balance sheet to each risk factor 2.Use these to project RBS to end-year (using stochastic asset model) 3.Read off 99.5 th percentile discounted loss

18. 18 Illustrative Example Liability is a 10-yr equity total return put option with strike at-the-spot –Interest rate of 5% –Volatility of 20% –Nominal of £1,644m –Current market value of put option of £100m Assume assets backing guarantee cost are invested in equities –And any assets required in excess of guarantee cost are invested in cash

19. 19 RBC under Univariate approach: Risk Contributions 99.5 th percentile equity return is -36% –Liability increases from 100 to 235 –Assets fall from 100 to 64 –Equity capital requirement is 163 [(235-100) – (100-64)]/ 1.05 99.5 th percentile rise in option-implied equity vol is 5% –Liabilities increase from 100 to 160 –Assets do not change in value –Vol capital requirement is 57 99.5 th percentile interest rate fall is 1.5% –Liabilities increase from 100 to 157 –Assets do not change in value –Interest rate capital requirement is 54

20. 20 RBC under Univariate approach: Allowing for diversification Sum of capital requirements is £274m But this assumes perfect correlation Assume correlations of: –-0.3 between equities / interest rates –-0.4 between equities / option-implied vol –+0.1 between interest rates / implied vol Implies capital requirement of £185m –Diversification benefit of 32%

21. 21 RBC under Multivariate approach Use a number of sensitivity tests: –20% equity fall increases liabilities from 100 to 159 –40% equity fall increases liabilities from 100 to 259 –0.85% interest rate fall increases liabilities from 100 to 130 –2% option-implied interest rate rise increases liabilities from 100 to 124 –Could use many more, e.g. 20% equity fall after 1% interest rate fall, etc… Use greeks to project liabilities in each 1- yr asset simulation

22. 22 Asset / Liability Projection as a function of equity returns

23. 23 Asset / Liability Projection as a function of vol changes

24. 24 Capital Requirement as a function of equity return

25. 25 RBC: Concluding Thoughts Current implementations of the multivariate approach produce similar capital requirements to univariate approach –In example, capital requirements were £187m and £185m But mulitvariate approach is inherently more flexible and transparent –Sophistication can be developed incrementally –More useful as a risk management tool (identifying and appraising candidate management solutions)

26. 26 Correlations: An Aside Most life offices are exposed to falls in equities and falls in interest rates –(Also true for Defined Benefit pension funds) Negative correlation assumption between equities and interest rates implies natural hedge –i.e. Big diversification benefit What if we reduce equity / interest rate correlation?

27. 27 Impact of Correlations on RBC

28. 28 RBC Benefit of Removing Interest Rate Risk

29. 29 Whats the right correlation?

30. 30 Using Stochastic Models as a Capital Management Tool

31. 31 Appraising hedging solutions Matching the risk exposures

32. 32 Appraising hedging solutions Estimating economic capital Neutralising equity exposure: reductions in ICA and RCM Option strategy improves gamma and vega matches: significant reduction in ICA, no impact on RCM

33. 33 Monitoring and managing a hedging strategy Liability risk exposures will change over time as financial markets move Any hedge is unlikely to be static for long periods. The extent to which this is the case will depend on choice of hedging solution – e.g. how well matched is equity gamma? Hedging performance can be regularly monitored (e.g. quarterly) and, when appropriate, re-balanced. e.g. cash guarantees equity delta can double when the yield curve falls by 100bp. Impact of Interest Rate and Equity Market Interaction on Realistic Guarantee Cost

34. 34 Concluding Thoughts Changes in regulatory / accounting / rating agency regimes mean significant step towards convergence in various capital / value / profit measures Reduces constraints to managing economic risks New valuation tools allow capital market solutions to be more effective at mitigating market risks in life assurance business

35. 35 Questions and answers