Earnings at Risk: A Unified Approach

1. Earnings at Risk: A Unified Approach April 27, 2004 Jay Glacy Andres Vilms

2. VaR: A Refresher • A monthly VAR of $10 million means that there is a 5% chance of “loss” in excess of $10 million. • VaR =  - 1.65 • A fair-value metric • Of limited usefulness and determinability for life insurers

3. Braving the Complexity Tsunami • “Alphabet soup” • C-3a, SarbOx, OCI, 99-20, FAS 133, et al • Can we strengthen the actionability of management information? • Can we move decisioning away from subjective rules of thumb to a rigorous framework enabling optimality?

4. Shortcomings of Duration • A fair-value, not accounting-based, quantity • Duration is a termination or wind-up value • Neglects important elements • Forward flows (renewal premiums, new issues) • Effects of reinvestment • Ignores distribution of value • Need a different metric for other risk factors • A trillion ways to create a portfolio of D = 5

5. Why Earnings at Risk? • GAAP results explain 96% of the share price movements of life insurers. • CFOs crave smooth, predictable and rising earnings. • A direct connection to share price through analysts’ DDM valuations. • Low turnover requires understanding of how assets accommodate liabilities over time.

6. The Earnings at Risk Framework • A concise measure of downside risk • Builds on existing ALM and CFT platforms • Expresses results in accounting terms • Captures all financial risks simultaneously • Contrasts relative exposures to various risks

7. Key Functionality • Robust economic scenario generation • Interest rate • Equity market • Credit • Mortality • Policyholder behavior • Robust GAAP functionality • EITF 99-20: income and impairment rules • FAS 91: MBS amortization • FAS 97: dynamic DAC management

8. Nested Scenarios • Two types of scenarios • Projection scenarios -- projections of future outcomes • Valuation scenarios -- for derivation of point-in-time values consistent with market conditions or regulatory requirements Valuation Projection

9. Evolution of 10-Year Treasury Rates Year

10. Emergence of GAAP Earnings To EaR Year

11. Cross-Section of Year 3 GAAP Net Income Mean 10th %

12. Implementation

13. Calculation of EaR • EaR is a statistic of a joint probability distribution -- the convolution of the probability distributions of individual risks • If distributions are simple enough, closed-form solution may be available -- e.g. “mean-variance” VaR approach used by banks • However, financial risk of insurers is too complex

14. Causes of Complexity Financial risk of insurers reflects capital market outcomes as filtered through • Asset/liability interaction • Market-sensitive behavior • Accounting and regulatory rules • Multiple periods  Monte Carlo simulation is necessary

15. Calculation of Insurer EaR (by Monte Carlo simulation) • Need stochastic projection-type scenarios that • Include all relevant risk factors (capital market and other) • Extend over all modeling intervals • Financial results are projected for each scenario • EaR is observed from cumulative probability distribution of the resulting earnings outcomes • Correlation effect = Multi-factor EaR  Single-factor EaR

16. Capital Market Scenarios • Scenarios should reflect company’s capital market forecast • History is richest source of data, considering • Length of observation period • Current market conditions • Risk-neutral basis is not appropriate for EaR analysis

17. Scenario Reduction Methods • Screening of random deviates for conformity to standard normal • Quasi-random sequences • Linear path space • More dependent on the mathematical structure of a particular problem

18. Modeling Interest Rates • Models of yield curve points (“key rates”) • Lognormal with forward drift • Cox-Ingersoll-Ross (incorporates mean reversion and volatility scaled by level of rates) • Principal components analysis -- statistical analysis identifies model factors that drive movement of entire yield curve • Can use “stylized facts” as criteria for reasonableness of modeled scenarios

19. Modeling Equity Returns • Lognormal model • Regime-switching lognormal • GARCH model of stochastic volatility • Equity style analysis

20. Modeling Credit Risk • More recent subject of research • Low frequency/high severity  difficult to fit a credible distribution • Definitional complications • Investment perspective is concerned mainly with market value changes • Realized credit losses are a function of both default incidence and recovery

21. Modeling Insurance Risks • Conceptually simple -- specify probability distribution and correlations with other risk factors • Little established use in life insurance industry • Mortality is best candidate • Reasonably well understood • Large volume of data -- good statistical credibility • Correlation with other risks probably immaterial

22. Application

23. Applications Enabled • Strategic asset allocation • Strategic line-of-business decisioning • Inforce management strategizing • Dynamic liability repricing • Reinvestment/financing • Risk management exercises • Financial management exercises • Financial statement sculpting

24. EaR for Risk Management • Track EaR over time to highlight material changes in risk exposure (“early warning” system) • Compare EaR across lines of business to prioritize risks for mitigation • Compare EaR across risk factors to understand company’s overall risk profile • Compare correlation effects across lines of business and across risk factors, to identify natural hedges

25. EaR for Financial Management • EaR can serve as a measure of economic capital • Compare EaR to regulatory capital to evaluate profit potential of different lines of business • EaR << regulatory capital  regulatory requirements create drag on profit • EaR >> regulatory capital  potential for outsize profits, but higher likelihood of ruin • Use EaR as basis for risk charge for performance measurement • Implicit assumption is that EaR (as specified) is a measure of market-compensated risk

26. Applying Optimization • Optimization Decision Variables • Model time 0 • Asset allocation • Business line mix • Derivatives (caps, floors) overlay • Model time 1+ • Reinvestment/financing strategy • Renewal crediting strategy • New business generation algorithm

27. Optimization in Action By Changing Minimize