1. Development of Asset Models: Calibration Issues Chris Madsen, ASA, CFA, MAAA American Re-Insurance Company CAS DFA Forum, Chicago July 19th-20th, 1999 Chris Madsen, ASA, CFA, MAAA American Re-Insurance Company CAS DFA Forum, Chicago July 19th-20th, 1999

2. Discussion Overview Overview of an integrated risk management system Asset model calibration issues Summary Overview of an integrated risk management system Asset model calibration issues Summary

3. Model Structure

4. Economic Assumptions

5. M2 Growth V2 Growth Inflation* GDP Growth* Interest Rates* (Forward, Spot, Yield) Equity Earnings Yield Equity Earnings Growth Asset Model * Currency Link (not currently modeled) Economic Model

6. SimulationDefining the r/i structure Modeling the portfolio Gross loss Net loss Ceded loss Retained premiums Ceded premiums Loss Simulation with DFA Loss data Premiums Customer requirements Limits Prices

7. Model Purpose Is the model for  Pricing?  Risk management? Is the model for  Pricing?  Risk management?

8. Types of Models* Rung 5: Total Integrated Risk Management Rung 4: Dynamic Asset and Liability Management Rung 3: Dynamic Asset-Only or Liability-Only Rung 2: Static Asset-Only or Liability-Only Rung 1: Pricing Single Securities Rung 5: Total Integrated Risk Management Rung 4: Dynamic Asset and Liability Management Rung 3: Dynamic Asset-Only or Liability-Only Rung 2: Static Asset-Only or Liability-Only Rung 1: Pricing Single Securities * Mulvey’s Risk Ladder

9. What are we trying to do? Determine economic parameters that generate the asset characteristics we want.  Note: Each asset is priced along each economic path. Goal: Generate scenarios of company financials to study efficient allocation of resources: Business mix, asset mix, capital and retro covers. Determine economic parameters that generate the asset characteristics we want.  Note: Each asset is priced along each economic path. Goal: Generate scenarios of company financials to study efficient allocation of resources: Business mix, asset mix, capital and retro covers.

10. Indexes 1926-1999

11. Asset Only Efficient Frontier...

12. …Falls Short on the Bottom Line

13. Economic Model Long interest rates  dl t = a l ( l  - l t ) dt + l t  l dZ l Short interest rates  dr t = a r ( r  - r t ) dt + r t  r dZ r Long interest rates  dl t = a l ( l  - l t ) dt + l t  l dZ l Short interest rates  dr t = a r ( r  - r t ) dt + r t  r dZ r

14. Calibration (Model Fitting) Relationships  within time periods  across time periods Relationships  within asset class/ economic variable  across asset class/ economic variable First step is economic calibration - this session focuses on asset model impact Relationships  within time periods  across time periods Relationships  within asset class/ economic variable  across asset class/ economic variable First step is economic calibration - this session focuses on asset model impact

15. Calibration (Model Fitting) Basic statistics (arithmetic mean, compound mean, st.dev., percentiles, min. & max., serial) Plausibility criteria (Becker - yield curve characteristics) Basic statistics (arithmetic mean, compound mean, st.dev., percentiles, min. & max., serial) Plausibility criteria (Becker - yield curve characteristics)

16. Basic Asset Class Statistics Historical:

17. Returns: 1926 - 1999 10 Year Compound Annual 10 Year Compound Annual

18. 10 Year Simulated

19. Actual (left) versus One Simulated Path (right)

20. Historical Standard Deviations

21. Correlation Matrix Annual versus monthly Time and trend dependency 1926-1999: 10 Year: Annual versus monthly Time and trend dependency 1926-1999: 10 Year:

22. Target Example History Simulation

23. Reasonability Check Risk return trade-off should be apparent (in general)

24. Simulated (10 Years)

25. Summary A number of characteristics must be monitored for asset model results to be labeled “reasonable” Calibration methodology and targets should match model purpose A number of characteristics must be monitored for asset model results to be labeled “reasonable” Calibration methodology and targets should match model purpose