A Stochastic Model of CPP Liabilities –Preliminary Results

1. A Stochastic Model of CPP Liabilities –Preliminary Results Rick Egelton Chief Economist CPPIB October 27, 2007 The views in this presentation reflect work in progress and do not represent the official views of the CPP Investment Board

2. Outline of Presentation • Model Objectives • Key model features • Demographic assumptions • Preliminary results

3. Model Objectives • Input to ALM optimal portfolio allocation and estimation of likelihood of plan restructuring • OCA sustainability criterion: expected asset/expenditure ratio in 60 years >= current asset/expenditure ratio

4. CPPLM – Demographic Block • Cohort population model • Stochastic fertility, mortality and net migration • Calibrated autoregressive processes

5. CPPLM – Contribution and Benefit Blocks • Cohort-based • Incorporates indexing formulae, retirement pension actuarial adjustment • Capture dynamic impacts of inflation and productivity on retirement and disability benefits

6. CPPLM – Economic Framework • Structural supply-side: neoclassical growth model • Long-run growth determined by working age population growth and productivity growth (technical progress) • Economy subject to demand and supply shocks • Only supply shocks have permanent real effects

7. CPPLM – Asset Returns • Monetary authority adjusts short rate in response to changes in excess capacity and deviation of inflation from target • Long rate = short rate plus term premium • Equity return depends on economic growth and equity premium

8. CPPLM –Estimation Methodology • General approach: error correction equations • Estimated as a system (Seemingly Unrelated Regressions); • captures error covariances needed for ALM portfolio optimization

9. CPPLM – Basic Structure Foreign* Economic Variables Foreign* Asset Returns Commodity Prices Canadian Demographic Variables Canadian Economic Variables Canadian Asset Returns CPP Contributions and Benefits CPP Fund Return

10. Result Caveats • Currently modeled: equity and bond returns; Canada, U.S. and Developed • Planned addition of other countries and assets classes will affect results • Equilibrium real interest rates not affected by long-run output growth • Scenarios are illustrative and are not forecasts

11. Stochastic Simulations • 10,000 draws • Innovation variances based on residual standard deviations • Cross-equation residual correlations

12. Mean fertility expected to remain low Demographic Assumptions Bounds are 95% confidence intervals “OCA” refers to the 21st Actuarial Report (31 Dec 2003)

13. Life expectancy continues to rise Demographic Assumptions

14. Net migration expected to be stable Demographic Assumptions

15. Demographic uncertainty widens after 2035

16. Key Assumptions • Mean long-run productivity growth = 1.7% • Mean long-run inflation = 2.0% • Long-run asset mix: 25% Canadian equity, 40% other developed equity*, 25% bonds, 10% inflation-indexed bonds* *not directly comparable with OCA asset classes; OCA considers world equity and real estate and infrastructure returns Assumptions are illustrative and are not forecasts

17. Increasing labour productivity and demographic uncertainty leads to rising expenditure/contribution uncertainty

18. Mean real energy prices remain elevated but with high uncertainty

19. Mean real non-energy commodity prices decline somewhat

20. Commodity price uncertainty generates real exchange rate uncertainty

21. The cumulative mean fund return has a 95% confidence band of 140 basis points Given a differing set of asset classes and mix, the OCA projects a 4.2% average cumulative return (4.1% terminal)

22. The mean asset-expenditure ratio is close to that of the OCA…

23. …and the probability that the asset-expenditure ratio will be lower in 60 years is slightly less than half Probability of lower A/E in 60 years = 0.457

24. Higher productivity growth lowers the expenditure-contribution ratio path... 0.5 p.p. higher productivity growth

25. …and boosts the total fund return… 0.5 p.p. higher productivity growth

26. text Improved net cash flow and a higher return raise the asset-expenditure path 0.5 p.p. higher productivity growth

27. …and significantly reduces the probability that the asset-expenditure ratio will be lower in 60 years 0.5 p.p. higher productivity growth Probability of lower A/E in 60 years = .093

28. Lower inflation raises the expenditure-contribution ratio path... 0.5 p.p. lower inflation • Slower real basic exemption decline lowers real contribution base • Higher real starting pension

29. text …leading to a lower asset-expenditure path 0.5 p.p. lower inflation

30. …and a higher probability that the asset-expenditure ratio will be lower in 60 years 0.5 p.p. lower inflation Probability of lower A/E in 60 years = .667

31. Next Steps • Expand countries and asset classes • Explore long-run relationship between real economic growth and real bond returns • Input to ALM portfolio optimization • Would provide optimal portfolio and restructuring probability

32. Annex

33. CPPLM – Demographic Block Fertility Immigration Mortality Population Age 16-64 Population Age 60+ Stochastic Exogenous Endogenous - Deterministic

34. CPPLM – Canadian Supply Block Working Age Population U.S. TFP Potential Hours Desired Capital Stock TFP Potential Output User Cost Long-run Relationship

35. CPPLM – Canadian Demand Block 90-Day T-Bill Rate Potential Output Labour Income Share Output Gap U.S. Output Actual Output Inflation Commodity Prices Short-run Relationship

36. CPPLM – Asset Returns Commodity Prices Canadian Economic Variables Canadian Asset Returns Foreign Economic Variables Foreign Asset Returns

37. CPPLM – Contributions Block Labour Income Share Actual Output GDP Inflation Labour Income Contributable Earnings Contributions

38. CPPLM –Benefits Block Labour Income/Worker Inflation and productivity YMPE Max Benefit When Person Age i Retired Fertility Avg Cumulative Inflation Since Retirement of Persons Age i Average Retirement Benefits/Person Age i Total Retirement Benefits/Person Age i Population Age i Retirement Age Distribution of Persons Currently Age i Immigration Mortality