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

Copyright © Canada Pension Plan Investment Board. All rights reserved. Outline of Presentation  Model Objectives  Key model features  Demographic assumptions  Preliminary results

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM – Demographic Block  Cohort population model  Stochastic fertility, mortality and net migration  Calibrated autoregressive processes

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM –Estimation Methodology  General approach: error correction equations  Estimated as a system (Seemingly Unrelated Regressions);  captures error covariances needed for ALM portfolio optimization

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM – Basic Structure Canadian Economic Variables Canadian Asset Returns Foreign* Economic Variables Foreign* Asset Returns Commodity Prices Canadian Demographic Variables CPP Contributions and Benefits CPP Fund Return

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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

Copyright © Canada Pension Plan Investment Board. All rights reserved. Stochastic Simulations  10,000 draws  Innovation variances based on residual standard deviations  Cross-equation residual correlations

Copyright © Canada Pension Plan Investment Board. All rights reserved. Mean fertility expected to remain low Demographic Assumptions Bounds are 95% confidence intervals “OCA” refers to the 21 st Actuarial Report (31 Dec 2003)

Copyright © Canada Pension Plan Investment Board. All rights reserved. Life expectancy continues to rise Demographic Assumptions

Copyright © Canada Pension Plan Investment Board. All rights reserved. Net migration expected to be stable Demographic Assumptions

Copyright © Canada Pension Plan Investment Board. All rights reserved. Demographic uncertainty widens after 2035

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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

Copyright © Canada Pension Plan Investment Board. All rights reserved. Increasing labour productivity and demographic uncertainty leads to rising expenditure/contribution uncertainty

Copyright © Canada Pension Plan Investment Board. All rights reserved. Mean real energy prices remain elevated but with high uncertainty

Copyright © Canada Pension Plan Investment Board. All rights reserved. Mean real non-energy commodity prices decline somewhat

Copyright © Canada Pension Plan Investment Board. All rights reserved. Commodity price uncertainty generates real exchange rate uncertainty

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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)

Copyright © Canada Pension Plan Investment Board. All rights reserved. The mean asset-expenditure ratio is close to that of the OCA…

Copyright © Canada Pension Plan Investment Board. All rights reserved. …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

Copyright © Canada Pension Plan Investment Board. All rights reserved. Higher productivity growth lowers the expenditure-contribution ratio path p.p. higher productivity growth

Copyright © Canada Pension Plan Investment Board. All rights reserved. …and boosts the total fund return… 0.5 p.p. higher productivity growth

Copyright © Canada Pension Plan Investment Board. All rights reserved. text Improved net cash flow and a higher return raise the asset-expenditure path 0.5 p.p. higher productivity growth

Copyright © Canada Pension Plan Investment Board. All rights reserved. …and significantly reduces the probability that the asset-expenditure ratio will be lower in 60 years Probability of lower A/E in 60 years = p.p. higher productivity growth

Copyright © Canada Pension Plan Investment Board. All rights reserved. Lower inflation raises the expenditure- contribution ratio path p.p. lower inflation Slower real basic exemption decline lowers real contribution base Higher real starting pension

Copyright © Canada Pension Plan Investment Board. All rights reserved. text …leading to a lower asset-expenditure path 0.5 p.p. lower inflation

Copyright © Canada Pension Plan Investment Board. All rights reserved. …and a higher probability that the asset- expenditure ratio will be lower in 60 years Probability of lower A/E in 60 years = p.p. lower inflation

Copyright © Canada Pension Plan Investment Board. All rights reserved. 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

Annex

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM – Demographic Block FertilityImmigrationMortality Population Age Population Age 60+ Stochastic Endogenous - Deterministic Exogenous

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM – Canadian Supply Block Working Age Population Potential Hours Desired Capital Stock TFP U.S. TFP Potential Output User Cost Long-run Relationship

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM – Canadian Demand Block Short-run Relationship Commodity Prices Labour Income Share Potential Output U.S. Output Actual Output Gap Inflation 90-Day T-Bill Rate

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM – Asset Returns Canadian Economic Variables Canadian Asset Returns Foreign Economic Variables Foreign Asset Returns Commodity Prices

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM – Contributions Block Labour Income Contributable Earnings Labour Income Share Actual Output GDP Inflation Contributions

Copyright © Canada Pension Plan Investment Board. All rights reserved. CPPLM –Benefits Block Immigration Mortality Labour Income/Worker Fertility YMPE Average Retirement Benefits/Person Age i Max Benefit When Person Age i Retired Avg Cumulative Inflation Since Retirement of Persons Age i Retirement Age Distribution of Persons Currently Age i Population Age i Total Retirement Benefits/Person Age i Inflation and productivity