Optimal funding of pension schemes Denis Latulippe Pierre Plamondon September 2004

1. Optimal funding of pension schemes Denis Latulippe Pierre Plamondon September 2004

2. Criteria for choosing afunding method • Stability of the contribution rate • Strengthen the contribution – benefit connection • Ensure generational fairness • Strengthen fiscal discipline • Maintain public confidence • Minimizing the contribution rate • Smart funding: increased funding during periods of high rates of return and weak salary increases • Solvency • Compulsory funding of private-plan commitments • Not particularly pertinent to public plans • Macroeconomic impacts • Effect on savings and the labour force • Effect on financial markets • Institutional capabilities and political choices The two elements covered by the study

3. Economic variables that influence the inflows and outflows of a pension plan Growthin the numberof workers Contributions Totalinflows Growth in wages Investment income Reserve Interest rates Benefits Total outflows Inflation Administration

4. Factors that determinethe contribution rate • Pure pay-as-you-go basis • Ratio of pensioners to contributors • Salary levels and growth • Maturity of the scheme • Full-funding basis • Discount rate and other actuarial assumptions • Amortization of experience deficiencies (differences between experience and assumptions) • Amortization of past service Gradual variations in the contribution rate More short-term variations in the contribution rate

5. Demographic and economic trendsof the OECD countries Observations: • Aging of the population • Increase in the dependency rate • Slowing of manpower growth • Volatility in the increase of wages and interest rates and negative correlation between these variables Conclusions: • Vulnerability of pay-as-you-go plans • Increased importance of funding • Need for protection against the volatility of contribution rates resulting from uncertainty over future increases in wages and rates of return on investments Objective of our action

6. Wage increases and interest ratesin Canada (1966-2000)

7. Impact of the demographic and economic environment on the contribution rate (Canada) Source: Canadian Institute of Actuaries, 1996

8. Simulation ofthree funding options Applied to a public plan (projection method): 1. Pure pay-as-you-go 2. Partial funding, maintaining a reserve ratio of 3.0 times the cash outflows (stabilization reserve) 3. Full funding, maintaining a reserve ratio of 25.0 times the cash outflows (assumed to be equal to the present value of accrued benefits) In contrast to the method generally used for private plans, in which the contribution rate is based on the present value of future benefits.

9. 14% 12% 10% Pay-as-you-go 8% Partial funding 6% Full funding 4% 2% 0% 2003 2013 2023 2033 2043 Projection of the contributionrate for the base scenario(with no fluctuation in the economic variables)

10. Fluctuations in the economicvariables analyzed

11. Working assumptions • The contribution rate is re-examined every 5 years. • The reserve objective is 50 years following the valuation date (which corresponds to amortizing the net gains and losses over 50 years). • The economic and demographic assumptions, for the years following the valuation date, are not changed for later subsequent valuations.

12. 14% 12% 10% Pay-as-you-go 8% Partial funding 6% Full funding 4% 2% 0% 2003 2013 2023 2033 2043 Fluctuation in therate of increase in wages

13. 14% 12% 10% Pay-as-you-go 8% Partial funding 6% Full funding 4% 2% 0% 2003 2013 2023 2033 2043 Fluctuation in the interest rate

14. Simulation with more rapidamortization of gains and losses • Simulation of the effect of a fluctuation in the rate of return supposing an amortization period of 5 years (instead of 50 years). Amortization period of deficits of private plans in Canada

15. 15% 10% 5% Pay-as-you-go Partial funding Full funding 0% 2003 2013 2023 2033 2043 -5% -10% Fluctuation in the rate of return and5-year amortization of deficits

16. Future work Possible refinements • Assumptions used • Actualization models used for private plans • Risk management : Keeping contingency reserves…

17. The financial point of view • Primary objective : stabilizing the contribution rate • Secondary objective: minimizing the contribution rate • Optimize the funding of a retirement scheme by considering the relation between the rate of increase in wages and the rate of return on investments.

18. The financial point of view Application of the portfolio theory: (Capital Asset Pricing Model) • Security A: rate of return corresponding to a portfolio composed of 50% bonds and 50% shares • Security B: rate of return equal to the rate of increase in wages

19. Methodology and assumptions • Assumptions for salary increases and rates of return are based on past statistical data and on the risk level of the current QPP risk portfolio. • Application of the CAPM requires the use of a risk-free rate : Different scenarios proposed

20. Optimal distribution of Québec Pension Plan income sources Average Rates       Risk-free 3.9 Standard deviation Wage increase 3.9 2.0 2.0 2.0 2.0 2.5 2.5 2.5 2.5 3.0 3.0 Invest. yield 7.4 3.5 4.0 4.5 5.0 3.5 4.0 4.5 5.0 3.5 4.0 Covariance -3.5 -4.0 -4.5 -5.0 -4.4 -5.0 -5.6 -6.3 -5.3 -6.0 (based on a coefficient of correlation of -0.5) Weight (contributions) 0.47 0.50 0.53 0.56 0.41 0.44 0.47 0.50 0.37 0.40 Weight (investment income) 0.53 0.50 0.47 0.44 0.59 0.56 0.53 0.50 0.63 0.60

21. Results of applying the portfolio theoryto the Québec Pension Plan Sensitive to: • the choice of the risk-free rate • the variability of the increase in wages and the variability of the rate of return on stocks and bonds • the covariance between the return on stocks and bonds and the wage increases Examples: • Risk-free rate equal to the wage growth (3.9%) (see Table) • Contributions: between 40% and 60% • Investment income: between 40% and 60% • Risk-free rate equal to the average interest rate on Treasury bills over the period 1998-2002 (4.4%) • Contributions: 30% • Investment income: 70% • Risk-free rate, wage growth and return on stocks and bonds equal to the average of the last 30 years • Risk-free rate significantly higher than wage growth • The model does not respond correctly

22. Future work Possible refinements • Models with multiple asset categories • Sensitivity analysis regarding the choice of a risk-free rate

23. Conclusions • A pension plan’s contribution rate is very sensitive to changes in the economic environment. • The interest rate level and salary increases influence the contribution rate in different ways depending on the choice of funding method. • Public plans can amortize the effects of these changes over long periods. • Fully funded private plans, which must amortize deficits over short periods, are more sensitive to fluctuations in the economic variables. • Two ways of immunizing a pension system against these fluctuations: • Partial funding of a public plan • A mixed (public-private) system • Partial funding is also appropriate from the portfolio theory point of view, especially in a context of high wage growth and low interest rates