1

Optimal funding of pension schemes

Denis LatulippePierre 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

Reserve

Contributions

Investment income

Benefits

Growthin wages

Interest rates

Growthin the number

of workers

Inflation

Totalinflows

Totaloutflows

Administration

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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

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Wage increases and interest ratesin Canada (1966-2000)

0%

2%

4%

6%

8%

10%

12%

14%

16%

1966 1971 1976 1981 1986 1991 1996

Rate

Wages Interest rate (long-term gvt. bonds)

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Impact of the demographic and economic environment on the contribution rate

(Canada)

1960senvironment

1990senvironment

Assumptions

Dependency rate (long term)Real increase in wages Real interest rate

0.33 2.0% 2.0%

0.40 1.0% 4.0%

Long-term cost (OAS + QPP)

Pay-as-you-go basisTotal funding basis

11.0%16.5%

14.5% 7.2%

Source: Canadian Institute of Actuaries, 1996

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Simulation ofthree funding options

Applied to a public plan (projection method):1. Pure pay-as-you-go2. 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.

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Projection of the contributionrate for the base scenario

(with no fluctuation in the economic variables)

0%

2%

4%

6%

8%

10%

12%

14%

2003 2013 2023 2033 2043

Pay-as-you-goPartial fundingFull funding

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Fluctuations in the economicvariables analyzed

Period

Scenario 1Fluctuating rate of

return

Scenario 2Fluctuating earnings

increases

Scenario 3Fluctuating rate of return and fluctuating

earnings increases

Difference with the base scenario as regards the

rate of return of the fund

Difference with the base scenario as regards the

rate of increase of earnings

Difference with the base scenario as regards the

rate of return of the fund

Difference with the base scenario as regards the

rate of increase of earnings

2001-20052006-20102011-20152016-20202021-20252026-20302031-20352036-20402041-20452046-2050

+ 5%– 5%+ 5%– 5%+ 5%– 5%+ 5%– 5%+ 5%– 5%

+ 3%– 3%+ 3%– 3%+ 3%– 3%+ 3%– 3%+ 3%– 3%

+ 5%– 5%+ 5%– 5%+ 5%– 5%+ 5%– 5%+ 5%– 5%

– 3%+ 3%– 3%+ 3%– 3%+ 3%– 3%+ 3%– 3%+ 3%

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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.

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Fluctuation in therate of increase in wages

0%

2%

4%

6%

8%

10%

12%

14%

2003 2013 2023 2033 2043

Pay-as-you-goPartial fundingFull funding

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Fluctuation in the interest rate

0%

2%

4%

6%

8%

10%

12%

14%

2003 2013 2023 2033 2043

Pay-as-you-goPartial fundingFull funding

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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

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Fluctuation in the rate of return and5-year amortization of deficits

-10%

-5%

0%

5%

10%

15%

2003 2013 2023 2033 2043

Pay-as-you-goPartial fundingFull funding

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Future work

Possible refinements• Assumptions used• Actualization models used for private plans• Risk management : Keeping contingency

reserves…

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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.

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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

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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

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Optimal distribution of Québec Pension Plan income sources

AverageRates       Risk-free 3.9Wage increase 3.9 2.0 2.0 2.0 2.0 2.5 2.5 2.5 2.5 3.0 3.0Invest. 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

Weight (contributions) 0.47 0.50 0.53 0.56 0.41 0.44 0.47 0.50 0.37 0.40Weight (investment income) 0.53 0.50 0.47 0.44 0.59 0.56 0.53 0.50 0.63 0.60

Standard deviation

(based on a coefficientof correlation of -0.5)

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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:1. Risk-free rate equal to the wage growth (3.9%) (see Table)

– Contributions: between 40% and 60%– Investment income: between 40% and 60%

2. Risk-free rate equal to the average interest rate on Treasury bills over the period 1998-2002 (4.4%)

– Contributions: 30%– Investment income: 70%

3. 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

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Future work

Possible refinements• Models with multiple asset categories• Sensitivity analysis regarding the choice of a

risk-free rate

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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