A Stochastic Model of CPP Liabilities –Preliminary Results
Rick EgeltonChief 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 © 2007. Canada Pension Plan Investment Board. All rights reserved.
Outline of Presentation
Model Objectives
Key model features
Demographic assumptions
Preliminary results
Copyright © 2007. 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
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CPPLM – Demographic Block
Cohort population model
Stochastic fertility, mortality and net migration
Calibrated autoregressive processes
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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
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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
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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
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CPPLM –Estimation Methodology
General approach: error correction equations
Estimated as a system (Seemingly Unrelated Regressions);
captures error covariances needed for ALM portfolio optimization
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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
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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
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Stochastic Simulations
10,000 draws
Innovation variances based on residual standard deviations
Cross-equation residual correlations
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Mean fertility expected to remain low
Fertility Rate
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound OCA
Demographic Assumptions
Bounds are 95%
confidence intervals “OCA” refers to the 21st Actuarial Report (31 Dec
2003)
Copyright © 2007. Canada Pension Plan Investment Board. All rights reserved.
Life expectancy continues to rise
Life Expectancy at Age 65
15.0
17.5
20.0
22.5
25.0
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound OCA
Demographic Assumptions
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Net migration expected to be stable
Net Migration - % of Population
0.00
0.20
0.40
0.60
0.80
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound OCA
Demographic Assumptions
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Demographic uncertainty widens after 2035
Population 65+/Population 16-64
0.0
0.1
0.2
0.3
0.4
0.5
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound OCA
Copyright © 2007. 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
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Increasing labour productivity and demographic uncertainty leads to rising expenditure/contribution uncertainty
Expenditure-Contribution Ratio
0.0
0.3
0.6
0.9
1.2
1.5
1.8
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound
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Mean real energy prices remain elevated but with high uncertainty
Real Energy Commodity Price (log)
4.0
4.5
5.0
5.5
6.0
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound
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Mean real non-energy commodity prices decline somewhat
Real Non-Energy Commodity Price (log)
4.0
4.5
5.0
5.5
6.0
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound
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Commodity price uncertainty generates real exchange rate uncertainty
Canada-US Real Exchange Rate (Log)
0.0
0.2
0.4
0.6
0.8
1.0
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
CTL Mean CTL Upper Bound CTL Lower Bound
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Average Real Cumulative Returns - Control
5.16
4.88
4.49
3.37
4.284.31
3.79
3.13
2.08
3.593.42
2.71
1.79
0.80
2.88
0
1
2
3
4
5
6
Canadian Equity Dev. Excl. CanadaEquity
Nominal Bonds Inflation IndexedBonds
Average RealCumul. CPP Return
High
Mean
Low
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)
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The mean asset-expenditure ratio is close to that of the OCA…
CPP Asset-Expenditure Ratio - Control
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
Mean Upper Bound Lower Bound OCA
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Asset-Expenditure Ratio: 2066 minus 2006 - Probability Distribution
0.00
0.02
0.04
0.06
0.08
"-10 to-9.5"
"-8.0to -7.5"
"-6.0to -5.5"
"-4.0to -3.5"
"-2.0to -1.5"
"0.0 to0.5"
"2.0 to2.5"
"4.0 to4.5"
"6.0 to6.5"
"8.0 to8.5"
"10.0to
10.5"
"12.0to
12.5"
"14.0to
14.5"
"16.0to
16.5"
"18.0to
18.5"
Control
…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
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Higher productivity growth lowers the expenditure-contribution ratio path...
0.5 p.p. higher productivity
growth
Expenditure-Contribution Ratio
0.7
0.9
1.1
1.3
1.5
2007 2012 2017 2022 2027 2032 2037 2042 2047 2052 2057 2062 2067 2072
CTL Mean CTL Upper Bound CTL Lower Bound
SHK Mean SHK Upper Bound SHK Lower Bound
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…and boosts the total fund return…
0.5 p.p. higher productivity
growth
Average Real Cumulative CPP Return
4.28 4.38
3.593.71
2.883.01
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Control Shock
High
Mean
Low
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textImproved net cash flow and a higher return raise the asset-expenditure path
CPP Asset-Expenditure Ratio
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
CTL Mean CTL Upper Bound CTL Lower Bound SHK Mean
SHK Upper Bound SHK Lower Bound OCA
0.5 p.p. higher productivity
growth
Copyright © 2007. Canada Pension Plan Investment Board. All rights reserved.
Asset-Expenditure Ratio: 2066 minus 2006 - Probability Distribution
0.00
0.02
0.04
0.06
0.08
"-10 to-9.5"
"-8.0to -7.5"
"-6.0to -5.5"
"-4.0to -3.5"
"-2.0to -1.5"
"0.0 to0.5"
"2.0 to2.5"
"4.0 to4.5"
"6.0 to6.5"
"8.0 to8.5"
"10.0to
10.5"
"12.0to
12.5"
"14.0to
14.5"
"16.0to
16.5"
"18.0to
18.5"
Control Shock
…and significantly reduces the probability that the asset-expenditure ratio will be lower in 60 years
Probability of lower A/E in 60 years = .093
0.5 p.p. higher productivity
growth
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Lower inflation raises the expenditure-contribution ratio path...
0.5 p.p. lower inflation
Expenditure-Contribution Ratio
0.7
0.9
1.1
1.3
1.5
2007 2012 2017 2022 2027 2032 2037 2042 2047 2052 2057 2062 2067 2072
CTL Mean CTL Upper Bound CTL Lower Bound
SHK Mean SHK Upper Bound SHK Lower Bound
•Slower real basic exemption decline lowers real contribution base
•Higher real starting pension
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text…leading to a lower asset-expenditure path
0.5 p.p. lower inflation
CPP Asset-Expenditure Ratio
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1971
1976
1981
1986
1991
1996
2001
2006
2011
2016
2021
2026
2031
2036
2041
2046
2051
2056
2061
2066
2071
CTL Mean CTL Upper Bound CTL Lower Bound SHK Mean
SHK Upper Bound SHK Lower Bound OCA
Copyright © 2007. Canada Pension Plan Investment Board. All rights reserved.
Asset-Expenditure Ratio: 2066 minus 2006 - Probability Distribution
0.00
0.02
0.04
0.06
0.08
"-10 to-9.5"
"-8.0to -7.5"
"-6.0to -5.5"
"-4.0to -3.5"
"-2.0to -1.5"
"0.0 to0.5"
"2.0 to2.5"
"4.0 to4.5"
"6.0 to6.5"
"8.0 to8.5"
"10.0to
10.5"
"12.0to
12.5"
"14.0to
14.5"
"16.0to
16.5"
"18.0to
18.5"
Control Shock
…and a higher probability that the asset-expenditure ratio will be lower in 60 years
Probability of lower A/E in 60 years = .667
0.5 p.p. lower inflation
Copyright © 2007. 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 © 2007. Canada Pension Plan Investment Board. All rights reserved.
CPPLM – Demographic Block
Fertility Immigration Mortality
Population Age 16-64
Population Age 60+
Stochastic
Endogenous - Deterministic
Exogenous
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CPPLM – Canadian Supply Block
Working Age Population
Potential Hours
Desired Capital Stock
TFP
U.S. TFP
Potential Output
User Cost
Long-run Relationship
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CPPLM – Canadian Demand Block
Short-run Relationship
Commodity Prices
Labour Income Share
Potential Output
U.S. Output
Actual Output
Output Gap
Inflation
90-Day T-Bill Rate
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CPPLM – Asset Returns
Canadian Economic Variables
Canadian Asset
Returns
Foreign Economic Variables
Foreign Asset
Returns
Commodity Prices
Copyright © 2007. Canada Pension Plan Investment Board. All rights reserved.
CPPLM – Contributions Block
Labour Income
Contributable Earnings
Labour Income Share
Actual Output
GDP Inflation
Contributions
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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 iTotal Retirement Benefits/Person Age i
Inflation and productivity