a stochastic model of cpp liabilities – preliminary results rick egelton chief economist cppib...

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


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


CPPLM – Demographic Block

Cohort population model

Stochastic fertility, mortality and net migration

Calibrated autoregressive processes


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


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


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


CPPLM –Estimation Methodology

General approach: error correction equations

Estimated as a system (Seemingly Unrelated Regressions);

captures error covariances needed for ALM portfolio optimization


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


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


Stochastic Simulations

10,000 draws

Innovation variances based on residual standard deviations

Cross-equation residual correlations


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)


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




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




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



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


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


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 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



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


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)


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



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


Higher productivity growth lowers the expenditure-contribution ratio path...

0.5 p.p. higher productivity

growth


0.7

0.9

1.1

1.3

1.5

2007 2012 2017 2022 2027 2032 2037 2042 2047 2052 2057 2062 2067 2072


SHK Mean SHK Upper Bound SHK Lower Bound


…and boosts the total fund return…


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


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


growth



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


growth


Lower inflation raises the expenditure-contribution ratio path...

0.5 p.p. lower inflation


0.7

0.9

1.1

1.3

1.5

2007 2012 2017 2022 2027 2032 2037 2042 2047 2052 2057 2062 2067 2072


SHK Mean SHK Upper Bound SHK Lower Bound

•Slower real basic exemption decline lowers real contribution base

•Higher real starting pension


text…leading to a lower 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



0.00

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



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


CPPLM – Demographic Block

Fertility Immigration Mortality

Population Age 16-64

Population Age 60+

Stochastic

Endogenous - Deterministic

Exogenous


CPPLM – Canadian Supply Block

Working Age Population

Potential Hours

Desired Capital Stock

TFP

U.S. TFP

Potential Output

User Cost

Long-run Relationship


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


CPPLM – Asset Returns

Canadian Economic Variables

Canadian Asset

Returns

Foreign Economic Variables

Foreign Asset

Returns

Commodity Prices


CPPLM – Contributions Block

Labour Income

Contributable Earnings

Labour Income Share

Actual Output

GDP Inflation

Contributions


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

a stochastic model of cpp liabilities – preliminary results rick egelton chief economist cppib...

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