Better pension deals with fair-value ALM

UvA, Netspar, AG - 2 november 2006Niels Kortleve

2

Better pension deals with fair-value ALM

Classical ALM has shortcomings

– Inconsistent with market value• Does not give correct weight to downside

• High cash flows can have low present value

– Mostly focused on averages only

Fair-value ALM is easy to understand

– Comparing euros in stead of different averages

– Measuring impact of policy changes on stakeholders

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2

2

3

3

Classical ALM inconsistent with market valueFair-value ALM attaches more weight to downside

1

Introduction

4

Choice between two deals• Suppose you have no control of your own future

– Probability of 50% to become millionaire

– Probability of 50% to become unemployed

• Someone is offering you two deals

– Deal one: receive € 1000 when millionaire

– Deal two: receive € 1000 when unemployed

• For which deal are you willing to pay most?

• Classical ALM says: both deals are equal

• Fair-value ALM attaches more weight to downside

– Scenario of becoming unemployed has high “state price”

– Scenario of becoming millionaire has low “state price”

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0.00005

0.005

state price

Fair-value ALM: more weight to downside

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

valu

e (e

uros

)

= Equities

time

6

Invest € 1 in equities or € 1 in bonds?

€ 1 in equities € 1 in bonds

5% quantile € 1.00 € 1.52

median € 2.67 € 2.05

95% quantile € 7.25 € 2.85

What is future value of investment after 15 years?

Which of these two investments do you prefer?

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0.00005

0.005

state price

State prices reveal what we already knew:Both investments have same present value

= Equities = Bonds

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

valu

e (e

uros

)

time

time

scen

ario

s

Economicscenario set

time

scen

ario

s

Cash flows per scenario

time

scen

ario

s

Set state prices

Classical ALM:

P(underfunding) Average indexation Average contributionPension deal

Fair-value ALM:

Balance sheet(in euros)

Stakeholder analysis

9

Classical ALM mostly focused on averagesFair-value ALM compares euros in stead of different averages

2

Example

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Example: fictitious pension fund

• Pension deal 1– Average pay DB– Fixed contribution: 14% of salary– Unconditional indexation with wage inflation– 50% equities, 50% bonds

• Adapting this deal step by step– What happens to classical ALM results?– What happens to fair-value ALM results?

• Our horizon is 15 yearsInitial funding ratio: 130% (nominal)

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Classical ALM results for pension deal 1

Horizon 15 years Ultimo 2005

P(FR < 100%) 12.4%

Average indexation 100%

Average contribution 14%

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Verloop van de dekkingsgraad

6

30

Funding ratio for pension deal 1

0

50

100

150

200

250

300

350

400

450

500

2006 2011 2016 2021

Fair-value ALM: more weight to downside

probability present value

87.6%

12.4%

time

13

assets liabilitiesinvestments 79 pensions 148contributions 45option deficit 30 option surplus 6

total 154 total 154

Balance sheet for pension deal 1

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Policymaker’s control panel: pension deal 1

P(FR < 100%): 12.4%

Average contribution: 14% Average indexation: 100%

assets liabilitiesinvestments 79 pensions 148contributions 45option deficit 30 option surplus 6

total 154 total 154

0

50

100

150

200

250

300

350

400

450

500

2006 2011 2016 2021

0

10

20

30

2006 2011 2016 2021

0

25

50

75

100

2006 2011 2016 2021

deal 2 deal 3

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Pension deal 2: contribution ladder

-10%

0%

10%

20%

30%

100% 120% 140% 160% 180%100% 130%

14%

160%

funding ratio

con

trib

uti

on

16

Pension deal 2: contribution ladder

Classical ALM:average contribution = 14%

0

10

20

30

2006 2011 2016 20210

10

20

30

2006 2011 2016 2021

Fair-value ALM:value of contribution = 45

Classical ALM:average contribution = 11.8%

Fair-value ALM:value of contribution = 51

Lower average but higher present value

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Policymaker’s control panel: pension deal 2

P(FR < 100%): 7.7%

Average contribution: 11.8% Average indexation: 100%

0

25

50

75

100

2006 2011 2016 20210

10

20

30

2006 2011 2016 2021

assets liabilitiesinvestments 79 pensions 148contibution 51option deficit 23 option surplus 4

total 152 total 152

0

50

100

150

200

250

300

350

400

450

500

2006 2011 2016 2021 deal 1 deal 3

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0%

25%

50%

75%

100%

100% 120% 140% 160% 180%

Pension deal 3: indexation ladder

100% 160%

funding ratio

in

dex

atio

n

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Policymaker’s control panel: pension deal 3

P(FR < 100%): 5.9%

Average contribution: 10.7% Average indexation: 71%

0

50

100

150

200

250

300

350

400

450

500

2006 2011 2016 2021

0%

25%

50%

75%

100%

2006 2011 2016 20210

10

20

30

2006 2011 2016 2021

assets liabilitiesinvestments 79 pensions 137contribution 46option deficit 16 option surplus 5

total 142 total 142

deal 1 deal 2

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Fair-value ALM compares euros in stead of different averages

pension deal 1

pension deal 2

pension deal 3

P(FR < 100%) 12.4% 7.7% 5.9%

Average indexation 100% 100% 71%

Average contribution 14% 11.8% 10.7%

Present value option deficit (euros) 30 23 16

Present value pensions (euros) 148 148 137

Present value contribution (euros) 45 51 46

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Fair-value ALM measures impact of policy changes on stakeholders

3

Stakeholder analysis

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Which stakeholders pay for policy changes?

• Cohort = stakeholders of same age group

• Transfers between cohorts because of policy change– > 0: cohort profits from change

– < 0: cohort loses from change

• Assumptions– Range of cohorts is 5 years

– Our horizon is 15 years

– Initial funding ratio: 130% (nominal)

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Fair-value generational accounting computes transfers between cohorts: zero sum game

assets liabilities

investments 50 pensions 90contributions 40option defecit 10 option surplus 10

total 100 total 100

assets liabilities

investments 20 pensions 20contributions 8option defecit 2 option surplus 2

total 30 total 22

assets liabilities

investments 20 pensions 40contributions 15option defecit 5 option surplus 5

total 40 total 45

assets liabilities

investments 10 pensions 30contributions 17option defecit 3 option surplus 3

total 30 total 33

cohort loses 8

cohort gains 5

cohort gains 3

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Example: pension deal 1

-10

-5

0

5

10

5 15 25 35 45 55 65 75 85 95

nominal pension

contribution

>>

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Example: pension deal 1

-10

-5

0

5

10

5 15 25 35 45 55 65 75 85 95

indexation

nominal pension

contribution

26

Example: pension deal 1

-10

-5

0

5

10

5 15 25 35 45 55 65 75 85 95

extra claim

indexation

nominal pension

contribution

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Result: transfers in pension deal 1

-5

0

5

5 15 25 35 45 55 65 75 85 95

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-5

0

5

5 15 25 35 45 55 65 75 85 95

Young participants lose in pension deal 2(contribution ladder)

PENSION DEAL 1

-1

0

1

5 15 25 35 45 55 65 75 85 95

EXTRA TRANSFERS

-5

0

5

5 15 25 35 45 55 65 75 85 95

PENSION DEAL 2

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-6

-4

-2

0

2

4

6

5 15 25 35 45 55 65 75 85 95

-6

-4

-2

0

2

4

6

5 15 25 35 45 55 65 75 85 95

-4

-2

0

2

4

5 15 25 35 45 55 65 75 85 95

Retirees lose in pension deal 3(contribution ladder and indexation ladder)

PENSION DEAL 1

EXTRA TRANSFERS

PENSION DEAL 3

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-6

-4

-2

0

2

4

6

5 15 25 35 45 55 65 75 85 95

-4

-2

0

2

4

5 15 25 35 45 55 65 75 85 95

-6

-4

-2

0

2

4

6

5 15 25 35 45 55 65 75 85 95

Young participants lose when initial funding ratio is 100% in stead of 130% (pension deal 3)

INITIAL FR: 130%

EXTRA TRANSFERS

INITIAL FR: 100%

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Concluding remarks

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Better pension deals with fair-value ALM

Classical ALM has shortcomings– Inconsistent with market value

• Does not give correct weight to downside• High cash flows can have low present value

– Mostly focused on averages only

Fair-value ALM is easy to understand– Comparing euros in stead of different averages

– Measuring impact of policy changes and initial funding ratio on stakeholders

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Appendix

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Because of Dutch “doorsneepremie” young participants pay too much contribution

0%

5%

10%

15%

20%

25%

30%

25 30 35 40 45 50 55 60 65

leeftijd

prem

ie a

ls p

erce

ntag

e va

n sa

lari

s actuarieel benodigde premie

werkelijk betaalde premie (doorsneepremie)

Source: “Leeftijdsolidariteit in de doorsneepremie”(Boeijen, Jansen, Tamerus, Kortleve)

actuarial required

actually paid (“doorsneepremie”)

age

con

trib

uti

on

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“Doorsneepremie” leads to huge transfers

Participant (salary € 50 000) works between ages 46 and 65

Actuarial required contribution: € 350.000Actually paid contribution: € 290.000

Gain: € 60.000

Participant (salary € 20.000) works between ages 25 and 35

Actuarial required contribution: € 22.000Actually paid contribution: € 36.500

Loss: € 14.500

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Source: “Leeftijdsolidariteit in de doorsneepremie”(Boeijen, Jansen, Tamerus, Kortleve)