Download Niels Kortleve

Better pension deals with
fair-value ALM
UvA, Netspar, AG - 2 november 2006
Niels Kortleve
Better pension deals with fair-value ALM
Classical ALM has shortcomings
1
– Inconsistent with market value
• Does not give correct weight to downside
• High cash flows can have low present value
2
– Mostly focused on averages only
Fair-value ALM is easy to understand
2
2
– Comparing euros in stead of different averages
3
– Measuring impact of policy changes on stakeholders
1
Introduction
Classical ALM inconsistent with market value
Fair-value ALM attaches more weight to downside
3
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
4
–
Scenario of becoming unemployed has high “state price”
–
Scenario of becoming millionaire has low “state price”
Fair-value ALM: more weight to downside
0.00005
10
state price
value (euros)
8
6
4
2
0
0
1
2
3
4
5
6
7
8
time
5
= Equities
9
10
11
12
13
14
15
0.005
Invest € 1 in equities or € 1 in bonds?
What is future value of investment after 15 years?
€ 1 in equities
€ 1 in bonds
5% quantile
€ 1.00
€ 1.52
median
€ 2.67
€ 2.05
95% quantile
€ 7.25
€ 2.85
Which of these two investments do you prefer?
6
State prices reveal what we already knew:
Both investments have same present value
0.00005
10
state price
value (euros)
8
6
4
2
0.005
0
0
1
2
3
4
5
6
7
8
9
time
7
= Equities
= Bonds
10
11
12
13
14
15
Set state prices
scenarios
scenarios
Economic
scenario set
time
Fair-value ALM:
time
Balance sheet
(in euros)
Stakeholder analysis
Cash flows
per scenario
scenarios
Pension deal
Classical ALM:
P(underfunding)
Average indexation
Average contribution
time
2
Example
Classical ALM mostly focused on averages
Fair-value ALM compares euros in stead of different averages
9
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 years
Initial funding ratio: 130% (nominal)
10
Classical ALM results for pension deal 1
Horizon 15 years
11
Ultimo 2005
P(FR < 100%)
12.4%
Average indexation
100%
Average contribution
14%
Verloop
van
de dekkingsgraad
Funding
ratio for
pension
deal 1
Fair-value ALM: more weight to downside
500
450
probability
present value
87.6%
6
12.4%
30
400
350
300
250
200
150
100
50
0
2006
2016
2011
time
12
2021
Balance sheet for pension deal 1
assets
investments
contributions
option deficit
total
13
liabilities
79 pensions
45
30 option surplus
154 total
148
6
154
Policymaker’s control panel: pension deal 1
Average contribution: 14%
Average indexation: 100%
30
100
75
20
50
10
25
0
2006
2011
2016
2021
P(FR < 100%): 12.4%
0
2006
2011
assets
investments
contributions
option deficit
500
450
400
350
300
250
2016
2021
liabilities
79 pensions
45
30 option surplus
148
6
200
150
total
100
154 total
154
50
14
0
2006
2011
2016
2021
deal 2
deal 3
Pension deal 2: contribution ladder
contribution
30%
20%
14%
10%
0%
100%
100%
-10%
15
120% 130%
140%
funding ratio
160%
160%
180%
Pension deal 2: contribution ladder
Lower average but higher present value
30
30
20
20
10
10
0
2006
2011
2016
2021
Classical ALM:
average contribution = 14%
Fair-value ALM:
value of contribution = 45
16
0
2006
2011
2016
2021
Classical ALM:
average contribution = 11.8%
Fair-value ALM:
value of contribution = 51
Policymaker’s control panel: pension deal 2
Average contribution: 11.8%
Average indexation: 100%
30
100
75
20
50
10
25
0
2006
2011
2016
2021
0
2006
2011
2016
2021
P(FR < 100%): 7.7%
assets
investments
contibution
option deficit
500
450
400
350
300
250
liabilities
79 pensions
51
23 option surplus
148
4
200
150
total
100
152 total
152
50
17
0
2006
2011
2016
2021
deal 1
deal 3
Pension deal 3: indexation ladder
indexation
100%
75%
50%
25%
0%
100%
100%
120%
140%
funding ratio
18
160%
160%
180%
Policymaker’s control panel: pension deal 3
Average contribution: 10.7%
Average indexation: 71%
100%
30
75%
20
50%
10
0
2006
25%
2011
2016
2021
0%
2006
2011
2016
2021
P(FR < 100%): 5.9%
assets
investments
contribution
option deficit
500
450
400
350
300
250
liabilities
79 pensions
46
16 option surplus
137
5
200
150
total
100
142 total
142
50
19
0
2006
2011
2016
2021
deal 1
deal 2
Fair-value ALM compares euros in stead of
different averages
20
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
3
Stakeholder analysis
Fair-value ALM measures impact of policy changes on stakeholders
21
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
–
–
–
22
Range of cohorts is 5 years
Our horizon is 15 years
Initial funding ratio: 130% (nominal)
Fair-value generational accounting computes
transfers between cohorts: zero sum game
assets
investments
contributions
option defecit
total
assets
investments
contributions
option defecit
total
liabilities
50
40
10
pensions
90
100 total
10
100
20
8
2
investments
option defecit
total
contributions
option defecit
total
23
option surplus
20
2
22
cohort loses
8
liabilities
20
15
5
pensions
option surplus
40 total
assets
investments
pensions
30 total
assets
contributions
option surplus
liabilities
40
5
45
cohort gains
5
liabilities
10
17
3
pensions
option surplus
30 total
30
3
33
cohort gains
3
Example: pension deal 1
nominal pension
10
contribution
5
0
5
-5
-10
24
>>
15
25
35
45
55
65
75
85
95
Example: pension deal 1
indexation
10
nominal pension
contribution
5
0
5
-5
-10
25
15
25
35
45
55
65
75
85
95
Example: pension deal 1
extra claim
indexation
10
nominal pension
contribution
5
0
5
-5
-10
26
15
25
35
45
55
65
75
85
95
Result: transfers in pension deal 1
5
0
5
-5
27
15
25
35
45
55
65
75
85
95
Young participants lose in pension deal 2
(contribution ladder)
5
5
0
0
5
-5
15
25
35
45
55
65
75
85
5
95
PENSION DEAL 1
15
25
35
0
-1
28
15
25
35
45
55
55
65
PENSION DEAL 2
-5
1
5
45
65
75
EXTRA TRANSFERS
85
95
75
85
95
Retirees lose in pension deal 3
(contribution ladder and indexation ladder)
6
6
4
4
2
2
0
0
-2
5
15
25
35
45
55
65
75
85
95
-2
-4
-6
5
15
-4
PENSION DEAL 1
25
35
2
0
15
25
35
45
55
65
75
-2
-4
29
55
65
PENSION DEAL 3
-6
4
5
45
EXTRA TRANSFERS
85
95
75
85
95
Young participants lose when initial funding
ratio is 100% in stead of 130% (pension deal 3)
6
6
4
4
2
2
0
0
-2
-4
-6
5
15
25
35
45
55
65
75
85
95
-2
5
15
-4
INITIAL FR: 130%
25
35
2
0
15
25
35
45
55
65
75
-2
-4
30
55
65
INITIAL FR: 100%
-6
4
5
45
EXTRA TRANSFERS
85
95
75
85
95
Concluding remarks
31
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
32
Appendix
33
Because of Dutch “doorsneepremie” young
participants pay too much contribution
contribution
premie als percentage van salaris
30%
actuarial
required
actuarieel
benodigde
premie
25%
20%
werkelijk
betaalde
actually
paidpremie
(doorsneepremie)
(“doorsneepremie”)
15%
10%
5%
0%
25
30
35
40
45
50
55
leeftijd
34
Source: “Leeftijdsolidariteit in de doorsneepremie”
(Boeijen, Jansen, Tamerus, Kortleve)
60
65
age
“Doorsneepremie” leads to huge transfers
Participant (salary € 50 000) works between ages 46 and 65
Actuarial required contribution:
Actually paid contribution:
€ 350.000
€ 290.000
Gain:
€ 60.000
Participant (salary € 20.000) works between ages 25 and 35
Actuarial required contribution:
Actually paid contribution:
€ 22.000
€ 36.500
Loss:
€ 14.500
<<
35
Source: “Leeftijdsolidariteit in de doorsneepremie”
(Boeijen, Jansen, Tamerus, Kortleve)