Longevity risk in future Dutch pension
schemes
W.J.P. (Wessel) Schouten
Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam
Faculty of Economics and Business Amsterdam School of Economics
Author: W.J.P. Schouten
Student nr: 10363300
Email: wessel schouten@hotmail.com
Date: December 15, 2017
Supervisor: Supervisor:
Dr. S. (Servaas) van Bilsen Drs. M.J. (Martin) Jonk AAG
Second reader:
the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Longevity risk in future Dutch pension schemes — W.J.P. Schouten iii
Abstract
In this research, a very topical subject is highlighted, namely longevity risk in a future Dutch pension scheme. This pension scheme (variant IV-C-R of the SER report) has an individual pension capital, which is invest via a life cycle. The pension scheme does not have a buffer itself with all the participants for longevity risk. In this thesis we look at sharing this risk via an exchange contract between the participants.
This thesis looks at the possibility of hedging the macro longevity risk of the retirees with the active population. The retirees will pay a risk premium to the actives, so their pension payment will not vary over time from the longevity risk. The actives have more upwards and downwards risk in there pension capital, which they can takeover.
Based on this thesis, the impact and importance of the longevity risk (especially macro longevity risk) is made clear for the new pension scheme. It also contains some suggestions for pension communication and further research on this subject.
Keywords Li-Lee, Kannist¨o, Mortality model, Longevity risk, Mortality risk, Future pension scheme, Variant IV-C-R, Risk sharing, Risk premium, Pension Funds, Life expectancy, Life cycles, Micro longevity risk, Macro longevity risk, Investment risk, Pension communication, UPO, PPR
Preface vi
1 Introduction 1
2 The Dutch pension system 3
2.1 Current pension schemes . . . 3
2.1.1 First pillar . . . 3
2.1.2 Second pillar . . . 4
2.1.3 Third pillar . . . 5
2.2 Future pension schemes . . . 5
2.2.1 Variant IV-C-R . . . 6 3 Methodology 7 3.1 Mortality table . . . 7 3.1.1 Data . . . 7 3.1.2 Assumptions . . . 7 3.1.3 Definition . . . 7 3.1.4 Dynamic model. . . 8
3.1.5 Closure of the mortality table . . . 8
3.1.6 Impact on the life expectancy . . . 9
3.2 New pension scheme . . . 9
3.2.1 Assumptions . . . 9
3.2.2 Simulation . . . 10
3.2.3 Model . . . 10
4 Calculations on the longevity risk in future pension scheme 13 4.1 Number of simulations . . . 13
4.2 Results of the macro longevity risk . . . 13
5 Premium for longevity risk hedge 17 5.1 Calculations on the risk premium . . . 17
5.2 Results. . . 18
6 Communication 23 6.1 Pension awareness . . . 23
6.1.1 Misunderstanding about pension . . . 23
6.1.2 Trust of participants in current pension sector . . . 24
6.2 Pension communication . . . 25
6.3 How to present the new pension scheme to the participants . . . 25
6.3.1 Chances . . . 25
6.3.2 Risks. . . 26
6.3.3 New UPO . . . 26 iv
Longevity risk in future Dutch pension schemes — W.J.P. Schouten v
7 Conclusion and recommendations 28
7.1 Conclusion of the results . . . 28
7.2 Recommendations for further research . . . 29
A Tables & Graphs 30
A.1 Assumed variables mortality table . . . 30
A.2 Assumed variables of the new pension scheme . . . 32
In the Preface, I would like to seize the opportunity to explain my choice for the subject of this research. Also, I would like to thank my supervisors.
The pension sector has struggled with big problems since the crisis. The current pension schemes are not payable anymore and we need to go to a new pension scheme. Also the ”doorsneepremie systemathiek” does not fit the dutch population anymore, where nowadays there are a lot of retirees. The pension sector need to be more transparent and the feeling that pension is far away need to be vanished. People can earn and save a lot money from this working condition without even knowing it.
The new pension scheme will bring some risk with it, one of them is still the longevity risk. Which is increasing due to the increasing life expectancy. Because of the importance of the future Dutch pension scheme, I decided to carry out a study on this matter.
I would like to thank my supervisors for helping me bring my thesis to a successful conclusion. I wrote my thesis in collaboration with Willis Towers Watson. My supervisor at Willis Towers Watson, really pleased me. My supervisor Martin Jonk has a lot of theoretical and practical knowledge on this subject, so I barely got stuck with the calculations on the new pension scheme. At the University of Amsterdam, Servaas van Bilsen was my supervisor. He helped me with technical points on sharing the longevity risk, but also on ways to present the research in this thesis. I really appreciated his feedback and meetings we had during my research.
Wessel Schouten Amsterdam, 2017
Chapter 1
Introduction
Life expectancy of the Dutch population is increasing. There are more older people as percentage of the population than before as shown in the graph below, which is retrieved from data of the Dutch Bureau of Statistics (CBS).
Figure 1.1: distribution of the dutch population
In calculating the contribution to the pension plan, the mortality tables are used. If pensioners turn out to live longer than was expected based on those mortality tables, the pension fund will have to pay out benefits longer than accounted for in calculating the contributions. The risk of the pay out period being longer than expected, is called longevity risk.
The liabilities of pension funds will increase, so the solvency (ratio) will decrease since it does not affect the assets. Up until now, the increase in liabilities is not paid for directly. It is paid from existing assets which weakens the funding ratio.
The longevity risk consists of two elements, the so called micro- and macro longevity risk. In some literature longevity risk is defined as macro longevity risk and mortality risk is defined as micro longevity risk, in this thesis the longevity risk is the two risk together. The micro longevity risk is coincidence and appears when the population of the pension funds is not large enough to follow the mortality chances. The difference between the expected mortality and the real mortality life for a large (so there is no micro longevity risk) pension fund is called the macro longevity risk. So when the mor-tality chances increase for the whole population due to for example better health care or more safety. These risks together are the difference between the expected mortality and
the mortality that occurs in every pension fund. These risks can be hedged, but to give a good overview of the macro longevity risk, the micro longevity risk is eliminated in chapter four. The hedge for the macro longevity risk contains the risk that the assumed mortality table is not the reality. The risk can be mapped by using various scenarios. Chapter four contains an analyses of the macro longevity risk and chapter five describes ways to hedge this risk.
In the paper of De Crom et al. (2011), several options to hedge against longevity already exist. Among these:
• a swap, where the pension fund’s payment(s) are fixed and the insurer’s pay-ment(s) depend on the actual mortality data;
• a buy-in, where all or partly the pension fund’s liabilities are hedged by buying annuities (that replicates the liabilities) with an insurer;
• a buy-out, where the insurer take over all the fund’s liabilities;
• a survivor bond. The payoff from a survivor bond is the same as with a longevity swap. The difference between the two is that a survivor bond has more counterpart risk. A longevity swap exchanges only the differences and not the underlying risk, where a survivor bond does.
Also, Bauer et al. (2009) mentioned a longevity option.
What we currently see at insurance companies and pension funds in the Netherlands is a natural hedge against longevity instead of the hedging options mentioned above. This means that an insurer who is exposed to longevity (due to annuities in its portfolio) has death benefits in its portfolio, too. That way the insurer is exposed to the risk of people living longer than expected (which is of importance in pension products) and the risk of people living shorter than expected (which is of importance in life insurance products).
This thesis contains research on a new way of hedging the longevity risk of the re-tirees. Because of the new individual pension scheme, it may be preferable for retirees to hedge the longevity risk with the active population by paying a risk premium. Whereby the following questions raises and are researched in this thesis.
• What is the impact of changing the mortality tables (longevity risk) on pension payments (for different ages)?
• Can the longevity risk of the retirees in variant IV-C-R (an individual pension scheme) be hedged by the active participants?
• What is the risk premium that the retirees must pay to the active participants to hedge their longevity risk?
• Is it necessary to share the longevity risk in the future pension schemes between all the generations?
• What are the pros and cons of hedging longevity risk?
Chapter 2
The Dutch pension system
The Netherlands is known as a country with a great pension system. This follows for example from the Melbourne Mercer Global Pension Index (2nd place) or from the Pensions Sustainability Index published by Allianz (4th place). According to the Global Assets Pension Study 2017 from Willis Towers Watson the Netherlands has a total pension assets of USD 1,296 billion, this is 168% of their gross domestic product. The Dutch pension system knows its origins from the late 19th century. Halfway the 20th century, the AOW was introduced to give everybody a fixed basic state pension.
Figure 2.1: the pillars in the Dutch pension system
2.1
Current pension schemes
2.1.1 First pillar
The fixed basic income is part of the first pillar of the Dutch pension system. The first pillar includes state regulations that provide for an income for people older than their state pension age or after decease. In the act increasing state pension age and pension directive age of July 2012, the government has linked the state pension age to the pension directive age. This is specified in the act of speeding up the step-by-step increase of the state pension age of June 2015. The results of these laws are shown in the figure below. Because of consistency matters, in this figure the deterministic mortality table of the ”Actuarieel Genootschap” (see chapter three) is used, where as the law prescribes that this must be the CBS mortality table.
Figure 2.2: the development of the state pension age Two forms of old age provisions are involved:
• General Old Age Pensions Act (AOW). This statutory social security (state) old age pension provides all residents of the Netherlands older than their state pension age with a flat-rate pension benefit that in principle guarantees 70 percent of the net minimum wage;
• Surviving Dependants Act (ANW). A surviving dependants pension is a flat-rate benefit payable to the surviving partner after the other partner passes away and after the decease of parents.
The AOW benefit is a fixed amount which is based on the net statutory minimum wage. The level of the benefit does not depend on any former income or on contributions paid in the past. People that lived in the Netherlands during the period before their retirement are insured, the persons who have never paid contributions are also entitled to an AOW benefit when they reach their state pension age. The flat-rate AOW benefit depends on the domestic situation of the retiree. It also depends on the marital status, the benefit is different for single people, single parents and married couples. Via the pay-as-you-go system in the first pillar, the AOW is financed by contributions calculated over every insured with a salary (of at least the minimum required) and is limited to a maximum of 17.9 (plus ANW 0.1 percent in 2017) percent. Once this contribution is no longer adequate to cover costs as a result of the ageing population, the deficit will be met from the public funds. All taxpayers contribute to this system, including retirees who do not pay any AOW contribution. The tax authorities collect the AOW contributions through income tax. The administrative body for the AOW is the Social Insurance Bank (SVB).
2.1.2 Second pillar
The second pillar is an additional arrangement and consists of collective pension schemes. Almost every employee can claim a pension through the second pillar, which is financed by capital funding. The capital consist of premiums, contributions paid in the past and returns on the investment over the build up contributions. The yearly pension premium is paid by the employee together with the employer. This labor-based pension is addi-tional to the AOW, and so adds to it. Besides an old-age pension, most pension plans provide benefits for surviving relatives. Sometimes, it includes a right to benefits for inability to work. The Dutch state encourages saving for a pension, by not taxing the contributions, the so-called pension claim. However, the final pension payment is liable to tax. This is a deferred taxation rule called ”omkeerregel”. The fiscal legislation re-quires that the right to AOW is taken into account for determining the pension amount. The pension fund or insurance company mostly have a third party to administrate these pension schemes. The Dutch law prescribes that the company and pension fund must
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 5
be strictly separated, which means pension funds are legally and financially indepen-dent from the companies. Most of the pension assets as mentioned in the beginning of this chapter are managed by pension funds. In the Netherlands there are three different types of pension funds:
• Industry-wide pension funds (for a whole sector, such as the metal industry, gov-ernment, retail sector),
• Corporate pension funds (for a single company or a corporation),
• Pension funds for independent professionals such as architects and dentists. Pension funds are non-profit organizations. The pension funds will therefore not be directly affected if a company gets into financial difficulties. The capital is divested by company and can only flow back under very strict conditions.
2.1.3 Third pillar
The third pillar is formed by individual pension products and is voluntarily. These are mainly used by the self-employed and employees in sectors without a collective pension scheme. Anyone can increase his pension till the desired amount. They can for example save, invest or buy an annuity in this pillar, where this often takes advantage of tax benefits.
2.2
Future pension schemes
The pension schemes (second pillar) must adjust to the demographic, economic and social developments. Especially after the crisis, when the investment returns have been disappointing (currently recovered), interest rates are low (which results in higher pen-sion liabilities) and the life expectancy is increasing (which results in an increase of the pensionable age). There has been a lot of research in developing a new pension system. The new improved premium act ”Wet verbeterde premieregeling” made it pos-sible for a participant to keep investing their pension capital after retirement. The ”Sociaal-Economische Raad” (SER) researched on behalf of the cabinet, the design of the additional pension to strengthen the current pension scheme. The time line of this development is shown below.
Figure 2.3: time line of decisions to a new pension system including the new improved premium act
The SER came up with four variants for a new pension system, where collectivity, risk sharing (also between generations) and accrual of pension played a central role. Cur-rently two variants remain and are more detailed elaborated, where the main difference is the benefit (1) versus contribution (4) scheme (shown in table below).
Figure 2.4: the analysed variants of the SER
As mentioned by Heemskerk et al. (2017) a PPR (personal pension account (with risk sharing)) summarizes variant IV-A, B and C. Heemskerk et al. (2016) says that the core of the proposal of a PPR is to separate different functions of a pension contract (save money for later, invest, partner pension, sharing longevity risk), to make clear which risks are for the individual, and which risks are hedged by the financial markets/the col-lective. This thesis contains only an analyses of variant IV-C-R, because this individual variant does not have a buffer itself with all the participants for longevity risk. In this thesis we look at sharing this risk via an exchange contract between the participants.
2.2.1 Variant IV-C-R
The age independent premium IV-C-R goes to an individual pension capital, which is invested via a life cycle. The pension capitals are combined with a collective buffer for sharing the investment shocks. The buffer is maximized and the surpluses above are added to the pension capital of the participants. By law, the positive or negative shocks of the investment result can be spread out over a period of 5 years. But the Senate proposed to extend this period to 10 years. Negative investment return does not lead directly to a pension cut, because it can be spread out over a longer period. Also the pension cuts are on average smaller in size, but the benefit of spreading out the shocks seems to be limited, there is less indexation on short term. Spreading out the negative investment returns leads also to an extra risk. The shifting of the negative investment on short term can result in a bigger deficit on long term. Also on short term the chance of indexation is smaller with spreading out the investment shocks. The financial report of the SER (2015) shows that after transition to this new pension system the retirees are worse off. The middle agers are also going backwards mainly from abolishment of the premium ”doorsneepremie”, they paid to much premium when they were young and cannot profit from it at old age. Whereas the new pension system is preferable for the younger people. A final question from the report is if the double transition (abolishment of average premium and new pension scheme) gives enough compensation for the abolishment of the average premium itself.
Chapter 3
Methodology
This chapter contains in the first section the model for calculations on the mortality table. The second section describes the model for the new pension scheme. The chapter ends with insights on the longevity risk, where the premium for hedging is calculated in chapter five.
3.1
Mortality table
This section elaborates on the mortality model of the Koninklijk Actuarieel Genootschap that is used in this thesis, describes the fitting procedure and shows the results.
3.1.1 Data
The mortality data is based on the Dutch population, but also on other European countries with a Gross domestic product (GDP) above the average. Because of the positive correlation between the welfare and the life expectancy, the GDP is a good measurement for the other countries of the mortality data. The data covers the period 1970 till 2014 for Europe countries, for the Netherlands it is till 2015. The data comes from the Human Mortality Database completed with data from Eurostat. The dutch data for 2015 is from Dutch Bureau of Statistics (CBS). The total set includes 100 million deaths. From this data, the Koninklijk Actuarieel Genootschap has calculated the parameters (Appendix A) that are used in the models.
3.1.2 Assumptions
The following assumptions are made for the model for calculation of the mortality tables. The data contains the Europe and Dutch mortality, based on the GDP of the country. For ages till 90 the Li-Lee model is used and for extrapolation of the higher ages the model of Kannist¨o is used. There is only public data used. The correlation between Europe and the Netherlands as well as the correlation between man and woman are taken into count in calculating the mortality tables.
3.1.3 Definition
The mortality table gives for each gender for the ages x ∈ X = {0,1,2,...,120} and years t ∈ T ≥ 2016 the best estimate for probability of dying in one year. The hazard rate µx(t) from Promislow (2014) is used in this model:
qx(t) = 1 − exp(− 1 Z 0 µx+s(t + s)ds) = 1 − exp(−µx(t)) (3.1) 7
3.1.4 Dynamic model
For the ages till 90 years, x ∈ ˆX = {0,1,2,...,90}, the Li-Lee model is used for both genders (superscript g). Where M stands for a male and V for a female. Whereby the assumed variables are shown in Appendix A.1.
ln(µgx(t)) = ln(µg,EUx (t)) + ln(µg,N Lx (t)) (3.2)
ln(µg,EUx (t)) = Agx+ BxgKtg (3.3)
ln(µg,N Lx (t)) = αgx+ βxgκgt (3.4)
The Ktgis calculated by a random walk with drift. And the κgt is a first order autoregres-sive model without a constant. Which means that in expectation the Dutch mortality development follows the Europe trend. The assumed variables are shown in Appendix A.1.
Ktg = Kt−1g + θg+ 1stochasticgt (3.5)
κgt = agκgt−1+ 1stochasticδgt (3.6)
Where the one is a dummy variable, which is one if the model is stochastic and 0 for the deterministic variant.
Time series simulation
If the dummy as described before is one, the normal distribution is used to simulate the time series Zt = (Mt , δtM, Vt , δtV). It has mean zero and covariance C. Zt can be
calculated by Zt= ˜ZtH with HTH = C, where ˜Ztis a row vector with four independent
standard normal distributions. The assumed variables are shown in Appendix A.1.
3.1.5 Closure of the mortality table
For ages above 90 years x ∈ ˜X = {90, 91, ..., 120}, the method of closure of Kannist¨o is used (for ages over 120, the mortality rate is equal to the mortality rate for 120). This method is based on a logistic regression of the table for the ages y ∈ {80, 81, ..., 90}.
µx(t) = L( n X k=1 wk(x)L−1(µyk(t))) (3.7) With L(x) = 1 1 + exp(−x), L −1 (x) = − ln(1 x − 1) (3.8)
The weights for the regression are given by:
wk(x) = 1 n+ (yk− ¯y)(x − ¯y) Pk j=1(yj − ¯y)2 = 1 11 + (yk− 85)(x − 85) 110 (3.9)
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 9
3.1.6 Impact on the life expectancy
The results from the scenarios sets are 1000 different mortality tables. The development of the life expectancy for a man and woman who are born in the year the mortality table starts, are shown in the figures below. The life expectancy is calculated by the following formula of Promislow (2014):
ex = ∞
X
t=0
kpx (3.10)
Which results in terms (because of sloping through mortality table) of this thesis in the following formula. eg0,i= 120 X t=0 t Y j=0 (1 − qgj,i+j) (3.11)
Where i is the start year of the mortality table and year of birth. It shows that the life expectancy increases in the future for both genders and that women have a higher life expectancy than men. Furthermore the development of life expectancy is less volatile for women, whereas the lines in the graph for men are wider spread.
Figure 3.1: Life expectancy of a man (left) and a woman (right)
3.2
New pension scheme
This section describes the calculations that are performed in this thesis. In the calcula-tions, we make use of the present value of future pension benefits. Therefore, we need to establish a method to calculate this present value. The first subsection discusses the data and the assumptions that we use in this thesis. The next subsection mentions the factors that are used to calculate this present value and how these factors are calculated. It also provides the longevity risk structure.
3.2.1 Assumptions
The assumptions that are made in this thesis are as followed. Only old age pension is taken into account, there is no partner pension. The pension payments are made in the beginning of the year. The simulations are done end of the year. The rate of return is equal to the risk free rate, which is 1%. The premium paid by the participants follows the table of the Appendix. The full time salary is constant for all the participants and equal to 37000. The franchise is 14050. The population exists of 5000 men and 5000 women, so equally divided pension offset and are normally distributed over the ages. There are no leavers (besides death) or entrants. The start distribution of participants and capital is formed from one participant age 15. The participant survives every year and the actuarial factors are based on the expected mortality table. A graph of this distribution is shown in the Appendix A.2 (figure A.4).
3.2.2 Simulation
The model in the next subsection to construct the pension scheme of variant IV-C-R uses a couple definitions. kG
t,i is the number of participants in year t for age i and gender
G (M is male, V is female). The range of t is from 0 to 50, coming from the boundaries of the mortality table. The number of participants (2n) is determined in section one of the next chapter. The participants are standard normally distributed for the first year.
kG1 ∼ n · N (0, 1) (3.12)
kt,i= kt,iM + kt,iV (3.13)
Afterwards they will survive following a Bernoulli drawing with their survival chance as expected value (so the age cohort follows a binomial distribution), this will vary (taking other scenarios) over the runs of the model.
kt+1,i+1∼ Bin(kt,i, pt,i) (3.14)
Where the survival chances pt,i (for a male px,t,i and female py,t,i) are gender neutral
based on the start distribution of the pension fund. %male = k
M 1 W1
k1W1
(3.15) pt,i = %male · px,t,i+ (1 − %male) · py,t,i (3.16)
It will be mentioned if there is a change (as described below) in the expected value of the Bernoulli drawing in formula 3.14. The model of the next subsection is in all the run based on deterministic mortality table. Only the Bernoulli drawing depends on the 1000 simulations, because this is the real mortality of the fund.
• In the first run to determine the micro longevity risk, the survival chances of the deterministic table are used as described in section one of this chapter.
• In the second run to determine the macro longevity risk, all the 1000 mortality tables are used, the mortality chances are the expected value of the Bernoulli drawing.
3.2.3 Model
In the model µ is the return on the investment portfolio. r is the risk-free rate. PG is the pensionable salary for an individual. So the salary minus the franchise as described in the assumptions. P remiumi is the premium % for age i of an individual, the table
for P remiumi is shown in Appendix A.2 (table A.4). The premium paid equals:
Si= P G · P remiumi (3.17)
The model calculates the pension capitals (Wt,i) for every age at any time. Followed
from the assumptions, the total pension capital can be calculated by multiplying the individual pension capital with the number of participants in that state. There is a biometric return (based on expected mortality) included in the calculations for the pension capital. The biometric return θt,i from Bovenberg et al. (2014) is of the following
form, where the mortality rates are always from the deterministic mortality table. θt,i =
Wt,iqt,i
pt,i
(3.18) A participants can get a pension benefit each year after retirement. But because of the life cycle, the participants still invests every year after his retirement. So the cash flow
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 11
depends on the return of the investment portfolio, this is the reason that this cash flow needs to be calculated every year. The discount factor and the actuarial factor from Promislow (2014) for this old age pension is as followed, where the chances are always from the deterministic mortality table:
vm= 1 1 + r m (3.19) ¨ at,i = ∞ X m=0 vmmpt,i (3.20)
At the end of the year the actual mortality result (Macro and Micro) is calculated based on the paper of Bovenberg et al. (2014), which is a percentage of the total capital in their group. The actual mortality is determined by the release of pension capital:
βtA=
67
X
i=0
(kt−1,i−1− kt,i)Wt,i (3.21)
βtR=
121
X
i=68
(kt−1,i−1− kt,i)Wt,i (3.22)
And used to compare the real release of pension capital β with the expected from the biometric return θ. There is made a distinction between actives and retirees, because the release of pension capital is based on status. Where the superscript ”A” stands for the active population and ”R” for the retirees. The first run of the model uses the deterministic mortality table for the simulation of the participants as well as the calculation of the model. The difference in release of capital (formula 3.23 and 3.24), the mortality result, is called the micro longevity risk (in the formula M icroAt or M icroRt). This is caused by the size of the population in the fund.
M icroAt = β
A t −
P67
i=0kt,iθt,i
P67
i=0kt,iWt,i
(3.23)
M icroRt = β
R t −
P121
i=68kt,iθt,i
P121
i=68kt,iWt,i
(3.24) The individual pension capital is calculated based on the paper of Bovenberg et al. (2014). The individuals start with zero capital at age 14. And start paying a premium the year after.
Wstart,0:14= 0 (3.25)
Before pensionable age the pension capital is calculated as followed. The mortality result is assigned at the beginning of the year, the same applies to the premium paid. Then there is a biometric and risk-free interest return over the capital described above.
Wt+1,i+1= (Wt,i(1 + M icroAt ) + Si)(1 + θt,i)(1 + µ) (3.26)
After pensionable age the pension capital is calculated almost the same, but now there is a pension payment purchased, which is calculated by the formula below. The principal of actuarial fairness is used, the pension benefit is calculated at pensionable age, where the coming service of the future pension benefits is equal to the accrued capital. Next year the pension benefit will be recalculated with the capital at t + 1 (so with the capital of formula 3.28).
Instead of a premium payment, there is a reduction from a pension payment. The capital is invest, so the return is r instead of the risk-free rate µ (in this thesis µ and r are equal).
Wt+1,i+1= (Wt,i(1 + M icroRt) − ct,i)(1 + θt,i)(1 + r) (3.28)
To give a good view of the macro longevity risk, the micro longevity risk is subtract from the mortality results in the second run. All the mortality tables (h as described below formula 3.31 is from 1 to 1000) from section one are used in the simulation of the second run to calculate the macro longevity risk. The risk that the real mortality table differs from the expected mortality table (deterministic).
M acroAt = β
A t −
P67
i=0kt,iθt,i
P67
i=0kt,iWt,i
− M icroAt (3.29)
M acroRt = β
R t −
P121
i=68kt,iθt,i
P121
i=68kt,iWt,i
− M icroRt (3.30)
In the second run, the model described in this section is calculated. In formula 3.26 and 3.28, the M icro variable is replaced by the M acro variable. Which effects the result of the accrued capital W from the fact that now 1000 mortality tables are used to calculate the variable M acro instead of only the deterministic for the M icro variable.
For calculations on the risk premium, the M acrot must be saved in a matrix for
every simulation. We therefore define the following matrix.
M (h) = M acroR(h) (3.31)
Where h is the simulation that is used (from 1 to 1000). So M acroR(1) is a row vector which contains for every t the M acroRt of the first simulation, that uses mortality table 1. Results on the two runs described above are showed in the next chapter.
Chapter 4
Calculations on the longevity risk
in future pension scheme
This chapter contains an overview of the macro longevity risk. At first the amount of simulations is established to subtract the micro longevity risk. After which the macro longevity risk is calculated by looking at the deviation of expected stochastic mortality chances from the mortality tables and the realized (simulated) fund mortality.
4.1
Number of simulations
With the speed of convergence the number of simulations can be determined. The mor-tality result is calculated for various numbers of simulations, which is shown in table 4.1 & 4.2. The difference between the (expected) mortality table and the simulated (real) mortality is calculated. For this micro longevity risk, the expected mortality result (so the longevity risk) must be zero and have a small standard deviation. Otherwise there is still a big impact from the size of the fund. If the size is small, the simulated (real) mortality deviates from the (expected) mortality tables chances. From the tables below we can conclude that if we simulate a fund that has at least 10000 participants, the mi-cro longevity risk will vanish. The small result will be subtract to give a good overview of the macro longevity risk in the next subsection.
Table 4.1: mortality result actives
Participants Minimum Maximum Mean Standard deviation
100 -0.1618 0.0088 -0.0015 0.0129
1000 -0.0063 0.0053 0.0000 0.0011
10000 -0.0028 0.0047 0.0000 0.0006
Table 4.2: mortality result retirees
Participants Minimum Maximum Mean Standard deviation
100 -0.0255 0.0106 -0.0005 0.0041
1000 -0.0093 0.0064 -0.0001 0.0016
10000 -0.0032 0.0017 0.0000 0.0005
4.2
Results of the macro longevity risk
The macro longevity risk is different for every year and simulation. It is calculated the same as above, but now not only for the expected mortality table, but for all the 1000 mortality tables from the first section of chapter 3. Again the mortality risk is the difference between the simulated (real) mortality and the (expected) mortality tables
chances, but now without the micro longevity risk. The risk premium for this example can be calculated from formula 5.2 of the next chapter. An overview of the statistics of the macro longevity risk will therefore also be taken over all the years and simulations. The tables below show the risk for actives and retirees as percentage of the total capital of the group. The risk is significant, meaning in worst case it is a cut of 1.9% a year for the retirees of their pension capital. But on average it is positive, so the retirees profit from the fact that others die earlier than expect. It also shows that the retirees are more sensitive than the actives for the macro longevity risk. This can be explained by the fact that their mortality chances are higher, so a surviver requires more capital than was expected by the mortality table.
Table 4.3: mortality result actives
Minimum Maximum Mean Standard deviation
Macro longevity risk -0.0043 0.0171 0.0000 0.0006
Table 4.4: mortality result retirees
Minimum Maximum Mean Standard deviation
Macro longevity risk -0.0113 0.0185 0.0000 0.0016
The accrued pension capitals and pension payments are shown below for all the scenar-ios. The development of the pension capital is based on a 15 year old gender neutral. For the pension payments the cash flow of a 67 year old gender neutral is taken into account.
Figure 4.1: pension capital before risk premium collection due to fluctuations in mor-tality (no investment risk)
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 15
Table 4.5: statistics pension capital
Year Minimum Maximum Mean Standard deviation
1 1599 1599 1599 0 10 19886 20004 19946 19 20 45763 46360 46065 98 30 82836 84689 83561 282 40 135922 139845 137567 643 50 214699 225968 218664 1558
The figure and table show that the pension capital does not fluctuate much over time. Active people have a low mortality chance, so this will not vary much over the scenarios. They can take some risks from the retirees to get a higher pension capital at age of retirement. The active population are more willing to take some risk to get a higher pension. If the returns are bad, they still can easily influence their pension accrual, because they still have a salary.
Figure 4.2: pension payments before risk premium payment
Table 4.6: Statistics pension payment
Year Minimum Maximum Mean Standard deviation
1 12217 12217 12217 0
10 11712 12705 12230 158
20 11058 13734 12215 423
30 10373 15352 12351 792
It shows that the pension payments fluctuate over the years, which is caused from the mortality result. This is not preferable for retirees, they mostly want a constant or in-creasing with inflation cash flow over the years. Retirees pay a fixed percentage of their pension capital as risk premium every year in the next chapter to provide a decreasing (or increasing, depends on the risk premium) fixed pension payment. The active popu-lation will take over the macro longevity risk from the retirees.
The total fund capital (actives and retirees) develops as showed below for each sce-nario. The lines are decreasing, because we have a pension fund without accession and retirees buy an annuity with their pension capital. There will be no entrance of new participants and the individuals of the pension fund can die. As we saw before the most risk is after pensionable age. After sharing the macro longevity risk (next chapter), the actives will get more risk in their accrued pension capital. So the volatility in the total pension capital will increase over the years compared with the current situation, they will effect the future years more than retirees.
Figure 4.3: total pension capital before risk premium collection due to fluctuations in mortality (no investment risk)
Chapter 5
Premium for longevity risk hedge
5.1
Calculations on the risk premium
After subtraction of the micro longevity risk which is calculated in the previous chapter, the macro longevity risk premium can be calculated. This is done for every year t in the future, by repeating the two runs of chapter three. Where the model is still deterministic and the Bernoulli simulation is based on the stochastic scenarios, h is from 1 to 1000. This means the runs are almost the same as before, but now with risk sharing (formula 5.3 & 5.5), so there is a risk premium. The risk premium (RP) in formula 5.1 (where year t is the column of matrix M ) is not constant over the years, which means that the future cash flows are also not constant for the retirees. The premium in 5.2 is constant, which is more preferable from perspective of the retirees, because their cash flow will be constant over the years. There are more risk principles than the two based on the book of Kaas et al. (2008) and noted below, but those are not part of this thesis.
RPt= E[Mt] +
1
2V ar[Mt] (5.1)
RP = E[M ] + 1
2V ar[M ] (5.2)
From the example in the previous chapter we get from formula 5.2 a risk premium of approximately 0.02% each year of their pension capital.
Then we run a new model to see the impact of the risk premium on the cash flows of retirees and capital of the actives. The new model has two different equations compared to the model described in chapter 3.2.3.
Before pensionable age:
Wt+1,i+1= (Wt,i(1 + M acroAt,i+ M acroRt,i) + Si+
RPP121
i=68Wt,i
P67
i=0kt,iWt,i
)(1 + θt,i)(1 + µ)
(5.3) After pensionable age:
Wt+1,i+1= ct+1,i+1· ¨at+1,i+1 (5.4)
Wt+1,i+1= (Wt,i(1 − RP ) − ct,i)(1 + θt,i)(1 + r) (5.5)
This leads to a decreasing cash flow for the retirees, because of the subtraction of the premium. The end of this chapter contains some other perspectives to make this pension payment constant over time. The results show that the actives get more capital before the pensionable age.
5.2
Results
To compare the model with risk sharing with the example of the previous chapter, we look at the following graph and table. These are also shown for the model without risk sharing in chapter four (figure 4.1 & table 4.5)
Figure 5.1: pension capital after taking the macro longevity risk of the retirees
Table 5.1: statistics pension capital
Year Minimum Maximum Mean Standard deviation
1 1599 1606 1603 2 10 19355 20516 19900 166 20 43027 49547 46058 930 30 74941 95248 83832 2810 40 116560 168661 138677 6633 50 174276 298642 223728 14222
The graph and table above show that there is now more risk in the accrued pension capital. This comes from the macro longevity risk of the retirees that the actives have taken over. The pension capital can be higher, but also lower on the retirement age then without sharing the macro longevity risk. For the first 20 years, the accrued pen-sion capital is almost the same as without macro longevity risk sharing. However the uncertainty (standard deviation) is higher in the model with risk sharing. This means the maximum pension capital will increase, also the minimum will decrease compared with the situation before. The average pension capital of the later years is higher in this model, whereby the standard devision is much larger than before. Actives want to take some extra risks to get a higher pension capital, because they still can influence
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 19
the capital when they are in a bad scenario. This also means that young individuals have a longer term to restore any adverse shocks on the financial market with their human capital (Bodie, Merton & Samuelson, 1991). Risky investments should therefore be attractive to young households as mentioned in the thesis of Hereijgers (2013).
The distribution of the pension capital at pensionable age is determined as followed. Originally the mortality tables are normally distributed and the number of scenarios is large enough to expect a normal distribution. The first graph below shows the expected values from the normal distribution versus the values of the data. The second graph shows, the distribution of the data against a normal distribution. The skewness γ1 =
E[(X−µ)σ 3] = 0.495, which confirms the arguments before. The Jarque-B`era value is
n−k+1 6 (γ
2 1+
γ22
4 ) = 78.68, where the kurtosis is γ2 =
E[(X−µ)4]
E[(X−µ)2]2 = 0.952. The test is
Chi-squared distributed with two degrees of freedom. This gives a p-value of 0.006 and rejects the H0 (start hypothesis), which says the data is normally distributed. The cumulative
distribution function is FX(x) = Φ(x−µσ ), so the 2.5% worst scenarios is approximately
195852, which is less but not bad compared with the pension capital where the macro longevity was not shared.
The same comparison (figure 4.2 & table 4.6) as for the actives can be made for the retirees with the following figure (scale is kept almost the same) and table.
Figure 5.3: pension payments after risk premium payment
Table 5.2: statistics pension payment
Year Minimum Maximum Mean Standard deviation
1 12217 12217 12217 0
10 12201 12201 12201 0
20 12184 12184 12184 0
30 12165 12165 12165 0
40 12139 12139 12139 0
Now the retirees have almost a constant pension payment. They know at retirement age what their pension payments are, from the fact that the standard deviation equals zero for all the years. The decreasing line comes from the premium payment to the active population. A remark by this figures is that in this thesis the investment return is as-sumed constant and equal to the risk free rate. When life cycles are taken into count, retirees will have fluctuations in their pension payment. This comes from the investment return, which is not constant over the years and will be most of the times different from the risk free rate. If the actuarial factors take the risk premium into account, retirees can still have a constant payment stream. It is also possible to subtract the total risk premium at the beginning of retirement, because it is a fixed percentage. This will make the pension payment constant over time as well.
The total pension capital develops as showed below. Where we see an increase in volatil-ity of the total pension capital, which is mentioned in the chapter before. The fluctuation
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 21
in accrued pension capital for the actives will also effect their situation when they retire and with the current pension fund (no accession) the retires are important in the later years. This means that the risk of the pension funds increases, which is not preferable.
Figure 5.4: total pension capital after taking the macro longevity risk of the retirees Again to make clear what the difference is between the model with and without risk sharing, we can look at the total capital for the actives and retirees in a single scenario. The development for both models are shown below.
Figure 5.5: Development of the total capital for actives and retirees for both models We see that the retirees are better of in the first years of the model without risk sharing. In this scenario the macro longevity risk of the retirees was positive for the first years. After paying a risk premium, the actives take over this risk. Because of the take over of this positive risk and the intake of the risk premium, the actives are better of in the model with risk sharing. In the later years the pension capital of the retirees restores and grows above the model without risk sharing. The positive advantage of the actives flows away, because of this development, they often take over negative macro longevity
risk of the retirees. The lines are mostly decreasing because actives reach their age of retirement (a lot of actives retire in the first years) and retirees buy their pension payment with their pension capital. So in short, they both are a little better in the model with risk sharing for this scenario. We see that the pension capital is less volatile for the retirees after risk sharing and the actives can profit from taking over the risk. A remark hereby is that it can also be a opposite scenario, where actives take over a negative risk of the retirees. Their total pension capital will decrease in such a scenario.
Chapter 6
Communication
Changes for the pension sector are big, when the pension system changes to the new variant IV-C-R. Communication is very important to hold the support for the collective system. Also communication is the way to inform the participation about the effect of this change on their pensions.
The Dutch central bank concludes in the report ”Staat van Toezicht”(2016) that the reformations are needed to hold their pension system in the future. Challenges are the expectations of the participant, redistributions and the one-size-fits-all approach. Besides the changes of the legal and actuarial point of view, the pension communication can be used to prevent big misunderstandings about the new pension system.
This chapter describes pension communication from perspectives of the participa-tions and is partially based on the report of the SER about communication. The first section discusses their knowledge, attitude and trust in the pension system. The next section mentions the lack in the current pension communication. The third section pro-vides a proposal for a new form of presenting pensions to the participants.
6.1
Pension awareness
The biggest challenge in pension communication is to establish attention from the par-ticipants to their pension. Research from TNS Nipo (2013) shows that most (71%) of the participants are not open (read, deepens or interest) to get information about their pension.
Nibud (2015) concludes that more than half of the Dutch people do not know whether their pension income is high enough to pay their expenses. Research from Pension fund Zorg en Welzijn (2014) shows that the estimation about the expected outcome of pension income decreases and the insecurity about this estimation increases. The group that do not know what to expect about their pension income after retirement has grown in the past years. AFM (2015) says that people act like others around them do. There is a lack of awareness for pension in their surrounding, so the participations do not see other active people.
Motivaction (2011) concludes in their research that a big part of the investigated people find it difficult to understand their pension accrual. Also Nibud (2015) concludes that 40% finds pension difficult to understand.
6.1.1 Misunderstanding about pension
Motivaction (2016) shows in their research that 80% (this was 55% in 2011, also re-searched by Motivation) of the participants belief that their pension premiums are paid to finance the current retirees. This growth might be caused by the growing attention for the average premium. Participants belief that the second pillar is a pay-as-you-go system. This leads to a lack of trust for the active population, because the group of
retirees are growing. Their research also concludes that the participants do not know the extra value of investing their money. They see investments as a risk, which can cause a change and so low pension incomes.
Last years there was a continuous negative communication about the pensions. Abatement, low coverage ratios and no indexation give participations the feeling that they get less pension income after retirement. 26% (45% by the AFM research, 2015) of the requested people by Motivaction (2016) belief that if you build up pension, you will earn 70% of the last earned salary. Based on the research of 2011, there is a large group that thinks that they get less pension than they paid premium.
6.1.2 Trust of participants in current pension sector
The report of the Dutch central bank (Staat van toezicht, 2016) shows that the trust in the financial sector decreased over the past years, especially for pension funds. This is caused by the crisis and the negative information/effects afterwards. The following graphic shows the results for the financial sector.
Figure 6.1: Trust of the participants in banks, insurers and pension funds
The lack of freedom of choice is also a topic that influence the trust in the pension sector. Different research has demonstrated that there is a desire for freedom of choice. Participants want to influence the way that their money is invested and guarantees that they have. However other more advanced research has shown that this desire turned out to be less important than described above, but it is still trigger zone.
Known from behavioral science perspective, participants have desire for anatomy and control (Taylor 1989, Deci 1981). The freedom of choice leads to more appreciation of the pension products. Opposite of it is that the choice are not always better and there can raise a feeling of regret. Participants are afraid to make a bad choice, but can not make a good comparison (Schwartz, 2004). Currently there are some choices to make in the pension system, for example ”hoog-laag”. Therefore a good default is very important. In practice participants want more control, but choice for the save contract of the default, which is most of the time as the current system.
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 25
6.2
Pension communication
The neuromarketing research (Vonken en Iking, 2016) shows that people have negative emotions when they get confronted with pension. Terms as net pension, pension before tax, coverage ratio, investments, solidarity and collectivity are unconsciously negative appreciated. People also link pension rather to dying, illness or poverty than positive things (Lamme, 2015). These negative feelings towards pension lead to the fact that people do not read their pension communication.
People do not get confronted enough with their pension, because it is far away. They often do not know that their employer pays a big part of their pension premium, because they did not own the money at any time. So they did not have the feeling that the money was their own. This is known as the endowment effect in behavioral science. Various experiments shows that the value of the object increases when people own the object (Ariely, 2012). Because the pension accrual probably does not feel as the participants own, people do not value the money the same as for example their bank money. The fact that people do not know how much money they get from their accrual confirmed this. Also the SER (2015) concludes that the connection between premium, costs, investments and results are not clear defined. The effect is that people feel indeed that pension is far away. But people do not have emotional connection to their future self, they just form an abstract view and wishes of them future self (Ersner - Hershfield et al., 2009). This means that they find it difficult to do something do their future self (Vonken en Iking, 2016). Effort for the situation now weights more than for the future. Behavioral delay get stimulated when choice are difficult (Prast en van Soest, 2014).
Pension communication as the UPO now leads to money illusion. People get the tendency to think in nominal instead of real terms (Prast en van Soest, 2014). Bodie en Prast (2011) point out that this explains why people have a stronger feeling against cutting their pension than not indexing their accrual pension.
The fact that the pension system nowadays deviates from the expectations set by people through the above describes casualties leads to a negative view of the system. In (collective) defined contribution schemes people see every year their pension result from the paid premium. They know their risks and do not have guarantees.
6.3
How to present the new pension scheme to the
partic-ipants
The big difference between the current pension scheme and variant IV-C-R is the indi-vidual pension capital. Instead of build up pension claims, there is a indiindi-vidual pension capital. Benefits can be purchased at retirement with this capital.
6.3.1 Chances
Because it is individually administrated, participants have a clear view of the develop-ment of their capital with the new UPO (uniform pension summary) that is proposed in subsection three, a lot of disadvantages can be taken away. For example, people see that pillar 2 of the pension system is not a pay-as-you-go system, because it is their own capital and there is no average premium for everyone. So younger people do not pay for the older people anymore. Furthermore participants see that just a small component is used for solidarity purposes. The benefits of the investments become clear and they see the added value of it. Participants also see that the growth of their capital is not just their paid premium. Because of the fact that they see their pension capital growing, not only by the paid premium, participants will reason from a profit perspective. An other opportunity is the frequency of interacting of the pension fund with the participants. The changes in their pension capital can be communicated every year, quarter or even
month, which results in the fact that participants will feel a better connection with their pension fund. These changes in communication will also bring some risks, which are explained in the next subsection.
6.3.2 Risks
The new UPO makes negative return on various components very clear. People can get a risk aversion of these news messages. But they will probably relate it to the state of the economy, which is probably bad during the negative returns. Because of the recovery plans in the current system, cuts in peoples pension are lots of years after a crisis. Whereas the investments were bad during that period, not the years after the crisis. Another risk is the communication for retirees. Retirees will see a decreasing pension capital, because of their pension payment. However the pension payment is based on the life expectancy of participants in the pension fund. Participants will get their pension payment from the pension funds if they live longer than expected (this has nothing to do with the longevity risk), because other people will live shorter. But it will be a challenge to communicate this to the participants when they see their pension capital decreasing towards zero. Furthermore the realization for the capital that is needed to purchase a life long annuity is a challenge to communicate. Participants will see a big pension capital and can not always translate it to the height of an annuity. Furthermore the height of the annuity will be decided by the pension fund. Where participants can take up their capital in case of illness or early death.
6.3.3 New UPO
The UPO (”Uniform pensioen overzicht”) is an uniform pension summary, it describes the pensions of the participants. By Dutch law it is mandatory for a pension funds to provide every year an UPO to the participants for their current employer. For the jobs at previous employers, people get their UPO every five years. As pointed out in previous sections, the pension system is going to change and so is the UPO. The UPO will be an overview of the changes of the individual pension capital over a certain period. Below a proposal for the new UPO.
Table 6.1: Example UPO for a retiree
Development pension capital Old age pension
Capital last year e220009
Risk premium payment e-44
Pension payment e-13048
Micro longevity risk (through risk premium payment) e600 Macro longevity risk (through risk premium payment) e1247
Investment return e2088
Capital end year e210897
Micro longevity risk
There is a difference between the expected mortality and the real life mortality for a pension fund. If the pension fund has a large number of participants then the mortality will approach the expected mortality. The amount of money that the deceased had is spread over the survivors. The difference between the biometric return (this is based on the expected mortality) and the actual realization (based on the real mortality) is the micro longevity risk. This risk is caused by the size of the pension fund and can be positive or negative.
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 27
Macro longevity risk
The expected mortality is based on 1000 scenarios. There can always be a deviation from this expectation. For example when people suddenly become older than expected. The risk that comes from these different scenarios is called the macro longevity risk. For the retirees it is preferable to have a constant pension payment. When they carry the macro longevity risk this pension payment can fluctuate (positive or negative). The risk can be insured by the active participants by paying a premium. After that, the active participants carry the risk of the suddenly increase in survival of the total population. Investment risk
Investments involve a lot of risks including possible loss of principal. All types of invest-ments bring other risks for the asset portfolio. These portfolio lead most of the time to a better (so is positive, but also sometimes negative) return on the invested capital than the risk-free rate, which is taken into account in this thesis. The return is needed to compensate for inflation and to give indexations. In the new pension system it is pos-sible to choose a life cycle, that gives the investment strategy (even after retirement). The degree of risk assessment will influence the risk of the portfolio and so the return.
Conclusion and recommendations
The pension schemes (second pillar) must adjust to the demographic, economic and social developments. Especially after the crisis, when the investment returns have been disappointing (currently recovered), interest rates are low (which results in higher pen-sion liabilities) and the life expectancy is increasing (which results in an increase of the pensionable age). There has been a lot of research in developing a new pension system. The new improved premium act ”Wet verbeterde premieregeling” made it pos-sible for a participant to keep investing their pension capital after retirement. The ”Sociaal-Economische Raad” (SER) researched on behalf of the cabinet, the design of the additional pension to strengthen the current pension scheme. The variant with per-sonally pension capital with risk sharing scored the best and is an interesting variant. All the new pension schemes will have transition issues, so there is a lot of research needed before the government will implement a new pension scheme.
This thesis provided a closer look on sharing the macro longevity risk, especially for variant IV-C-R of the SER report, which is mentioned by Heemskerk et al. (2017) as a PPR. This pension scheme has an individual pension capital, which is invest via a life cycle. The pension scheme does not have a buffer itself with all the participants for longevity risk, so the longevity risk is not shared directly as in the most current pension schemes. It may be an idea to let the results on the longevity risk flow through the existing buffer of the variant IV-C-R. At retirement there will be a addition of money to the buffer and by changing of mortality table the result will be subtract. Since the increasing of the life expectancy, longevity is becoming a big problem to pension funds and their participants. Currently there are some ways to hedge the longevity risk, but in variant IV-C-R it is possible to hedge it for retirees with the active population.
7.1
Conclusion of the results
The macro longevity risk (before sharing) was significant large, meaning in worst case scenario a cut of almost 2% a year for the retirees. The actives have little risk, so they possibly can take over some risk. The pension payments are not constant over time, which is not preferable for the retirees. They cannot takeover downwards risks, because they do not have a salary anymore.
After sharing the macro longevity risk between the retirees and active population, both the groups are better of. The retirees get a constant decreasing pension payment, because of the low risk premium (0.02%) they need to pay to the actives. If the actuarial factors take the risk premium into account, retirees can still have a constant payment stream. It is also possible to subtract the risk premium at the beginning of retirement, because it is a fixed percentage. This will make the pension payment constant over time as well. The actives can reach a higher pension capital, but have more risk during their accrual. Where the 2.5% worst case scenario has still a relatively good pension capital compared with the situation before sharing the risk.
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 29
From communication perspective variant IV-C-R has several important chances for the pension sector. The misconceptions about the yearly change (for example the ac-crual) in pension capital can be taken away. The perspective of pension will go towards the present day, so people will see more gain in capital than the current focus on pension cuts. The communication between the provider and participant will be more transparent. A negative consequence is that a large amount of pension capital can lead to unjustified wealth for the participants, where a lot of money is needed to purchase a proper pension payment after retirement.
7.2
Recommendations for further research
In chapter 3, the assumptions that have been used in this thesis are stated. In further research, these assumptions could widened to give a more realistic view of the results of this new pension scheme. The assumed pension fund can be split in for example three funds, which contains a young, middle age and old funds. It can influence the conclusions about sharing the risk, because it is only possible when there are enough actives in the population. If there are far more retirees in the fund (so a high average age), the macro longevity risk for the retirees will increase. There also will be less active participants to share this risk with, so the risk premium will increase as well as the volatility in pension capital of the active population after taking over the macro longevity risk. The salary is constant over time which is not realistic, but works to make the effects of this research clear. If the salary increases with the age, the pension capital will increase faster at old ages. This means the macro longevity risk will increase, because the fluctuation in mor-tality chances are higher at old ages. The consequences are the same as for the increase in average age. Here the entrance of new actives people will weaken this effect.
This thesis is based on the mortality tables of the ”Actuarieel Genootschap”, which is common for calculations on pensions in the Netherlands. However these mortality tables are really important in this thesis and have a big impact on the outcomes. In further research it may be interesting to take into count some other mortality tables as well. Which are based on an other mortality models than the Lee-Li model.
In the new pension scheme it is possible to invest the pension capital after retirement. In this thesis are the investment returns assumed equal to the risk-free rate, so retirees will have a constant payment. It is more realistic to take into count some life cycles, which contain more risk. An important point hereby is that the risk is separated from the longevity risk. Another big assumption is to leave out the partner pension. This will influence the conclusion and possibly provides a little hedge by itself.
Tables & Graphs
A.1
Assumed variables mortality table
Figure A.1: variable AG
x and αxG
Figure A.2: variable BG
x and βxG
Longevity risk in future Dutch pension schemes — W.J.P. Schouten 31
Figure A.3: variable KtG and κGt
Table A.1: variable θG and aG
θM θV aM aV
value -2.127 -2.066 0.980 0.976
Table A.2: H (choleski)
H (choleski) M δM V δV
M 1.427 0.192 1.569 -0.355
δM 0.379 -0.042 1.012
V 0.676 0.215
δV 0.692
Table A.3: C (covariance)
C (covariance) M δM V δV
M 2.035 0.273 2.238 -0.507
δM 0.273 0.180 0.285 0.316
V 2.238 0.285 2.920 -0.455
A.2
Assumed variables of the new pension scheme
Figure A.4: distribution start capital ages
Table A.4: Premium old age pension Age classes premium
15 till 19 5,7% 20 till 24 6,3% 25 till 29 7,3% 30 till 34 8,5% 35 till 39 9,8% 40 till 44 11,4% 45 till 49 13,3% 50 till 54 15,5% 55 till 59 18,2% 60 till 64 21,6% 65 till 67 24,9%
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