Taking out a lump sum to pay off mortgage debt
Chantal Sijs
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: C. Sijs BSc
Student nr: 10193995
Email: chantalsijs@hotmail.com
Date: July 15, 2016
Supervisor: prof. dr. ir. M.H. (Michel) Vellekoop Second reader: dr. Servaas van Bilsen
This document is written by Student Chantal Sijs who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is 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.
Abstract
This thesis investigates when it is preferable for Dutch participants to take out a lump sum at retirement to pay off the mortgage debt. This research adds to the discussions about reforming the Dutch pension system. The possible types of freedom of choice are discussed and the current situation in the Netherlands for mortgage debt is described. Furthermore, the possibilities to reduce the mortgage debt with pension capital dur-ing the accumulation phase and at retirement. With the use of the logarithmic utility function the advantage/disadvantage is calculated for participants when taking out a lump sum to pay off the mortgage debt under two different scenarios. First, the results are calculated without habit formation. Secondly, the results are calculated with habit formation. Besides different theta’s are investigated for one specific mortgage interest rate and pension annuity interest rate. The results show different best strategies for dif-ferent theta’s. If a fixed pension annuity interest rate and habit formation are assumed, then the best strategy is the same, while for the term structure of interest rates, the strategies differ. Further research is needed to make a conclusion for the participants in general.
Keywords Freedom of choice, lump sum, mortgage debt, habit formation, reform of pension plan.
Preface vi
1 Introduction 1
2 Literature study and research questions 3
2.1 Freedom of choice . . . 3
2.1.1 Freedom of choice in participation . . . 3
2.1.2 Freedom to take out a lump sum . . . 4
2.1.3 Freedom of choice of pension fund for the employee . . . 5
2.1.4 Freedom of choice for pension fund for the employer . . . 7
2.1.5 Freedom in choosing the asset mix . . . 7
2.1.6 Freedom of choice of the accrual rate . . . 8
2.1.7 Collective freedom of choice for employees . . . 9
2.2 Mortgage debt in the Netherlands . . . 9
2.2.1 Current situation in the Netherlands . . . 9
2.2.2 New mortgage rules . . . 10
2.3 Reducing mortgage debt in the accumulation phase . . . 11
2.3.1 Proposal Reformist Social Union . . . 12
2.3.2 Possible disadvantages and outcome of the plan . . . 12
2.3.3 Comparison with other countries . . . 13
2.4 Reducing mortgage debt at retirement . . . 15
2.4.1 Advantages and disadvantages . . . 15
2.4.2 Comparison with other countries . . . 15
2.5 Research question . . . 15
3 Methodology 16 3.1 Data . . . 16
3.2 Assumptions . . . 16
3.3 Habit formation . . . 17
3.4 Calculation of pension capital . . . 17
3.5 General model . . . 18
4 Results and analysis 21 4.1 Analysis of input data . . . 21
4.2 Fixed pension annuity interest rate without habit formation . . . 22
4.2.1 Fixed payoff lump sum ofAC100.000 . . . 22
4.2.2 Optimized lump sum payoff . . . 23
4.2.3 Optimized yearly payoff . . . 24
4.3 Term structure of interest rates without habit formation . . . 25
4.3.1 Fixed payoff lump sum ofAC100.000 . . . 25
4.3.2 Optimized lump sum payoff . . . 25
4.3.3 Optimized fixed yearly payoff . . . 26
4.4 Fixed pension annuity interest rate with habit formation . . . 26
4.4.1 Fixed payoff lump sum ofAC100.000 . . . 26 iv
4.4.2 Optimized lump sum payoff . . . 27
4.4.3 Optimized yearly payoff . . . 28
4.5 Term structure of interest rates with habit formation . . . 29
4.5.1 Fixed payoff lump sum ofAC100.000 . . . 29
4.5.2 Optimized lump sum payoff . . . 30
4.5.3 Optimized yearly payoff . . . 30
4.6 Overview based on different theta’s . . . 31
4.6.1 Results with theta is equal to 1.000 . . . 31
4.6.2 Results with theta is equal to 1.500 . . . 32
4.6.3 Results with theta is equal to 500 . . . 32
5 Conclusion 33
Appendix A: Interest rate DNB 34
Appendix B: AG mortality table 35
Preface
In front of you lies the Master thesis “Freedom of choice in pension plans: Taking out a lump sum to pay off mortgage debt”. This thesis has been written for the Master Ac-tuarial Science and Mathematical Finance and is the final requirement for graduation. From March to July 2016 I have been working on this thesis and from day one I was dedicated to write a thesis that would be useful. In this thesis taking out a lump sum to pay off mortgage debt is explored as part of freedom of choice in pension plans. I have chosen this subject because there have been several discussions about reform for the Dutch pension system. In particular, the freedom of choice in pension plans is often discussed. If I talk with other people about their pension, I always notice the lack of knowledge they have. I have the feeling that people are interested in this subject and that my thesis can add significant value.
During my literature study, I fortunately did not encounter major problems. The pur-pose of this thesis changed during the process and therefore the chapter about the literature study has been rewritten several times. I was able to find enough literature about the pension plans in other countries and especially Netspar has published a couple of articles that were very useful for my study.
I would like to thank some people who have helped me the in past couple of months to realise my thesis. First of all I would like to thank my supervisor dhr. prof. dr. ir. M.H. Vellekoop. Without his support, ideas, enthusiasm and knowledge it would have taken me much longer to come up with this final result. Many thanks for your help! Secondly, I would like to thank my parents, brother and friends for their support.
Enjoy reading and hopefully you will know afterwards a bit more about the possi-ble reforms for your pension plan.
Chantal Sijs BSc,
Chapter 1
Introduction
In the Netherlands pension is important. The Dutch government supports retirees with a state pension, in Dutch called AOW, and this has resulted in a solid, trusted base. On the top of this, the Netherlands has a system of occupational pensions. This combination makes the Dutch system robust and this is the major reason that the Netherlands con-sistently finishes highly in the ranking of the Melbourne Mercer Global Index (Klijnsma, 2015). This index provides a comparison of the many varied pension systems around the world. In the last report of the Melbourne Mercer Global Index the Netherlands ranked second after Denmark (Australian Centre For Financial Studies and Mercer,2015). How-ever, due to ageing, low investment returns and low interest rates, the pension system has to be reformed in order to be able to cope with the current problems. One of the problems is that pension funds can no longer meet their liabilities and therefore they have to cut the pension entitlements.
In order to try to solve this problem, the last couple of years the pension system has gone through several changes. One of these changes is that the government has adjusted the pension tax rules in 2015 (Rijksoverheid, wdb). Under these new rules, pension accrual is only possible for a salary up to a limit of AC100.000. Besides, the accrual rate for the average pension scheme has been decreased from 2,15 percent to 1,875 percent per year of service. Also, the state pension age has been increased to 66 years in 2018 and 67 in 2021. Another change is the introduction of a variable pension benefit that allows for investment after retirement. As a result, people may have a higher pension. Unfortunately, these changes are not enough to solve all the problems.
More and more people feel insecure about their pension (Klijnsma, 2015). The fi-nancial crisis has shown that pension benefits are not as certain as previously thought. Pension funds are forced to stop indexation and sometimes even to cut the pension entitlements. More insight for participants into their retirement and more involvement in decisions about their pension may contribute to recovering confidence in the pension system (Ponds, Steenberg & Vonken,2016). Besides, the labour market is changing. The level of education of participants is higher, the diversity among workers has increased, as well the mobility on the labour market.
To investigate the possibilities for reform of the Dutch pension system, the Ministry of Social Affairs and Employment launched the National Pension Dialogue in 2014 ( Kli-jnsma,2014). In the National Pension Dialogue, four questions are investigated to gain knowledge about how the pension system should be changed to maintain the strong elements of the current Dutch system. Due to these strong elements it is possible to save for a pension in a collective way, which is based on solidarity, with relatively low costs (Klijnsma,2014a). However, the system should be strengthened in several points: more transparency, simpler and better tailored to the different characteristics and needs of participants. Especially the last point, has been often discussed in the last couple of months.
Nowadays participants are given more and more responsibility and therefore they are taking more risks. This comes with a greater need for control for the participants. A study of the Sociaal en Cultureel Planbureau (2015) has shown that especially the younger participants (18-34 years old) and highly educated participants would like to have more influence on their own pension. Besides, half of the younger participants is not satisfied with the fact that they help to pay elderly for their pension. From these points of view it seems reasonable to give participants more freedom of choice in their pension plan. Countries like Denmark, Sweden, Chile and Australia give already more freedom of choice.
On the other hand, a recent study by the APG (2015) shows that participants are ambiguous regarding pension choices. To the question whether participants want to have more freedom of choice, the majority of the participants responded with yes. However, at the same time, to the question whether participants want their pension to be ad-justed automatically for them, the majority says yes as well. Moreover, the Sociaal en Cultureel Planbureau (2015) showed that solidarity is an important aspect for 65 per-cent of the surveyed participants, while nearly half of the surveyed participants prefer freedom of choice to solidarity. Conversely, certainty about the pension benefits is still most important for the participants. Therefore, the question whether the participants want to have freedom of choice in their pension plan is difficult to answer.
Another often recurring discussion in the Netherlands has been about the payoff of the mortgage debt. The Netherlands is a country with a lot of pension capital, but also with a lot of mortgage debt (Nederlandse Vereniging van Banken,2014). In each country that already has more freedom of choice it is possible to take out a lump sum to pay off the mortgage debt. There have been several discussions whether the Netherlands should follow these countries in order to lower the mortgage debt. The question is under which circumstances the participants prefer to take out a lump sum to pay off their mortgage debt. This thesis will investigate this question.
The sequel of this thesis is as follows. Chapter 2 contains a literature study and fo-cuses on the different types of freedom of choices that are possible in a pension system. This chapter also discusses the current situation of the mortgage debt in the Nether-lands. Chapter 3 contains the methodology of the research of this thesis. It describes the data, assumptions, general model and an explanation of the use of habit formation. The next chapter, chapter4, describes the final results of the calculations and analyzes these results. Finally, chapter5 presents the conclusion.
Chapter 2
Literature study and research
questions
In this chapter different types of freedom of choice are discussed together with the cur-rent situation of the mortgage debt in the Netherlands. In section2.1the different types of freedom of choice are introduced. Next, we discuss the advantages and disadvantages of each type of freedom and review in which countries the types of freedom of choice are already introduced. Section2.2describes the mortgage debt in the Netherlands and the discussions about lowering the mortgage debt. Next, section2.3 discusses taking out a lump sum during the accumulation phase in order to pay off the mortgage debt and describes possibilities in other countries. Lastly, section 2.4discusses taking out a lump sum during the retirement phase to pay off the mortgage debt.
2.1
Freedom of choice
2.1.1 Freedom of choice in participation
The Dutch pension system contains three pillars. The first pillar is the state pension (AOW), which provides a compulsory insurance plan yielding a retirement pension for everyone living in the Netherlands aged 65 and higher (Kok & Hollanders,Kok & Hol-landers). The second and third pillar are supplementary pension plans. The second pillar is the occupational pension, which is part of the terms of employment, agreed upon in negotiations between social parters. When there is enough representation, the social partners can request the government to force employees in that particular indus-try to join the pension plan (Kok & Hollanders, Kok & Hollanders). This obligation to join a pension plan is hardly a divisive issue in the Netherlands. However, there have been discussions about the self-employed and the employees without a collective pension plan and whether they should be saving for their pension (Lever, Ponds, Cox & Garc´ıa Huitr´on,2015). They are not obliged to participate in the second pillar, but they have the opportunity to join the third pillar, which contains the personal, private pensions.
That the obligation to participate is hardly problematic in the Netherlands, was shown in research by the Dutch Central Bank (Vereniging van Bedrijfstakpensioenfond-sen,2015). More than three quarters of the surveyed participants consider the manda-tory participation as an advantage. They say that they have no time and energy to think about their retirement. They also fear that they are not disciplined enough to save for their pensions themselves. A disadvantage of obligated participation is that employees do not have a choice whether they want to participate.
The pension system in the Netherlands is an example of the Social Partner model, whereby the government supports self-regulation by the public sector in the second
pil-lar with appropriate regulation (Lever et al.,2015). Besides the Netherlands, Denmark, Sweden and Switzerland also have a Social Partners model. In countries with a Reg-ulated Choice model, such as Australia and Chile, participation in a pension plan is made mandatory by the government. Participants have to pay contribution annually to individual DC accounts managed by government regulated financial institutions. The Regulated Choice model is also effective in Sweden, but then as a funded addition to the first pillar. Participants can choose between 850 pension funds in Sweden (de Beer, de Deken, Hollanders, Kuiper, Salverda & van der Zwan,2014). In the Induced Choice model there is a lot of freedom of choice in combination with defaults. Countries like the US, New Zealand and the UK use this model. In this model participation is not mandatory. However, a couple of countries have started a special program to support participation. In 2007 New Zealand started the so-called Kiwisave-program to support individuals to participate in a pension plan (Lever et al., 2015). New employees are automatically enrolled but they have the right to opt-out. In 2007, the government of the UK has introduced the National Employment Savings Trust (NEST). The NEST-plan is intended for employers who do not offer a pension NEST-plan or are not connected to an overarching plan of a sector or specific group. Their employees are automatically enrolled in the NEST-plan. The Provident Fund model is more commonly used in Asian countries, such as Malaysia and Singapore. The main feature of this model is that it is a system with capital-funded social security and with a central role for the government. The government has decided that individuals are obliged to accrue capital in own bank accounts. They can use this money for specific situations, such as disability, financing of houses, family, financing of study and pension.
Just as in the Netherlands, in Denmark and Sweden workers without collective labour agreements and the self-employed are not obliged to participate in the occupational pension plan. However, in Sweden the emphasis in the pension system is on the first pillar, which is income-related and is also mandatory for the self-employed. In Australia there is no savings obligation for the self-employed. In Chile, the self-employed have re-cently become obliged to participate. The introduction of the mandatory participation was gradually, initially with the possibility to opt-out and with a gradually increasing contribution percentage. The experiences in Chile and the UK suggest that automatic enrollment with the possibility to opt-out may be a useful intermediate for employees without a collective plan and the self-employed to build more pension, without limiting their options (Lever et al.,2015).
2.1.2 Freedom to take out a lump sum
In the Netherlands pensions are paid out as an annuity. The participant has the op-portunity to choose for a high-low pension, in which participants for a maximum of ten years receive a higher pension and after that receive a lower pension, or visa versa. The variation between high and low is maximally 100:75 (APG, 2015). This ratio is the ratio between a temporary and a lifelong pension. The (low) lifelong pension is 75 percent of the (high) temporary pension. This ratio is not used often. In addition, partner pension can be converted into a higher old-age pension or vice versa. By con-trast, this option is used often. In several countries there is the option to take out a lump sum. The advantages and disadvantages of taking out a lump sum will be discussed next. The most important advantage is that participants lower the risk of losing their ac-crued pension entitlements. People with a shorter life expectancy are more likely to prefer to take out a lump sum than people who expect to live long. If someone dies early, then he/she will lose his/her accrued pension entitlements and the assets will be distributed among the surviving policyholders. A lump sum will lower this risk, because the participant will (partially) get the accrued pension entitlements at the time of
re-tirement (if the participant is still alive then). People who expect to live longer will probably receive their accumulated pension entitlements for the largest part, so their potential loss will be smaller.
Besides, due to the economic crisis, pension entitlements are not certain anymore. Low investment returns and low levels of interest rates have resulted in the fact that pension funds may not have enough assets to meet all the future pension obligations. This has led to a lack of indexation and cutting of pensions and pension entitlements. Furthermore, ageing is also a huge problem. Because of the rising number of retirees, the number of workers (contributors) per retiree declines. Research ofDe Nederlandsche Bank(2016a) in request of the Ministry of Social Affairs and Employment shows that if the financial situation not changes this year, 27 pension funds may have to cut the pension entitlements in 2017. If participants are able to take out a lump sum, they know for sure that they obtain that particular part of their pension capital.
Gaining control of the investment strategy is another advantage of taking out a lump sum. The individual will be able to make decisions on his/her own on how to invest his/her money or hire a financial advisor or investment manager to assist with the process (Investor Guide, 2016). If the participant is able to take out a lump sum during the accumulation phase, then he/she will also have full control of (and access to) any or all of the money in the account when needed. Further, if the individual dies his or her spouse, children or other heirs will have access to any money left in the account. A disadvantage of taking out a lump sum is that participants can spend too much money at once and as a result outlive their assets (Investor Guide,2016). Furthermore, individuals can make bad investment decisions and unnecessarily lose money. Partici-pants who are willing to take out a lump sum should be informed very well in order to prevent behavioural biases.
Another disadvantage is solidarity. In countries such as Sweden, Chile and Australia, the emphasis is less on sharing longevity risk, because a part of the capital is often used as a lump sum (CPB,2006).
There are countries that give already the freedom to take out a lump sum. Lever et al. (2015) state that taking out a lump sum is even possible in countries with a Social Partner model. For instance, in Denmark fifty percent of the pension entitlements are paid out as an annuity, 35 percent as a phased withdrawal for at least ten years and fifteen percent as a lump sum. In Chile, there are strict rules about how pension en-titlements may be spent. For example, at the time of retirement, part of the pension entitlements must be used to buy annuities in order to realise the minimum amount of income that is arranged by the government (Dellaert, Ponds, Bovenberg, van Ewijk & Nijman,2014). The remaining assets may be used to purchase more annuities or to take a lump sum. The countries with the Provident Fund model know a lot of variation. In Malaysia, participants must withdraw the remaining capital of the individual accounts at once, whereas in Australia, New Zealand and the US there are only few rules about the distribution phase. Besides, the amount of annuitisation is very low. In these coun-tries a lump sum is allowed, even during the accumulation phase, for certain purposes, such as housing, health care, education or a job change.
2.1.3 Freedom of choice of pension fund for the employee
In the current Dutch pension system participants are not allowed to choose their own pension fund. In the Netherlands approximately 75 percent of the participants are obliged to join the occupational pension plan, which is agreed by the social partners (unions and the employers). If participants are not satisfied with their pension fund, they do not have the opportunity to switch to another pension fund. Giving participants this opportunity has a couple of advantages and disadvantages.
An important advantage of freedom of choice of pension fund by the employee is that, if pension funds do not perform well, participants can switch to another pension fund. This opportunity will provide more competition between the funds and force them to perform better. Better performance could include higher yields, more stable yields, lower imple-mentation costs or a (social) investment policy that is more in line with the preferences of the participants (de Beer et al.,2014).
Also, this type of freedom of choice better suits the larger variation in contracts and careers in today’s job market. Nowadays, almost every individual changes jobs several times, sometimes with periods of unemployment in between. As a result, individuals have to change several times to different pension funds. Therefore, they are not able to accrue a full pension, despite the possibility to transfer their accrued pension to their new pension fund. The ambition of a pension fund is to achieve seventy percent of the average loan (at a DB plan) and this can only be achieved if employees stay at the same employer for forty years. Especially if individuals become self-employed and are not connected to a pension fund, it is not possible to achieve this ambition. If the participant could stay at the same pension fund, this would not be a problem.
Another advantage is that participants can switch to another pension fund if they prefer a different investment policy. For example, young people can switch to pension funds that invest relatively risky (e.g. primarily in equity), which provides a higher re-turn and thus can offer a discount on the premium. However, this requires sufficient transparency about the investment policy of the pension funds and adequate financial knowledge among the participants in order to make an informed choice. Therefore, from this point of view this type of freedom of choice is an advantage, for participants who have this knowledge.
A disadvantage of this type of freedom are the higher implementation costs due to higher transaction and administration costs. This is the result of the larger variation in or within pension plans. In general, pension funds will have higher administration costs to record individual participants, who each bring along their own pension plan. Where most of the pension funds now only carry one or a few plans, so a large number of participants apply to the same rules, they will have to adapt their administration to the pension plans applicable for the participants. If pension funds do not have an enrollment obligation, they will likely refuse individual participants or will charge them high fees in order to reduce the costs. For small pension funds these costs will be so high that they will be gradually forced out of the market and therefore only a small number of pension funds will remain. Eventually, it is conceivable that, as with the health care system, the market will ultimately be in hands of four or five large institutions. As a consequence, actual freedom of choice will barely be present, especially since large pen-sion funds will probably not enter into fierce competition with each other and therefore a tacit truce may be observed, once the market has been divided. Furthermore, the advertising costs will also increase, because pension funds try to attract participants with favourable risks.
Another disadvantage of freedom of choice of pension fund by the employee is the so-called ‘herd behaviour’, where participants simply follow the behaviour of others without making a well informed decision by themselves. If those who lead the herd make the right decisions and choose the options that in general benefit the total population, herd behaviour does not have to have negative consequences. Moreover, due to herd behaviour the pension fund can become undercapitalized. This means that the pension funds do not have enough assets for every participant who want to leave the pension fund. For several participants it is possible to transfer their pension entitlements, but if a lot of participants want to do that, this will be a problem. As a result, the pension entitlements of the remaining participants will probably be cut. Also, it will be harder
for the pension funds to spread risk, because there are less participants (e.g. regarding investment income and life expectancy). More generally, herd behaviour could lead to large movements between pension funds, which could jeopardise the stability of pension funds and in the worst case will lead to liquidation of some of the pension funds. If every year a large part of the participants would switch, then it is almost impossible for the pension funds to have a stable and consistent long-term investment. However, it is likely that a small percentage of the participants will switch to another pension fund if this type of freedom of choice is introduced.
Moreover, it is questionable whether solidarity is still possible when this type of freedom of choice is introduced. In the current Dutch pension plan, solidarity between young and old is mandatory. This applies to both the state pension and the additional occupational pension. Due to average contribution, the younger participants pay too much than is actuarially fair, while the elderly pay too little. Therefore, the elderly are subsidized by the younger participants. There is in fact a real chance of segregation between young and old when young participants switch to pension funds with relative young participants. When the premiums are also lower, then this allows the younger participants to escape solidarity that is expressed in the average contribution. However, due to the acceptance obligation that pension funds have, it is possible that there will be a withdrawal if the elderly, the younger and the different age groups come together in a large pension fund. Thus, the solidarity between age groups will be resolved. It will also reduce the division of investment risk between generations as the younger generation, when an appeal is made on their solidarity, can move to another pension fund. As a result, it will be very difficult to remain the majority of the DB nature of the current pension plans. Therefore, employers who still have a DB plan, will eventually switch do DC plans.
There are already few of countries that provide the freedom of choice for pension funds. Such as Chile and Australia (Lever et al.,2015). The government in both countries pro-motes competition among financial institutions, which are active in the pension market. In Australia the establishment of a uniform pension product, called MySuper, will lead to cost reduction. Australia is considering setting up a similar bid procedure as in Chile.
2.1.4 Freedom of choice for pension fund for the employer
The introduction of freedom of choice in pension funds for the employer is in theory comparable with the freedom of choice for pension fund for the employee, but it works differently in practice. An important difference is that the choice of the pension fund by the employer always refers to the pension plan of all employees. The implementa-tion costs are lower, because the employer makes the decision for the entire company and not per employee. Furthermore, the employers are more likely to make a rational choice, because they have the necessary knowledge. In the Netherlands, a large number of companies already have this freedom of choice and it appears to work well in practice (de Beer et al.,2014).
The disadvantage of this type of freedom of choice are the same as the disadvantages of freedom of choice for pension fund by the employee.
2.1.5 Freedom in choosing the asset mix
This type of freedom of choice means that employees have the opportunity to change the standard asset mix. They will be able to choose another variant with more or less investment risk. In the Netherlands, freedom of choice in asset mix is not possible in DB plans, but it is possible in DC plans.
The advantage of this freedom is that employees are able to choose the amount of investment risk they want to have (de Beer et al., 2014). If employees choose for more investment risk than the standard amount, then the chance of having a higher return will increase and vice versa.
A disadvantage of this type of freedom of choice is that employees can lose money it they make a wrong decision. Thus, there is more risk. Besides, it would be better to limit the possible choices for the asset mix. If there are too many possibilities, then the extra costs that go along with this type of freedom of choice may not weight up against the benefits (Lever et al.,2015).
This type of freedom of choice is possible in Australia, the US, the UK, New Zealand and Sweden. In Sweden, in the past years there has been a shift from collective plans to individual DC plan, that offer more freedom of choice. As a result, freedom of choosing the asset mix is more often possible. In Chile, this type of freedom of choice is restricted. Employees can choose between five investment profiles, which differ in degree of invest-ment risk. The restriction is that elderly and retirees are not allowed to invest in the most risky funds.
2.1.6 Freedom of choice of the accrual rate
This type is closest to the current situation in the Netherlands. Many pension plans already offer their participants certain options, such as partner pension, the possibility of part-time pension, high-low pension and flexibility regarding the age at which the pension payments commence. Investment freedom is only possible in DC plans, but due to the trend from DB plans towards DC plans, it is more and more often possible to have this type of freedom of choice.
Participants may differ in their preferences regarding pension income when it comes to the pension plan itself. The advantage of the freedom of choice of the annual accrual rate is that participants can save according to their current situation. If a participant has high expenses, then he/she can choose to save less and, on the other hand, if a participant wants to save more because of more wealth, he/she can choose a higher annual accrual rate. Also, if a participant wants to retire early, he/she can accrual more annually, while, on the other hand, another participant may choose a lower annually accrual rate in order to work longer.
The problem for this freedom is that people may not save enough if there is no lower bound (Lever et al., 2015). People prefer to consume today rather. A lower bound is necessary to protect participants against undersaving. If the choice of accrual rate de-pends only on the characteristics of the participants, this type of freedom of choice could have consequences on the funding ratio of the pension fund. Suppose that young participants choose for a low accrual rate and the older participants for a high accrual rate. Then the subsidy from the younger to the elderly will decrease through the average premium. As a result the funding ratio will fall and hence the possibility of necessity to cut pensions will increase. It will become more difficult to provide indexation for pension entitlements.
Another problem of this type of freedom of choice is that it will be difficult to keep solidarity. This is due to the composition of the workforce of the companies. It can cause a separation between companies with a young and old workforce, so intergenerational solidarity decreases directly.
2.1.7 Collective freedom of choice for employees
With this type of freedom of choice, (former) participants of the pension fund will get more collective control over the content and implementation of the pension plan. On the one hand, a representation of the (former) participants receives a competency with respect to the agreements that the social partners make about the pension plan, while on the other hand the pension fund board has to ask the representative board an ap-proval for the implementation for the pension plan.
Although the participants do not determine the content of the pension plan in this scenario, they have a large potential impact because they may reject the agreements of the social partners. Hence, they enforce the social partners to meet their needs. There-fore, this is an advantage of this type of freedom of choice. Besides, they can exert a significant influence on the implementation of the pension scheme, because they have to approve major decisions of the pension fund board (de Beer et al.,2014).
A disadvantage of this type of freedom is that participants will only be able to ex-ercise this influence if a (qualified) majority is able to transcend their own particular interests and to adopt a joint position. If the participants agree on the decisions of the social partners, this will significantly increase the support of the pension plan. However, it is uncertain whether a representative board will get enough trust of the (former) participants.
All these types of freedom of choices are summarized per country in Table 2.1. In the table a distinction is made between solidarity and freedom of choice and this table is published in research of CPB (2006). Note that every country has the opportunity to choose between taking out a lump sum or an annuity. This option has been often discussed in the Netherlands too. Taking a lump sum could help to reduce the mortgage debt.
2.2
Mortgage debt in the Netherlands
This section describes the current situation of the mortgage debt in the Netherlands.
2.2.1 Current situation in the Netherlands
The Netherlands is a country with a high mortgage debt. In 2015 the total mortgage debt in the Netherlands was AC651 billion (Centraal Bureau van de Statistiek, 2015). Figure 2.1shows that the Netherlands has, after Denmark, the highest mortgage debt. The figure also shows that the Netherlands has a lot of pension capital compared to other countries. Moreover, the Dutch have saved a lot of money. The high pension capi-tal results in a gross domestic product (GDP) of 189 percent, which is by far the highest GDP of the sixteen countries, as can be seen in the figure. This high GDP means that people who almost retire will get benefits which are not much lower than their last salary. As a result, people do not feel the urge to pay off their mortgage debt entirely. In other countries, such as Belgium and Italy, the mortgage is fully paid off and there-fore their fixed costs per month after retirement are less than the Dutch. As as result, the Belgians and Italians need to save less pension capital (Nederlandse Vereniging van Banken,2014).
Despite the other equity components of the Dutch, such as savings and pension capital, the mortgage debt is a persistent worry for Dutch regulators, who see it as a major risk for the economy. According to DNB, this debt makes the economy much more vulnerable to shocks in the housing market, interest rates and employment. From a financial
stabil-Current Dutch system Denmark Sweden
Participation Employees under CAO Employees under CAO Employees under CAO Solidarity
Longevity risk Yes Yes (partly) Optional
Investment risk Yes Yes at guaranteed,
no at DC
Yes at guaranteed, no at DC With who is risk
shared?
Current and future
participants Current participants
Current participants and self-chosen collective Are the property
rights individual? No
Yes, with the exception of collective reserve
Yes, with the exception of collective reserve Freedom of choice
Participation No No No
Pension provider No No Yes
Asset mix No Not at guaranteed,
DC yes
Not at guaranteed, DC yes
Choice between lump
sum and annuity? No Yes Yes
Chile Australia
Participation Employees under CAO Employees under CAO Solidarity
Longevity risk Optional Optional
Investment risk No No
With who is risk shared?
At annuity: participants of self-chosen collective
At annuity: participants of self-chosen collective Are the property
rights individual? Yes Yes
Freedom of choice
Participation No No
Pension provider Yes Yes
Asset mix Yes Optional
Choice between lump
sum and annuity? Yes Yes
Table 2.1: Summary of freedom of choices in different countries. Source:CPB(2006).
ity perspective, DNB thinks the mortgage loan-to-value ratios, the maximum mortgage as percentage of the value of the house, are too high (Dalton,2011). The financial crisis has shown that a lot of people are left with a residual debt due to forced house sales at a lower price than their mortgage debt. To deal with these problems, the mortgages rules have been changed. This will be discussed next.
2.2.2 New mortgage rules
On January 1, 2013 new mortgage rules came into effect in the Netherlands. The goal is to make sure that people are able to pay their mortgage (Rijksoverheid,wda). The most important changes for this thesis are described below:
- Mortgage interest deduction only upon full repayment: when people first take out a mortgage to buy a house, they have to pay off the mortgage in thirty years, according to an annuity scheme, in order to be entitled to mortgage interest de-duction.
- Maximum height mortgage: in 2016, the Loan-to-Value (LTV) is decreased to 102 percent and it will be decreased to 101 percent in 2017. In 2018, the LTV will be decreased to 100 percent, which means that people are not allowed to get a higher mortgage than the value of the house.
Figure 2.1: Equity components of several European countries. Source:Nederlandse Vereniging van Banken(2014).
- National Mortgage Guarantee: the National Mortgage Guarantee (NMG) is a guar-antee on the mortgage up to AC245.000 in 2016. With this NMG people have less change on a residual debt and a forced sale of their house. This guarantee can be obtained along with the mortgage. Every year, the NMG is remeasured and is linked to the average house price.
- Mortgage conditions for starters more flexible: the mortgage conditions are more flexible for starters who expect an increase in income in the upcoming months. These starters can get a higher mortgage.
The most interesting change for the research in this thesis is that mortgage deduction is only possible upon full repayment. The basic principle of the annuity scheme is that people have to pay a fixed amount of money for interest and redemption each month. As a result, people will pay off more each month compared to a (partially) interest-only mortgage. Also, the tax benefits due to interest deduction decreases, because the inter-est payments decrease due to the payoff. This means that after thirty years the house is fully paid off.
An important question is whether the participants would take the opportunity to take out a lump sum if that would be an option. Besides, if they take out a lump sum, the question arises on what would they spent it. Ponds et al.(2016) investigated what the participants of the pension fund of ABP (the Dutch pension fund of the government and education in the Netherlands) would spend a lump sum on. The results are shown in Figure 2.2.
From the figure it can be seen that 53 percent of the participants would use the lump sum to pay off their debts: 46 percent would pay off their mortgage debt and seven percent would pay off other debts. Travelling (33 percent) is the next popular intention to use the lump sum, followed by the desire to maintain liquid assets (31 percent). Given this results, it is interesting to investigate whether it is possible whether participants would take out a lump sum from their pension capital in order to pay off their mortgage debt.
2.3
Reducing mortgage debt in the accumulation phase
In this section the possibility to take out a lump sum during the accumulation phase for special purposes, like housing, education or health care is investigated. There have
Figure 2.2: Intended use of lump sum (source:Ponds et al.(2016)).
been several discussions in the Netherlands about this. One of the discussions will be discussed next.
2.3.1 Proposal Reformist Social Union
In 2011 the Reformist Social Union (RMU) proposed to give employees more freedom of choice in the use of the employee’s part of the pension contribution (Ministerie van Sociale Zaken en Werkgelegenheid, 2015). With this proposal every employee gets the opportunity to limit the contribution of his/her pension accumulation to the employers part. The rest can then be used to pay off the mortgage debt (Klijnsma, 2014b). The idea of this plan is to make the Netherlands less vulnerable in times of financial crises. Moreover, this type of freedom of choice will stimulate the housing market and will help starters. The target group for this plan is people with a mortgage and a pension plan. The core of the idea of the RMU is that the part of the pension contributions which are paid by employees, can be used to pay off the mortgage debt. This results in a lower pension income. A limitation of this type of freedom of choice is that the pension accu-mulation may be too drastically reduced. As a result, the government set the employee part at a third of the total premium (Ministerie van Sociale Zaken en Werkgelegenheid, 2015).
The government agreed with the proposal of the RMU and Secretary of State Kli-jnsma gave the approval to the Ministry of Social Affairs and Employment to investigate whether it was possible to fit the idea into the current pension system. The Ministry of Social Affairs and Employment came up with two possibilities. The first possibility is to pay off the mortgage loan with a part of the pension premium and the second possibility is to pay off the mortgage loan with a part of the accrued pension capital (Ministerie van Sociale Zaken en Werkgelegenheid,2015).
2.3.2 Possible disadvantages and outcome of the plan
In order to investigate whether it is possible to fit the idea of the RMU in the current pension system, it is important to take into account the possible disadvantages. Theses are discussed next.
Distinction between buyers and renters
First of all, the question is whether there will be a distinction between buyers with a mortgage debt and others (for example renters), since the opportunity to pay off the mortgage debt with pension is only possible for employees with a mortgage loan. The treaty protection against discrimination relates to sex, sexual orientation, disability, age,
religion or belief and racial or ethnic origin. The distinction between renters and home owners is therefore law irrelevant and should not be a problem.
Distinction between men and women
Another possible disadvantage is that distinction between men and woman can be dif-ficult. On basis of the General Act on Equal Treatment, to prevent or to stop discrimi-nation on the ground of gender, employers are not allowed to discriminate between men and women (Ministerie van Sociale Zaken en Werkgelegenheid,2015). This prohibition on discrimination applies for pension accumulation, but also for the payoff of the mort-gage debt of the employee who uses the freedom of choice for the payoff of the housing debt.
Discrimination in pension plans is only possible if contributions are actuarially fair. In the proposed plan the employers part of the contribution is higher for women than for men, due to the longer life expectancy of women.
The payoff of the mortgage is higher for women than for men. Therefore, higher payoff on the house debt for women are in conflict with national and international rules for equal treatment. This unequal treatment between men and women can be prevented. The first possibility is to use the pension contribution that falls free when deploying the freedom of choice and divide it equally among all participants. This is equal to average contribution. However, this possibility will put pressure on the solidarity of a pension fund, because it will be advantageous for men to leave the pension fund. Another pos-sibility is thinkable in the surrender variant. Because the role of the employer is much smaller, the implementation problems are less in the surrender variant. Pension funds already do equivalent calculations at the surrender of small pensions.
Distinction between young and old
Because the return on the pension of the younger participants will be higher than the return on the pension of the elderly, a difference in the outcome of this type of the free-dom of choice between young and old exists. Employers have to put in less money for younger than for elderly, to reach the same pension result (Ministerie van Sociale Zaken en Werkgelegenheid,2015). As a result, if the younger participants will use the freedom of choice to pay off their mortgage debt, they will receive less pension entitlements than the elderly.
Conclusion Secretary of State Klijnsma
The Secretary of State Klijnsma concludes that the plan is legally impossible in the Netherlands. There are positive aspects to the plan, but she expects that it will contra-dict the European Law of Equal Treatment. In particular, the plan will be seen as age discriminating, because it is more attractive for the elderly to use freedom of choice than for the younger. In Australia, Switzerland and the UK, there are different laws about equal treatment and therefore it is possible to take out a lump sum in these countries. Other countries are discussed in the next paragraph.
2.3.3 Comparison with other countries
In this paragraph a comparison with other countries is made based on the choice of freedom to take out a lump sum during the accumulation phase. The situation in the UK, Switzerland, Australia, Sweden and Chile is discussed.
Since April 2015, participants in the UK have more choice and flexibility over how and when they can take money from their pension account (UK Government,2016). These changes have recently been introduced for participants who are 55 years old or older and have a pension based on a DC plan. These participants can now take 25 percent
of their pension wealth as a tax-free lump sum to spend on whatever the participants like. For example, they could use this money to enable them to work fewer hours, to retire early, to help top up their salary if they are still working or to release a cash sum. This 25 percent is the only part of the pension of the participants that is tax-free, so it is advantageous to take this offer. They can also take their whole pension wealth as cash or take small cash sums from their wealth. There are also circumstances in which participants are allowed to withdraw money from their pension even earlier than at the age 55. For example if they are in poor health or in a profession where retirement is lower than at the age of 55 (Pension Advisory Service,2016).
In Switzerland participants may withdraw money from their pension account early ac-quire property for personal use, to repay mortgage loans or to acac-quire shares in a housing cooperation. There are a couple of conditions when participants withdraw pension from their pension account early (Conf´ed´eration Suisse, wd). If participants sell a property that is purchased with an early withdrawal, they must refund the amount withdrawn. Moreover, early withdrawals reduce the voluntary old age, survivors’ and invalidity pen-sions. Allianz (2012) states that early withdrawals are possible every five years and, at the latest, three months prior to the normal retirement age. Where purchases have been made, the resulting benefits cannot be withdrawn as a lump sum within the following three years. The minimum amount of an early withdrawal is CHF 20,000. Exceptions are made for unit certificates or similar holdings that are being purchased or in the case of vested benefit policies.
Australia has a superannuation, which is an agreement people make to accumulate funds for their retirement (Lever et al., 2015). Superannuation is encouraged by the government and supported with tax benefits. The benefits can be divided into three categories: preserved benefits, restricted preserved benefits and unrestricted non-preserved benefits (Australia Government, 2015). The preserved benefits include all contributions and earnings for the period after June 30, 1999. The term preservation means that the participant can not withdraw assets until the age of 55 and so the funds are preserved for retirement. The actual preservation age depends on date of birth and varies between 55 and sixty years old. Participants are required to make prescribed minimum contributions to special pension funds. Restricted non-preserved benefits are all the contributions between July 1, 1983 and June 30, 1999 and can only be paid to participants on compassionate grounds, such as medical costs, disability, to modify your home or vehicle for special needs because of disability. Unrestricted non-preserved benefits include money held in the participant’s fund that they can access at any time, if the pension fund allows it.
In Sweden it is possible to take out a lump sum of the income-based old-age pen-sion at the age of 61 at the earliest. The participant can withdrawal 25, 50, 75 or 100 percent of the full amount (Fritzes Customer Service,2010). There is no upper age limit to withdrawal. Pension income and premium pension may be claimed independently of each other. However, guaranteed pensions may not be withdrawn before the age of 65. People who have not earned enough credit for an income based pension are entitled to a guaranteed pension. A fully guaranteed pension requires forty years of residence in Sweden between the ages of 25 and 64.
In Chile, employees have a choice of the age at which they begin to withdraw their money from the pension system. The normal retirement age is 65 for men, sixty for women (Vial Ruiz-Tagle & Castro,1998). After this age, workers may begin withdraw-ing funds regardless of the amount accumulated. Employees are also permitted to make early withdrawals of any balance that exceeds the necessary capital to pay a pension
equivalent to seventy percent of the pensionable salary and is at least 120 percent of the minimum pension. For these workers, further contributions are voluntary rather than mandatory. Besides, during an initial three-year period, a disabled worker receives a temporary DB payment directly from his pension provider (the AFP). If a worker is certified as permanently disabled after the three-year provisional period, he has the choice between a lifetime annuity or a gradual withdrawal of money from his account.
2.4
Reducing mortgage debt at retirement
As discussed in the previous section, taking out a lump sum during the accumulation phase is not possible in the Netherlands. In countries like Denmark, Sweden, Chile and Australia participants have the opportunity to take out a lump sum at retirement. Next, it will be discussed if this is also possible in the Netherlands.
2.4.1 Advantages and disadvantages
The basic idea of combining pension and mortgage is that people need less pension income if they own a home. Indeed, a house owner who (partially) pays off his mort-gage debt, will generally have fewer overheads than a renter who pays monthly rental. The advantage of taking a lump sum at retirement compared to the proposal of the RMU is that at retirement there is a responsible choice possible between housing and pension. The participant knows better what his financial situation is, so he can make a more informed decision. Besides, the pension capital will be a lot bigger than during the accumulation phase, whereby the housing market could really be helped (APG,2015). Also, at retirement there is no age discrimination. Every participant who retires has the choice to take out a lump sum.
TheAPG(2015) has investigated the opportunity to take out a lump sum at retirement and they came up with a couple of disadvantages. They state that a disadvantage of taking out a lump sum is that virtually nobody stays forever in the same house. After retirement it is not inconceivable that a retiree wants to move, for example, because the house is too big, because it is not suitable for occupation by older people, or because the house is too expensive (if there is a partial mortgage). If retirees have to sell their house with a big loss, this will have big consequences for their way of living. Besides, if retirees want to enjoy life by spending a lot of money, this is much easier to realise with a pension (with the use of a high-low construction) then through the overvalue of their house. Therefore, it can be stated that a house has more financial risk than a pension, because with a house there is relatively much invested in one illiquid investment. More-over in case of a financial setback, a pension guarantees more than a house, because if people need financial support of the government, they have to first eat their home, while their pension protects them against that.
2.4.2 Comparison with other countries
In every country where it is possible to take out a lump sum at the accumulation phase, it is also possible to take out a lump sum at retirement. This is the case in the UK, Switzerland, Australia, Sweden and Chile. Besides, as mentioned in paragraph2.1.3, in Denmark and Malaysia it is also possible to take out a lump sum at retirement.
2.5
Research question
After this literature study, the option of taking out a lump sum at retirement to pay off the mortgage debt will be investigated in the next chapters. These results will show whether the Netherlands should follow the reformation of other countries.
Chapter 3
Methodology
This chapter describes the data and defines the methodology used in this thesis. To determine when the participant prefers to take out a lump sum, the utility function will be used. In this chapter the data that is used for the calculations is described first in section 3.1. Section 3.2 describes the assumptions that are made to do the calculations. Next, section3.3describes the habit formation, which is used to make the utility calculations more realistic. The calculation of the pension capital is described in section 3.4. Finally, section3.5describes the general model.
3.1
Data
To calculate whether taking out a lump sum from the pension capital is more prefer-able for participants, two scenarios are compared. In the first scenario a fixed pension annuity interest rate is assumed and in the second scenario a term structure of interest is assumed. The fixed pension annuity interest rate is chosen a priori and lies within the range of one percent to eight percent. This range is chosen to have a good overview for different percentages. For the term structure of interest rates, the interest rate curve of De Nederlandsche Bank (2016b) is used. The curve is used, which was published on March 10, 2016. To estimate the survival rates, the Projection Table AG2014 for mortality table is used, which is published by the Koninklijk Actuarieel Genootschap (2015).
3.2
Assumptions
First of all, it is assumed that the participant has a DC plan. This assumption is made, because at a DC plan the participant can convert the accrued pension capital into a commitment to a lifelong annuity. Secondly, it is assumed that the participant is a house owner and therefore he has a mortgage that is not yet fully paid off. The participant has the possibility to take out a lump sum to pay off the mortgage debt. On the mortgage he has to pay interest and this interest rate lies within a range of one percent to eight percent. Further, it is assumed that the participant is a male with age x and he is married with his wife, who has age y. He retires at age 67 and the age difference between him and his wife is more or less three years. This age difference is mostly chosen in pension plans. Besides, the participant has a life insurance, so that we do not have to take into account the remaining mortgage debt at death for calculating the optimized utility. As a result, at the moment of death of the male the entire mortgage debt will be waived and therefore the survivors inherit no mortgage debt. It is assumed that the participants has no additional savings at retirement, so his wealth W is equal to zero. The accrued pension capital depends on several factors and this capital is calculated in the next section. To take also into account past consumption, the habit formation is included in the utility function.
3.3
Habit formation
There are several researches published about habit formation. All these researches use habit formation to weaken the time-separability assumption. Because of habit forma-tion the participant has a momentary utility funcforma-tion that depends on both current and past consumption (Chapman,1998). High rates of consumption in the recent past imply lower utility from a given current consumption rate. In these models, current consumption decisions have an effect on the entire path of future consumption through the habit index.
Habit formation models can be distinguished along two different dimensions.Gomes & Michaelides (2013) states first that, while some papers, such as Campbell & Cochrane (1999) and Chan & Kogan (2002), use an external habit specification where the habit depends on the consumption of a reference group (for instance, aggregate consumption), others assume that the habit depends on the individuals own past consumption, such as Samuelson (1969) and Constantinides, Donaldson & Mehra (2002). Second, Gomes and Michaelides state that some models specify the argument in the utility function as the difference between consumption and habit (additive habit models, such as Constan-tinides et al. or Campbell and Cochrane), while in others utility is a function of the ratio between consumption and habit (multiplicative habit models, such asAbel(2015) or Chan and Kogan).
In this thesis, the habit process is specified in terms of individuals’ own consumption, since the aim of this thesis is not to solve an equilibrium model. As a direct consequence, consumption responds gradually to financial shocks. For the utility function, the ratio between consumption and habit will be considered.
The ratio habit formation is modelled as follows (Gomes & Michaelides,2013):
θt+1= θt· (1 − γ) + γ · Ct (3.1)
where θt denotes the reference level (also knows as the habit level) at time t. θ0 will be
assumed in the next chapter. Ctis the consumable income at time t. The importance of
the habit is controlled by the parameter γ, where γ ∈ [0, 1]. If γ = 0 habits do not affect the utility function, which then becomes the standard utility function. In the research ofvan Bilsen(2015) γ is set to twenty percent. This percentage will also be used in this thesis.
3.4
Calculation of pension capital
In order to calculate the pension capital of the participant, a progressive scheme is needed. The steps of the progressive scheme are described below.
Step 1 : Annual salary
To estimate the yearly salary the participant has had during his career, some assump-tions have to be made. We assume four different salary paths: low and flat, low and increasing, high and flat and high and increasing. The assumptions that are used for the calculations are shown in Table3.1.
Step 2 : Annual contribution
The formula for the annual contribution is as follows:
Low&flat Low&increasing High&flat High& increasing
Starting salary 20000 20000 36000 36000
Carrier 25-45 2% 4% 2% 4%
Carrier after age 45 0% 1% 0% 1%
Table 3.1: Possible salary path of the participant.
where the contribution rate is a percentage and is often age-related. The franchise is that part of the salary over which no pension is built up and therefore no contribution is paid. Step 3 : Annual return
In a DC plan, the benefits are not directly distracted from the paid contributions, but depend on the returns on the invested contributions. The formula of the annual return is as follows:
Annual returnt= Annual contributiont· (1 + it), (3.3)
where it denotes the annual increase of the investment at time t.
Step 4 : Pension capital
The final formula for the pension capital is equal to:
Pension capitalt+1= Annual returnt+ Pension capitalt· (1 + it), (3.4)
where the Pension capital0 is chosen in the next chapter.
3.5
General model
In order to calculate the utility, the following progressive scheme is needed. Step 1 : Mortgage debt
First, it is assumed that time zero is equal to January 1, 2016 and that the participant is 67 years old and retires on that date. Every month the participant pays interest over the mortgage debt and he has to pay off a part of this mortgage debt. For the interest payments there are two possibilities. The first possibility is that the interest rate pay-ment is part of a fixed paypay-ment that the participant makes yearly (α = 1). In other words, the fixed payment depends on the mortgage payoff and the interest rate pay-ments and this fixed payment is set at time zero. Because the mortgage debt decreases every year, the interest rate payments decreases every year and therefore the mortgage payoff increases every year. The second possibility is that the interest rate payments are made separately from the fixed payments (α=0). This means that the fixed payment only depends on the mortgage payoff. The formulas in the progressive scheme are based on yearly variables, whereas in real life these payments have to be made monthly. The remaining mortgage debt per year is equal to:
mortgaget= mortgaget−1− fixed payofft, (3.5)
where mortgaget ≥ 0 and mortgage0 is chosen in the next chapter. If mortgaget−1 is
equal to zero than the fixed payofft is equal to zero.
The fixed payofftper year is equal to:
fixed payofft= payoff mortgaget− interest paymentt−1· α, (3.6)
where the fixed payofft is set at time zero. The interest paymentt−1will be explained in
Step 2 : Interest rate payments
If a fixed mortgage interest rate is assumed for a couple of years, which is set at thirty years in the new mortgage rules, then the interest payment per year is equal to:
interest paymentt= mortgaget· mortgage interest ratet if mortgaget≥ 0, (3.7)
where the mortgage interest ratetis the fixed mortgage interest rate at time t that needs
to be paid for the mortgage debt. Step 3 : Annuity factor
The annuity factor is the expected capital that is needed to payAC1 per year until death. The annuity factor needs to be calculated differently for a fixed pension annuity interest rate and for the term structure of interest rates.
The annuity factor with the use of a fixed pension annuity interest rate is as follows: Annuity factort= 1 +
Annuity factort+1·tpxy
1 + fixed interest rate , (3.8)
where fixed interest rate is the assumed fixed pension annuity interest rate and tpxy is
equal to:
tpxy =tpx+tpy−tpxy. (3.9)
In this equation,tpxdenotes the t-year probability of survival for a male currently aged
x. tpy denotes the same probability but then for a women currently aged y and tpxy is
the probability that both x and y are alive in t years. As mentioned before, the Pro-jection Table AG2014 for mortality rates is used to calculate these survival rates. The ages are from x = 0 until x = 120 and the annuity factor is set at one at age x = 120. It is important to note that we only need to calculate the annuity factor at time zero, one and two. This is because only the pension capital at t = 0 is needed, which depends on these annuity factors.
The variable pension annuity interest rate requires another calculation. The interest rate curve that De Nederlandsche Bank (2016b) publishes every month is in terms of the so-called spot rates. For an annuity factor however, forward rates are necessary. The formula for the forward ratetat time t is as follows:
forward ratet=
(1 + spot ratet)t
(1 + spot ratet−1)t−1
− 1, (3.10)
where the forward ratet is equal to zero at t = 0 and the forward rate is equal to the
spot rate at t = 1. The formula for the Annuity factort is as follows:
Annuity factort= 1 +
Annuity factort+1·tpxy
1 + forward ratet
. (3.11)
Step 4 : Benefits
In order to calculate the pension benefits, the capital at time zero needs to be calculated first. If the participant takes out a lump sum to (partially) pay off his mortgage debt then β = 1 and otherwise β = 0. The capital at time zero is equal to:
Capital0 = Pension claim0− Lump sum0· β, (3.12)
where the Lump sumtis the lump sum that can be taken out at time zero. The Pension
The yearly pension benefit0 is calculated as follows:
Yearly pension benefit0 =
Capital0
Annuity factor0
. (3.13)
It is assumed that the yearly pension benefit0 is fixed until death.
The total consumable per year is as follows:
Ct= Consumable per year = Yearly pension benefit0· (0, 7 + 0, 3 ·tpx)
+AOW
−payoff mortgaget·tpx
−interest paymentt· (1 − α) ·tpx,
(3.14)
where the yearly benefit0 is multiplied by (0, 7 + 0, 3 ·tpx), because only if the participant
is alive, he gets full pension benefits. If the participants dies, his wife gets seventy per-cent of the accrued pension rights (in form of partner pension). AOW is the support of the Dutch government, the first pillar pension. How much AOW pension the participant gets, depends on the the marital status and on the numbers of years that he has been insured for AOW (Kok & Hollanders, Kok & Hollanders). Up to retirement everyone with a taxable income has to pay AOW contributions.
Step 5 : Utility
The participant aims to maximize Et(Ut), where Et is the conditional expectation
op-erator at time t and the logarithmic utility function is given by (Abel,2015): Ut= X t≥0 (1 + δ)−t· ln Ct θt ·tpxy, (3.15)
where δ stands for the subjective rate of time preference. The (1 + δ)−t is smaller or equal to one, because people prefer to consume today rather than tomorrow. The θt is
Chapter 4
Results and analysis
In this chapter the results of the calculations are shown and discussed. Section4.1shows the analysis of input data. Section 4.2 describes the results of a fixed pension annuity interest rate without habit formation. Next, section4.3describes the results with habit formation. Section4.4 shows the results of the term structure of interest rates without habit formation and section4.5describes the results with habit formation. Finally, sec-tion 4.6gives an overview based on different theta’s.
For every calculation the housing wealth0 is set equal to AC200.000 and the pension
capital0 equal to AC500.000. The AOWt is set equal to AC598,60, which is the AOW of
the year 2016 (AOW pensioen,2016). This AOW is assumed to be fixed. Moreover, we assume that the fixed payoff only depends on the mortgage payoff, thus α is equal to zero. This is assumed, because in the case that α is equal to one, the minimum fixed payoff is for every mortgage interest rate different. This is because people are obligated to pay interest over their mortgage debt every month. In case of habit formation, the reference level at time zero is set equal to 1.000. In the reference level, γ is set equal to twenty percent.
4.1
Analysis of input data
For the calculations based on the term structure of interest rates, the curve is shown in Appendix A. The corresponding graph is shown in Figure4.1.
Figure 4.1: DNB interest rate on March 31, 2016.
The figure shows that the interest rate for the upcoming four years is negative and for the first nineteen years lower than one percent. The interest rate in the last couple of months is historically low and that has consequences for the pension of the participants.
Therefore, the results of the term structure of interest rates will be different than the fixed pension annuity interest rate, where a fixed interest rate is assumed in the range of one percent until four percent. The mortality rates of the Projection Table AG2014 for males and females for the year 2016 are shown in Appendix B. The graph of the survival probabilities for males and females respectively are shown in Figure4.2.
Figure 4.2: Survival probabilities.
4.2
Fixed pension annuity interest rate without habit
for-mation
This section investigates the problem for a fixed pension annuity interest rate without habit formation. The total utilities will be compared with each other.
4.2.1 Fixed payoff lump sum of AC100.000
First, we expect that at high mortgage interest rates the participant wants to take out a lump sum, otherwise he has to pay a lot of money for interest. To investigate when taking out a lump sum is attractive, the utility is optimized for different mortgage interest rates and a fixed pension annuity interest rate with respect to β. In Table 4.1
the fixed payoff is set equal toAC10.000, while in Table 4.2the fixed payoff is set equal toAC0. rpension annuity rmortgage 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,01 0 (726) 0 (820) 0 (907) 0 (990) 0 (1.067) 0 (1.141) 0 (1.210) 0 (1.275) 0,02 0 (688) 0 (785) 0 (876) 0 (961) 0 (1.041) 0 (1.117) 0 (1.188) 0 (1.254) 0,03 0 (647) 0 (748) 0 (843) 0 (931) 0 (1.014) 0 (1.092) 0 (1.164) 0 (1.233) 0,04 0 (603) 0 (709) 0 (808) 0 (900) 0 (986) 0 (1.066) 0 (1.141) 0 (1.211) 0,05 1 (580) 1 (670) 0 (771) 0 (867) 0 (956) 0 (1.038) 0 (1.116) 0 (1.188) 0,06 1 (564) 1 (655) 1 (741) 0 (832) 0 (924) 0 (1.010) 0 (1.090) 0 (1.164) 0,07 1 (564) 1 (640) 1 (728) 1 (810) 0 (891) 0 (980) 0 (1.063) 0 (1.139) 0,08 1 (528) 1 (624) 1 (714) 1 (797) 1 (875) 0 (949) 0 (1.034) 0 (1.114) Table 4.1: The table reports taking out a fixed lump sum, (β = 1) or not (β = 0), where the fixed payoff
is equal to AC10.000 per year. The numbers in brackets denote the total utility.
In both tables it can be seen that the higher the interest mortgage rate, the lower the utility. Besides, the higher the pension annuity interest rate, the higher the utility. This
