An Alternative Financial Assessment Framework for Pension Funds

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An Alternative Financial Assessment

Framework for Pension Funds

Improving the Current and Future Financial Situation of Pension

Participants

D.J.W. Telkamp

11122943

MSc in Econometrics Track: Financial Econometrics Faculty of Economics and Business Amsterdam School of Economics

MSc in Mathematics Track: Stochastics Faculty of Science Supervisors: Prof. dr. H.P. Boswijk Dr. A. Khedher Drs. H.J.M. de Bock Ir. C. Krijgsman Second readers:

Prof. dr. ir. M.H. Vellekoop Prof. dr. P.J.C. Spreij

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Statement of Originality

This document is written by Duco Jan Willem Telkamp, who declares to take full responsibility for 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.

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Abstract

This thesis evaluated the new Financial Assessment Framework (nFTK) for Dutch pension funds, while closely monitoring the financial situation of pension participants. The aim was to answer the question: “Can the nFTK be adjusted in order to improve the assessment for long-term risks of underfunding, while lowering the indexation risk of pension participants?” To answer the re-search question, an ALM model was written and implemented in MATLAB. Various investment strategies, stock models, interest rate models and inflation models were considered in order to obtain a general overview of the nFTK. In particular, a stock model based on mean reversion was introduced. Moreover, the recent Pension Agreement and Advice of the Committee Parameters (see [1] and [2]) was taken into account.

Two different alternative financial assessment frameworks were introduced and analyzed. While the first financial assessment framework is based on higher discount rates, the second introduced financial assessment framework lowers the required own funds for pension funds. The introduc-tion of the New Required Funding Ratio, which effectively reduces the required own funds for pension funds, significantly improves the financial situation of pension participants. The advan-tages of the Required Funding Ratio are: higher payouts to pension participants, more equality between generations and less or no incentive to change the asset allocation in case a pension fund is underfunded. The newly proposed New Required Funding Ratio perfectly aligns with the goal of the Pension Agreement: paying out pensions to older generations, while still creating buffers to take care for younger generations. Even under the relatively modest assumptions on asset returns in our simulations, the pension system remains affordable.

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Acknowledgements

The first person I would like to thank is Karma Dajani from Utrecht University, the supervisor of my bachelor’s thesis. She was not directly involved in this master’s thesis, but she referred me to InAdmin RiskCo. Without her, I would not have known about the possibility of writing my master thesis at InAdmin RiskCo.

Next, I would like to thank Asma Khedher of the University of Amsterdam for supervising my thesis on behalf of the study Mathematics. Not only did she provide very useful comments and suggestions, her enormously positive attitude kept on motivating me at all times. I would also like to thank Peter Boswijk of the University of Amsterdam for supervising my thesis on behalf of the study Econometrics. He even agreed to supervise the thesis before meeting me, portraying his unconditional support. His thorough feedback was highly beneficial to this thesis.

Furthermore, I would like to thank everyone at InAdmin RiskCo for providing a supportive and professional environment to conduct my research project. Especially the daily supervisor Bert de Bock for offering the opportunity to write my thesis at InAdmin RiskCo and guiding me therein. The discussions with Cees Krijgsman about the Dutch pension system were also valu-able to the thesis. Moreover, my gratitude goes out to my tvalu-able tennis opponents at InAdmin RiskCo, with special mention of Eppo and Connor.

Last but not least, I would like to thank my family, girlfriend and friends, who made my time at the University of Amsterdam and InAdmin RiskCo even better.

Duco Telkamp, August 2019

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1 Introduction

In June 2019, the Pension Agreement was presented by the Dutch government (see [1]). This agreement in principle was achieved by the Dutch government, employers’ and employees’ orga-nizations in order to renew the Dutch pension system. Among other things, it was introduced to prevent pension cuts and increase the public support for the Dutch pension system. However, pension cuts are still a real possibility and criticism has not disappeared (see for example [3], [4] and [5]). In this thesis, we will analyze the situation of Dutch pension funds under the current regulations and propose alternatives. First, we introduce the Dutch pension system and its po-tential drawbacks (Section 1.1), then the research question and methodology (Section 1.2) and the structure of the thesis (Section 1.3).

1.1 Introduction to the Dutch pension system and its potential issues

The assets of pension funds in the Netherlands combined are, in comparison to the GDP, the highest in the world, according to [6]. In order to protect the pension funds’ assets, the Dutch government introduced the Financial Assessment Framework (FTK) in 2006 (see [7]). After the financial crisis, a lot of pension funds were heavily underfunded under the FTK . This led to pension cuts in order to meet the FTK regulations. In 2015, the new Financial Assessment Framework (nFTK) was introduced to provide more stability for pension funds for volatility on the markets (see [8]). Most importantly, the nFTK tried to prevent abrupt shortening of pen-sions by calculating Funding Ratios, the assets divided by the liabilities, in an averaged version (12 month average). Moreover, indexing pensions became more difficult under the nFTK.

Even under the nFTK, with prevention for abrupt shortening of pensions, pension cuts are a real possibility as of 2019. Possible pension cuts for three large pension funds in 2020 would affect 2 million people, according to [9]. The Pension Agreement of June 2019 (see [1]) tries to prevent this by lowering the Minimal Required Funding Ratio for pension funds to 100%, which means that if the liabilities have been higher than the assets of the pension funds for 5 years, pen-sions need to be cut. Before the Pension Agreement, pension cuts were needed if the assets were less than 104.2% of the liabilities for 5 years (see [10]). Hence, the Pension Agreement prevented possible pension cuts by lowering the required funds for pension funds. However, shortly after the Pension Agreement, the Advice of the Committee Parameters was presented (see [2]). As a result of [2], pension funds should use lower discount factors and expected returns to calculate with. These changes pose significant concerns for pension funds and its pension participants as indexing pensions and preventing pension cuts will be more difficult in the nearby future. In fact, pension cuts might be necessary sooner than originally estimated after the Pension Agreement (see [3]).

While pension cuts may be prevented because of the Pension Agreement (possibly nullified by [2]), indexing pensions is out of the question for a large number of pension funds. The reason for this is that the Funding Ratios of pension funds are considered to be too low under the nFTK.

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Moreover, the core of the nFTK has not changed in the Pension Agreement: it is still based on managing short-term risks of assets and liabilities. The nFTK tries to approximate the losses of pension funds in the 2.5% worst-case scenarios, over a one-year horizon. The Funding Ratio of a pension fund (the total value of assets divided by the total value of liabilities) should be higher than the Required Funding Ratio, where the one-year 2.5% worst-case scenarios mentioned above determine the Required Funding Ratio. While managing the current financial position is crucial to pension funds, the goal should be to provide a stable and healthy pension for all its pension participants. Restricting indexation and cutting pensions based on current bad economic situa-tions especially hurt the older pension participants. On the other hand, if pension funds change their asset allocation to less volatile assets (with lower returns) in order to lower the required funds imposed by the nFTK, it is possible that future pension payments are affected.

1.2 Research question and methodology

In order to involve the long-term risk of pension funds and the (lack of) indexation risk of pension participants, we evaluate the current nFTK, taking into considerations the Pension Agreement and the recent Advice of the Committee Parameters. Central to this thesis is the question:

“Can the nFTK be adjusted in order to improve the assessment for long-term risks of under-funding, while lowering the indexation risk of pension participants?”

We notice that the term “indexation risk” is more than just the risk of no indexation. It also covers the risk of pension cuts, as in that case the pension participants are struck even more by inflation. To address the central question of the thesis, we simulate an Asset and Liability Management (ALM) model, similar to [11]. We try to mimic the current situation of a Dutch pension fund as of 2019, that is: an underfunded pension fund. For our ALM model, we need to simulate stock returns, a term-structure, inflation rates and demographic changes. Furthermore, we need to make assumptions about the asset allocation of the pension fund in our ALM model. We also consider a strategy for our pension fund where the asset allocation can be changed by the pension fund in order to lower its (short-term) risk profile to comply Required Funding Ratios of the nFTK. Next to the nFTK as under the Pension Agreement, we use two adaptations of the nFTK. For the first adaptation of the nFTK, we increase the discount factors with which the pension fund calculates. This results in higher Funding Ratios and therefore (partly) prevents pension cuts and leaves more room for indexation in the near future.

The second adaptation is more revolutionary and we propose this as an alternative to the current nFTK. In this alternative we drastically change the calculation of the Required Funding Ratio. As mentioned before, the current nFTK calculates the Required Funding Ratio using 2.5% worst-case scenarios for its assets and liabilities, over a one-year horizon. The New Required Funding Ratio is an alternative which uses the Required Funding Ratio, but also assumes a real (after inflation) return of the portfolio to decrease the Required Funding Ratio. In this way, the index-ation and repair policies of a pension fund are not only based on the worst-case scenarios over

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a one-year horizon, but also take into account that pension funds have a certain return on their portfolio. The factor with which the current Required Funding Ratio is decreased, is based on the real return of the portfolio over a ten year period. Just as in the case of the current formula of the Required Funding Ratio, the real return is based on the composition of the portfolio of the pension fund.

As mentioned above, we need to simulate stock returns, a term-structure, inflation rates and demographic changes for our ALM model. The stock model we use is a geometric Brownian motion. However, instead of a regular geometric Brownian motion, we propose to include a mean reversion parameter and calibrate the model to S&P500 returns. Moreover, we compare the simulation results in case of a stock model with mean reversion versus the case of a stock model without mean reversion. The term-structure and inflation rates are based on the Jarrow and Yildirim methodology as discussed in [12] and [13]. The parameters of the Jarrow and Yildirim model are estimated using the Dutch CPI index, the term-structure provided by the Dutch central bank (DNB) and inflation swap rates provided by InAdmin RiskCo (see Appendix A). The calculation of liabilities and the strategies of the pension fund in our ALM model is based on analysis of [11] and in particular the Appendix thereof (see [14]). The demographics of our pension fund are based on the Dutch population in 2018 and the predicted mortality rates of the Dutch Royal Actuarial Association (AG) as of 2018 (see, [15] and [16]). Contrary to similar analysis of the nFTK in [11], we calculate the Required Funding Ratios of the nFTK in our model, instead of assuming a constant value for it. The implementation of our ALM model is built from scratch in MATLAB.

1.3 Structure of the thesis

The structure of the thesis can be summarized by a review of literature, followed by the method-ology, results and analysis of the nFTK and its adaptations. In Section 2, an overview of the Dutch pension system and its regulations is given (Sections 2.1, 2.2, 2.3, 2.4 and 2.5), together with the current position of Dutch pension funds (Section 2.6). Moreover, a description of the recent Pension Agreement and the Advice of the Committee Parameters is given in Section 2.7.

In Section 3, the ALM model is discussed. The introduction of our ALM model can be bro-ken down in the discussion of our stock model (Section 3.1), the term-structure and inflation rates (Section 3.2), the composition of our asset portfolio (Section 3.3), the setup of the liabilities of our pension fund (Section 3.4) and the explanation of how we implemented the calculation of the Required Funding Ratio (Section 3.5).

After the overview of the Dutch pension system (and its regulations) and the explanation of the ALM model, the results of our simulations are described in Section 4, accompanied by the introduction and analysis of the two adaptations of the nFTK in Sections 4.1, 4.2 and 4.3. In Sections 4.4, 4.5, 4.6 and 4.7, we extend our analysis by changing the model in various ways, before summarizing our analysis in Section 4.8.

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The conclusion of our analysis and the answer to our research question can be found in Sec-tion 5. We propose some methods to extend our research in SecSec-tion 6.

Lastly, we note that this thesis contains a lot of tables and figures placed inside the sections or at the end of the thesis. Appendix D (E) contains tables (figures) that are not placed within the text of the thesis. An English and Dutch list of abbreviations can be found in Appendix B.

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2 The Dutch pension system, its regulations and recent

developments

In this section pension systems and specifically the Dutch pension system are introduced. We find the following layout:

• Sections 2.1, 2.2 and 2.3 contains a general introduction of the Dutch pension system, • Section 2.4 introduces the new Financial Assessment Framework (nFTK),

• Section 2.6 describes the current situation of Dutch pension funds, • Section 2.7 gives an overview of recent developments of the nFTK.

The general introduction of the Dutch pension system in Sections 2.1, 2.2 and 2.3 is mainly based on [17]. The overview of recent developments of the nFTK summarizes the recent Pension Agreement in [1] and the Advice of the Committee Parameters in [2].

2.1 The three pillars

The Dutch pension system consists of three pillars. The first pillar is the state pension (AOW, short for “Algemene Ouderdomswet”), the second pillar consists of the collective pension schemes and the third pillar consists of individual pension products. We will discuss the three pillars in Section 2.1.1, Section 2.1.2 and Section 2.1.3.

Figure 1: The three pillars in the Netherlands. The second pillar translates as “employees’ pension”, the third pillar translates as “individual pension products”. Picture obtained from [18].

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2.1.1 First pillar

The state pension provides a basic income, linked to the statutory minimum wage. Married couples and couples living together receive 50% of the minimum wage per person. Pensioners living alone receive 70% of the minimum wage. The state pension is not limited to people with the Dutch nationality: every person who has lived or worked in the Netherlands between the age of 15 to 65 has a state pension and is entitled to the state pension benefit from the age of 65 (the AOW Age) according to [17]. This AOW Age has in fact been increased and its (future) value can be found at [19]. Every year that a person lives in the Netherlands and is insured in the Netherlands, he or she accrues 2% of the state pension rights.

The state pension is a pas-as-you-go system. This means that the pensions are paid by the current workforce in the form of contributions. Additional funding for the state pensions are paid by the government.

2.1.2 Second pillar

The second pillar is made up by collective pension schemes, managed by pension funds. These pension funds are operating (legally and financially) independent from the company the employee works at. The pensions are financed by capital funding, which means that pensions are paid from historic contributions and returns on investment of these contributions. Hence, pension funds have an incentive to have a high return on investments to safeguard the current and future pen-sions.

We separate between three different types of pension funds:

• Industry-wide pension funds, • Corporate pension funds,

• Pension funds for independent professionals.

The industry-wide pension funds are for a whole sector, such as civil service, construction, retail, et cetera. Corporate pension funds are for single companies or corporations. As an example of a pension funds for independent professionals we can think of the Pension fund Medical Specialists (Stichting Pensioenfonds Medisch Specialisten or SPMS).

The second pillar is not mandatory for individuals. However, the government can make a pension scheme mandatory for an entire sector or profession. As a result of this, more than 90% of em-ployees have a pension scheme with their employer. The advantage of having a uniform level in an entire sector or profession is that changing jobs within this sector or profession without losing pension rights is easier. Another reason for the semi-mandatory nature of pension schemes under the second pillar is that the Dutch government wants to create solidarity through compulsory participation.

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As stated before, more than 90% of the employees belong to a pension fund. The size of pension funds differs: the largest (ABP, pension funds for government and education) has over 450 billion euros in invested capital, while smaller ones with invested capital of only a couple of million euros also exist.

In the second pillar a member builds up pension rights via a fixed percentage per year. All members pay the same contributions to the pension fund. Factors as age, gender, health and income are not taken into account when determining the amount of contribution to be paid. The system thus has a strong basis in solidarity.

2.1.3 Third pillar

The third pillar consists of individual pension plans. These plans are mostly used by the em-ployees in sectors without a collective pension scheme. The third pillar is a way to save for extra old-age benefits. Saving in the third pillar is often stimulated by the government in the form of tax benefits.

2.2 Schemes

Next to the difference in pillars, there are different pension schemes. A pension scheme determines the way your pension is organized. The two main forms of pension schemes are Defined Benefit (DB) and Defined Contribution (DC). Furthermore, hybrid schemes such as Collective Defined Contribution (CDC) pension schemes also exist. Most of the people have an average salary scheme (a form of DB, see below). We briefly introduce the pension schemes.

2.2.1 Defined Benefit

In DB schemes, the level of pension depends on the number of years worked in combination with your salary. There are two options: the Average Salary Scheme (“middelloonregeling”) and the Final Salary Scheme (“eindloonregeling”).

In a Final Salary Scheme, the pension rights are increased to the level of the new pension basis. In the Average Salary Scheme, the average salary is the pension basis. Every year an employee works, he or she builds ups a fixed percentage of his salary. The pension is mostly fixed (hence the term “Defined Benefit”), contrary to the pension premium which depends on the state of the pension funds. However, the pension can also be reduced or indexed for inflation or wages, depending on the pension funds financial situation.

Under the nFTK, pension funds do not have to maintain reserves for future indexation (see Section 2.4). Contrary to this, pension funds must demonstrate that they will be able to realize their indexation plans in the long term, as indicated in [17].

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2.2.2 Defined Contribution

Contrary to DB, the DC scheme fixes the pension premiums or contributions instead of the pension benefits. The amount of pension benefits depends on the contributions and the return on investment over these contributions. The investment risk and the interest rate risk (see Section 2.5.1) lie with the employee, contrary to DB.

2.2.3 Collective Defined Contribution

In CDC pension schemes, the pension is based on salary and the number of years a person participates in a scheme are based on the DB scheme. However, the contributions are fixed for some years. If the contributions turn out to be insufficient for the built up pension rights, then the benefits will be lowered.

2.3 Regulations

The second pillar is monitored by two regulators, the Dutch Central Bank (DNB) and the Dutch Authority for Financial Markets (AFM).

The DNB assesses the financial position of pension funds. The aim is to examine whether pension funds are financially healthy and whether they can expect to fulfill their current and future obligations. The current framework for the Dutch pension funds is the new Financial Assessment Framework (nFTK), part of the Pensions Act. The nFTK is introduced in Section 2.4.

The AFM mostly monitors the behaviour of pension funds, in particular with respect to the obligation to provide proper information to its members. Pension administrators are obliged to properly inform the pension participants about their pension rights. Members should receive an annual pension statement and information about the pension scheme when joining.

2.4 The new Financial Assessment Framework

In this thesis, we will be focusing on the second pillar of the Dutch pension system, the em-ployees’ pension and its pension funds. The Dutch law has several regulations for these pension funds and relevant law is introduced below. As mentioned in Section 2, most of these regulations are from the new Financial Assessment Framework (nFTK).

The nFTK is mostly concerned with the Funding Ratio (FR), which is defined as the current value of assets divided by liabilities. We will also use the notion of Policy Funding Ratio (PFR), which is just the 12-month average of the Funding Ratio. The FR and the PFR are used in-terchangeably in this thesis, as the distinction is only to reduce variability in the Funding Ratio.1

1_{Specifically: under the FTK the FR is meant. Under the nFTK, the PFR is meant. In our ALM model from}

Section 3, we use the FR, since we simulate our ALM model on a yearly basis.

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The Dutch Pension Law (Pensioenwet) dictates that pension funds are obliged to have a Min-imal Required Own Funds (MROF).2 _{The MROF can be calculated by the pension fund. The}

Minimim Required Funding Ratio (MRFR), which is defined to be 1+MROF, is set by adminis-trative order and is mostly between 104% and 105%.3 _{When the PFR is below the MRFR for 5}

years, immediate measures have to be taken in order to be above the level again.4 _{This means}

that within six months, pensions are reduced. Hence, in economic hard times, indexation for the working and retired pension participants is off the table.

Under the same Pension Law, there is also the setup for the Required Own Funds (ROF) to which a pension fund should have access to.5 _{A pension fund should determine the ROF such}

that with a certainty of 97.5% a funding deficit in the next year is prevented. A funding deficit occurs when the PFR is below the Required Funding Ratio (RFR). The Required Funding Ra-tio is the desired Funding RaRa-tio of a pension funds and is defined to be 1+ROF. When the Policy Funding Ratio is below the RFR, a Ten-Year recovery plan should be presented and im-plemented. In this case, indexation, pension entitlements and premium are adjusted. When the PFR is above the Indexation Funding Ratio (IFR), (partial) indexation may take place. The Indexation Funding Ratio is 110% under the nFTK. If the PFR is above the Full Indexation Funding Ratio (FIFR, the lower bound for full indexation) and the RFR, the gap between the Pension Entitlements (PE) and the Full indexed Pension Entitlements (FPE) may be reduced, repairing the previously damaged indexation for the pension participants. Ultimately, if the PFR is larger than the Reduction Indexation Funding Ratio (RIFR), full indexation has happened for ten consecutive years and the PE equal the FPE, the pension premium may be reduced.

Figure 2: An overview of the conditions, steps and adjustments within the nFTK as in [11].

2_{Art. 131 lid 1 Pw.} 3_{Art. 131 lid 2 Pw.} 4_{Art. 140 Pw.} 5_{Art. 132 Pw.}

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Extensive rules and guidelines about the calculation of the ROF have been set out by adminis-trative order. First of all, in principle a standard model should be used. If the standard model does not sufficiently fit the risk profile of the pension fund, the pension fund could develop addi-tional (partially) internal models (see [20]). A fully internal model is in principle also permitted, but prior consent from DNB (De Nederlandsche Bank: The Dutch (Central) Bank) is needed.6

Taking a look at the annual reports of the following five big pension funds: PMT, PME, ABP, bpfBOUW and PFZW(see [21], [22], [23], [24] and [25]), all mentioned pension funds reported the use of the risk factors of the standard model.7 _{For simplicity purposes and because the standard}

model seems to be used frequently, at least within the big Dutch pension funds, we will refrain from analyzing specific internal models.

2.5 The standard model

In what follows, we will be explaining the nFTK rules and guidelines under the standard model (see [20]). The standard model of the nFTK has the following ten risk categories or shocks, denoted with (Si)i∈{1,...,10}:

• Interest rate risk (S1),

• Stock and real estate risk (S2),

• Currency risk (S3),

• Commodity risk (S4),

• Credit risk (S5),

• Technical insurance risk (S6),

• Liquidity risk (S7),

• Concentration risk (S8),

• Operational risk (S9),

• Active management risk (S10).

All of these risks should be calculated with a 97.5% certainty level based on a one-year horizon. In principle, the ROF is then equal to P10

i=1Si. However, this holds only if the correlations

between all categories are equal to 1. Under the standard model, it is assumed that there is a diversification effect, in other words not all shocks occur at the same time. Taking into account this diversification effect, the ROF is calculated as:

ROF = v u u t 10 X i=1 S2 i + 2ρ1,2S1S2+ 2ρ1,5S1S5+ 2ρ2,5S2S5< 10 X i=1 Si. (1)

In the setup of the nFTK, we have ρ1,2 = ρ1,5 = 0.4, if for the interest rate risk a decrease in

interest rates is assumed (see Section 2.5.1) and ρ1,2 = ρ1,5 = 0 else. The correlation between

stock and real estate risk and credit risk is set at: ρ2,5 = 0.5. The previously mentioned

diversi-fication effect is the difference between the sum of the risk terms and the ROF. This effect can be quite large, as will be illustrated later (see Section 2.6).

Before discussing the risk categories and there calculations, a remark about the Committee

6_{Artt. 26 en 28 Regeling Pensioenwet en Wet verplichte beroepspensioenregeling}

7_{Note: at the time of writing (March 2019) not all annual reports of 2018 of these pension funds were available}

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Parameters. The Dutch Law dictates that at least every five years a committee should be ap-pointed to set rules about the parameters from the nFTK standard model.8 _{This committee is}

called the Committee Parameters and it gave its last Advice in June 2019 (see [2]).

2.5.1 Interest rate risk

As most pension funds have a higher duration for their liabilities than their assets, there is interest rate risk. This risk lies mostly in decreasing interest rates, as in that case the assets decrease relative to the liabilities. DNB gives bonds, inflation linked bonds, convertibles and interest derivatives as examples of assets sensitive to interest rate risk.

In the Dutch Law (see [26]) interest rate factors are given in order to derive a interest rate increase or decrease for the nominal and real interest rate, under the interest term-structure given by DNB (see Table 1). To calculate the interest rate shock S1, the interest rate

term-structure is multiplied by the interest rate factor. Suppose that the duration of a liability is for example 4%, then we should account for a decrease in interest rates of 0.96% or an increase in interest rates of 1.28%.9 _{Notice that the values in the fifth and sixth column of Table 1 can be}

obtained from column two and three respectively.10 _{The reason for this is that the Dutch Law}

and DNB assume that 50% of the nominal interest rate shock is visible in the real interest rate shock and the other 50% of the real interest rate shock comes from inflation.

Duration Increase Decrease

1 2.05 0.49 2 1.79 0.56 3 1.65 0.61 4 1.55 0.64 5 1.49 0.67 6 1.44 0.70 7 1.40 0.71 8 1.37 0.73 9 1.35 0.74 10 1.34 0.75 11-15 1.33 0.75 >15 1.32 0.76

(a) Nominal factors

Duration Increase Decrease

1 1.53 0.75 2 1.40 0.78 3 1.33 0.81 4 1.28 0.82 5 1.25 0.84 6 1.22 0.86 7 1.20 0.86 8 1.19 0.87 9 1.18 0.87 10 1.17 0.88 11-15 1.17 0.88 >15 1.16 0.88 (b) Real factors

Table 1: The prescribed interest rate factors for nominal (Table 1a) and real (Table 1b) interest rate shocks as of March 2019.

Pension funds need to calculate the change in value for assets and liabilities, when applying

8_{Art. 144 Pw.}

9_{As (0.76 − 1) × 4% = 0.96% and (1.32 − 1) × 4%) = 1.28%} 10_{By applying the map x →}x−1

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the increase or decrease in interest rates. After this, the relative loss of the worst-case scenario obtained is then the required S1. To illustrate the calculations involved, let us consider an

example.

Example 2.1. Suppose our liabilities consist of paying 1AC in 30 years time. Let the (fixed) interest rate equal 2%, hence the current value of this 1AC is 0.55AC= 1

(1+2%)30

. Also, let us have a total portfolio of stocks of 0.30AC and a ten year zero-coupon bond with interest rate 2% and a face value of 0.30AC. We assume that the zero-coupon bond was purchased today at the price of 0.25AC. Our current Funding Ratio is therefore equal to 1 =0.30+0.25_0.55 .

In order to calculate the interest rate shock, we look at the zero-coupon bond and our liabili-ties. First of all, our liabilities have a duration of 30 years and the zero-coupon bond has a duration of 10 years. In case of a negative interest rate shock, we get the following new interest rates:

• New interest rate zero-coupon bond: 1.5% (= 2% · 0.75), • New interest rate liabilities: 1.52% (= 2% · 0.76).

In case of a positive interest rate shock, we get the following new interest rates:

• New interest rate zero-coupon bond: 2.66% (= 2% · 1.33), • New interest rate liabilities: 2.64% (= 2% · 1.32).

This gives us the following new values in case of a negative shock:

• New discounted value of zero-coupon bond: 0.26 =_1.0151.021010 · 0.25

,

• New discounted value of the liabilities: 0.63 =_1.01521.023030 · 0.55

,

• New value of the Funding Ratio: 0.89 = 0.30+0.26 0.63 .

And in the case of a positive shock of interest rates, we obtain the following:

• New discounted value of zero-coupon bond: 0.23 =_1.02661.021010 · 0.25

,

• New discounted value of the liabilities: 0.46 =_1.0641.023030 · 0.55

,

• New value of the Funding Ratio: 1.15 = 0.30+0.23 0.46 .

We see that the negative interest rate shock is the worst-case scenarios the Funding Ratio is here 0.89 < 1.15. Here the Funding Ratio decreases 11%. Hence, S1 equals 11%.

In case we would have no bonds and a portfolio consisting of 0.55AC in stocks, S1 would have

been 13%. If we would have no stocks and a portfolio consisting of a ten-year zero-coupon bond with face value 0.55AC, S1 would have been 8%. In general, having more fixed income means a

lower interest rate shock.

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Lastly, notice that we calculate the interest rate shock based on an immediate increase or de-crease of interest rates, whereas the actual standard model of the nFTK applies shocks on a yearly basis.

As we saw in Example 2.1, having more fixed income means a higher protection against interest rate shocks. It seems that the interest rate shocks gives incentive to invest more in fixed income.

2.5.2 Stock and real estate risk

The second risk category under the nFTK is the stock and real estate risk (S2) as described in

[27]. Under the FTK, the stock and real estate risk was divided into four categories: “mature markets”, “emerging markets”, “private equity” and “(direct) real estate”. Indirect real estate is assumed to be under the category of mature markets, as it bears more similarities with stocks than with direct real estate according to [28].11 Committee Parameters concludes this in [28], as indirect real estate mostly includes a leverage effect because of the presence of loan capital with additional risk.

Now, let us denote the S2 shock with respect to mature markets as SM M, emerging markets

as SEM, private equity as SP E and real estate as SRE. In order to find the shocks per category,

a decrease of 25%, 35%, 30% and 15% is assumed for SM M, SEM, SP E and SRE, respectively.

If we denoted the fraction of assets invested in mature markets as FM M, emerging markets as

FEM, private equity as FP E and real estate as FRE, we obtain the following:

SM M = FM M× 25%,

SEM = FEM× 35%,

SP E = FP E× 30%,

SRE = FRE× 15%.

The percentages for the mature markets and the emerging markets were the result of analyzing MSCI indices, while watching for survivorship bias (badly performing stocks are removed from indices, possibly causing a upward slope bias) and fat tails (strong negative results occur more often than expected under a normal distribution) (see [28]). For private equity, the percentage is exactly between mature and emerging markets. Careful thoughts have been devoted to self se-lection bias (well-performing private equity funds tend to present externally sooner), back filling bias (data of private equity funds are retroactively added to indices) and again survivorship bias. However, apparently the percentage from private equity is mostly motivated by the sentence: “Private equity clearly has a higher risk profile then stocks mature markets.” as we find in [28].

The S2 shock was then calculated using a similar “square root formula” as with the formula

for the total ROF. In this case, the correlations are set at 0.75 for all categories. Defining

11_{Indirect real estate is investing in a company or (real estate) fund, which invests in real estate. Direct real}

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S = {M M, EM, P E, RE}, we find: S2= v u u u t X i∈S S2 i + 3 4 X i,j∈S i6=j SiSj

The correlation between categories of 0.75 is motivated in [28] by the Committee Parameters using [29], where a correlation of 0.74 between European listed stocks and private equity after accounting for serial correlation was found. Lastly, it is noted in [28] that varying volatility is more appropriate for stocks, but that time-varying volatility did not improve the FTK model.

The nFTK has a slightly different model for finding the stock and real estate risk factor. For the calculation of S2, there are four categories considered:

• S2A is the shock for stocks mature markets and listed real estate,

• S2B is the shock for stocks emerging markets,

• S2C is the shock for non-listed stocks (mature markets),

• S2D is the shock for non-listed real estate.

The correlation between categories is (as under the FTK) set at 0.75. The constant decrease in the different scenarios is 30%, 40%, 40% and 15% respectively. This means an increase of 5 percentage point for stocks in mature markets and stocks in emerging markets, when compared to the FTK. Moreover, it means an increase of 10 percentage point for non-listed stocks.

2.5.3 Currency risk

Currency risk is the risk that the value of assets in foreign currency decreases as a result of the decrease of the foreign currency with respect to the own currency. For Dutch pension funds, this is mostly the risk of changes in the US dollar, the UK pound and the Japanese Yen relative to the Euro as claimed in [28]. Originally, a decrease of 20% of all currencies with respect to the Euro was assumed in [28]. This was based on Table 11.1 in [28], reproduced in Table 2. The constant decrease of currency over all countries was based on the specific currencies and their weights. The Committee Parameters in [28] used data from 1999 − 2004 for the exchange range and based the weight factors on data from 2003. The Committee Parameters concluded (in 2006) that adding the period 2004 to June 2006 did not change much. However, they noted that relatively more currency risk was in emerging markets, which was neutralized by lower volatility in the Argentinian Peso. It was already noted that if for a pension fund the weights of mature versus emerging markets was very different from the standard model (and its weights in 2004), an internal model would be more appropriate.

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Currency Weight

US Dollar 35%

British Pound 24%

Argentinian Peso (proxy emerging markets) 13%

Japanese Yen 8%

Swedish Crown 7%

Swiss Franc 7%

Australian Dollar 6%

Table 2: The weights for different currencies assumed under the original FTK

Under the nFTK, the constant volatility of 20% was deemed inappropriate and the system changed. In the standard model under the nFTK for the currency risk a risk scenario is prescribed (see [30]). For this, countries are divided into two categories: mature and emerging markets. We have the following notation:

SA= the ROF for currency risk for mature markets,

SB = the ROF for currency risk for emerging markets,

SAi = the ROF for currency risk for mature market i,

SBi = the ROF for currency risk for emerging market i.

For every market, the shock SAi or SBiis calculated. The first with respect to a 20% decrease in

the currency, the latter with a 35% decrease in the currency. After finding the shocks for every market, the ROF for currency risk S3 is calculated by the following formulas:

SA= s X i S2 Ai+ 2ρA X i<j SAiSAj, SB = s X i S2 Bi+ 2ρB X i<j SBiSBj, S3= q S2 A+ S 2 B+ 2ρA,BSASB.

These formulas greatly remind us to the calculation of the total ROF and its diversification effect. In the standard model for the ROF for the currency risk, the correlations are set at: ρA= 0.5,

ρB= 0.75 and ρA,B= 0.25.

DNB provides a small example for calculating the ROF for currency risk, which is given in Example 2.2.

Example 2.2. Suppose that we have a portfolio with 50% US Dollar (U SD), 25% British Pounds (GBP ) and 25% Chinese Yuan (CN Y ). We have mature markets A = {U SD, GBP } and

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emerging market B = {CN Y }. We find the following values12_: SAU SD = 20% × 50% = 10%, SAGBP = 20% × 25% = 5%, SA= q S2 AU SD+ S 2 AGBP+ 2ρASAU SDSAGBP = p 1% + 0.25% + 2 × 0.5 × 10% × 5% = 13.23%, SBCN Y = 35% × 25% = 8.75%, SB= q S2 BCN Y = 8.75%, S3= q S2 A+ SB2 + 2ρA,BSASB = p 1.69% + 0.81% + 2 × 0.25 × 9%× = 17.59%.

As percentages are used, normally the market value of the total foreign assets should then be multiplied by this factor to obtain S3. So, suppose the total value (in euros) is 50% and 50% in

foreign currencies as laid down above. Then S3 would be 9% (= 50% × 18%).

It is furthermore noted by DNB that for determining the ROF per currency the “net exposure” should be taken into account, in other words the sensitivity for a decrease in a currency with respect to the Euro when accounting for currency hedging. This makes sense, as it seems absurd to assume risk when there is no risk (in case of perfect hedging).

2.5.4 Commodity risk

The fourth risk factor in the ROF standard model is the commodity risk (S4). Commodity risk

entails the risk of pension funds investing in commodities and losing (part) of their investment by fluctuation of the value of the commodity.

The standard model in [31] assumes a global, well diversified portfolio for commodities, but volatility is still assumed to be quite high. In the prescribed risk scenario a devaluation of 35% of commodities is assumed, there is no differentiation between commodities. There is no mo-tivation found by DNB, the Dutch Law nor the Committee Parameters since the Advice from 2006 when the devaluation was assumed to be 30% (see [28]). The then given motivation and described method was the Goldman Sachs Commodity Index (GSCI) on the period 1970-2001. It was then found that taking only more recent years into account would increase the volatility to 35%.

The value of S4 is the total negative effect on the value of commodity related assets. Hence,

suppose that the fraction of commodities with respect to the assets is γ ∈ [0, 1], then S4 =

| − 0.35γ| = 0.35γ. However, one should be aware that derivatives of commodities may have less or more impact than 35%.

2.5.5 Credit risk

According to [32], credit risk for pension funds under the nFTK is the risk that credit spreads change and therefore the value of assets such as bonds. Under [32], credit spread is the difference

12_{Rounding off at every step to 2 decimals (so to percentages).}

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between the return on fixed income and the riskless return. When credit spreads increase, the value of bonds decreases. Under the FTK, a upward shock of 40% on the average credit spread of the pension fund (see [28]). To find the constant shock of 40%, the credit spread of investment grade corporate bonds in Standard & Poors (rating BBB or higher) over the period 1999-2004 was used in [28]. The volatility over the data was 16%, which meant a shock of less than 37% with confidence 97.5%.13 DNB rounds this to 40%, motivated by the fact that pension funds may also invest in non-investment grade corporate bonds and that only systematic risk is taken into account, while pension funds may also suffer concentration risk.14

The nFTK changed the calculation of S5 quite a bit. The change is now not in percentages,

but in basis points (bps). The following assumption is made for shocks: • AAA rating: +60 bps,

• AA rating: +80 bps, • A rating: +130 bps, • BBB rating: +180 bps, • Lower or no rating: +530 bps.

It is not clear were these values come from, however the distinction between different ratings seems appropriate. The last category (no rating) seems a bit too wide: there might be a huge difference in risk between assets in this class (see for example [34]). These ratings should prefer-ably be determined by a qualified third party. If no (appropriate) rating by a qualified third party is available, then the pension fund may also determine the rating (see [32]).

To determine the credit risk, the pension funds should increase the credit spreads with the above mentioned basis points. Let us denote the fractions (in total assets of the pension funds) of the bonds/credit sensitive products as FAAA, FAA, FA, FBBB and FLN respectively.

Then, let Vi be the (non-negative) decrease in value of bonds/credit sensitive products of rating

i ∈ {AAA, AA, A, BBB, LN }. The decrease in value Vi is determined by using the specified

basis points for category i ∈ {AAA, AA, A, BBB, LN }. We find:

S5= FAAAVAAA+ FAAVAA+ FAVA+ FBBBVBBB+ FLNVLN.

The only thing to determine is to find the risk per asset for various bps increases. For this, we consider a simple example.

Example 2.3. Suppose we have a ten year AA rated zero-coupon bond with a fixed interest rate of 1% and a five year BBB rated zero-coupon bond with a fixed interest rate of 5%. The AA rated bond (denoted X) has face value 1,000AC and the BBB rated bond (denoted Y ) has face value 500AC. We assume that both bonds have been purchased today. We find the discounted values (DVX, DVY) and the values after shocks (V SX, V SY) of the bonds:

13_{It is not explained how this is done, but assuming normality, an absolute shock over more than 37% has a}

probability of approximately 0.025.

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• DVX= _1.011,00010 = 905.29,

• DVY = _1.055005 = 391.76,

• V SX = _1.0181,00010 = 836.61,

• V SY = _1.0635005 = 368.39.

Using this, we find the decrease in value of the bonds (VX, VY) and we find the fraction of the

value of the bonds (FX, FY):

• VX =DVX_DV−V SX

X = 7.59%,

• VY =DVYDV−V SY Y = 5.97%,

• FX= _{391.76+905.29}905.29 = 69.80%,

• FY = _{391.76+905.29}391.76 = 30.20%.

This results in a credit risk shock of:

S5= VXFX+ VYFY = 7.10%.

Notice however, that we calculated the credit shock based on an immediate shock, whereas the actual standard model of the nFTK calculates the shock on a yearly basis.

2.5.6 Technical insurance risk

DNB notices in [35] that technical insurance bases constitute a significant risk for the pension fund. Therefore, the sixth shock (S6) under the nFTK is the technical insurance risk. Within

the standard model, in principle only the mortality risks are taken into account, unless other technical insurance risks have a significant impact on the ROF, according to [35].

No prescribed calculations are given to calculate S6, but DNB does propose a method. Within

this method, three categories are found: process risk, mortality uncertainty (abbreviated as TSO, also called the macro-longevity risk (see for example [36])) and negative stochastic deviations (abbreviated as NSA, also called the micro-longevity risk (see for example [36])).

Firstly, the process risk is the risk for possible irregular negative results in technical insurance results, taking into account the actual value of the technical provision. It only considers the negative effects in a time span of one year, with a confidence level of 97.5%. The process risk is set out in percentages of the technical provisions.

Secondly, the TSO should be taken into account. The TSO should be such that the lower the average age within the pension fund, the higher the TSO. The TSO should be determined for the whole duration of the liabilities and are determined as the difference between the 75th percentile of the distribution of the value of the liabilities and its expectation.

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Lastly, DNB motivates that the NSA is needed for the sensitivity of the ROF for the risk that the average age in case of participants dying deviates from the bases for valuation of the technical insurances. As with the TSO, the NSA should be determined for the whole duration of the liabilities and are determined as the difference between the 75th percentile of the distribution of the value of the liabilities and its expectation.

2.5.7 Liquidity risk

The seventh risk category is the liquidity risk (S7, see [37]). As set out in [37] by DNB, pension

funds face the risk of not having enough liquidity in order to meet financial obligations in times of stress on the financial markets. The first obvious example is pension payments. On the other hand, pension funds might need to give collateral for swaps, futures and similar derivatives. In the standard model however, the liquidity risk is set at 0. DNB motivates this by claiming that pension funds are assumed to be sufficiently careful such that the liquidity risk is not significant for the ROF. A warning by DNB is given that if liquidity risk turns out to be significant or if the standard model gives results substantially deviating from the real risk profile, that a pension fund should consult with DNB.

2.5.8 Concentration risk

As DNB sets out in [33], pension funds also face concentration risk if it lacks a proper diversi-fication of assets. Therefore, the eighth risk category is concentration risk (S8). Concentration

risk occurs when a big share of the assets is invested in a specific class of assets, region, country or similar. DNB sets the sensitivity of the ROF with respect to concentration risk to 0. It is motivated by the same argument as for the liquidity risk: DNB assumes that pension funds have been sufficiently careful in setting up a diversified portfolio. Again a warning by DNB is given that if the risk turns out to be significant or if the standard model gives results substantially deviating from the real risk profile, that a pension fund should consult with DNB .

2.5.9 Operational risk

DNB describes the operational risk under the nFTK in [38] as the risk originating of failing internal processes, human or technical shortcomings and unexpected external events. Therefore, the ninth risk category is operational risk (S9). As examples, the failure of IT systems, natural

disasters, fraud and inadequate calculation of premia and an inadequate execution of the pay-ment process are pay-mentioned in [38]. Again, as with the last two categories, DNB assumes that operational risk is sufficiently controlled such that is it not significant in determining the ROF. So, the operational risk is set at 0 and consulting DNB is needed in case of substantial differences from the standard model.

2.5.10 Active management risk

The last risk factor in the standard model is the active management risk (S10). The active

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As DNB sets out in [39] that the degree of active management is mostly determined via the tracking error with respect to the benchmark for the selected portfolio. No regulations are given within the standard model, just as under the previous three categories. Pension funds need to determine the amount of active management risk themselves. DNB only notes in [39] that the ROF for active management is determined as the maximal loss by active management which will occur with probability 2.5%. For the time being, the risk scenario for active management risk is only applied to the stock risk.

2.5.11 Correlations

The non-zero (and trivial) correlations ρi,j (for i, j ∈ N≤10) are not motivated by DNB or

Committee Parameters. The nonzero correlations of the nFTK are motivated by the DNB or Committee Parameters. We briefly go through these correlations.

2.5.11.1 Shocks S1 and S2: ρ1,2

The correlation between S1 and S2 is in [28] motivated by the Committee Parameters through

referring to [40], where it is found that diversification effects among equities are smaller in bear markets. Furthermore, it is stated that when stock prices fall, interest rates also fall. The reason stated is that bonds are deemed to be a safe replacement for stocks in times of uncertainty. At first, a correlation of 0.65 between the stock risk and the interest rate risk is assumed, which is in [28] proposed to be reduced to 0.5 in the case of increasing interest rate factors. Under the nFTK, the correlation is reduced to 0.4 in case the interest rate risk is based on falling interest rates and set to 0 in case of increasing interest rates.

As a final remark, we note that in calculations done by the Committee Parameters in [41], the correlation between the interest rate risk and the stock and real estate risk is set at 0 instead of the prescribed ρ1,2 = 0.5. The given motivation for this is that for determining the ROF we

look at extreme scenarios and it is therefore necessary to estimate how correlations behave in such extreme scenarios. This is a very interesting argument: is the nFTK not in its core for calculating the position of pension funds in extreme scenarios?

2.5.11.2 Shocks S1 and S5: ρ1,5

The interest rate risk and the credit risk is in the standard model assumed to be correlated with correlation ρ1,5 = 0.4 if the shock S1 is based on falling interest rates and ρ1,5 = 0 else. Notice

that DNB claims in [42] that in most cases, the most negative scenario (the S1 shock) is based

on falling interest rates.

2.5.11.3 Shocks S2 and S5: ρ2,5

The stock and real estate risk and the credit risk is in the standard model assumed to be correlated with factor ρ2,5 = 0.5. Under the FTK, this correlation was set at 0. However, this

has been changed in the nFTK and no motivation from DNB or Committee Parameters has

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been discovered. No mention of the increase is found before the legislation was presented, not even in [41], the Advice of the Committee Parameters, 10 months prior to the effective date of the nFTK. It is not immediately apparent why a positive constant correlation is appropriate for the two risk factors. In times of high inflation, a positive correlation between stock and bond returns seems to exist and in times of low inflation, a negative correlation between stock and bond returns appears to exist (see [43]).

2.6 Regular values

To get an idea of the magnitude of the risk categories within the ROF, we consider again the five big Dutch pension funds PMT, PME, ABP, bpfBOUW and PFZW. We look at the value of the risk categories in the years 2016 and 2017 per pension fund (see [44],[45],[46],[47],[48],[21],[22], [23],[24],[25]). The results of the pension funds are summarized in Table 18, Table 19, Table 20, Table 21 and Table 22.15 _{First of all, the risk categories S}

7, S8 and S9 are assumed 0 in

every pension fund of our analysis. This is in line with the assumption of the standard model of the DNB (see Section 2.5.7, Section 2.5.8 and Section 2.5.9). Secondly, most pension funds greatly increased their own funds over the period 2015-2017, but only bpfBOUW came close to having the ROF (18% out of 25.5% in 2017). To give an idea of the size of the categories, we summarized the results by taking the equally weighted average of the percentages in Table 3.16

Factor S1 S2 S3 S4 S5 S6 S10 P_iSi ROF DE OF

Average 5.1% 17.5% 4.8% 1.4% 4.1% 3.1% 2.0% 38.2% 23.8% 14.5% 1.8%

Table 3: The equally weighted average of the pension funds over their equally weighted average in the period 2015-2017. We use the following abbreviations: “DE” for Diversification Effect and “OF” for Own Funds. Again, ”ROF” stands for Required Own Funds.

It is clear that the shock concerning stocks and real estate is contributing the most to the ROF. This is quite interesting, when we take a look at the average positions of pension funds in Table 4, where the category fixed income is generally the largest. Apparently, the nFTK gives incentive to invest less in stocks (and real estate). This is remarkable, as Committee Parameters noted in [28]: “An important consideration for using the unconditional scenario is that the solvability test should maintain a neutral point of view for future stock exchange developments. To put it differently: the magnitude of the required own funds may not contain an implicit signal that the risk on investing in stocks in a period is deemed to be relatively high or low. This would give an unwanted incentive to change the asset allocation because of a short term perspective and not because of a long term ALM vision.”

15_{Some pension funds set the liabilities in euros, we converted it to percentages by dividing by total liabilities.} 16_{Of course the pension funds have different sizes, but a weighted average could put too much weight on the}

biggest pension fund. The idea was to give a general overview of the magnitude of the shocks, diversification effects and the (required) own funds.

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Category Billions Percentage Fixed income 718.667 54.3% Stocks 383.199 29.0% Hedge funds 25.341 1.9% Real estate 126.178 9.5% Alternative investments 73.445 5.6% Commodities 0.64 0.0% Other investments -3.037 −0.2% Currency overlay -1.862 −0.1%

Table 4: Positions of Dutch pension funds in Q4 2018, based on [49].

That the situation as of 2018 is quite troublesome, can be seen in Figure 3, were the Policy Funding Ratio for different Dutch pension funds is shown. Partly based on this worrisome situation, the Pension Agreement came in 2019. We will elaborate on the Pension Agreement and the Advice of the Committee Parameters of June 2019 in Section 2.7.

Figure 3: Situation of Dutch pension funds in 2018 according to [9]. The horizontal axis is the Required Funding Ratio, the vertical axis is the Policy Funding Ratio. The size of the sphere indicates the size of the pension fund. The colors indicate the situation of a pension fund: green means healthy and full indexation, yellow means partial indexation, orange means no indexation, but no pension cuts and red means serious risk of pension cuts.

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2.7 Pension Agreement and Advice Committee Parameters

In this section, we extend the introduction of the Dutch pension system, the nFTK and its standard model in Sections 2.1, 2.2, 2.3, 2.4 and 2.6, by two major recent events: the Pension Agreement and the Advice of the Committee Parameters. The Pension Agreement is discussed in Section 2.7.1 and the Advice of the Committee Parameters in Section 2.7.2.

2.7.1 Pension Agreement

On 5 June 2019, an agreement in principle was achieved between the government, employers’ organizations and employees’ organizations regarding the renewal of the Dutch pension system. We (briefly) summarize the Pension Agreement in this section, which is laid down in [1].

The motivations for the Pension Agreement are described in [1]. It is mentioned there that over the last decade, vulnerabilities of the system were exposed by the risen life expectations and the changes in the labour market and financial markets. Financial shocks can not be absorbed because of longevity risks, endangering the system. Moreover, the crisis of 2008 and the regime of low interest rates showed that the financial market is decisive for the degree of certainty and the (preservation of) purchasing power. Also, the returns on investment are as of 2019 not used for indexing pensions, but for replenishing buffers. The lack of indexation causes persistent dis-cussion, undermining the public support for the current pension system.

The exact details for cutting pensions and determining indexation based on the (Policy) Funding Ratio are not known yet (as of August 2019), but [1] gives the foundations on which these rules should be based. First of all, (negative) shocks in returns on investments may only to some extent be passed on to future generations. To reach this goal, the (Policy) Funding Ratio may not be lower than 90% and not below 100% for more than 5 years. In this way, no more than 10% of the pension premiums can be used to pay for deficits. Moreover, the pension entitlements may only vary based on asset results and developments in life expectancy.

As noted in [1], if there are any pension cuts, they are lower (as the MRFR is now 100% instead of around 104.2%). Moreover, it is noted that the 100% is a turning point: if the (Pol-icy) Funding Ratio is lower than 100%, the pension cuts are higher than under the nFTK, while if the (Policy) Funding Ratio is higher than 100%, indexation is easier. However, the new rules have not been developed.17

2.7.2 Advice Committee Parameters

Based on the Dutch Pension Law, at least every 5 years an independent committee sets rules about:

• the minimal percentage of the price and wage inflation,

17_{The Dutch Bureau for Economic Policy Analysis (Centraal Plan Bureau, CPB) has however developed some}

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• the maximal return on fixed income,

• the maximal risk premiums on stocks and real estate, • a uniform set of economic scenario’s,

which should take the financial-economic development in the past and realistic insights of future financial-economic expectations into account.18 _{The independent committee is called the}

Com-mittee Parameters, which came up a couple of times before in this thesis. Coincidentally, the latest Advice of the Committee Parameters came out in June 2019 (see [2]), shortly after the Pension Agreement. We first summarize the major results, important for our understanding and analysis of the nFTK, compared to the Advice of the Committee Parameters in 2014 (see [41]). Then, we shortly elaborate on the effects of the Advice of the Committee Parameters and the reception thereof.

Firstly, we obtain the values in Table 25. We notice that the returns on assets are lower than in [41], but the same holds for the minimal expected price and wage inflation. We do recognize that the percentage (point) change of returns on assets is quite somewhat higher than for the price and wage inflation, when we compare [41] to [2].

However, we think that the most important change of [2] is the change in the Ultimate For-ward Rate (UFR) methodology. The UFR is calculated using a 20-year average of forFor-ward rates. The yield curve converges to the UFR-asymptote, starting from a maturity of 20 years. In Figure 18d, a nice illustration is given of this methodology from the DNB. Notice that as of June 2019 it is known that the yield curve only starts converging from 30 years instead of 20 years (see [2]). The UFR will now be based on the 120-months average of the 30-years for-ward rate, instead of the 120-months average of the 20-years forfor-ward rate. Moreover, the First Smoothing Point (FSP) is increased from 20 to 30 years. The FSP is the point from which the term-structure starts converging to the UFR. For example, we clearly see the application of the FSP (of 20 years), in Figure 18d. The result of these changes is that the actual market of interest rates receives a more central role in calculating the discount factors for pension funds. As the current interest rates are quite low, this results in low values for the UFR. For example, the Committee Parameters notes that the UFR under their new methodology was 2.1% as of end 2018. Of course, the UFR can increase a lot, if interest rates increase, but it will still be based on the 120 months average of the 30-years forward rates, and it will not change rapidly. From now on, we assume throughout the thesis that the UFR is fixed and equal to 2.1%, in order to simplify results and our analysis. As an unweighted 120-months average will not quickly change, this does not seem much of an assumption. Moreover, liabilities with a duration of less than 30 years are under our model still determined under the actual term-structure of our simulations and these liabilities make up the largest proportion of the liabilities (see Section 3.4).

The new Advice of the Committee Parameters was not received very well, see for example [5]

18_{Art. 144 Pw.}

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and [51]. Most criticism was aimed at the UFR method, which resulted in lower discount factors. Criticizers claimed that the positive effects of the Pension Agreement (easier index pensions) are cancelled out by the negative effects of the new UFR (lower discount factors, hence harder to index pensions and faster cuts in pensions).

2.7.3 Evaluating the new Financial Assessment Framework and alternatives

In the current section, we discussed relevant material of the nFTK and the regulations for pension funds. We proceed by writing an ALM model in Section 3, taking into consideration the regulations as closely as needed for a good analysis. Here we discuss how our pension fund is set up, hence how it invests in assets, calculates its liabilities and determines the pension entitlements of pension participants. We moreover motivate the assets our pension fund can invest in and the term-structure applicable. After the discussion of our ALM model, we will simulate our pension fund 20 years ahead. The results are presented in Section 4, where the nFTK is evaluated in Section 4.1 and alternatives are discussed in Section 4.2 and Section 4.3. To give a general overview, we consider alternatives for the investment strategies of the pension fund, alternative stock returns and an alternative term-structure setup in Sections 4.4, 4.5, 4.6 and 4.7.

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3 Asset and Liability Management model

In order to evaluate the nFTK, we want to set up and simulate an Asset and Liability Manage-ment (ALM) model. The setup of the ALM model is crucial, as we want the assessManage-ment of the nFTK to be as realistic as possible. The implementation of our ALM model is in MATLAB and it is built from scratch.

We consider two assets: stocks and (zero-coupon) bonds. Next to that, we also need infla-tion rates in order to assess the impact of inflainfla-tion on the pensions of pension participants. The modelling of stocks is done in Section 3.1 and the modelling of interest and inflation rates is done in Section 3.2. The liabilities of our ALM model are very important in order to adequately eval-uate the nFTK. Moreover, we need to incorporate pension funds strategies, keep track of pension entitlements and make assumptions about wages and demographics. The complete setup for the pension fund is considered in Section 3.4.

Lastly, we explain how the nFTK regulations are used in our model in Section 3.5. We summa-rize our model in Figure 4, where the separate parts of the model can be found in the sections mentioned above. We first import the input data. The different types of data are used to find parameters for our term-structure model, our stock model and for the demographic structure. These models separately generate scenarios which are imported to a model for our pension fund. The model for our pension fund then produces simulation output, which we can analyze.

Demographic data Stock index

CPI index Nominal term-structure

& inflation swaps

Demographic structure Stock model

Term-structure model

Simulated stock returns Simulated CPI/interest rates, bond returns

Model for pension fund Simulation output

Input data

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3.1 Stock model

In order to obtain a realistic ALM model, we need to be able to simulate stock returns. We will simulate stock returns by setting up a stock price process (St)t≥0. First, we assume a geometric

Brownian motion in 3.1.1, which is assumed to be known to the reader and therefore discussed briefly. Then, we extend the geometric Brownian motion by introducing mean reversion in Section 3.1.2.

3.1.1 Stock model

The starting point of our stock model is the underlying probability spaceΩ, F , (Ft)t∈[0,T ], eP

. We start by assuming that the stock prices (St)t∈[0,T ]follow a geometric Brownian motion. Thus,

we find the following dynamics for (St)t∈[0,T ]:

dSt= µStdt + σStdWtS, µ ∈ R, σ ∈ R≥0, t ∈ [0, T ], S0> 0, (2)

and where WS

t is a Brownian Motion adapted to the filtration (Ft)t∈[0,T ]. Applying Itˆo’s formula

on the stock price (St)t∈[0,T ], with function f (St) := log St, we find:

d log St= µSt 1 St dt −σ 2_S2 t 2 1 S2 t dt + σSt 1 St dW_tS= µ −1 2σ 2 dt + σdW_tS. (3)

As we will be simulating stock prices for discrete time steps for this continuous-time model, we need to find the discrete version of (3). For this, we assume that we only have stock prices available at certain points in time. The time step between the available stock prices is equidistant. Hence, instead of (St)t≥0, we need (Si)i∈T, where T = {0, 1, . . . , T }. Moreover, we denote

ri= log Si+1

Si as the log return. We can then us the actual log-normal distribution of (St)t≥0 to

rewrite (3) as:

log Si+1 = log Si+

µ − 1 2σ 2 + σ W_i+1S − WS i , ri= µ −1 2σ 2 + σZi, where Zi:= Wi+1S − W S i ∼ N (0, 1) . (4)

Now, suppose that we find a series of log returns (ri)i∈{0,...,T −1}, derived from (Si)i∈T, to which

we want to fit the parameters µ and σ. Denote µ_br as the empirical mean, bσ

2

r as the

empiri-cal variance, respectively, of (ri)i∈{0,...,T −1}, obtained by averaging and averaging the squared

deviations fromµ_br, respectively. We find as estimators for µ and σ2:

b µ =_bµr+ 1 2bσ 2 r, b σ2=_bσ_r2. (5)

These estimators are based on Maximum Likelihood by noting that (Zi)i∈{0,1,...,T −1}, where

Zi :=

ri−(µ−1₂σ2)

σ , is a sequence of independent and identically Standard Normal random

vari-ables (see Appendix C). As an estimator of the volatility we simply take_bσ =√σ_b2_.19

19_{The notation}

b

σ2 _{for an estimation of the variance might seem ambiguous, as we should actually denote it}

c

σ2_{. However, we will from now on always estimate the variance and use the square root of the variance as an}

estimation of the volatility. Therefore, we stick to the (aesthetically more pleasing) notation ofbσ

2_.

An Alternative Financial Assessment Framework for Pension Funds