A partial buy-out optimization based on
the expected future indexation level
Wilmer Lodder
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: Wilmer Lodder
Student nr: 10624163
Email: wlodder77@hotmail.com
Date: November 24, 2015
Supervisor: Dr. T.J. Boonen (UvA) Second reader: ...
A partial buy-out optimization — Wilmer Lodder iii Abstract
This thesis examines in which situation a partial buy-out could be inter-esting to de-risk the pension fund’s balance sheet. So can such a de-risk solution be beneficial to the buy-out group and the remainder of the fund? We examine the case of a partial buy-out of only pensioners. Such a partial buy-out will be attractive to both the pension fund and the insurer. This because the pension fund will be able to adjust its risk profile to match the risk position of the younger remainder of the fund and the insurer will be able to comply with a lower solvency requirement due to the introduction of the matching adjustment in Solvency II. We analyse the fifteen year de-velopment of three model pension funds (young, average and old) for the entire pension fund and the remainder of the fund after the partial buy-out. At the partial buy-out we examine two possible options of splitting the as-sets between the buy-out group and the remainder of the fund. The two options are related to splitting the assets based on: the expected indexation level and the current funding ratio. This thesis shows that a carve out is more interesting at a higher funding level. The tipping point if a pensioner carve out is interesting to both groups is around a funding level of 110%. It shows also that a pensioner carve out is less interesting for older pension funds (pension funds with a lower duration). It is most likely that for these pension funds a complete buy-out will be a better solution than a carve out. Another conclusion is that splitting the assets based on the funding ratio never leads to the optimal results. So at a pensioner carve out the pension-ers should never receive the same funding level as the remainder of the pension fund. A last conclusion is that the interest rate vision is crucial to the results.
Keywords Pension buy-out, Partial buy-out, Pensioners buy-out, new financial review framework, Asset liability management, De-risking solution, Indexation risk
Disclaimer
The views expressed in this paper are those of my own and do not necessarily represent the views of Towers Watson.
Preface vi
1 Introduction 1
2 Pension buy-outs in the Netherlands 3
2.1 A brief introduction to the Dutch pension system . . . 3
2.2 The pension buy-out market . . . 3
2.3 Nominal buy-out or buy-out including inflation . . . 5
2.4 Differences between CPI and HICP . . . 5
2.5 The new Financial Review Framework. . . 6
3 Data description 7 3.1 Mortality rates . . . 7
3.2 Economic scenario sets . . . 7
3.2.1 Economic rates and return on investments . . . 8
3.2.2 Yield curves . . . 9
3.3 Current yield curve . . . 10
4 ALM model 11 4.1 Participants and pension entitlements . . . 11
4.1.1 Age distribution of participants . . . 11
4.1.2 Development of participants. . . 12
4.1.3 Salaries and pension bases . . . 13
4.1.4 Accrual of pension entitlements . . . 14
4.2 Liabilities . . . 15
4.2.1 Cash flow of future benefits . . . 15
4.2.2 Present value of liabilities . . . 16
4.2.3 Duration of liabilities. . . 16
4.3 Assets. . . 17
4.3.1 Premiums and benefits . . . 17
4.3.2 Value transfers . . . 18
4.3.3 Hedging interest rate risk . . . 18
4.3.4 Annual return and total assets. . . 19
5 Carve out 20 5.1 Pensioner carve out . . . 20
5.2 Price of carve out . . . 21
5.3 Sharpe ratio . . . 22
6 Results 24 6.1 Assumptions . . . 24
6.1.1 Fixed assumptions . . . 24
6.1.2 Asset allocation assumption . . . 25
6.2 Results . . . 25 iv
A partial buy-out optimization — Wilmer Lodder v
6.2.1 Average pension fund with a funding ratio of 110% . . . 26
6.2.2 Sensitivity of the duration . . . 27
6.2.3 Sensitivity of the funding ratio . . . 29
6.2.4 Results based on the set with vision. . . 32
7 Conclusions 35 7.1 Summary of the results . . . 35
7.2 Main conclusions . . . 36
7.3 Further research . . . 37
Glossary 38
Appendices 40
While writing this thesis I realized that a study of five years nearly come to an end. Of these, I studied four years of mathematics at the University of Utrecht and one year of actuarial science at the University of Amsterdam. I am satisfied and happy with it. Therefore I am thankful to everyone who has supported me. First, I would like to thank Tim Boonen, my supervisor at the University of Amsterdam, for his support, useful advice and the freedom he has given me during my research. Secondly, I would like to thank Lennaert van Anken, my supervisor at Towers Watson, for guiding me through my research, giving me useful instructions, technical advice and sharing his knowledge. I am also thankful to Towers Watson and all colleagues in Rotterdam for the opportunity to use all their resources and the amazing time to work with them. I am also grateful to my family and friends for their support and distraction. Especially my parents for their mental and financial support to complete my study. Finally, I would also like to thank my friend Michael for the amazing adventure during all years of study and trips we have made.
Chapter 1
Introduction
Since the financial crisis in 2008 pension funds are struggling to comply with their obligations. In recent years, interest rates and return on investments have decreased significantly and had at the end of 2014 never been that low. As a result of declining interest rates and return on investments, liabilities have increased and assets have not increased sufficiently enough as ex-pected, with the result that the funding ratios have decreased and pension funds came, or will come, under pressure. Due to the increased risk in the financial market it becomes increasingly difficult for pension funds to ensure their obligations. Pension funds will reduces pension en-titlements rather than provide indexation. Since the government has adjusted the Financial Review Framework (financieel toetsingskader (FTK)), pension funds must comply with more stringent rules for the valuation of its obligations and indexation policy. For example, pension funds must maintain a higher solvency buffer, which makes it more difficult to provide (full) indexation, and in some cases even reduce pension entitlements in order to comply with this requirement. This might lead to the result that accrued pension will not be compensated for inflation, which means less old-age pension for the participants.
Thus pension funds are looking for solutions to demonstrate effective risk management and reduce the risk of their liabilities (see Watkins (2011)). This can be done in many ways. For ex-ample by adjusting the investment policy (hedging interest rate risk), the premium policy or the policy of outsourcing the pension fund’s work, such as the pension fund’s administration or asset management. The outsourcing policy can be obtained by a pension buy-in or pension buy-out. At a buy-in the pension fund insures the pension entitlements of the participants, but the assets and the liabilities will remain on the pension fund’s balance sheet. Both the pen-sion fund and the insurance company should administrate the penpen-sion entitlements, which ensures double administration costs. Therefore a buy-in is not attractive for pension funds. At a buy-out the pension fund transfers its assets and liabilities to an insurance company to guarantee the pension entitlements sometimes including indexation. This possibly purchased indexation at a buy-out depends on the funding ratio of the fund. All the assets and liabilities will be off-loaded from the balance sheet and the fund liquidates. Such a buy-out is also known as a complete buy-out. Another solution is to consider a partial buy-out, where a part of the assets and liabilities will be transferred to an insurance company. The fund will off-load these transferred assets and liabilities from its balance sheet and remains with the remaining assets and liabilities.
A pension fund board has to balance the interest of all participants for their risk management decisions. These decisions may have different consequences for different participant groups. In particular, the interest of younger participants will be quite different than the interest of elderly. The policy of the fund must be in line with the supervisory framework. This frame-work provide a basis to ensure these various interests, but ultimately it is the responsibility of the board to comply with it. A partial buy-out can help the board to simplify this task. From a legal point of view, the most obvious choice for a pension fund is to transfer the pensioners
to the insurer and continue with active and deferred participants at the pension fund. In this thesis the name carve out indicates a partial buy-out, because partial buy-outs literally carve the pension fund into two parts. A partial buy-out where especially the pensioners’ liabilities are transferred, is called a pensioner carve out1.
With the introduction of the nFTK the rules for indexation become more strict which means that the prospects for future indexation are limited. Beside that, there is a risk of reductions in pension entitlements. Especially when a fund has a funding deficit, which means that the funding ratio is below the minimum required funding ratio. The larger a pension fund has a funding deficit the higher the risk of reductions. A pensioner carve out can realise a guaran-teed pension benefit for the pensioners. Possibly, depending on the funding ratio, with a fixed annual indexation. Pensioners are relatively risk averse which means that after the carve out the risk profile can be adjusted in such a way that it matches the risk position of the remain-ing participants. In addition, dependremain-ing on the actual fundremain-ing ratio, there may be a fundremain-ing release after the carve out. This means that the remainder of the fund obtains a higher funding ratio. The improved risk position and extra buffer can lead to a higher indexation potential for the remaining participants. Thus a pensioner carve out may have advantages for both groups (pensioners and remaining participants).
In this thesis we will examine for which situation a pensioner carve out will be interesting for a pension fund. Interesting in the sense of potential advantages for both the pensioner group and the remaining group. When there are disadvantages for at least one of the two groups, then a carve out is probably not advisable, and the supervisor will not agree with such a solution. We will use the potential indexation to measure if a carve out is interesting: the pensioners gets a guaranteed pension benefit and a fixed indexation percentage, depending on the actual funding ratio, and the remaining fund will adjust its risk position so the potential indexation will be higher. Especially the distribution of assets will be a discussion of both groups’ interest. A correct distribution is important, because this determines the amount of inflation an insurer may purchase and determines the amount of funding release for the remaining fund. Thus we will optimize the potential amount of annual indexation for both groups and take their inter-ests into account so that it will create a win-win situation.
Following on from this chapter, we will have at first a look at pension buy-outs in the Nether-lands in Chapter 2, where we will discuss different issues according to the Dutch pension buy-out market. Then we will discuss in Chapter3the data which is used in our calculations. This calculations are done with an ALM model and this model will be discussed in Chapter4, where we describe the future developments of the pension funds, liabilities and assets. Then in Chapter5we will explain the pensioner carve out in further detail and define a measure to compare the results. At the beginning of Chapter6we discuss the assumptions and determine the current asset allocation of the pension funds. In the rest of this chapter we examine the results and discuss some sensitivities. Finally, we summarize the results and give a conclusion in Chapter7.
1The term (pensioner) carve out is a term introduced by Towers Watson. All rights are reserved by Towers
Chapter 2
Pension buy-outs in the Netherlands
In this chapter we will discuss a brief introduction to the general Dutch pension system and the current pension buy-out market in the Netherlands. We will also discuss the difference between a nominal buy-out and a buy-out including inflation, where we describe the difference between two types of inflation rates and which types insurers do actually offer. Finally we will have a look at some adjustments within the Financial Review Framework which have made a carve out interesting.
2.1
A brief introduction to the Dutch pension system
The Dutch pension system consists of three pillars. The first pillar is a social security (AOW), which is meant to be as a minimal income for a reasonable quality of life. For 2015 the annual amount of this social security is set to e 9,481 (per person) for a married couple and e 13,866 for an unmarried person. This security is funded by a pay-as-you-go system (PAYG) and is paid to the Dutch population from the retirement age. The retirement age will increase from 65 in 2013 to 67 in 2023 and is currently (2015) equal to an age of 65 years and three months. The second pillar is a pension accrued by employees during their working life. All employees within a company or industry are able to participate in a pension plan if this is offered by the employer. When the employer offers a pension plan, he is mandatory to offer this pension plan to all his employees. This additional pension will be accrued in a collective pension plan. The most common collective pension plan nowadays is an average wage defined benefit-plan. In an average wage defined benefit plan the participants accrue each year a fixed percentage of their pension base, which is equal to their pensionable salary minus the offset. These accrual rate and offset are defined in such a way that at the end of his career a participant has accrued at least 70% of his career average salaries. For 2015 the fiscal maximums of the accrual rate and offset for an average pay plan are set to respectively 1.875% and e 12,642.
The third pillar is an additional pension where individuals can establish their own life insur-ance contract with a financial institution. This is mostly used by self employed individuals, who are not covered by the second pillar, or sometimes by individuals who want an extra pen-sion income. As this kind of penpen-sion is very personalized, it will not be detailed any further. Pension buy-outs are related to the second pillar and focused on buying accrued entitlements of a (defined benefit) pension plan.
2.2
The pension buy-out market
In countries, such as the United States, Canada, United Kingdom and Ireland, there is a strong demand for pension buy-outs from the perspective of pension funds. This demand is also con-stantly increasing in the Netherlands. The total number of pension funds in the Netherlands
has decreased from 800 to approximately 300 in the last few years and it is expected that in the coming three years not more than a hundred pension funds will remain (De Horde (2014)). Especially small pension funds are interested in liquidation solutions, but in recent years it appears that also medium and large funds are interested in such solutions. Not all of these liquidated funds have transferred its obligations to an insurer. Around a third has searched a solution on the buy-out market and the other two-thirds have been merged with other pen-sion funds. Reasons for this increase of liquidations are the increasing risks, such as financial risks and longevity risk, more stringent laws, complex pension plans, which consists of dif-ferent plans for difdif-ferent group of employees, and the execution of plans, which is becoming increasingly complicated. Therefore the advantages of a buy-out is that the fund off-loads the risks from its balance sheet and reduce execution and governance costs. Buy-outs have also some disadvantages for pension funds. For example, pension funds can no longer take advan-tage from financial windfall profit and the potential future indexation will be limited. Besides that insurance companies must ensure pension entitlements with a certainty of at least 99.5%, which is higher than the certainty level for pension funds who must ensure at least 97.5%. This makes buy-out offers relatively costly. At the other hand, pension entitlements are more guaranteed due to this higher certainty level.
However, in recent years insurers are less interested in pension buy-outs (De Groot (2014)). Just now when there are large pension plans to buy, insurers respond with caution. Despite the fact that many insurers offer individual annuity, there are only four large insurance companies on the buy-out market in the Netherlands. The four insurers on the current buy-out market are Delta Lloyd, Aegon, a.s.r. and Nationale-Nederlanden. These four insurers are causing an oligopoly on the buy-out market. Table2.1shows an overview of some insurers and banks who offer individual annuities in the Netherlands. According to De Horde (2014), it is expected that in future years also foreign insurers will enter this market, which should be positive for pen-sion funds.
Insurance companies Banks
Nationale-Nederlanden Erasmus Leven ABN AMRO
Aegon Allianz SNS Bank
Delta Lloyd de Goudse verzekeringen ING
Reaal a.s.r. RegioBank
Zwitserleven OHRA Rabobank
Centraal Beheer Achmea
Table 2.1: List of insurance companies and banks who offer individual annuities in the Nether-lands according to http://www.apple-tree.nl/, which is an independent site where annuities of different providers are compared with each other.
According to De Groot (2014), the main reason of the low interest in buying pension enti-tlements of pension funds, is the current situation on the financial market. The current low yields provide higher pension liabilities and duration, so that insurers have more difficulties to match this with the duration of their assets. But, as of 1 January 2016, insurers have to have implemented Solvency II1. Insurers can request permission of the supervisor (DNB) to use
the Matching Adjustment (MA). The MA is an adjustment on the risk-free yield curve which insurers use for the valuation of annuities or pension obligations. This gives insurers a better opportunity to match benefit cashflows with their (long-term) assets (see Porteous & Martin (2015)). Beside that, the liabilities of pensioners have a lower duration than the the total pen-sions funds’ liabilities. The combination of the MA and only pensioners’ liabilities will make this sort of buy-outs more interesting for insurers.
A partial buy-out optimization — Wilmer Lodder 5
2.3
Nominal buy-out or buy-out including inflation
At a nominal pension buy-out the insurer purchases only accrued pension entitlements with-out any future compensation for inflation. But for a pension buy-with-out including inflation the insurer has to guarantee the annual amount of indexation whatever the financial situation will be. Therefore the insurer has to purchase a price inflation. The Dutch national price infla-tion index is based on the consumer price index (CPI) of the Netherlands. This index measures changes in price level of consumer goods and services purchased by Dutch households. The annual percentage change in a CPI is used as a measure of inflation. Most pension funds uses the CPI as benchmark for applying indexation on pension entitlements. CPI inflation can not be purchased at any of the current insurers in the Netherlands. Only at some insurers (Delta Lloyd and A.S.R.) it is possible to purchase European price inflation. This European price in-flation is a weighted average of price indices of European Union member states who have adopted the euro, which is measured by the Harmonised Index of Consumer Prices (HICP). The HICP index is an indicator of price and inflation stability for the European Central Bank (ECB), which will be used as measure to compare inflation rates between the EU member states. The ECB aims to maintain annual inflation rates as measured by the HICP below, but close to, 2% for the medium term.
An alternative of a buy-out including HICP inflation is a buy-out including a fixed inflation rate. This fixed inflation rate is a fixed annual growth of pension entitlements and can be purchased at all insurance companies. We will not discuss the possibility of purchasing fixed inflation rates any further. In the rest of this thesis, we will only use the HICP inflation for buy-outs including inflation.
2.4
Differences between CPI and HICP
Figure 2.1: CPI and HICP price inflation development in months over the last 10 years. Source: http://nl.inflation.eu/inflatiecijfers/historische-hicp-inflatie.aspx.
Even though it is only possible to purchase HICP price inflation through a buy-out, there are some differences between the HICP and CPI price inflation, which pension funds mostly use to index pension entitlements. These differences are partly due to the different calculation methods used for both indices. For example, the HICP takes the consumption of tourists into account, while the CPI does not. On the other hand, the CPI takes consumption taxes into account and the HICP does not. Moreover, in spite of these differences, both measurements
are strong correlated and usually almost equal. The following graph shows the development of both inflation rates for the years 2005 until mid 2015.
Over the recent 10 years the CPI and HICP inflation indices have been almost equal. The dif-ferences between the CPI and HICP in the recent years could be explained by the different calculation methods for the category housing. In the HICP method the increase in rents is charged to only tenants, while the CPI also charges the property owners. So changes in rents has more influence on the CPI index. From 2013 the rents have increased sharply, because of a policy adjustment for rents, with the result that the CPI inflation has become significant higher than the HICP inflation.
2.5
The new Financial Review Framework
Since the beginning of 2015 the government has adjusted the Financial Review Framework (FTK), which is the regulatory set of rules for Dutch pension funds’ balance sheets, premiums and indexations. The FTK is relied upon pension fund oversight for evaluating funding require-ments, mandating funding recovery plans and determining permissible changes to benefit lev-els (reduction and indexation of pension entitlements). According to the revised framework (nFTK) pension funds must comply with more stringent rules for the valuation of pension lia-bilities and indexing pension entitlements. Three changes in the nFTK in comparison with the FTK which have made a carve out interesting are:
• pension funds must hold a higher solvency buffer in order to realize the legally required degree of actuarial certainty;
• discount rates are based on a lower, risk-free discount rate (new ultimate forward rate approach);
• stricter funding rules for indexation, while reductions of pension entitlements, if neces-sary, will be spread over time.
With the above mentioned adjustments, a partial buy-out has become interesting. The first adjustment is simple to explain. Pension funds must withhold a higher solvency buffer of 25% and a degree of actuarial certainty of 97.5%, which result to less indexation possibilities and more risk of possible reductions. The second adjustment leads to a decreasing funding ratio which also results in less indexation possibilities. The more strict rules of the last adjustment includes, for example, the following: indexation is not allowed at funding ratios below 110%, full indexation is allowed only at funding ratios higher than 130% and reduction of pension entitlements must be applied when funding ratios are below 105% on six consecutive years. Thus also this adjustment leads to a lower indexation potential. Based on these adjustments a pensioner carve out may be a solution to have a higher indexation potential.
Chapter 3
Data description
This chapter defines the data which will be used in the ALM model. We will describe the used projection table to define the mortality rates of the population. This will be used to develop the number of participants over time and to determine the pension funds’ obligations. And we will also describe the economic scenario sets, which consists of different future economic scenarios, to provide an expected development of the pension fund.
3.1
Mortality rates
For calculating pension liabilities, the best estimate assumption for mortality is usually based on a generational table. We will use AG prognosetafel 2014 as the mortality table in this Thesis, which is the most recent mortality (projection) table published by the Dutch Actuarial As-sociation. This mortality table takes recent mortality levels into account and estimate future mortality rates for the entire Dutch population. The estimation is based on both mortality data of the Netherlands and mortality data of European countries of similar wealth to the Nether-lands. The mortality table is based on an underlying stochastic model and gives the estimated mortality per age for the years 2014 until 21841. Beside the AG2014 mortality table, we take
also an experience mortality into account. This can be seen as a correction on the AG mor-tality table for the working population. For this category a correction is needed, because the working population has in general a higher age expectation. For the experience mortality we use the Towers Watson 2010 Ervaringssterfte tafel. This is a general used correction table for the entire Dutch working population.
3.2
Economic scenario sets
For the ALM study we will use the economic scenario sets available within Towers Watson. These scenario sets are defined by the Global Investment Committee (GIC) of Towers Watson. The GIC department proposes every three months a new scenario set which will be based on four general economic assumptions, namely: current financial market conditions, historical returns, financial market consensus and economical theories. We assume two type of sets: one set where the yield curve will increase over time (set with vision) and one set where the yield curve develops based on the current economic assumptions (set without vision). We will use the scenario sets based on economic assumptions of the last three months of 2014. A set con-sists of 1,000 different scenarios with a prognosis for the coming 15 years. Each scenario has a different return on investments, economic developments, nominal term structures and term structures with an Ultimate Forward Rate (UFR). All these rates and yields of a scenario are correlated with each other. The term structure with UFR has an asymptote, which is estimated
1see http://www.ag-ai.nl/view.php?action=view&Pagina Id=480for more information about the AG2014
pro-jection table.
on 4.2%, and is also known as the DNB term structure. This term structure is equal to the nomi-nal term structure up to a maturity of 20 years and thereafter convergence to the UFR. The DNB term structure is determined by the Dutch Central Bank for the valuation of pension liabilities.
3.2.1 Economic rates and return on investments
The economic scenario sets with and without vision have the same economic rates and re-turn on investments. Only the yield curves are different. In the ALM model are the following rates and return on investments used: the Dutch price inflation rate, salary development and different return on investments. Where we first have a look at the inflation rates and salary developments and then we discuss the different return on investments.
The price inflation rates in the scenario set are based on the Eurozone HICP indices as de-scribed in Section 2.3. So the accrued pension entitlements in the model will be indexed on the basis of HICP indices, and not CPI indices, which will make it easier to compare future indexation between the carve out group and the remaining fund. The arithmetic mean and standard deviation of the price inflation index and salary developments of the 1,000 scenarios and future 15 years are shown in Table3.1.
Notation Economic rate Arithmetic mean Standard deviation
i Price inflation index 1.62% 1.73%
λ Salary development 2.06% 1.93%
Table 3.1: Arithmetic mean and standard deviation of price inflation index and salary devel-opment. These numbers are based on the average of the 1,000 scenarios and future 15 years. The salary development is slightly higher than the price inflation index, meaning that the salaries will increase more than the national inflation on prices. Per scenario the rates are cor-related, thus when there is deflation at a certain time in a certain scenario, salaries will not be increased for the compensation of inflation. This is not always true; there are deflation scenar-ios where the salaries will increase slightly. In case one of the rates is negative, we will use a floor of 0% for both rates meaning the growth will not decrease. Note that the salary growth for making career is not related to these salary development rates. Salary increase for making career will be discussed in Section4.1.
Table3.2shows the arithmetic mean and standard deviation of different returns on investments for the future 15 years and the 1,000 scenarios.
Notation Investment categorie Arithmetic mean Standard deviation
r1 Worldwide equities 7.50% 17.40%
r2 European equities 7.46% 21.60%
r3 Directly invested property 5.04% 9.90%
r4 Commodities 3.33% 10.14%
r5 Corporate bonds 2.69% 5.24%
r6 Government bonds (dur 6) 1.84% 3.64%
r7 Government bonds (dur 15) 1.26% 8.33%
r8 High yield bonds 3.49% 10.64%
r9 EMD HC 3.02% 9.77%
Table 3.2: Arithmetic mean and standard deviation of price inflation index and salary devel-opment. These numbers are based on the average of the 1,000 scenarios and future 15 years. The above mentioned investment categories will be used in the model of this thesis. Note that the first four investment categories are investments in equities and the other five categories
A partial buy-out optimization — Wilmer Lodder 9 are investments in bonds. The mentioned bonds are all based on European bond categories. We have used two types of government bonds: one with a duration of 6 and one with a duration of 15. The duration of a bond is the weighted average of the times of all payments. EMD HC means Emerging Market Debt in Hard Currency which are bonds issued by less developed countries.
3.2.2 Yield curves
Concerning the yield curves the two economic scenario sets differ from each other. In the set without vision, the yield curve develops on the basis of the current economic assumptions. We called it the set without vision, because in current economic assumptions the yields would slightly grow on maturity. The other set has a vision of increasing yields over time. Both sets consist of nominal yield curves and DNB yield curves which is the nominal yield curve with an UFR. Figure3.1shows the average growth of the nominal and DNB yield curves for some future times of the set without vision. The yield curves do increase in the first twenty maturi-ties and remain constant or even decreases afterward. Over time the yields increase more and more slightly and end up constant. For the DNB yields it is easy to see that the yields converge to the UFR after maturity 20.
Figure 3.1: The average growth of the nominal yield curves (striped lines) and the DNB yield curves (solid lines) for some future moments in time (t = 1, 4, 7, 10, 15) of the set without vision.
The average growth of the nominal and DNB yield curves for some future times of the set with vision is shown by Figure3.2. Here the yield curves increase for all maturities in the first ten time periods, thereafter the yields remain nearly constant. For pension funds it means that based on the growth of the interest rates, the liabilities will decrease in the first ten future years and thereafter will remain nearly constant.
Figure 3.2: The average growth of the nominal yield curves (striped lines) and the DNB yield curves (solid lines) for some future moments in time (t = 1, 4, 7, 10, 15) of the set with vision.
3.3
Current yield curve
Before we do the ALM study, we have to need a fixed term structure for the valuation of the liabilities of the pension funds. At the end of every month DNB publishes a new term structure. With this curve, pension funds will be able to valuate its liabilities. Since the beginning of 2015, DNB has adjusted the establishment of the term structure (see DNB (2015)). The so called three-month-averaging was no longer applied by the establishment of the term structure. The reason for leaving out the three-month-averaging in the establishment of the term structure is that the nFTK introduces a twelve-month-average funding ratio, which replaces the point estimate funding ratio. Thus because of an already applied averaging method, DNB has leaved it out the establishment of the term structure. The economic scenario sets are based on the economic assumptions of the last three months of 2014, therefore we will use the DNB term structure of the end of 2014 without the three-month-averaging for the begin valuation of the liabilities. Figure3.3shows this yield curve and also the nominal yield curve of the end of 2014.
Figure 3.3: The nominal yield curve (striped line) and the DNB yield curve (solid line) of the end of 2014 without three-month-averaging. Source: http://www.dnb.nl/statistiek/ statistieken-dnb/financiele-markten/rentes/index.jsp
Chapter 4
ALM model
In this chapter we will describe step by step how the future development of the model pension funds is done. For this we do an asset liability management (ALM) study based on a scenario approach (Boender et al. (2007)). We use the Towers Watson economic scenario sets to develop a model pension fund for the coming 15 years for 1,000 scenarios. By taking the averages of the scenarios we will get a good view of the expected funding ratio growth. First we describe the development of the participants within the pension fund and the appropriate pension en-titlements. Next we will discuss the development of the liabilities and finally the development of the assets.
4.1
Participants and pension entitlements
In this section we describe how we have created fictitious pension funds. We will use three typical model pension funds: an old fund, an average fund and a young fund. First we will have a look at how the distribution of the participants over the ages for the starting year is done and thereafter we determine the development of the participants for the future years. Further we will determine the salaries and pension bases of the participants for all ages. Finally, we will describe the accrued pension entitlements and policies for indexation and reduction. 4.1.1 Age distribution of participants
For the starting year we have to distribute the total number of participants over the ages to create a model pension fund. An employee will participate the pension fund from the age of 20 and will leave the fund at the age of 100. Therefore, all participants should be distributed among the ages of 20 to 100. For this distribution we use a scaled normal distribution. Assume ˜X normal distributed with mean µ and standard deviation σ, so ˜X ∼ N(µ, σ ). A normal distribution is a continuous distribution, so the probability that ˜X is exact x is equal to 0. Thus before we are able to apply this to the distribution of the participants over the different ages, we approximate age x by taking an interval around x in stead of exactly x. Therefore we will use the probability that ˜X is in interval [x−0.5, x+0.5] to determine the fraction of the total number of participants which is aged x. Furthermore, we assume that participants enter the pension fund at the age of 20 and leave (die) at the age of 100, so we have x ∈ {20, 21, . . . , 100}. Because of this we need to make a correction for the probabilities P( ˜X ≤ 19.5) and P( ˜X > 100.5), so that the summed fractions will be equal to one. We assume that the fraction of a participant aged x is equal to
f rx = P(x − 0.5 ≤ ˜X < x + 0.5) P(19.5 ≤ ˜X < 100.5)
. (4.1)
Appendix A proves that the sum of fractions is equal to one. 11
Now we are able to determine the number of participants per age. Assume Ntotal as the total number of participants within the pension fund and assume Nx,t as the number of participants aged x at time t. For t = 0 we have
Nx,0= f rx ·Ntotal,
for all x ∈ {20, 21, . . . , 100}. Note that the number of participants will be real numbers, because the fractions f rx are real numbers. In practice, this is off course not possible, but we will not round off Nx,0, because in that case the sum of the fractions would not be equal to one anymore. The effect of this on the calculations will be negligibly small. Note further that P100
x=20f rx = 1, so the total number of participants at t = 0 is indeed equal to P100x=20Nx,0= Ntotal.
For the creation of the above mentioned three model pension funds, we use different values of µ and σ. We assume µ = 45 and σ = 15 for a young fund, µ = 60 and σ = 15 for an average fund and µ = 75 and σ = 15 for an old fund. Furthermore, all three pension funds have a total number of participants equal to Ntotal = 5, 000. The figure below shows the distribution of the participants at time t = 0 for these three model pension funds.
Figure 4.1: Distribution of the participants for the three model pension funds at t = 0.
4.1.2 Development of participants
For the participants development for the future years, we consider mortality, resignation and new entrants. Assuming that the underlying companies will not grow or shrink, the new en-trants will keep the total number of active participants constant over time.
The AG2014 mortality table (see Section 3.1) defines the mortality rates for the years τ = 2014, . . . , 2184. Because we will describe the model in times t and not years, we assume t = 0 as the (end of) year 2014, thus τ = t + 2014. Suppose the mortality rates as qxx,t for males and qyx,t for females, meaning that someone aged x at time t will die before reaching age (x + 1) at time (t + 1). Suppose also qxxexpas the experience mortality correction for males aged x and qyexpx for females aged x. These corrections are independent of time. Because of the different mortality rates for males and females, we must consider a distribution of males and females within the pension fund. Therefore assuming Male% as the percentage of males and Female% as the percentage of females with Male% + Female% = 1, which are also independent of time.
A partial buy-out optimization — Wilmer Lodder 13 Than the mortality rate at time t is equal to
qx,t = Male% · qxx,t ·qxxexp+ Female% · qyx,t ·qyexpx , (4.2) for all x ∈ {20, 21, . . . , 100} and t ∈ {1, 2, . . . , 15}. Thus the number of deceased participants aged x at time t will be equal to qx,t ·Nx,t.
For the probability of resignation we have defined a vector, which gives per age the probability that someone will be resigned (see Appendix B). Suppose νx as the probability that someone aged x will be resigned. Note that if x is larger than the pensionable age (xop), νx is equal to 0. Appendix B shows this probability ladder. The number of resigned participants aged x in year t will be equal to
νx ·Nx,t. (4.3)
For every case of decease, resignation or retirement of an active participant, a new participant will enter the fund. In this way, the underlying companies of the pension funds keep their total number of employees constant. Like the probability of resignation, we define a probabil-ity vector. These probabilities must sum up to one to keep the number of active participants constant (see Appendix B). Suppose ηx as the probability that someone aged x will enter the fund. Note that the participants of age 20 only consists of new entrants and if x is larger than the pensionable age than ηx = 0. The total number of new entrants aged x at time t is given by ηx · *. , Nxop−1,t−1+ xop−2 X i=20 (qi,t −1+ νi)Ni,t −1+ / -. (4.4)
When we summarize the above mentioned formulas, we obtain the following formula for the total number of participants:
Nx,t = (1 − qx−1,t−1−νx−1)Nx−1,t−1+ ηx · *. , Nxop−1,t−1+ xop−2 X i=20 (qi,t −1+ νi)Ni,t −1+ / -, for all x ∈ {20, 21, . . . , 100} and t ∈ {1, 2, . . . , 15}. Note that for the development of the number of participants over time, the number of participants is not a natural number, but also Nx,t will not be rounded off.
4.1.3 Salaries and pension bases
For the calculation of pension bases for all ages and times, we need to determine the salaries first. We assume that all participants of a certain age have the same salary. Suppose Sx,t as the salary of a participant aged x at time t and suppose Sstar t as start salary, which is the salary of a participant aged 20 at time 0. For every year older the salary will always increase with a constant percentage based on the age. We define this general salary increase with a ladder. Suppose ρx as the general salary increase for a participant aged x. This ρx will be higher for younger participants than for the elderly. Besides the general increase, the salaries will also increase with the salary development index as described in Section3.2.1. Suppose λt as the salary development index at time t. If in a certain scenario λt < 0, we will assume λt = 0. Therefore the salary of a participant aged x at time t is equal to
Sx,t = Sstar t ·(1 + ρ x)x−20 for t = 0; Sstar t ·(1 + ρ
x)x−20·Qti=1(1 + max{0, λi}) for t = 1, . . . , 15, (4.5) for all x ∈ {20, 21, . . . , xop−1}. The pensioners do not receive any salary, so Sx,t = 0 for all xop ≤x ≤ 100 and t ∈ {0, 1, . . . , 15}.
The pension base is defined by reducing the salaries with an offset. Suppose Ot as the offset at time t. The annual growth of the offset is based on the inflation rates which are mentioned in Section3.2.1. If the inflation is negative at a certain time t (deflation), then the growth of the offset is equal to zero. Supposing it as the inflation at time t, the growth of the offset is equal to Ot = O0· t Y j=1 (1 + max{0,ij}), (4.6)
for all t ∈ {1, 2, . . . , 15}, where O0is the offset at time 0.
Supposing Gx,t as the pension base of a participant aged x at time t, the pension base is ob-tained by subtracting (4.6) from (4.5), which is equal to
Gx,t = max Sx,t −Ot, 0 , (4.7)
for all x ∈ {20, 21, . . . , 100} and t ∈ {0, 1, . . . , 15}. 4.1.4 Accrual of pension entitlements
Here we will discuss the annual pension accrual and the annual growth (indexation or reduc-tion) of the already accrued pension entitlements. First we determine a policy for indexation and reduction of pension entitlements based on the previously mentioned nFTK framework, afterwards we focus on the total accrued pension entitlements.
Indexation policy. A pension fund may increase accrued pension entitlements for the com-pensation of inflation, called indexation. This indexation is based on the inflation rate it. As-sume that pension entitlements do not decrease in the case of deflation. According to the nFTK, pension funds may apply indexation when the fund has a funding ratio of at least equal to the minimum required funding ratio level (FRmin), which is defined in the nFTK and is indepen-dent of time. In case the funding ratio is above a certain level, funds may apply full indexation (equal to the inflation rate of that year). This funding ratio FRmax
t depends on the expected cash flow of inflation discounted by the expected return on assets. Supposing iexp as the ex-pected inflation rate and rAexpas the expected return on assets, the indexation cash flow at time t is determined as the vector
−→ CFindex t = (1 + iexp)0.5·CFt,1 (1 + iexp)1.5·CF t,2 ... (1 + iexp)99.5·CF t,100 .
Afterwards the present value (or discounted value) is equal to PVtindex = CF−→indext T 1/(1 + rAexp)0.5 1/(1 + rAexp)1.5 ... 1/(1 + rAexp)99.5 , with (CF−→index
t )T as the transposed indexation cash flow vector. This multiplication can be written as
PVtindex =X100 `=1
(1 + iexp)`−0.5·CFt,` (1 + rAexp)`−0.5 . The required funding ratio for full indexation FRmax
t is determined by FRmaxt = Lt ·CRminL+ PVtindex
A partial buy-out optimization — Wilmer Lodder 15 with Lt the pension liabilities at time t, which will be described in Section4.2. If the funding ratio is between FRmin and FRmax
t , then the indexation is determined by linear interpolation between 0 and it (Hoeveraars and Ponds (2007)). So the indexation It at time t is equal to
It = 0 if FRt ≤FRmin; F Rt−F Rmin F Rmax t −F Rmin ·it if FRmin < FRt < FRmaxt ; it if FRt ≥FRmaxt , (4.8) for all times t ∈ {1, 2, . . . , 15} and FRt as the funding ratio of the pension fund at time t.
Reduction policy. When the funding ratio of the pension fund is below the minimum re-quired capital (MRC) for six consecutive years, pension funds must reduce pension entitle-ments in such a way that after the reduction the funding ratio will be at least equal to the MRC (according to the nFTK). So when the funding ratio is below the MRC for six consecutive years (FRt −5 < MRC, FRt −4 < MRC, . . . , FRt < MRC), we apply the following reduction
κt = MRCFRt −1, (4.9)
with κt as the reduction percentage at time t.
With the indexation and reduction policy we are able to determine the annual pension accrual and growth of the accrued pension entitlements. The active participants will only accrue old age pension based on an average wage pension plan. Supposing OPx,t as the accrued pension entitlements of a participant aged x at time t and ap% as the accrual percentage, the accrued pension entitlements are equal to
OPx,t = OPx−1,max{0,t−1} ·(1 + It −1+ κt −1) + Gx,t ·ap%, (4.10) for all x ∈ {20, 21, . . . , 100} and t ∈ {0, 1, . . . , 15}. Note that OPx−1,t = 0 for x = 20 and Gx,t = 0 for all x > xop.
4.2
Liabilities
All participants of a pension plan pay an annual premium for the pension accrual of that particular year. Pension funds have the responsibility of paying benefits when a participant retires. Therefore they determine an expected cash flow of future payments and discount this cash flow to obtain the present value of the funds’ liabilities. Because one euro today is worth more than one euro in 10 years, the discount rates are depending on the actual yield curve. Thus first we determine the expected cash flows of future benefit payments and then we describe the discounting of these cash flows to obtain the pension funds’ liabilities.
4.2.1 Cash flow of future benefits
Before we determine the cash flow, we have to determine the total amount of accrued pension entitlements for every time t. Suppose−OP−→t as a vector of the pension entitlements at time t, with on the rows the total pension entitlements per age. So we have
−−→ OPt = OP20,t ·N20,t OP21,t ·N21,t ... OP100,t ·N100,t ,
for all t ∈ {0, 1, . . . , 15}. We define the survival probability matrix Psurvival
t , where the indices are equal to the probability that the fund must pay the benefit. This means for an active partici-pant the probability of surviving until the pensionable age and for a pensioner the probability of surviving that particular age. We assume the ages on the rows and the maturity on the columns. So the survival matrix is equal to
Psurvivalt = ˆp20,t+1 . . . ˆp20,t+100 ... . . . ... ˆp100,t+1 . . . ˆp100,t+100 , (4.11) with indices ˆpx,` = 0 if x < xop−` + 1; (px,`−1)0.5·Q`−1 i=1(px−i,`−1−i) if x ≥ xop−` + 1, with px, ¯t= 1 − qx, ¯tand qx, ¯tas defined in equation (4.2).
Now we obtain the expected cash flow of accrued pension entitlements CFt by multiplying the transposed vector of total pension entitlements with the survival probability matrix. So
−→ CFt = −−→ OPt T Psurvivalt = CFt,1 CFt,2 ... CFt,100 , ∀ t ∈ {0, 1, . . . , 15}. (4.12)
4.2.2 Present value of liabilities
For the calculation of the present value of the pension funds’ liabilities, we use the yield curves from the Towers Watson economic scenario sets (see Section3.2.2). Pension funds value their liabilities on the basis of the DNB yield curve. Thus given these yields, we are able to obtain the discount rates. The given yields are spot rates, so suppose the vector→sp−t = [spt,1, . . . , spt,100]T as the yield curve at time t. First we put these spot rates into a forward rate vector−f w−→t = [f wt,1, . . . , f wt,100]T (see Hull (2011)). With these forward rates we are able to determine the discount rates. With the assumption that pension payments will be paid by mid year, the discount rate vector will be equal to
−→ pvt = pvt,1 ... pvt,100 , with indices pvt,` = (1 + f wt,`)−0.5· `−1 Y j=1 (1 + f wt, j)−1. (4.13) Next we obtain the liabilities Lt by multiplying the transposed cash flow vector with the dis-count rate vector, so
Lt = −→ CFt T −→ pvt = 100 X `=1 CFt,`·pvt,`, ∀ t ∈ {0, 1, . . . , 15}. 4.2.3 Duration of liabilities
The duration of the liabilities is the weighted average time of all payments. On the basis of the duration we know if the pension fund is a young, average or old fund. For example, for a young pension fund, which consist of especially young participants, it will take on average a long time before these participants receive their pension payments, thus for a young fund the duration will be high. And vice-versa for an old pension fund.
A partial buy-out optimization — Wilmer Lodder 17 The duration is introduced by Macaulay (1938) in its simplest form, where the liabilities are discounted by a fixed interest rate. However interest rates are not fixed, so the Macaulay du-ration was generalized by Weil (1973) and Ho (1992) to calculate the dudu-ration based on a yield curve. This duration DurLt is determined as follows
DurLt = P100
`=1` · CFt,`·pvt,`
Lt −0.5, (4.14)
for all t ∈ {0, 1, . . . , 15}. Note that the duration is based on the liabilities mentioned in the subscript. The subtraction of 0.5 is done because we have assumed that pension payments are paid by mid year.
4.3
Assets
In this section we will describe the development of the assets. The assets of the pension fund develops every year with incoming premiums, pension payments, value transfers and return on investments. We will discuss each component below.
4.3.1 Premiums and benefits
All active participants pay annually premiums to accrue yearly pension entitlements and all pensioners receive pension payments. The annual pension payments can be obtained easily by the first maturity of the cash flow given by equation (4.12). So the benefits at time t are equal to CFt,1.
Concerning the annual premiums, we will use a so called cost covering premium. According to the Pension Act1, the cost coverage premium must comply with the following complements:
1. the actuarial required premium to purchase new liabilities; 2. a raise to preserve the required capital;
3. a raise for execution costs.
Item1can be obtained by calculating the present value of the pension accrual. Therefore sup-poseOP−−→accrual
t as the vector of the pension accrual at time t, with on the rows the ages 20 until 100. So −−→ OPtaccrual = G20,t ·ap% · N20,t ... G100,t ·ap% · N100,t .
The cash flow vector of pension accrual at time t can be obtained by using the survival prob-ability matrix of equation (4.11), leading to
−→
CFaccrualt = OP−−→taccrualTPsurvivalt = CFaccrual t,1 CFaccrual t,2 ... CFaccrual t,100 .
Multiplying the transposed cash flow vector with the discount rate vector from equation (4.13) gives us the liabilities of pension accrual at time t:
Laccrualt = CF−→taccrualTpv−→t = 100 X
`=1
CFt,`accrual ·pvt,`,
for all t ∈ {1, 2, . . . , 15}. To satisfy the above mentioned item 2and3, we have to increase these liabilities with the required capital (RC), which is independent of time, and execution costs. The latter will be accomplish by adding the total amount of execution costs on the total amount of premium. Suppose Ct as the total amount of execution costs, the total amount of premium PRt paid by the active participants at time t will be equal to
PRt = Laccrualt ·(1 + RC) + Ct, (4.15)
for all t ∈ {1, 2, . . . , 15}. Note that only the total amount of premium is important for the de-velopment of assets and not the amount of premium per participant or per age group. But the premium percentage can be easily obtained by dividing PRt with the total sum of premium bases (which is usually equal to pension bases) at time t, which is equal to P66
i=20Gi,t ·Ni,t.
4.3.2 Value transfers
All participants of a specific age have accrued the same amount of pension entitlements, so we have to assume value transfers to compensate the assets for the accrued entitlements of new entrants who join the fund instead of the retired participants. The entitlements (liabilities) of the retirees will remain within the fund, with their part of the assets, and new entitlements (li-abilities) of new entrants will enter the fund, so there is a compensation for the assets needed. The amount of liabilities of new entrants who enters instead of resigned participants should also be compensated. Therefore it is necessarily to know the amount of liabilities of all resigned participants and all new entrants in a specific year.
The number of resigned participants per age and the number of new entrants per age are given respectively by equations (4.3) and (4.4). With equation (4.10), we are able to calculate the total amount of accrued pension entitlements by multiplying the number of participants per age with their amount of accrued pension entitlements. Then we have a vector of total accrued pension entitlements which leaves the pension fund and a vector of entitlements which enters the fund. The present value (or liabilities) can be obtained by multiplying these vectors with the discount rate vector given in equation (4.13). Then we have Lleave
t and Lentert for all times t. By using the funding ratio of time t, the amount of transferred and incoming assets is known and will be obtained by
Aleavet = Lleavet ·FRt and Aentert = Lentert ·FRt. (4.16) On the basis of these value transfers, the change in assets will be equal to
VTt = Aentert −Aleavet . (4.17)
4.3.3 Hedging interest rate risk
A common risk for pension funds is the interest rate risk. Most funds have a hedging strategy to moderate the effect of changing interest rates on the funding ratio (Boyle & Hardy (1997)). The main reason to hedge this risk is to protect the funding ratio against declining yields; in case yields decrease, liabilities will increase. The pension fund wants to hedge the effect of changing yields with a certain percentage, call it the intended hedge percentage. The invest-ments in bonds cover already a part of the interest rate risk. The difference will be covered by the hedging overlay2. On the basis of this overlay, assets will change in the same way (as
the liabilities) so it moderate the effect of changing yields on the funding ratio. Depending on decreasing or increasing yields, the hedging overlay can be positive or negative. When yields decrease, liabilities will increase, so the hedging overlay will be positive (assets should increase). Vice-versa for increasing yields.
A partial buy-out optimization — Wilmer Lodder 19 For the calculations of the hedging overlay, we use the nominal yield curves from the economic scenario sets. The yields of this economical scenario sets are nominal spot rates. We compare the liabilities based on the one-year rolling forward rates of time t −1 with the liabilities based on the forward rates of time t to measure the effect of changed yields. To obtain the one-year rolling forward rates, we roll-forward the forward rates by one year, which mean that the forward rate of maturity two will be maturity one of the roll-forward vector, maturity three will be maturity two, etc. So the indices of the roll-forward vector at time t will be given by
L
f wt,` = f wt −1,`+1= (1 + spt −1,`+1) `+1 (1 + spt −1,`)` −1.
The discount rate vector based on these rolling forward rates can be easily obtained in the same way as in equation (4.13). To avoid possible confusion, we will use the notation Lt(f wt) and Lt(f wLt) to indicate the liabilities based on respectively the forward rates and the rolling forward rates. The effect of the yield changes on the liabilities will be equal to
∆Lt = Lt(f wt) Lt(f wLt)
−1.
Suppose ϕ as the intended hedge percentage and γt as the hedging overlay at time t, the hedg-ing overlay is determined by the difference between the intended hedge and the percentage of assets invested in bonds. The latter can be written as β ·DurB
DurL , with β as the percentage of assets invested in bonds, DurB as the duration of bonds and DurLas the duration of liabilities (see equation (4.14)). Thus the hedging overlay is equal to
γt = ∆Lt · ϕ − β · DurB DurLt(f wt −1)
!
, ∀ t ∈ {1, 2, . . . , 15}. (4.18) 4.3.4 Annual return and total assets
The main growth of the assets will be accomplished by the return on investments. The total amount of assets will be invested in equity and bonds. Suppose α as the percentage invested in equity and β as the percentage invested in bonds, with β = 1 −α. The investments in equity and bonds will be subdivided in different investment categories, which are defined in table
3.2. The equity investments consist of 40% in worldwide equities, 20% in European equities, 20% in property (invested directly) and 20% in commodities. The bonds investments consist of 25% in European corporate bonds, 30% in European government bonds with a duration of 6 years, 25% in European government bonds with a duration of 15 years, 10% in high yield bonds and 10% in emerging market debt in hard currencies. The total return on equity and bonds at certain time t will be respectively equal to
rtequity = 40% · rt,1+ 20% · rt,2+ 20% · rt,3+ 20% · rt,4, and
rtbonds = 25% · rt,5+ 30% · rt,6+ 25% · rt,7+ 10% · rt,8+ 10% · rt,9.
Together with the hedging overlay as defined in equation (4.18), the total annual return on investments is equal to
rttotal = α · rtequity + β · rtbonds+ γt.
We have assumed that the premium, benefits, value transfers and execution costs are paid by mid-year, so half of these payments will be considered as annual investments. The total assets at time t is equal to At = At −1+ 1 2·(PRt + VTt −CFt,1−Ct) ·(1 +rttotal) +1 2·(PRt+VTt−CFt,1−Ct)), (4.19) with A0 = L0·FRstar t. Note that we use a cost covering premium, thus the total amount of execution costs Ct will be covered by the premium. The premium is paid at the same time as the costs and therefore the value of Ct will not be relevant.
Carve out
In this chapter we will explain the carve out in further detail and why we have chosen to carve the pensioners out of the fund. We will also discuss the price of a carve out i.e. the required funding level for a pensioner carve out for the three model pension funds. And finally, we will determine the Sharpe ratio which will be used later to optimize the results.
5.1
Pensioner carve out
The pensioner carve out is a partial buy-out where only the pensioners’ obligations will be transferred to the insurer, see Figure5.1. The pensioner carve out is a solution for de-risking the balance sheet and could have advantages for both the pension fund and the insurance com-pany. But why the decision to off-load only the pensioners’ liabilities from the balance sheet?
Figure 5.1: Graphic overview of a partial buy-out where the pensioners are transferred to the insurer – the pensioner carve out. Note that we assume only actives and pensioners in this thesis. Source: Beard (2014).
For a pension fund there are two important differences between pensioners, deferred and ac-tive participants. One difference is the risk profiles. Younger participants can take more risk on investments than older participants, because they have a larger horizon to absorb any poor investment performance before they receive their pension benefits. Therefore these pension-ers have a more risk avpension-erse profile than deferreds and actives. Thus when the pensionpension-ers will be transferred to the insurer, the pension fund can adjust its risk profile by taking more risk in investments. The other important difference comes from a legal point of view. Legally,
A partial buy-out optimization — Wilmer Lodder 21 ferreds and pensioners may be treat otherwise as actives. We will not discuss this any further. As mentioned earlier, insurers have to have implemented Solvency II by 1 January 2016. Ac-cording to Solvency II, insurers may apply the matching adjustment (MA). When the insurer applies the MA, it will ensure cash flows consisting of less risk, so the insurer will be able to apply a lower solvency ratio. The cash flows of active and deferred participants consist of more risk than the cash flows of pensioners, because the cash flows of actives and deferreds have also a risk of disability or value transfer, thus the solvency ratio for only pensioners’ cash flows is lower. Because of this lower required solvency level, the price of a partial buy-out of only pensioners will also be lower.
Because of these two advantages (the possibility of adjusting the fund’s risk profile and the possibility of applying the MA) makes a partial buy-out of only pensioners interesting for both the pension fund and the insurer.
The three model pension funds have different distributions of participants, so they have dif-ferent total amounts of pension entitlements. Therefore the future benefit cash flows and du-rations are different. The future benefit cash flows of the actives, pensioners and total fund for all three model pension funds are shown in Appendix C. Table5.1summarizes the amount of liabilities and duration of liabilities of all participants, actives and pensioners for the three model pension funds.
All participants Actives Pensioners
L0 DurL0 L0 DurL0 L0 DurL0
Young fund 977,421,151 21.4 791,286,800 24.3 186,134,351 9.1
Average fund 1,627,749,879 15.2 934,608,597 20.2 693,141,282 8.4
Old fund 1,753,021,531 10.6 546,068,511 17.7 1,206,953,019 7.5
Table 5.1: The amount of liabilities (in e) and duration of liabilities (in years) for the three model pension funds before and after the pensioners carve out. Note that for all three pension funds hold the following: Lall
0 = Lactives0 + Lpensioner s0 .
5.2
Price of carve out
In the case of a nominal buy-out, the price of the buy-out is equal to the amount of the liabili-ties. In practice this is not entirely true, because the insurer applied a different term structure for the valuation of the pension liabilities in comparison with a pension fund. Insurers use the nominal term structure with an additional spread for the valuation. The difference between both valuation methods is small, so we will assume that pension funds and insurers use the same term structure. By doing so, the price of a nominal buy-out will be equal to the amount of liabilities. In this case the pension fund transfers a funding ratio of 100% to the insurer, which means that when the pension fund has a funding ratio higher than 100%, the funding ratio of the remainder of the fund increases immediately (funding benefit). In case the pension fund has a funding ratio below 100%, the funding ratio of the remainder of the fund will decrease. In this thesis we will not examine cases where the funding ratio would be below 100%. At a nominal buy-out the bought pension entitlements are fixed and there is not any potential indexation for the future. But it is possible to do a buy-out including indexation, where the indexation is based on the Euro zone HICP as described in Section2.3. In this case the price of the buy-out will be higher than the price of a nominal buy-out, so a higher required fund-ing level is needed. With the extra amount of assets, the insurer purchases a fixed amount of annual indexation. At that moment the pension entitlements and the annual indexation are guaranteed to the pensioners.
As above described the required funding level for a nominal buy-out is equal to 100%. For a buy-out including indexation the required funding level depends on the duration of the pen-sioners’ liabilities. Table5.2shows the duration of the pensioners’ liabilities and the approx-imate required funding level for a buy-out including full (100%) HICP inflation of the three model pension funds.
Model pension fund Duration Required funding ratio
Young fund 9.1 114%
Average fund 8.4 112%
Old fund 7.5 110%
Table 5.2: The duration of the pensioners’ liabilities with the approximate required funding ratio for a buy-out including full inflation for the three model pension funds (at a buy-out including full indexation the insurer purchases 100% HICP inflation).
For purchasing a partial percentage of indexation, the required funding ratio will be deter-mined by linear interpolation between the required funding level for a nominal buy-out (100%) and the required funding level for a buy-out including full indexation (see Table5.2). In ac-cordance to Hoevenaars & Ponds (2008) the distribution of the assets for the remaining group and leavers will be based on the liabilities of both groups. The pension fund splits its assets in the same way as the ratio between the liabilities. This means that when an old pension fund has a funding ratio of 105%, the actives’ amount of assets will be 105% of their liabilities and the same applies to the pensioners. With this amount of assets it is possible to purchase 50% HICP inflation for the pensioners.
It is not possible to purchase more inflation than 100% HICP, so the price of the buy-out will never be higher than the required amount of assets for full indexation. For example, when an average pension fund has e 120,000,000.- of assets and e 100,000,000.- of liabilities, with e 60,000,000.- of liabilities for the actives and e 40,000,000.- for the pensioners, then the funding ratio is equal to 120%. The carve out price for the pensioners including full indexation will be equal to e 44,800,000.- (112% · e 40,000,000.-). The funding benefit will be equal to e 3,200,000.-(48,000,000.- -/- 44,800,000.-), which results in a funding ratio of approximately 125% for the remainder of the fund.
5.3
Sharpe ratio
The Sharpe ratio is a measure to calculate the risk adjusted return of an investment and is introduced by Sharpe (1966) and Sharpe (1993). The Sharpe Ratio measures the expected value of the excess of the return of an investment over a benchmark return, usually the risk-free rate, and takes the volatility or risk (standard deviation) of the excess return into account. the Sharpe ratio S is defined as
S =σµr r,
with µr the expected value of the excess of the return of an investment over the risk-free rate and σr the standard deviation of the excess return. This ratio is a way to measure the goodness of an investment by adjusting for its risk. Thus a higher Sharpe ratio means a better investment. For the examination of the results, a similar ratio as the Sharpe ratio is used to measure the goodness of the expected applied indexation. For a certain time t the average applied index-ation or reduction of all scenarios is determined by ˆE[It + κt], with It as defined in equation
A partial buy-out optimization — Wilmer Lodder 23 (4.8) and κt as in equation (4.9), and the standard deviation is determined by p ˆvar[It + κt]. So in our case the Sharpe ratio at time t is given by
ˆSt = ˆ E[It + κt] p ˆ var[It + κt] , (5.1)
for all t ∈ {1, . . . , 15}. Then we use the average of the calculated Sharpe ratios as measurement of the goodness of the expected applied indexation. Thus in the continuation of this thesis we assume the Sharpe ratio ˆS as the average Sharpe ratio over time.
Results
In this chapter we will discuss the results of the carve out calculations. For different cases we apply the ALM model to analyse the development of the pension fund before the carve out (thus based on the entire pension fund) and compare this with the development after the carve out (only with the active participants). During the carve out we discuss how much HICP inflation can be purchased at the buy-out transaction and adjust the asset mix of the pension fund to optimize the expected future indexation of the actives. First we discuss the fixed assumptions, then we will have a look at the results of a given case and finally we will discuss different sensitivity cases.
6.1
Assumptions
Before we are able to do the carve out calculations we have to determine some assumptions. Here we will discuss fixed assumptions which we will keep constant during the analysis and the model pension funds’ asset allocation before the pensioner carve out.
6.1.1 Fixed assumptions
These assumptions below will remain constant during the calculations. We will discuss the assumptions briefly and separately, and summarize these in Table6.1.
The offset and accrual rate are based on the fiscal maximums of 2015 for an average wage pension plan which is determined in the Act of income taxes of 19641. In accordance with
Ar-ticle 18a (2), the fiscal maximum offset and accrual rate are set at respectively e 12,642 and 1.875% in 2015. In accordance with the nFTK and the Dutch Pension Act (PW)2, the minimum
required capital is defined as 105%, the minimum required funding ratio for indexation (index-ation floor) is defined as 110% and the required capital is determined on 25%.
The expected inflation rate is set at 2.00%, the expected return on assets is set at 6.75% and the intended hedge rate is determined on 75%. Because the pensionable age will increase to an age of 67 over time, we have assumed the pensionable age is fixed at 67. Furthermore we have also assumed a male/female ratio of 0.75/0.25 and a start salary of e 25,000.- for all three model pension funds.
Note that other assumptions, such as funding ratio at time t = 0 and asset mix, will be deter-mined in each case separately.
1In Dutch: Wet op de loonbelasting 1964. 2see Article 137 (1) and (2) PW.
