Generational Pension Plan Designs

Transcription

1 See discussions, stats, and author profiles for this publication at: Generational Pension Plan Designs Article in SSRN Electronic Journal October 2010 DOI: /ssrn READS 25 2 authors, including: Ronald Mahieu TIAS School for Business and Society 54 PUBLICATIONS 883 CITATIONS SEE PROFILE All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. Available from: Ronald Mahieu Retrieved on: 12 May 2016

2 Generational Pension Plan Designs Xiaohong Huang and Ronald Mahieu January 12, 2009 Abstract The lack of individualization in a collective pension plan and the lack of risk sharing in an individual pension plan motivate us to examine a hybrid plan for occupational pension provision. We propose a generational plan in which people from the same generation are pooled in a generational sub-plan. Each sub-plan can set its own policies independently. We investigate the performance of the hybrid on funding ratio, contribution rate, indexation rate, net present value and welfare, and find that a generational fund provides a higher net present value and welfare to its participants and a lower underfunding probability to its trustees. 1 Introduction Pension fund providers in many countries have experienced some rough times in the last decade. The hazard of underfunding and volatility of their balance sheets during the beginning of 21st century has provoked the rethinking of occupational pension contract design. Plan sponsors have become more reluctant to take the full responsibility for underfunding and risk is spread among other stake-holders, most prominently active participants and Huang is at RSM Erasmus University, and Mahieu is affiliated with Tilburg University, RSM Erasmus University, and Netspar. Corresponding author is Huang. addresses are xhuang@rsm.nl and r.j.mahieu@uvt.nl. The usual disclaimer applies. 1

3 retirees. In response, occupational pension plans have changed the designs of their funds into either conditional defined benefit (DB) plans, where the defined benefit is no longer guaranteed but conditional on the funding status, or the collective defined contribution (DC) plan where contributions from sponsors and participants are fixed and benefits are determined by the investment results. The conditional DB and collective DC plans indeed transfer risks from sponsors to pension fund participants, but this risk transfer may impact specific groups of participants differently. See also Hoevenaars and Ponds (2008). A few issues need to be considered. Firstly, since the participants now bear the funding risk, the plan participants would like to take into account their own conditions like age, expected salary paths and schedules of retirement, in order to manage their pension plan in an optimal manner (see e.g. Bodie, Merton, and Samuelson (1992)). But in the current conditional DB and collective DC plans, a uniform plan-wide investment policy is applied to all participants. Such non-individualization leads to a sub-optimal investment policy to those participants who have a different risk profile from the plan s representative participant. A second issue is that a clear specification of risk and return allocation among members is lacking in the conditional DB and collective DC plan. When underfunding or overfunding occurs, the issue of division of responsibilities is often left to a costly negotiation among heterogenous stake-holders. Any resulting unfair treatment of different generations could endanger the sustainability of the mandatory feature of such collective plans. To solve the above problems, a fully individualized pension plan such as a 401(k) plan in the US or a personal pension scheme in the UK could be an option. But the experiences in the US and the UK reveal other problems in their implementation. In addition, an individual pension plan is totally devoid of any risk sharing. To combine the benefits of a collective plan and an individual plan while discarding their respective drawbacks, we investigate a 2

4 hybrid plan called a generational plan. In such a plan, people of different generations are allocated to their respective generational funds. Each generational fund has its own particular policies towards investment, contribution and indexation decisions. The idea of generational plans originated from Teulings and de Vries (2006) where they suggest creating generational accounts in a collective plan. In their paper they focus on the theoretical optimal portfolio choices for the different generational accounts and calculate the welfare loss for the various deviations from the optimal choices. Our paper develops their concept of a generational account, and transfers it into a fully fledged generational pension plan, in which not only portfolio choice but also contribution and indexation policies can be adjusted to accommodate individual generations. Cui, de Jong, and Ponds (2006) and Gollier (2006) optimize over investment policies only and conclude that a collective plan is more valuable than an individual plan. We should expect to be able to further improve on those results. Through numerical simulations, we examine the performance of our new generational plans in terms of the funding ratio, contribution rate, indexation quality, accrued annual benefit, net present value and welfare. We compare the performance with current conditional DB plans. Our main finding shows that our new design achieves lower underfunding probabilities, which are valued by trustees and supervisors, and provides higher values and welfare to participants. Therefore we conclude that a generational plan can be a very promising design choice for future occupational pension provision arrangements. This paper is structured as follows. First, we present some more information on different pension designs in Section 2. In Section 3 we present the models for the pension designs that we use in our numerical analysis. In this section the new generational design is also introduced in more detail. Section 4 presents our data and the setup of the simulation analysis. In Section 5 the results are presented, and some concluding remarks are presented in Section 6. 3

5 2 Collective, individual and generational pension plans 2.1 Collective DB and individual DC plan in the US and UK A pension plan in this paper is focused on the occupational pension plan where employees and their employers set aside a proportion of the salary for employees retirement income. There are two broad types of the occupational pension plan: a collective and an individual one. In collective plans, contribution, investment and indexation policies are centrally managed by pension plan trustees. In individual plans, individuals are responsible for all the mentioned decisions. A decade ago, the occupational plan was dominated by a collective DB plan. In such a plan, the promised retirement benefits to participants are defined by a formula of working years and salary path, and not related to the plan performance. It was seen as a delayed salary and meant to attract loyal employees (Bodie (1990)). Any deficit in the pension liabilities was made up by the plan sponsors and the current and future participants. When the situation is healthy, all parties are happy with the arrangement. When things turn sour, however, the DB arrangement is no longer affordable. The poor stock market performance in the early 21 century squeezed the asset values, and falling interest rates inflated the market value of pension liabilities. The resulting serious underfunding in many DB plans put a lot of planing pressures on the sponsors and the contributing participants. Due to aging the premium base has been shrinking while the pool of retirees has been increasing. Solely raising the contribution rate is no longer feasible and effective to turn around the underfunding situation. In addition, new accounting rules make a company s balance sheet liable to the changes in the planing status, so sponsors would like to shed the influence from its pension plans. A change of pension plans was needed. 4

6 In the US, where individuals are supposed to be more financially literate and more individualization is demanded than in any other countries, funding risk is totally transferred to individuals. Collective DB is replaced by 401(k) (Munnell and Perun (2006)). Under such an arrangement, the employer and participants put aside an amount of money in an individual account, then the participants decide their own investment and at retirement they will annuitize their savings on the 401k account to pension benefits. The practical implementation, however, suffers a series of problems. Firstly, not every participant is financially sophisticated enough to make the optimal dynamic decisions on saving, investing and annuitizing. Secondly, people suffers from behavioral constraints such as irrationality and lack of self-discipline. Thirdly, the annuitization exposes individuals to annuity risks. Such problems lead to a serious shortage of retirement income provision and sub-optimal life-time consumption. Theoretical and empirical details can be found in Bovenberg, Koijen, Nijman, and Teulings (2007), Munnell and Sunden (2006), and Koijen, Nijman, and Werker (2006). In the UK, the personal pension scheme is replacing the collective DB to relieve the financing pressure on the government and the sponsors, but it suffers from the similar problems as in the US, as discussed in Blake (2006). 2.2 Collective conditional DB plans in the Netherlands The ineffectiveness reflected in the US and UK practice and the highly embraced value of social solidarity in the Dutch society render an individual plan not a solution to the underfunding problem in the Dutch pension plans. Instead, the traditional DB plans in the Netherlands have mostly shifted to the conditional DB plans, where the previously inflationprotected benefits are no longer guaranteed (Ponds and Van Riel (2006)). Each year the indexation of the pension benefit to retirees or accrued rights by working participants to 5

7 inflation is contingent on the funding status. Such arrangement mitigates the underfunding situation partially, but there are still at least two problems with this conditional arrangement. Firstly, the conditional plan still offers no individualization in saving and investment strategy, this may lead to welfare loss to participants, as pointed out by Bovenberg, Koijen, Nijman, and Teulings (2007). Steenkamp (2004) also challenges the collective investing in a collective plan that one single asset allocation, geared to the average participant of the plan is problematic. Secondly, the conditional plan exposes all its participants to the volatile pension rights and benefits. With only one return from a plan s common ivestment pool, questions arise as to how risks and return should be allocated fairly among its participants. The current conditional plan does not specify the rules or establish a direct link between risk bearing and return awarding. This can lead to two issues. Firstly, When a overfunding or especially an underfunding situation presents itself, it will be very hard for various participants with differing interests to reach a consensus on benefit appropriation and loss allocation (Teulings and de Vries (2006)). Secondly, maturing plans with aging participants tend to take more conservative investment. This is to the disadvantage of young participants since they can not exploit the risk premium on the one hand and have to pay a higher contribution rate on the other hand (Ponds and Van Riel (2006)). All these problems lead to a welfare loss from a participant s perspective. 2.3 Generational pension plans To avoid the sophisticated financial management of retirement saving and income in the individual plans and to make up for the missing individualization in the collective plan, 6

8 we propose a hybrid plan and name it a generational plan. In such a plan, people of the same generation are pooled in one fund. In the generational plan operated by a pension plan, there can be multiple generational funds depending on how many generations are living at the same time and how much individualization the plan wants to achieve. Within a generational fund, investment, contribution and indexation policies can be tailored to the preferences of the participants in a particular generational fund, which is almost impossible in a collective plan. In addition, people can share risks with other people in the same generation, though limited in scope compared to a collective plan, but better than an individual plan where risk sharing is totally missing. 2.4 Comparison between collective DB and generational plans Built on the previous research results (Cui, de Jong, and Ponds (2006) and Gollier (2006)) that a collective plan is more valuable than an individual plan, we continue to show that a generational plan is more valuable than a collective plan. Theoretically, given the differing interests between the working participants and the retirees, a set of uniform policies applied in a collective plan is obviously inappropriate and suboptimal to participants, but a generational plan can accommodate such needs by allowing for individualized contribution, indexation and investment policies, and this should lead to a higher value to participants. A generational plan is also devoid of negotiation costs and in a better position to adjust to changes. When an external shock occurs, the conflict of interest among participants in a collective plan is hard to coordinate. The conditional indexation in the current DB plan aggravates such conflict. In a traditional collective DB plan, only the contribution and investment policies are the tools to recover from an underfunding situation. Now in a collective conditional DB plan, indexation is also available for adjustment. The contribution 7

9 rate only matters to the working participants who are still paying, while indexation rate matters more to the retirees than to the working participants as it is immediately realized in the benefit payout, so when there is a change in funding status, adjustment to contribution or indexation at what extent becomes a power play and a time-consuming negotiation process between the working participants and the retirees. In a generational plan, such conflict is non-existent, accordingly any relevant cost can be saved. A collective plan has an important feature in intergenerational risk sharing (IRS). It is reflected in the existence of a buffer/reserve, which can smooth shocks over multiple generations as long as the collective plan is not bankrupt. In a generational plan, only intra-generational risk sharing is present in that people of the same generation share risks with each other. They are different in the scope of risk sharing. The former is over an infinite period of time, while the later is only over the lifetime of a generational plan. We simulate the development of the two plans and find that the positive impact from IRS does not dominate the negative impact from uniform policies. The ability in taking flexible contribution policy makes the generational plan a superior plan to a collective one in both normal economic condition (shown in Test 1) and a lower equity premium economy (shown in Test 2). Risk sharing enables a plan to be more risk tolerant (Shiller (1999)). Even though the risk sharing in a collective plan is very extensive, its risk taking in investment and the magnitude of change in asset allocation is often limited and confined to a certain degree. This is because the composition of its participants simply do not allow either too risky investment or a sharp change in the investment policy. A generational plan, however, due to its life cycle pattern, can take a high risk in its early phase by investing very aggressively to exploit equity premium. When it is close to retirement phase, it can gradually move to more conservative investment strategy. A generational plan is in a better position than a collective plan to exploit risk premium as shown in Test 3. 8

10 Aging is a acknowledged fact. In our paper we assume away the longevity risk, and we consider the aging caused by lower birth rate. It means that in future there will be less young people than old people. This fact does not directly influence the capital-funded collective plan, as less people means less assets as well as less liabilities. But aging has an indirect influence on the investment policy. An increasing proportion of retirees in a pension plan will mean a more conservative investment policy defended by the retirees (Ponds and Van Riel (2006)). This in return means a lower investment return and consequently a higher contribution rate and a lower indexation for the working participants. Test 4 is designed to show a conservative investment policy adopted by a collective plan has a negative influence on its performance. On the contrast a generational plan is not affected. More/few people in a certain generation simply means a large/small generational plan, and no indirect influence on its investment policy is expected. 3 Design of collective and generational pension plans 3.1 General assumptions We make the following assumptions so to focus on more relevant issues discussed in this paper. Firstly, we ignore the role of sponsors. It is a trend that sponsors will gradually withdraw their roles as risk bearing when there is underfunding and return appropriation when there is overfunding. They will simply assume a responsibility to pay a fixed amount of contribution to the plan every year. Therefore in our following description of collective and generational plans, we focus on plan participants and trustees. 9

11 Secondly, both plans are of a DB average earnings scheme, referring to that pension rights/benefits are based on the life-time average salary. If we assume a replacement rate of 70%, years of service is 40 years, life-time average annual salary is LT AS, then for every year of service, the newly accrued right is NAR = 1 LF AS 70%. Thus every year a participant accrues 40 the same amount of new pension rights. Thirdly, we assume a stationary state for the collective plan, where the distribution of the age cohorts and their respective nominal pension rights are constant over time. So the market value of the liabilities only vary with yield curve and indexation. The interest of plan participants are the most important. As one participant can only join in one generational fund, we will use one generational fund within a generational conditional DB plan to compare with a collective conditional DB fund/plan 1. The conditional DB plan starts with a given status in aggregate premium collection and benefits payout, with simulated asset return and yield curve and given investment policy, development of assets and liabilities determines contribution rate and indexation rate for the next period. Such process go on infinitively. For the generational plan, it starts with an initial premium payment. This premium payment entitles a pension right which infers liabilities. With the same simulated asset returns and yield curve, funding ratio is computed to determine contribution rate and indexation rate. Contribution policy is only valid for the working years, when the participants in the plan retire, only indexation and investment policy are relevant. The contribution and indexation policies have implication for participants as they are used to compute net present value and welfare. 1 As a collective plan has only one plan, collective fund and collective plan are used interchangeably here. 10

12 3.2 Modeling a collective conditional DB plan In a collective conditional DB plan the premiums collected from all its participants are put in one monetary pool and invested as a unity in various assets, in order to pay the promised benefits to current and future retirees. To model the development of its assets and liabilities, we set some initial values concerning the initial assets (A 0 ) and liabilities (L 0 ), the initial premium base/pensionable salary (P base) and the initial benefit payout (Bbase). These initial values describe the current situation of the collective plan under study. The age composition of its participants is assumed constant over time and people of the same age in a certain year are assumed to earn the same salary. Each year the premium base increases with the salary growth rate (sal), and the pension benefit payout increases with the cumulative indexation (cumind) 2. Therefore the total assets of the collective plan changes positively with the investment return (r A,t ) and the premium collection (P t as contribution rate), and negatively with the benefits payout as follows: A t+1 = A t (1 + r A,t ) + P t P base (1 + sal) t cumind Bbase (1) The market value of the liabilities is the discounted value of the future expected benefits payout. The change of the liabilities comes from three sources: actuarial factors, inflation and yield curve factors (Bauer, Hoevenaars, and Steenkamp (2005), p420). The assumption of stationary plan allows us to temporally ignore the changes due to the actuarial factors. In addition, it also allows us to use a fixed duration for the collective plan. Each year the expected cash flow of benefits payout increases with the granted indexation (ind t )in that year. We approximate the influence from the yield curve each year with the return of a 2 The effect of salary growth on the benefit payout is already counted in the life-time average salary when computing the accrued right/benefit. 11

13 constant maturity (CM) bond with the same duration as that of the plan 3. We call the CM bond return as the liability return (r L,t ) to refer to the change in the value of liabilities caused by the yield curve change. Given an initial value of the liabilities, the value of liabilities (L t ) each year increases with the liability return and the indexation as follows: L t+1 = L t (1 + r L,t ) (1 + ind t ) (2) At the end of each year, the funding ratio is computed as A t /L t to determine the contribution rate P t+1 and indexation rate ind t+1 for the coming year according to the rules in the policy ladder Modeling a generational DC plan A generational plan serves people of similar characteristics and it has a life cycle like an individual plan. During the working years the plan collects contribution and makes investment. The change of the assets comes from two sources, premium collection and investment return. A t+1 = A t (1 + r A,t ) + P t Salary (1 + sal) t (3) where Salary is the initial average salary level of the generation. During the working years the change of liabilities come from the change in accrued rights 3 By this approximation, only small parallel shift in the yield curve is captured. This could be a limitation of the modeling of liabilities 4 Policy ladder is a set of rules specifying how indexation and contribution rate should be for the different values of the funding ratio. 12

14 and corresponding yield curve. Except that initial accrued right is AR 1 = NAR (1 + ind t ), from year 2 till retirement the total accrued future annual benefit is AR t+1 = (AR t +NAR) (1 + ind t ). AR t refers to the nominal amount of money a participant will receive each year after he retires if he works for t years and leaves the plan. Discounting these expected annual benefits with the corresponding yield curve, we can compute the value of the liabilities. As NAR is constant over time, the change of the liabilities comes from two sources, yield curve change and indexation. L t+1 = postryrs 1 n=0 AR t (1 + yieldcurve wkyrs+n ) wkyrs+n (4) where postryrs is the period of years when participants receive pension benefits and wkyrs is the period of working years. As of retirement (t = 40), besides continuing its investment, the plan starts to pay out benefits as defined in AR t. So the assets on the one hand increase with the investment return, while on the other hand decrease with the benefits payout. It is computed as A t+1 = A t (1 + r A,t ) AR t (5) As no new rights is accrued as of retirement, NAR = 0 and the total accrued right only increases with indexation AR t+1 = AR t (1 + ind t ). The value of the plan liabilities is the discounted value of the benefit payout with decreasing years of payment. L t+1 = postryrs+wkys t 1 n=0 AR t (1 + yieldcurve n+1 ) n+1 (6) At the end of each year, the funding ratio is computed, according to the policy ladder 13

15 contribution rate P t+1 and indexation rate ind t+1 are determined. The generational plan is an independent DB plan, so after the last payment there might be a surplus or a deficit in the plan as A postryrs+wkys L postryrs+wkys. In our modeling we do not impose any bottom boundary as we believe plan can buy some option or insurance to avoid deficit situation. 3.4 Dimensions for comparison A good plan caters the interests of major stakeholders like the participants and the sponsors. Following the industry practice, we look at the following 6 aspects to compare a collective plan and a generational plan, as can also be seen in Bauer, Hoevenaars, and Steenkamp (2005) and Ponds and Van Riel (2006). a. Funding ratio Funding ratio is defined as the value of assets divided by the value of liabilities. It is the first important parameter that the plan trustees care about, as it reflects the overall health of a plan, over which solvency requirement is imposed. Funding ratio is also important to participants, as it decides how much contribution rate to pay for the coming year and how many indexation is granted to their accrued rights/benefits. Underfunding probability measures the one-side volatility of funding ratio, and it is an important measure monitored by pension supervisors. b. Contribution rate The contribution rate measures how much participants pay into the plan. In a collective plan, the contribution collected from the working participants is used to pay the benefits to the retirees and the left is to earn investment return. In a generational plan, in its early phase the contribution is solely to earn investment return. Upon retirement, contribution rate 14

16 becomes 0 and the plan counts on the accumulated assets and some continued investment to pay retirement benefits. The contribution rate is dependent on funding ratio and specified in the policy ladder. c. Indexation quality Each year contingent on the funding ratio, indexation is granted to protect accrued rights/benefits from inflation (when inflation is 0 or negative, no indexation is granted). The 100% indicates a pension s liability is fully indexed to the price inflation in that year. This percentage is labeled indexation quality in the paper. d. Accrued annual benefits(ar) From the perspective of a participant, the accrued annual benefits represents the exact amount that a participant will expect to receive annually as of retirement if he decides to leave the plan at a certain moment. Accrued annual benefits over time is determined by the sum of previously accrued rights and the newly accrued, multiplied by the indexation rate. So it reflects the effect of all the previously granted indexation. e. Net present value of a plan This is a composite parameter that a newly entering participant should consider when choosing a plan. Participants pay premium at a rate of P t into the plan during the working period and receive benefits as defined in AR t from the plan as of retirement. The net present value from participating a pension plan can be computed as the discounted cash inflow of benefits minus the discounted cash outflow of contributions. In our simulation, participants are assumed to work for 40 years and die in 15 years after retirement, so the present value is computed as the sum of 14 discounted benefits receipt minus the sum of 40 discounted premium payments. 15

17 f. Welfare analysis There is uncertainty involved in the net present value a participant can draw from a pension plan, therefore we use a utility function to facilitate the comparison. we use CRRA power utility function as T E 0 [ e δt U t dt] (7) 0 U t (w) = w1 λ t 1 1 λ where wealth (w t ) during the working phase is defined as salary minus premium payment, wealth after retirement is simply the benefits received by participants. 4 Data and simulation 4.1 Data description We use quarterly data from the Center for Research and Security Prices (CRSP) of the University of Chicago for the period 1952Q2 to 2004Q4. 5 The return on stocks (including dividends) and the dividend yield are for a portfolio that includes all stocks traded on the NYSE, NASDAQ, and AMEX. Dividends are twelve-month moving sums of dividends paid on the just mentioned portfolio that includes all stocks traded on the NYSE, NASDAQ, and AMEX. The dividend yield is the ratio between the dividends and the prices. The return on bonds is the return to a 10-year constant maturity T-bond representing a long term bond investment. Its quarterly return can be obtained according to the loglinear 5 The starting date 1952Q2 comes after the Fed-Treasury Accord that allowed short-term nominal interest rates to freely fluctuate. 16

18 relationship between log return and log yield as described by Campbell, Lo, and MacKinlay (1997) that ln(1+r n,t+1 ) D n ln(1+y n,t ) (D n 1)ln(1+Y 4 n 1,t+1) where D n is Macaulay s duration, calculated as (1 (1 + Y n,t ) n )/(1 (1 + Y n,t ) 1 ). Y n,t is the annualized yield of a n-year constant maturity bond at time t and n is 10 here. Such yield data is directly obtainable from US Federal Reserve Bank. The derived r n,t+1 is the simple quarterly return of a n-year constant maturity bond at time t. The real interest rate is the ex-post real return on 90-day T-bills (i.e. the difference between the yield on T-bills and the inflation rate). Inflation rate is sampled at a quarterly frequency 6 from Consumer Price Index-All Urban Consumers (CPI-U, seasonally adjusted,1982:q4=100) from US Bureau of Labor Statistics. We use return on the 90-day T-bill as our measure of the short term nominal interest rates. Yield spread is the difference between the yield on a zero coupon 10-year T-bond and the return on a 90-day T-bill. All returns/rates are translated to quarterly values for simulation. Yield curve data is constructed from the monthly euro swap rate sampled during Jan 1999 and June 2007 for 1 till 10 year, 12-, 15-, 20-, 25-, 30-year, and it is obtained from DataStream. 4.2 Estimation The return dynamics of the financial assets are modeled with one lag Vector Autoregressive (VAR(1)) as in Campbell and Viceira (2005), where the stock and bond returns are described by their lagged values and the lagged values of real interest rate, nominal interest rate, 6 Monthly CPI figure is very seasonal and creates timing problem. This motivates our use of quarterly data. 17

19 dividend yield and yield spread as in Equation (8). z t+1 = A + Bz t + ɛ t+1 (8) where z t is a vector of stock return, bond returns, real interest rate, nominal interest rate, dividend yield and yield spread, A is a 6 1 constant vector, B is a 6 6 coefficient matrix for z t, and ɛ t+1 N(0, Ω). The statistical description, the estimates of coefficients and covariance matrix are shown in Table 1, 2 and 3 respectively. As in Diebold and Li (2006), the yield curve is modeled by a three factor model as in Equation (9) y t (τ) = β 1t + β 2t ( 1 exp λτ λτ ) + β 3t ( 1 exp λτ λτ exp λτ ) (9) y t (τ) refers to the interest rate for a maturity of τ-years. Factors β 1t, β 2t and β 3t respectively govern the level, slope and curvature of the yield curve. λ determines the maturity at which the loading on curvature or β 3t reaches its maximum. In accordance with the common practice, we pick 30 months for τ. So the value for λ should be that maximizes the loading on β 3t at 30 months. Every year, we regress yield of different maturities (namely, 1-10, 12, 15, 20, 25 and 30 years) on factor loadings of 1, 1 exp λτ, and 1 exp λτ exp λτ, λτ λτ we get a OLS estimates of β 1t, β 2t and β 3t. With the times series of the three βs, and using the following AR process we estimate the coefficients to describe the βs. β i,t+1 = c i + γ i β i,t + ɛ i,t+1, i = 1, 2, 3 (10) Using the estimates of coefficients and variance of the residuals of Equation (10), we can forecast future βs. Then plugging such forecasts in Equation (9) we can generate the future yield curve. 18

20 4.3 Assumptions in simulation General plan characteristics A participant starts working at age 25, retires at 65, and earns an initial annual salary of euro. His salary grows at 2% per year. So the life time average salary (LTAS) is euro 7. At the end of each year he pays premium to a plan, a collective or a generational one, at a contribution rate of P t out of his salary to build pension rightsar t. He makes contributions for 40 years. For every year of service, he accrues additional new rights (NAR) of euro 793 8, where 70% is the assumed replacement rate. Together with the previous accrued rights, the total accrued right increases with yearly granted indexation. As of retirement at the age of 65 he starts to receive benefits for 14 times and dies at the age of 80. Due to the conditional indexation the pension benefits continue to change each year after retirement. In the collective plan, with the assumption of constant age composition, the duration of a collective plan is constant and fixed at 15 years. So the impact of yield curve change on the liabilities can be approximated by the return of a 15-year CM bond, which is calculated from the simulated 15-Year yield. The initial values of the assets, of the liabilities, the premium base and the benefit payment are assumed to be 200, 160, 32.5 and 6.1 respectively 9. Then the assets and liabilities develop as described in section 3.2. In the generational plan, the development of only one generational fund is simulated. The initial funding ratio is set at 0. Then the assets and liabilities develop as described in section computed as (1+0.02) /40. 8 NAR = 45301/40 70%. 9 Values are taken from ABP results in 2006 for an example. Absolute values do not matter and only relative proportions matter here. 19

21 The initial premium rates for both the collective and the generational plan are set at 10%. The boundary for the premium rate is set between 0 and 20%. Both plans only invest in the stock and the bond Policy ladders The policy ladder for contribution rate is described in Figure 1. In the collective plan, the contribution rate is set at [0, 20%] for the funding ratio threshold of [100%, 200%]. When the collective funding ratio is below 100%, the contribution rate is 20%. When the funding ratio reaches 200%, the contribution rate is 0. Linear rule applies when funding ratio is between 100% and 200%. In the generational plan, we set a stricter threshold of [100%, 600%] initially, then loosen it gradually as the generational plan matures. Just before the retirement, it becomes [100%, 200%] as in the collective plan. There are two reasons for this setup. Firstly, the liability is very small at young age due to the fact that the present value of the accrued right is small. So the funding ratio is often large in the beginning. If using the same funding ratio threshold as in the collective plan, then the beginning contribution rate will be very small. But later contribution will be very large when the funding ratio declines over time. To avoid such rapid increase of the contribution rate, we impose a higher upper threshold to induce a high contribution rate in the early phase. Secondly, the early contribution is more valuable than the later one as it earns investment return and allows to fully exploit equity premium. Such difference in the setup of funding ratio threshold helps to mitigate the impact from timing of the contribution. As of retirement, the contribution rate in the generational plan is 0. The policy ladder for indexation 10 is described in Figure 2. The indexation rate is set as [0, 10 In our paper indexation to pension rights and benefits are the same. 20

22 100%] of the then-inflation for the funding ratio threshold of [100%, 110%] in both plans. No indexation is granted when the funding ratio is below 1, while full indexation to inflation is given with the funding ratio higher than 110%, and linear rule applies when the funding ratio is in between Description of four tests 4 tests are designed to see how two plans perform under declining equity premium, differentiated investment and aging. Table 4 gives the specifics of the 4 setups. Test 1 is the baseline situation. Equity premium is taken as the difference between stock and bond return from the simulation. No aging is considered, and both plans have constant age composition. Both plans adopt the same investment policy over time, namely 50% stocks and 50% bonds. In Test 2, we decrease the simulated equity premium by 1%, which we obtain by deducting the generated stock return by 1% while keeping the generated bond return intact. Investment policy and other plan characteristics are the same as in Test 1. In Test 3 we employ a more tailor-made investment policy in the generational plan to reflect its position in its life cycle. Specifically it has an allocation of 80% stock - 20% bonds in the first half of working period, 50%-50% in the second half, and 10% stock - 90% bond after retirement. The investment policy is made such that the time-average of stock and bond allocation in the generational plan is equal to the time-average of that in the collective plan. In the collective plan, still policy applies because it is unlikely for a collective 11 Indexation policy only applied for one year, so no catch-up for the missing indexation of previous years. So once a missed indexation, forever a missed indexation. This is also the reason that the threshold for full indexation is as low as

23 plan to take dramatically time varying investment policy as in the generational plan. Other conditions are the same as in Test 1. In Test 4, a conservative asset allocation of 40% stocks and 60% bonds, a consequence of aging, is applied to the collective plan, while still a constant 50%-50% for the generational plan. Other conditions are the same as in Test 1. 5 Simulation results and analysis With the estimates of Equation (8) for the asset returns and Equation (9) and (10) for yield curve, we simulate 500 scenarios for stock and bond returns for a period of 54 years (the assumed lifetime of a generational fund). The average annual stock and 10-year bond return simulated for each year and the simulated average yield curve can be seen in Figure 3. The overall averages for stocks and bonds are 9.86% and 6.27% respectively, with an equity premium of 3.59%, which means in Test 2 the equity premium is 2.59%. 5.1 Test 1 results Funding ratio and underfunding probability The solid lines in Figure 4 displays the expected funding ratio and the underfunding probability in each year over time for both collective and generational plans. The expected funding ratio in the collective plan shows a rising trend over time. The underfunding probability for each year is declining. The driving force is that the assets growth net of investments and contribution collections is higher than the liabilities change caused by the benefits payout 22

24 and the yield curve. In the generational plan, the funding ratio starts high because the contribution is much higher than the present value of the accrued rights in the early phase 12. As the accrued rights and the liabilities accumulate, the funding ratio declines. In the year of retirement (year 40), it hits the lowest and also at this point the accrued rights reaches the highest. After retirement the funding ratio climbs up for two reasons. One is the declining liabilities due to the fact that part of the accrued rights are being paid out as benefits. The other is the growing assets as part of the assets not yet used for benefits payout are still earning investment returns. The exploding of the funding ratio in the last few years of its life cycle indicates that on average people have accrued more assets than they need from a lifetime perspective. In total the generational plan s funding ratio exhibits a leaning V-shape. The V-shaped expected funding ratio also induces an inverted V-shaped underfunding probability Contribution rate Figure 5 shows the contribution rate and its standard deviation for each year during the working period, averaged across 500 simulations. After retirement no more contribution is paid. In the collective plan, due to the ever increasing funding ratio its average contribution rate declines monotonously over time. Its variation over time increases as well because of the increasing volatility of the funding ratio. Regarding the generation plan, the decreasing funding ratio threshold in the premium policy and the decreasing funding ratio together make the contribution rate stable firstly and then declines somewhat in the end. 12 Making the contribution rate higher than needed in the beginning is to avoid abrupt increase of the contribution rate in the later phase. 23

25 5.1.3 Indexation quality Figure 6 shows the mean and standard deviation of the indexation rate granted each year. Since the inflation rate for each year is different, so we use the percentage of inflation that is indexed to show the indexation quality. In the collective plan, due to the lower funding ratio in the early working years, the indexation is relatively low, but then increase to almost full extent when the funding ratio is very high in the end. Because of the indexation rule ([0,100%] for a funding ratio threshold of [100%, 110%]), and with a rising funding ratio very probably bigger than 110%, the indexation rate will also be more and more likely to reach its maximum, and consequently shows a declining volatility. In the generational plan, due to the V-shaped funding ratio, the pattern for indexation quality is also V-shaped. The lowest point of indexation occurs at the time of retirement when the funding ratio plunges into the valley. The volatility of indexation increases first and then declines after retirement, an inverted V-shape due to the V-shaped funding ratio Accrued benefit The above reflects the indexation quality for each year, but the annual rights accrued, shown in Figure 7, reflects the cumulative indexation. This is important because it determines the annual benefits a participant can receive as of retirement. Bearing the goal of fully indexed annual benefits, the collective and generational plan respectively offer 85.6% and 87.4% on average as a percentage of the full cumulative indexation as of retirement. The generational plan has a higher cumulative indexation is mainly due to the high granted indexation rate in the early phase when the funding ratio is very high. 24

26 5.1.5 Comparison Table 5 shows the comparison between the two plans over different dimensions. Firstly, both plans are overfunded on average during the simulated period. In comparison the generational plan achieves a higher life-time funding ratio than the collective plan in either the best, or the worst and the average simulated scenario. The average underfunding probability over the life time is also lower in a generational plan. Secondly, the generational plan asks for a higher contribution rate (11.3%) than a collective plan (9.9%) on average. In the best simulated scenario indicated by the min value, the collective plan charges a rate as low as around 0.8%. But in the worst scenario indicated by the max value, the collective plan charges a higher life-time contribution rate. This reflects that in the healthy conditions when there is an affluent buffer, a participant is better off to be in a collective plan than in a generational plan. Because in the generational plan, people have to save for their future, a high funding ratio still requires some contribution like 6%, while in the collective plan people often enjoy the contribution holiday when there appears a good status. But in a miserable situation, a participant is better off in a generational plan because the conservative premium policy (i.e. a high funding ratio threshold 13 ) prepares a buffer for the bad situation and results in a lower life-time rate. The conservative premium policy also leads to less time variation of contribution rate in the generational plan than in the collective plan (4.4% compared to 5.4%.). Thirdly, indexation rates in both plans are very high, and this is due to the low funding ratio threshold for full indexation. But the generational plan on average grants a slightly 13 Principally a collective plan can also adopt a conservative policy to allow for a low contribution rate only when funding ratio is very high, but this is not practical as the current payers would not be willing to pay. 25

27 higher indexation rate than the collective plan (97.7% compared to 93.8%) due to a higher average contribution rate. The generational plan also delivers a stabler indexation rate over time due to the high average level of funding ratio. It is not concluding to compare the average contribution rate or the indexation quality alone. Each plan charges contribution rate or grants indexation rates at different points in time. The early contribution rate weighs more than the later contribution as the former earns returns over a longer period. The early granted indexation weighs less than the later indexation as the former applies to less rights than the later but it can also weigh more as the former is the base for the future indexation. Therefore we use the net present value, accounting for both the timing and the amount of contribution and indexation to reflect the value a participant will expect to draw from a particular plan. The upper left graph in Figure 8 shows that both plans add value to participants. We perform the paired sample t-test to compare the means of the net present values, and find that the generational plan brings more net present value than the generational plan, marginally in a statistically significant way. From a welfare perspective, the generational plan also provides a higher expected utility than the collective plan (99.5% < 1.) This results from a strict and stable premium policy, and it is consistent with the common sense of the benefits of precautious saving. In conclusion, in a environment of 9.86% stock return and 6.27% bonds return on average, a investment policy and a reasonable premium and contribution policy can help both plans overfunded. Being able to impose a strict premium policy for precautious saving, the generational plan charges a higher premium, and grants a slightly higher indexation. It achieves a lower underfunding probability to trustees, and provides more net present value and welfare to participants. 26

28 5.2 Test 2, 3 and 4 When equity premium is lower in Test 2, both plans performance worsen, as shown in Table 6, a higher premium, a lower indexation and a more vulnerable to underfunding situation. But comparatively, the generational fund is still more valuable to the collective plan. When the generational fund makes its investment in a life-cycle pattern in Test 3, it can afford to charge a lower premium while increasing the indexation, if we compare the right columns in Table 6 and 7. Yet this leads to a higher volatility in funding ratio, contribution and indexation rate. In combination, however, it provides a higher net present value and welfare in Test 3 than in Test 1. Consequently with this additional flexibility in investment policy, the generational plan is even better than the collective plan. Though the time average asset allocation in both plans are the same, the generational plan is able to take a risky investment in its early phase when its funding status is very healthy. Such investment strategy allows the generational plan in a better position to exploit the equity premium, therefore leads to a even better performance when compared with the collective plan. Conservative investment induced by aging in Test 4 and Table 8 lowers the funding ratio in the collective plan, consequently a higher premium is charged. The average indexation is improved, this is caused by the higher indexation in the early phase when the plan is overfunded and becomes less volatile due to the conservative investment. Overall, the collective plan is still inferior to the generational plan. In the computation of the net present value a plan offers, we do not include the assets left in the generational plan when all the participants in the plan die. Figure 9 shows the box plot of the assets left in 4 tests. We find most of time they are positive. There are also cases where a negative value is left which means the plan was in deficit with the highest 27

29 deficit of euro per person. This could lead to a problem in the plan operation. As a generational plan is self-sustained, the deficit means that for the last year a participant might not get retirement income at all. A practical remedy is that a generational plan could buy a put option from other generational plans by giving up the upside potential while obtaining certain guarantees. This will be our further research direction. 6 Concluding remarks The lack of individualization in a collective plan and the lack of risk sharing in an individual plan motivate us to consider a hybrid plan for occupational pension provision. We investigate a new generational plan where people of the same generation are pooled in a generational sub-plan, which can set its own differentiated policies on investments, indexation and contributions. Our simulations show that a generational plan can have an isolated premium policy, which makes the plan preferable to a collective plan under both normal economic conditions and lower equity premium environments. Specifically, a generational plan delivers a higher funding ratio, a lower underfunding probability, charges higher premiums but also grants higher indexation (real pension payments). Overall the generational plan provides a higher net present value and a higher welfare to all generations. The generational plan is allowed to adopt a more tailor-made investment policy, which enables it to be in a better position to exploit the equity premium for different generations. Our simulations show that the generational plan provides a higher value and welfare to participants than the collective plan. Suffering from an aging pool of participants, the collective plan may have to employ more conservative investment policies. This further lowers the value of a collective plan when compared to a generational plan. 28