Intergenerational Risk Sharing in Individual Retirement Schemes

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1 Intergenerational Risk Sharing in Individual Retirement Schemes Mark-Jan Boes VU University Amsterdam Faculty of Economics and Business De Boelelaan 1105, 1081 HV Amsterdam The Netherlands tel Arjen Siegmann 1 VU University Amsterdam Faculty of Economics and Business De Boelelaan 1105, 1081 HV Amsterdam The Netherlands a.h.siegmann@vu.nl tel [We agree to be considered for publication in the Special Issue "Institutional and Individual Investors: Saving for Old-Age" of the Journal of Banking and Finance.] 1 Corresponding author, a.h.siegmann@vu.nl. We thank Jan Bertus Molenkamp, Lans Bovenberg and Wilse Graveland for useful comments and suggestions. 1

2 Intergenerational Risk Sharing in Individual Retirement Schemes This version: February 4, 2015 Abstract We analyze propose a new and pragmatic approach to intergenerational risk sharing in individual retirement schemes. Risk sharing is accomplished by payments from and to an insurance fund that is shared across generations. Pension shortfalls due to low investment returns are covered by this insurance fund. The simple rules governing the inflow and outflow of the insurance fund make it possible to implement in practice. From a simulation of overlapping generations with stochastic asset returns we find that the generation insurance scheme outperforms pure individual retirement saving by a significant margin: for the most risk averse participant, a 2.7%-point lower contribution gives equal utility. In addition, the generation insurance scheme is less sensitive to return volatility than individual accounts. Keywords: intergenerational risk sharing, insurance, defined-contribution, defined benefit. JEL-codes: B22, J26, G23, H55 2

3 1 Introduction In this paper we propose a system for retirement saving with a simple mechanism for intergenerational diversification. Participants build up retirement capital individually and an insurance fund provides intergenerational insurance against large shocks in investment returns. The generation insurance provides the benefits of a defined-benefit (DB) style of arrangement, without the drawback of opacity that is inherent with such a scheme. The payments into the fund, and payouts at retirement are structured as to minimize nominal losses and allow for an interpretation similar to that of a health insurer: everybody pays, but only those affected receive a payment. Pension systems provide participants with the means of living after retirement. They can usually rely on mandatory participation. An efficient pension system enhances welfare and reduces the likelihood of poverty in old age. Pension savings provide risk-bearing capital to the economy. Retirement income provides smoother consumption paths and prevents poverty in old-age. To achieve efficient pension outcomes with risky investments, however, intergeneration risk-sharing is necessary, to decrease investment and longevity risk. Therefore, fair and transparant pension systems that embed risk-sharing across generations need our attention. Existing funded pension systems are either of the defined-contribution (DC) or definedbenefit (DB) type. Defined contribution consists of individual retirement savings accounts and is the most easy to understand, transparent and portable. However, risk-sharing is absent: all the investment risks remain with the individual participant. Defined-benefit (DB) is considerably more efficient in terms of outcomes, see Beetsma and Bovenberg (2009). The efficiency is caused by the intergenerational risk sharing, by which shocks in the funding ratio are spread out over time and generations, see Gollier (2008) and Siegmann (2011). In addition, the annuity payments with indexation ambition take into account the risk of inflation and protect against longevity risk. Nonetheless, defined-benefit has serious problems. Despite its stand-alone attractiveness, there are several factors that work against the attractiveness of defined-benefit. First, employers are exceedingly not willing to carry the 3

4 burden of a contribution rate that changes from year to year. In bad years, they might have to make up for a funding shortfall. International accounting standards are forcing companies to put future uncertain pension obligations on the balance sheet, which is costly. It puts companies at a disadvantage compared to their competitors who do not have these obligations. Second, sponsors could abuse the intransparency of DB plans to hide funding shortfalls. For example, US companies are overstating projected returns and using too high discount rates for pension obligations, see Andonov et al. (2012). Similarly, governments are tempted to adjust the rules governing the discount rate to decrease current contribution rates. For example, there are proposals in the Netherlands to use a non-market ultimate forward rate (UFR) for discounting long-maturity liabilities, see Eling and Holder (2013). In the current market state, the immediate effect is a lower present value of liabilities and, for pension funds, a higher funding ratio. If this leads to higher real benefits for the current pensioners, this leads to net generational transfers from the young to the old. From a macroeconomic perspective, defined-benefit plans do not sit well in a mixed system with both DB and DC-plans, or with a mobile labor force. Accrued rights in a defined-benefit plan can only be transported to another pension fund if they have explicit agreements on this. Employees that change jobs and change pension system, or country, are left with partial pensions at different institutions. A related problem is the opacity of DB plans, which is a characteristic of this type of pension plan, caused by the intergenerational redistribution implicit in the contribution and funding policies. It is the opacity that makes tinkering with the discount rate possible, as the effects are difficult to judge for laymen. However, this also diminishes the trust in the pension system, with increased awareness among the public that complex financial systems might not be for the public good. For example, in the Netherlands, both young and older generations are now claiming that the system is not fair. If such a widespread dissatisfaction with the system cannot be resolved, the defined benefit pension system is destined to be reformed. As such, there is evidence that the dominance of DB-systems is already decreasing, see Broadbent et al. (2006). In this paper we propose a pension system that has the portability and transparency of individual retirement accounts, with intergenerational risk-sharing that is simple to explain 4

5 and understand. The core is an individual retirement savings account: Participants save a fixed fraction of their wage for old-age pension to purchase a fixed pension at retirement. Intergenerational diversification is provided by a generation insurance fund that grows with premiums paid by the participants. The contributions and payout of the generation fund are determined only once for the existence of the plan. The contributions into the insurance fund are governed by two parameters: a fixed fee, as a fraction of wages, and a variable contribution that is a fraction of returns over a high-water mark level of assets. The highwater mark is time and generation-specific. Our proposal builds on the known efficiency of intergenerational risk-sharing, see Gollier (2008). It is related to the analyses of alternative or hybrid pension plans, see Blommestein et al. (2009). In contrast to other proposals, we have a fixed contribution rate over the lifecycle and intergenerational risk-sharing is provided through an explicit insurance fund. We perform simulations of the performance of our plan using stochastic asset returns and interest rates in an overlapping-generations model. The approach of a Monte-Carlo simulation enables us to model a realistic evolution of returns, contributions and payouts of the insurance fund. For a given set of parameters, the outcome of the simulation is a certainty-equivalent pension at retirement for each value of risk aversion. Simulation outcomes show that the certainty-equivalent level of pension, as a fraction of average wage, is higher than a standard DC system (without insurance), for all levels of risk aversion that we consider. Comparing contributions for equal expected pension utility, we find that in the generation insurance the least risk averse participant has a one percent lower contribution. For higher risk aversions, the contributions are 2% and 2.7% lower, respectively, for the same expected utility of the pension outcome. On a baseline DCcontribution of 13% and 13.7%, respectively, this is economically significant. The paper proceeds as follows. Section 2 outlines of our proposal. Section 3 describes the simulation approach. Section 4 presents the results. Section 5 discusses implementation issues. Section 6 concludes. 5

6 2 Individual accounts with generation insurance The basic component of the scheme is an individual retirement account. Participants pay a fixed contribution rate as a fraction of wages which accumulates in the retirement account with investment returns. The life-cycle investment mix is set by the fund and is identical for each individual of a certain age. The add-on component is an insurance fund that pays out a compensation for each retiring generation who faces a pension shortfall below 70% of the average wage. The payout of the insurance fund is capped at a percentage of total assets of the fund, so that the fund is not emptied by one generation. If the total maximum payout from the insurance fund is not enough to cover the shortfall of the current retiring generation, the monetary payout to each participant is proportional to his pension capital. The premium for the generation fund consists of two parts. The first part is a fixed percentage of wages, for example, 1%. The second part consists of a percentage of, say, 20% of returns in the individual account, given that the returns are positive and previous year s assets exceed the high-water mark level. The high-water mark is equal to the highest level of assets in any previous period, hence the name. Collecting premia from excess returns is similar to the Save More Tomorrow scheme of Thaler and Benartzi (2004). In their scheme, employees are induced to save more by having a default fraction of wage increases being put in a savings account. It assumes employees are loss averse in nominal terms, so that they are reluctant to a decrease in their nominal income, see Kahneman and Tversky (1979), Kahneman et al. (1991). The second source of the insurance premiums is in a similar vein: it avoids nominal losses by charging an insurance premium only if the net returns on the individual account are positive and the asset value is above the high-water mark. The fee structure connects to the sense of fairness by investors that performance is only rewarded if it beats a previously high level of assets. In the pension scheme, the fee structure ensures that extra premia are only paid in times that participants will unequivocally perceive 6

7 as good : returns are positive, and the assets in the individual account are exceeding the previous highest level. 2 The high-water mark is important, as it constitutes a natural reference point for participants. People use historical highs to form a reference point beyond which they decode outcomes as losses. Investors of an acquiring firm are using similar frames when considering a takeover bid of a company, see Baker et al. (2012). The insurance fee structure leads to high premia in times of high investment returns. This is highly beneficial for the overall efficiency of the pension outcome. It can be framed as a Joseph-principle, whereby seven years of plenty are followed by seven years of famine. Only by saving the good harvests in the years of plenty the people can survive in the years of famine. It connects to a normative view on good financial policy, whereby irrational exuberance is not seen as unavoidable feature of financial cycles, but something that should be tempered, see Sedlacek (2011). A pension scheme that embeds such a feature is worthwhile to pursue for the benefit of participants and public welfare. In fact, the necessary buffer that regulators force DB pension funds to hold against adverse market conditions is a reflection of the same principle. Returns in good years increase the buffer, so that shocks can be absorbed. Our insurance fund resembles the buffer in a DB-system, with one of the differences being that the insurance fund invests in low-risk assets only. Given the risk profile of the possible pay-outs, it is imperative that the insurance fund invests in assets that have a low (or negative) correlation with the investment returns of participants. In practice, this will be a combination of low-risk assets, such as government bonds or money market funds, assets with low beta and volatility, and possibly assets with a negative correlation with risky assets, such as funds and securities with a short exposure to the stock market. The payout structure of the insurance fund is similar to that of Beetsma et al. (2012), who model a linear payout below a threshold of consumption. 2 In practice, the insurance could be made dependent on the level of the insurance fund as well. This might increase efficiency further, at the costs of added complexity and discretion by the pension fund board, which we try to avoid. 7

8 Part-time employees, of employees with less than a working life of 45 years with the same pension fund, receive payouts in proportion to their capital accumulated in their individual account. An implementation detail of our proposal is the choice of setting up a separate entity for the pay-out phase of the plan. Such an entity could provide the insurance against longevity risk and offer a (limited) protection to inflation, at lower costs than commercially available annuities. The entity would retain some of the opaqueness of a DB-system, but with a scope limited to only retired participants. Also, having only retirees in the post-retirement plan limits the intergenerational conflicts. A key feature of the proposal is that the rules governing the generation insurance fund, and its workings, could be explained in relatively simple terms. For example, it can be explained as a health insurance company that obtains insurance premiums, but only pays out to people who suffer from health problems and need treatment. Likewise, the generation insurance fund takes in insurance premiums and pays out if the investment returns or current interest rate lead to pension problems. 2.1 Economic Efficiency The system of individual accounts plus insurance fund increases the individuality relative to a collective defined-benefit system. It decreases opacity and makes people owner of the individual retirement account. The generation fund accomplishes intergenerational risk sharing, which is shown to be efficient, see Gollier (2008), Beetsma et al. (2012), Beetsma and Bovenberg (2009). A feature of the proposal is that investment risk decreases with age. This is optimal from a life-cycle perspective, where labor income becomes a decreasing proportion of lifetime wealth with age, see Campbell and Viceira (2003). At retirement, the accumulated capital is converted to an annuity which provides a stable pension. This improves on the downside to defined-benefit pensions, where retired participants share in the same investment risk as the active participants, which increases the associated risks to the funding ratio and potentially lead to indexation cuts. A defined benefit system has necessarily the same asset mix for all generations, ages and risk averters. This is a drawback of the system because ideally retirees 8

9 would like to take less risk and young participants on the other would be willing to take more risk. The story is that if a negative shock realizes for the funding ratio, the young participants or the sponsor will close the deficit by means of higher contributions or recovery contributions. However, this situation is not sustainable due to ageing of the population, which has reduced the portion of active participants in the pension fund. In other words, the burden on the active participants has or will become unrealistically heavy. Moreover, sponsors are less willing to pay recovery contributions because of the pressure this will have on the corporate s profit and loss. The scheme does not hinder labor mobility, as under defined-benefit, because the individual retirement account is easily transferred. Also, it should be possible to transfer the individualspecific contributions into the generation fund to another pension fund. If there is no systematic pattern in labor mobility, i.e., a pattern of older workers moving from one specific industry to another, one could even do without the transfer of the insurance fund-part. This is similar to what happens in health insurance: health insurers accept new clients without having them transfer their net insurance premia from their old insurer. 2.2 Can the market provide generation insurance? The possibilities of replication of the generation insurance in the market are limited. First, it would require the buying and selling of long-dated put options in large quantities. It could be done by using shorter-dated options, sold by younger generations to older generations. But if a payout is triggered, younger generations suffer a net asset loss, which could lead to intergenerational tensions that our plan is intended to diminish. Alternatively, if the put options were to be provided by outside participations through open markets, the whole pension plan becomes vulnerable to counterparty risk. And the positions themselves constitute a new source of stability risk, if the writers of the puts are concentrated at just a few large counterparties. Third, the contingent payout of the insurance fund depends on the pension shortfall of generations, which has no simple linear relation to stock market returns. Final pension is the accumulation of contributions with asset returns over 45 years, divided by a pension costs factor that depends on interest rates at retirement. At the very least, a put option that pays out in case of a pension shortfall is a complex exotic derivative, with doubts 9

10 on whether enough sellers could be attracted to make a market or, alternatively, whether the costs would be acceptable. 2.3 Accounting for differences in wage growth A typical problem of defined benefit pension systems is that high-growth earners are being subsidized by low-growth earners: pension rights are being earned as a fraction of wages, and high growth earners profit more from this than workers with a lower growth rate of their income. Such problems do not exist in a pure DC system, but might be re-introduced when having a generation-insurance fund. However, if the share of the payout for an individual is proportional to the monetary value of the transfer, there is no significant redistribution across low-growth and high-growth wage profiles. This is due to the fact that pension capital accumulated in N years is roughly proportional to the average contribution. Our simulations support this (not reported). The rule of payout share equals capital share is easily communicated and is fair: low-growth earners have contributed less over their working life and will also receive less from the fund. Under the rule, the payout in terms of final pension will be similar to what they could have received when being in a separate pension fund with similar low-growth earners. 3 Simulation approach We compute the performance of the pension plan using Monte-Carlo simulation in an overlapping generations model with yearly generations. We focus on the retirement outcome only, abstracting from labor income, consumption and housing wealth. Section 3.1 describes the evolution of individual pension assets, the evolution of the insurance fund assets and the computation of the final pension. Section 3.2 describes the characteristics of the employee population, the wage profile and the parameters used for generation economic scenarios. 3.1 Evolution of pension assets and the insurance fund A generation i at age t builds up pension assets A it, as follows: A it = A i,t 1 R it p + c W it, (1) 10

11 where R p it is the portfolio return and c is the contribution rate. W it is the wage of generation i at time t. The portfolio return is the return on the stock and bond investment, with a fraction of stocks, α t, that is initially 100% and declines from year t. In the baseline simulation, t is such that the fraction stocks declines with 10%-points each year from age 50, reaching 0% stocks at age 60. The sensitivity to this parameter is analyzed in Subsection 4.4. Every generation i has a high-water mark at time t, H it, that evolves as H it = max (H it 1, A t ), (2) i.e., the historically highest level of assets. The inflow into the insurance fund consists of two components. The first is the insurance fee f as a fraction wages. The second is a fraction κ of any positive asset growth in the pension account that exceeds the high-water mark. So, for any active generation i at time t, its contribution to the insurance fund is given by C it = f W it + { κr ita it 1 0 if A t 1 H t 1 and R it > 0. otherwise (3) Besides the contribution C t, the insurance fund grows with the short-term interest rate, R t 0, so that the evolution of the asset value of the insurance fund, IF t is simply IF t = IF t 1 R t 0 + C it. (4) In the first year of the simulation, the inflow into the insurance fund comes only from one generation. Beyond year 45, there are 45 active generations who each contribute to the insurance fund as in Equation (3). The first payout occurs when the first generation retires, i.e., at t = 45. From that point onwards, the sum of wages is constant (45 active generations) and payouts can be made each year, depending on whether the retiring generation has a pension shortfall. The payout is capped to a fraction F of the assets in the insurance fund, see below. 11

12 For each generation, the pension obtained at retirement is the final capital divided by the average wage, W, and the costs of a pension annuity. The annuity cost in money terms is denoted by a R0t, which is an actuarial factor that depends on the current interest rate and the demographics of the population (assumed fixed). This leads to a pension level in terms of the fraction of average wage, which is positive and otherwise not restricted. The pension shortfall is equal to max(0.7 Pension it, 0), i.e., it is the difference between 70 percent of the average wage and the unadjusted pension, but only if the pension is below 70%. The shortfall of generation i at retirement time t is denoted as PSF it. The monetary value of the pension shortfall is PSF it a R0t W. If a generation has a pension shortfall, the insurance funds pays out a fraction of its assets to (partly) compensate for the shortfall. Only up to a maximum fraction F of the insurance fund is paid in any year, so that the fraction of the pension shortfall paid is InsFraction t = min(psf it a R0t W, F I t ) PSF it a R0t, (5) where I t is the size of the insurance fund at time t. So, if generation i at time t has a pension shortfall, it receives a compensation up to a monetary value of F I t. If there is no shortfall, the payout of the fund is zero. With the compensation from the insurance fund, the adjusted pension for generation i becomes PensionAdj it = Pension it + InsFraction t. (6) In the absence of insurance, i.e., f = κ = 0, the second term on the right-hand side of (6) is zero, and the adjusted pension is equal to the outcome of a pure DC-system. In practice, one might not want to have an insurance payout surprise at retirement, but rather a payout mechanism that is structured so that soon-to-retire participants can form proper expectations about the pension they will receive. For example, a prediction could be communicated about the pension level at retirement and the payout to be received, depending on the value of the individual account, the interest rate, and the assets in the insurance fund. 12

13 3.2 Economic parameters We assume an aged population whose distribution is perfectly stable over the simulation period, using the Dutch demographics as predicted for 2060 by Statistics Netherlands (CBS). For the wage profile we take the average wage per age group in 2011, also from Statistics Netherlands. The demographic build-up and wage profile are depicted in Figure 1. INSERT FIGURE 1 HERE The age profile in panel A of Figure 1 takes into account an aged population with high longevity. For that reason, we assume a relatively high retirement age of The composition of the population is assumed stable, so that in each year, the same number of people from a specific age is assumed to be alive. Any significant fraction of non-survivors is only visible after the age of 68, so in the simulation model each age group is normalized to 1 and survival after 68 follows the demographic pyramid of Figure 1, panel A. The wage profile in panel B of Figure 1 is representative of wages increasing over the lifetime, leveling off, and slightly decreasing at higher ages. The decrease in wages at an older age can be seen as early retirement by a fraction of the population, accepting a lowerpaid job, or working part-time. We assume zero wage and price inflation, and choose parameters for the asset returns accordingly. We assume a fixed inflation rate of 2%. However, to facilitate the simulations, we work with an inflation of 0% and adjust the mean asset returns to reflect real returns, i.e., 2% lower than nominal average returns. Stock returns are normally distributed with a mean of 6% and volatility of 20%. The mean and volatility are within the range typically found in the literature. The interest rate is normally distributed with a mean of 2% and standard deviation of 1%. Stock returns and interest-rates are independent and identically distributed, and we assume no mean reversion. 3 The current Dutch retirement age increases stepwise from 65 in 2012 to 67 in 2021, for the pay-as-you-go part (AOW). After 2012, the retirement age evolves with the life expectancy. The occupational pension age becomes 67 per January 2014 and future age rises are not ruled out. 13

14 For the annuity costs of a pension, we assume that the term-spread is equal to the inflation rate, so that we use the current short-term interest rate to compute the costs of the final pension. The investment opportunities for the individual are stocks and bonds. Assuming a duration of Δ, we have a simple relation between bond returns and short-term interest rates R 0 t, given by R b t = 0.01 Δ (R 0 0 t R t 1 ). (7) where the first term in (6) implies a carry return, or term premium of one percent. The relation in (6) is similar to the one used in Hoevenaars et al. (2008). 3.3 Sample outcomes To illustrate the dynamics of the pension plan, sample outcomes for two scenarios of stock returns, interest rates and bond returns are in Figure 1. INSERT FIGURE 1 HERE The scenario in the top panel of Figure 1 has good returns for the generations. Under DC (the dashed line) the pension outcome drops below 0.70 after generation 68. All earlier generations have a high pension outcome, sometimes exceeding two times the average salary. For the pension system with generation insurance, the outcomes of all generations are equal to, or higher than 70 percent of the average wage. However, the contributions to the insurance fund lead to a pension level that is lower than under DC, for all generations up to the 68 th. For all following generations in this simulated scenario, the pension outcome is exactly Figure 1a is thus an example of a scenario where the years of plenty are used to build up an insurance fund that starts paying out in the years of famine. The scenario in the bottom panel of Figure 1 is an example of DC-outcomes dominating the outcomes with insurance fund for all but a few generations (between 14 and 35). This is a logical consequence of the system with an insurance fund: if returns are good for a long time, the insurance fund is not necessary, ex post. 14

15 4 Performance Evaluation 4.1 Baseline results In the baseline results we compare the descriptive statistics and utility outcomes of a simple DC-plan with our plan of generation insurance. To make outcomes comparable, we choose parameters for contribution and the fixed insurance fee so that c+f=0.11 for both plans. Table 1 shows our baseline results based on 500 simulations of 100 generations. For each parameter setup the same random numbers are used for generating the economic scenarios. INSERT TABLE 1 HERE The top row in Table 1 has the results for a pure DC scheme, i.e., without the insurance fund. The average pension is 0.85 of average wage, with a median of The standard deviation is 0.58, and the 90% confidence interval for final pension is (0.38,1.5). The final three columns give the certainty equivalent pension, using the power utility function with relative risk aversion of 3, 5 and 7. Chiappori and Paiella (2011) find a mean coefficient of 4.2 among Italian households, and 2.5 for households who hold risky assets. In the case of pensions, we expect a high degree of risk aversion, so that we should not take the risk aversion of a stock investor as typical. Therefore, we choose 3 and 7 as the lowest and highest degree of risk aversion, respectively, where utility is measured in terms of final pension relative to the habit level of 70% of average wage. For DC, the certainty-equivalent levels of pension for the three levels of risk aversion are 0.57, 0.48 and 0.42, respectively. The rows below the first row are in two groups, one with a fixed fee, f, of 1%, and one with a fee of 0. For readability, the highest mean and certainty equivalent pension, and lowest standard deviation per group, are made bold. The first block of rows has 9 simulation results for a setup with a fixed insurance fee of 1%, maximum payout F between 10 and 30%, and return sharing between 10 and 30% of positive returns beyond the high-water mark. For all levels of risk aversion, the system with an insurance fund and optimal configuration has a higher certainty equivalent pension than DC. For a risk aversion of 3, the improvement is 4 percentage points, from 0.57 to For =5 it increases from 0.48 to For the most risky participant ( =7), the highest CEQ-pension 15

16 (0.51) is achieved for a 10% payout fraction and 30% return sharing. This is 9 percentage points higher than the CEQ-pension under DC. The highest mean pension, 0.75, is achieved for the lowest fraction (10%) of return sharing, which is as expected, as the skimming of excess returns over a high-water mark decreases the expected mean value of the pension outcome. The optimal configuration is one with 30% return sharing and a 10% maximum payout of the insurance fund. It has a standard deviation of 0.15, compared to 0.58 for the DC-model. These results show that the proposed system resembles in a DB system in the sense that pension benefits are relatively stable. The second group of rows has the outcomes for a configuration without a fixed insurance fee. Under this configuration, similar outcomes are obtained, with maximum CEQ pensions for the three risk aversion parameters of 0.62, 0.56 and 0.50, respectively. The highest mean, and lowest standard deviations are achieved with a high fraction (30%) of returns paid into the insurance fund. However, the differences in CEQ pension for different values of κ are small. Further computations show that a higher fixed fee f, while keeping c+f constant does not lead to higher CEQs. 4.2 Average contributions for equal-utility plans To further compare our proposal with a traditional DC-plan, we compute DC-contributions that give equal pension utility as the optimal generation insurance schemes. We take the c/f/f/κ schedules with c+f=0.11 from Table 1 that have the highest utility for a risk parameter of 3, 5 and 7, respectively. Then, we do a grid search on the parameter c for the ordinary DCscheme that gives equal utility. The results are in Table 2, where the summary statistics and CEQ pension are reported for each combination of matching utility. INSERT TABLE 2 HERE The three rows in Table 2 represent the three parameter choices that give the highest utility, one for each risk aversion parameter. For γ = 3, the best plan has a contribution rate of 0.11, no insurance premium, return sharing (κ) of 0.2 and maximum payout (F) of 10% of the insurance fund. The matching DC-plan has a contribution rate of It has a higher mean return of 0.94 and standard deviation of

17 For the higher risk aversion parameters (5 and 7), the DC-plan that has the same certaintyequivalent pension (CEQ), has a higher mean and standard deviation. The higher mean return is necessary to achieve equal utility with the insured plan, which has downside protection. For the most risk-averse participant (a γ of 7), the difference in mean pension is large, 0.42, for equal CEQ-pension. For this participant, the insured system with a contribution rate of 10%, insurance fee of 1%, upside return-sharing of 30% and a maximum payout of 10% of the fund, has equivalent utility as the DC-plan with a contribution rate of 13.7%. Thus, for a 2.7%-point lower contribution rate and 30% upside return-sharing, generation insurance can achieve the same utility as a DC-plan. This is economically significant and illustrates the potential benefits that can be achieved with intergenerational insurance. 4.3 Shifts in intergenerational benefits A potential concern with the results in Table 1 is that the higher CEQ pensions relative to DC are not caused by the increased efficiency of the plan, but by a shift in intergenerational benefits. For example, with the insurance fund, early generations might be made worse off on average, subsidizing the later generations. If the increase in CEQ pension for later generations is more than proportional than the decrease for early generations, we might be measuring something different than an increase in efficiency, but rather a specific method of allocating costs and benefit over young and old generations. To measure shifts in intergenerational benefits we compute the difference in CEQ pension between our plan and the DC scheme, separately for the first 50 generations and the last 50 generations. We compute outcomes for parameter values from rows 2, 4 and 5 of Table 1, and the three risk aversion parameters. All three variants have a contribution of 0.10 and insurance fee of The results are in Figure 3. INSERT FIGURE 3 HERE Figure 3 uses black bars for the first 50 generations and white bars for the last 50 generations. The height of a bar is the increase in CEQ pension relative to DC. Under the parameter values of variant 2, with 10% return sharing and 10% maximum payout, there is quite a difference between the late and early generations, of around This points at an effect of the early generations filling the insurance fund, of which later generations benefit disproportionally. 17

18 However, the benefit for the early generations is still positive. For variant 4, there is no clear difference in benefits between early and late generations. For variant 5, the difference is roughly half of that in variant 2. The results in Figure 3 show that the benefits in intergenerational risk sharing are not always evenly distributed over generations (in expectation). The cause of this is a point for further research. However, the importance of this issue is somewhat diminished if the retirement scheme starts with a non-empty insurance fund. Given the existence of funded systems, having a sizeable insurance fund to start with might be the more realistic situation. 4.4 Heterogeneity in risk aversion In any life-cycle investment model, as in defined-contribution, the investment mix needs to be tuned to the horizon of the investor. In practice, this is achieved by determining an age after which the fraction invested in risky assets is decreased by a fixed percentage per year. For example, in Section 4.1 we have chosen the age of 50 to decrease the fraction in stocks by 10 percentage points per year, so that the investment in stocks decreases linearly, to zero at 60. The linear schedule impacts the riskiness of the pension outcome, but the optimal path crucially depends on the level of risk aversion of the participant. To determine whether heterogeneity in risk aversion is important, we perform simulation with different ages at which the fraction in risky assets starts decreasing by 10 percentage points per year. The outcomes are in Table 3. INSERT TABLE 3 HERE Table 3 shows that the mean and standard deviation of the pension outcome are increasing in the point at which reduction starts. This is as expected: a higher age at which reduction starts leads to a higher exposure to stocks over the investment horizon period, which leads to higher returns and higher risk. The certainty-equivalent (CEQ) pensions are most affected for the most risk-averse participant (γ=7). For him, the CEQ pension decreases from 0.54 to 0.35 when the age of reducing stocks increases from 40 to age 60. The decline is most pronounced between 18

19 reduction ages 52 and 60. This is caused by the high risk aversion that comes with a preference for safety, and has a low optimal investment in stocks. With low risk aversion (γ=3), the CEQ is not much affected by the reduction age. It moves between 0.60 and 0.62, with an optimum age of reduction between 46 and 56. For a risk aversion coefficient of 5, the CEQ-pension is almost constant for the reduction ages of 40 to 50, and equal to From age 50 to 60 it drops from 0.56 to For all levels of risk aversion, the optimum age to start reducing stocks is at 50 or earlier. In practice a less-than-optimal age slightly below 50 could be implemented as a compromise between the least and most risk-averse participants. One argument for a less risky allocation is that a less risky allocation can always be compensated by investments in a third pillar pension. A typical third pillar would consist of individual pension arrangements to supplement an occupational pension, and/or a first pillar pay-as-you-go pension, see Worldbank (2005). Less risk-averse workers can use personal investments to determine the riskiness of their total retirement income. One argument against a less risky arrangement is that the intergenerational benefits are greater for more risky returns, see Gollier (2008). 4.5 Sensitivity to stock return volatility The literature suggests that intergenerational benefits are increasing with economic uncertainty, as the value of insurance against shocks increases, see Gollier (2008). To test the extent of this effect in our setup, we compute CEQ-pensions for lower and higher values of stock return volatility, relative to our baseline stock volatility of The results are in Table 4, with a separate panel for each risk aversion parameter used. INSERT TABLE 4 HERE Starting with Panel A, i.e., a risk aversion coefficient of γ = 3, we observe that the CEQpensions of both schemes are decreasing in volatility. This is consistent with the intuition that the utility of a pension is negatively affected by volatility. An interesting observation is the fact that the generation insurance scheme has a markedly lower sensitivity to volatility than DC: the CEQ-pension is 0.05 higher or lower under lower and higher volatility, while the outcomes under DC change by 0.10, which is double as high. 19

20 The sensitivity to volatility follows the same pattern for the other risk aversion parameters, as shown in panel B and C of Table 3. The CEQ-pension under DC is higher resp. lower by 0.10 for a lower resp. higher volatility, while the generation insurance scheme is much less affected. 4.6 Stochastic volatility There is strong evidence that conditional volatility is negatively related to stock returns, see for example Glosten et al. (1993) and Poon and Granger (2003). This might have an effect on the performance of a pension system, with the impact on DC and generation insurance not similar in magnitude. We use an alternative model to generate stock returns to test this. We simulate stock returns from an adapted discrete version of the model of Heston (1993) for computing option prices under stochastic volatility. Annual stock returns have a fixed mean and stochastic variance, given by R t = μ + σ t ε 1t, (8) where σ t is the conditional variance at time t and ε 1t a standard normal disturbance. The process for σ t is given by σ t = σ t 1 m(σ t σ) + σ σ V t, (9) with m the speed (between 0 and 1) of adjustment from the current level of volatility to the average level, σ, of The parameter σ σ is the volatility-of-volatility and V t is a disturbance term that is correlated to the disturbance term of stock returns, ε 1t, in the following way: V t = ρε 1t + 1 ρ 2 ε 2t, (10) where ε 2t is a, independent of ε 1t, standard normal disturbance and ρ is a correlation parameter. We simulate from the model in Equations (8) (10) using m=0.2, and ρ = 0.5, and for three different values of the volatility of volatility, σ σ, namely 0, 0.01 and The results are in Table 5. INSERT TABLE 5 HERE 20

21 The results of Table 5 show that stochastic volatility makes the pension outcomes worse for both plans. This is the result of high volatility and negative returns appearing simultaneously, so that the worst returns become more pronounced. However, the effect on CEQ-pensions is roughly similar for the two types of plans. For example, for =5 the CEQ-pension of DC drops from 0.56 to 0.48 when σ σ increases from 0 to 0.02, and for generation insurance it drops from 0.56 to For the other risk aversion parameters, the the effect is similar in magnitude. We conclude that stochastic volatility has little influence on the comparative advantage of either plan. 5 Implementation issues 5.1 The pension annuity In practice, the pension annuity at retirement can be purchased from a commercial insurance company. However, it might be more beneficial for pensioners to have a separate non-profit entity providing the pension annuity. It can operate as a defined-benefit pension plan, and have lower costs than a commercial solution. The portfolio is not necessarily risk-free, to allow for indexation ambitions to be pursued. Most of the assets would be hedged for interest-rate risk, to match the interest-rate sensitivity of the liabilities. 5.2 Risk management For the purposes of this paper, we do not consider interest-rate hedges for the assets of active participants. Such hedges, e.g., swaps, could be used to facilitate a smooth transition from the pension capital to a yearly pension. We are fairly certain that such hedges will be beneficial, but in this setup it leads to unnecessary complications in modeling the pension outcomes. 5.3 Transitioning from existing DC or DB plans We want to offer some thoughts on how a transition from an existing DB or DC-plan to a plan with explicit generation insurance, such as ours, could be realized. Existing participants in a pension plan have a history of payments, assets and/or pension rights, and the associated expectations with regard to a final pension. Changes to the system will involve the transformation of assets or pension rights into the terms of the new system. 21

22 Transitioning from a DC-plan should be the easiest, as pension assets are clearly marked as such. Existing active (non-retired) participants continue to pay a contribution to their individual pension account, but by paying an insurance fee and/or the upside return sharing they obtain rights to the insurance payouts at retirement. Those rights would be proportional to the years in the new system. The transition from a DB system is more complex. Active participants to a DB-system build up pension rights, not assets, and these rights would have to be converted to assets. The assets then have to be split in an individual part and an insurance part. There are issues in the split in assets between (i) retired and non-retired participants, (ii) young and old participants, and (iii) the individual account and the insurance funds. First, splitting the pension assets between retired and non-retired participants can be done on the basis of the actuarial value of the nominal pension rights. The allocation of the surplus or shortfall needs to be negotiated between the retired and active participants, and the sponsor. Such a negotiation is similar to the yearly negotiation that takes place implicitly in the DBpension when contribution and indexation policies have to be determined. After the split, the assets of the retired generation are placed in a special payout-fund. Second, the total pension rights of non-retired participants need to be distributed over the generations. A complication is the fact that the actuarial value of pension rights of the younger generation (say, below 40) is usually lower than the present value of the contributions paid into the fund. The reason is that under DB, pension rights accrue with a fixed percentage per year, while the actuarial value increases with age. For older participants, the yearly increase in pension rights is worth more than their contribution. This is an essential feature of a DB-fund and drives the intergenerational solidarity embedded in DB. A negotiation about the asset value of the pension rights for young and old generation will have to find the middle ground between the present value of the contributions and the actuarial value. A final part of the transition is the allocation of assets between the individual account and the insurance fund. The desired initial size of the insurance fund determines the total fraction of assets that need to go in the insurance fund, and the contribution of each generation is a 22

23 function of the expected benefits of insurance. If the pension fund has a nominal funding ratio greater than 1, the surplus could be used to fill the insurance fund. 5.4 Taxation of pension contributions in the Netherlands The Netherlands has a peculiar tax treatment of contributions to a DC-plan, namely one in which the deductibility of pension contributions is progressive. For example, a worker of 60 years old can deduct five times as much contribution as a worker aged 20. This treatment of pension contribution for taxation is rooted in the prevalence of DB-schemes in the Netherlands, where pension rights are accumulated as a fixed percentage of the wage. Someone who starts in a DC-scheme with fixed contributions and switches to an employer with a DB-scheme at, say, age 40, could build up pension rights with tax-deducted contributions of more than 70% of average wage. The existing law stimulates a DC scheme to have a contribution rate that is increasing in age, growing with the present value of the pension rights earned in a year. This is a hurdle for the implementation of our proposal, which depends on a fixed contribution rate, and would need adaptation. 6 Conclusion We analyze a risk-sharing scheme that captures some of the benefits of a defined-benefit plan, but retains the simplicity of individual retirement saving. The benefits in risk-sharing across generation are achieved by setting up a generation insurance fund that takes in contributions and pays out when a generation has a pension shortfall. Economic ownership of this fund therefore lies with the fund s retirees. A key feature of the proposal is that the rules governing the generation insurance fund, and its workings, could be explained in relatively simple terms. For example, it can be explained as a health insurance company that obtains insurance premiums, but only pays out to people who suffer from health problems and need treatment. Likewise, the generation insurance fund takes in insurance premiums and pays out if the investment returns or current interest rate lead to pension problems. 23

24 The simulation outcomes that we present in this paper show that significant improvements over a DC-style pension plan can be achieved, measured in terms of the certainty-equivalent level of pension, as a percentage of the average wage. The magnitude of the benefits can also be computed in terms of the difference in pension contributions that give equal utility, which we do as well. There remain several hurdles in actually implementing a generation insurance fund, some of which are discussed in this paper. Negotiations between the stakeholders are necessary. However, given the interest of the sponsors of corporate defined benefit plans to switch to a different system, a combination of an individual account plus some form of insurance is worthwhile to consider. Defined benefit pension plans are nearing the end of their usefulness. Companies do not want to have to fund pension shortfalls, nor to compute the future value of shortfall, as forced by new accounting rules. Moreover, the opacity of the workings of defined-benefit enables some pension plan managers, sponsors and regulators to manipulate the liability discount rate to inflate funding ratios, which leads to wealth transfers between generations. The annual decisions on funding and investment decisions are recurring battles over the allocation of benefits, costs and risks to young and old generations. The drawbacks of DB call for transparent alternatives that retain some of the intergenerational risk sharing properties. In this paper we have proposed one such alternative. It remains to be seen whether the political support for a drastic overhaul of pensions will come anytime soon. However, society calls for a system that fits with the transparency that is required across the society as a whole. It is to be seen whether this required transparency can be delivered by the traditional DB-system, despite its widely recognized advantages. In our opinion, the system proposed in this paper is not only better than a DC-system but also offers a viable alternative to the DB-system. 24

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