1. Saving and investing over the life cycle and the role of collective pension funds Lans Bovenberg, Ralph Koijen, Theo Nijman and Coen Teulings June 2007

2. 2 Trend to individual arrangements Trend in many countries towards individual pension products rather than collective arrangements Main drivers:  Transparency (costs, risks, property rights)  Underfunding of collective schemes  Tailor-made pension solutions  International Accounting Standards: firm no longer residual risk taker  Desire to take savings and investment decisions (?)

3. 3 Traditional collective DB The distinction between individual and collective is often seen as a synonym for DC versus DB and the choice between them often seems also 0/1. Traditional collective DB:  No risk taking by individual  Pension contributions uniform and imposed collectively  Asset allocation uniform and imposed collectively  Forced participation in sector / firm specific fund  Purchasing power guarantee on pension entitlements (deferred real annuities imposed)  Crucial role trustees in governance

4. 4 Traditional individual DC Traditional individual DC usually  Risk taking by individual  No risk taking by sponsor  Savings decisions taken by individual  Investment decision taken by individual  Freedom to choose pension provider  No forced (deferred) annuities  No pre-set defaults, automatic enrollment etc.

5. 5 The Dutch hybrid model  In the Netherlands hybrid collective schemes have developed which contain elements of the traditional DB and DC setting No (or less) risk taking by sponsor Risk taking by individual  Nominal guarantee on entitlement  Indexation of nominal guarantee depends on coverage ratio of the fund Uniform savings decisions (pension contribution) collectively imposed Uniform investment decision collectively imposed Industry / firm specific pension funds Deferred annuities imposed Stringent supervision to combat underfunding

6. 6 Potential advantages hybrid collective model over individual DC More cost efficient (30 bp) Avoids behavioral biases, professional decision makers Enables borrowing against human capital Completes markets (longevity risk and (wage) inflation risk traded within fund) Potential for risk sharing with non-overlapping generations (“intergenerational solidarity”)

7. 7 Disadvantages hybrid collective model over individual DC Asset allocation of financial capital independent of age  Workhorse model suggests substantial risk taking in financial capital for the young (target date or life cycle funds)  No optimal consumption smoothing of shocks in contribution levels Uniform over individual characteristics  Differences in life expectancy socioeconomic groups  Differences in accumulated pension benefits  Differences in risk aversion etc. Property rights and exposures often not well defined or transparent

8. 8 Aim of this paper Panel / survey paper for Netspar participants and researchers Detailed analysis of saving and investing in the work horse life cycle model (“Merton, Bodie and Samuelson”) Numerical results on welfare effects of individual and collective schemes in this work horse model Survey of extensions of the basic model in the recent literature

9. Saving and investing over the life cycle in the basic model

10. 10 Basic model Individuals work for T years and spend D-T years in retirement Constant exogenous riskless labor income Single risky investment opportunity: the stock market Stock returns are i.i.d. normal No other financial assets than pension contract Smooth time separable CRRA utility with exponential discounting No bequest motive

11. 11 Benchmark parameters Rate of time preference: 2% Risk aversion5 Risk free rate:2% Equity premium:4% Volatility stock market:20% Working life (T)45 yrs Retirement (D-T)15 yrs

12. 12 First best individual contract Contribution dependent on age and past returns Asset allocation of over-all wealth constant f = expected excess return / (risk aversion * variance) Asset allocation of financial wealth dependent on age and past returns: f t * = f (1 + H t / F t ) where  H t reflects human capital  F t reflects financial capital Expected asset allocation resembles investment in life cycle fund

13. 13 Financial, human and total wealth without access to stock market

14. 14 Expected asset allocation financial wealth Expected share of financial wealth invested in risky assets

15. 15 Asset allocation financial wealth Expectation, 10% and 90% quantiles and two simulated scenario paths of the share of financial wealth invested in risky assets

16. 16 Optimal consumption path (contribution level) Trajectories of the consumption paths of individuals entering at respectively time t=1 and t =31. Shocks in the asset price are absent except at time t=20 and t=40, when a negative shock is imposed.

17. 17 Distribution of future consumption Expectation, 10% and 90% quantiles and two simulated scenario paths of the consumption path over the life cycle

18. 18 Characteristics of first best contract without intergenerational risk sharing Expected asset allocation resembles investment in life cycle fund Actual asset allocation initially quite volatile Initial pension contribution is low (7% versus 15% in case without risk taking) Pension contribution quite volatile which reduces the welfare gain

19. 19 Welfare loss of sub-optimal contracts Measure of welfare loss: Annual change in consumption in reference contract that generates same welfare level as contract considered Reference contract: First best contract without intergenerational solidarity No use of equity exposure at all-8.5% Risk aversion level of 3 imposed -5.0% Implementation cost of 0.3%-1.2% Implementation cost of 1.0%-4.0% Fixed asset allocation -5.3% Fixed contribution rate-6.6%

20. 20 Welfare loss of sub-optimal contracts Optimal constant policy r.t. to first best without intergenerational risk sharing: -7.0% Specific strategies with constant savings rate and asset allocation, relative to optimal strategy with constant rates and exposure

21. Borrowing constraints

22. 22 Borrowing constraints The first best solution assumes that individual can take unrestricted equity exposure If returns get negative their human capital is to be used as collateral for their debt. Adverse selection and moral hazard make it hard for financial institutions to ensure that loans will be paid back: “Junior cannot borrow”, Constantinides et al (QJE, 2002) The use of derivatives and / or mortgages can mitigate the problem for the individual, but requires very sophisticated strategies.

23. 23 Expected equity exposure optimal borrowing constrained contract Expected optimal equity share in financial wealth over the life cycle in the presence of a borrowing constraint

24. 24 Welfare analysis second best individual contract First best contract cannot be implemented by individuals: No borrowing against future human capital Often no equity exposure joint with annuities after retirement Behavioral biases Welfare effects ignoring behavioral biases: Joint effect is utility loss of 3.6% for benchmark model. With implementation costs of 0.3% (1.0%) the welfare loss increases to 4.6% (7.0%)

25. Risk sharing with non-overlapping generations

26. 26 Intergenerational solidarity Additional risk sharing is possible if trade is possible with non-overlapping generations This can not be contracted on financial markets; buffers (and deficits) of collective pension schemes aim to achieve this Welfare gain of 6.2% due to intergenerational risk sharing in optimal (age dependent) contracts if agent participates fully in investment risk 15 years before entry to labor market The argument assumes that negative buffers will not be avoided Probability of negative buffer is 35% Probability that buffer exceeds two working years is 28%.

27. 27 Intergenerational solidarity II Mandatory participation in sector or firm specific pension funds is often put forward as an instrument to make sure that collective pension deficits can not be avoided But:  Workers can leave firm / sector or reduce labor supply  Firm / sector can default Derivative structures (not unlike solvency requirements as in FTK and Solvency II) can be imposed to reduce potential size of deficit and retain some welfare gain of trade between non-overlapping generations

28. 28 Welfare gains of intergenerational risk sharing with capped deficits Strategies that benefit from intergenerational risk sharing but reduce the probability of substantial negative buffers on entry to the labor market using (synthetic) put options

29. Welfare analysis of stylized collective schemes

30. 30 Stylized collective schemes The collective schemes considered so far have age and wealth dependent contribution rates and asset allocations. We now consider DC, DB and hybrid schemes that impose uniform asset allocation and contribution rates The premium and benefit level consist of a base level (  b and b b ) as well as adjustment levels towards recovery (  t a and b t a ):   t =  b +  t a ; b t = b b + b t a   t a =  1 (1 – f t ) ;  b t a =  1 (1 – f t ) The asset allocation is also dependent on the coverage ratio f t of the fund: x t =  0 +  1 (1 – f t )

31. 31 Stylized collective schemes Model:   t =  b +  t a ; b t = b b + b t a   t a =  1 (1 – f t ) ;  b t a =  1 (1 – f t )  x t =  0 +  1 (1 – f t ) Note that  1 >= 0 and  1 <= 0. A (collective) DB scheme is obtained if  1 = 0. Likewise a (collective) DC scheme is obtained if  1 = 0. A hybrid scheme is obtained if  1 > 0 and  1 < 0. Hybrid schemes smooth shocks over active life and retirement, and allow for intergenerational risk sharing Parameters are optimized subject to a constraint on the half life of shocks in buffer

32. 32 Optimal parameters and welfare effects collective schemes Characteristics of collective schemes and welfare gains relative to first best contract without intergenerational risk sharing

33. 33 Findings on stylized collective schemes Optimal base premium and benefit same all cases More risk taking and risk sharing in hybrid schemes, which are more attractive than pure DB / DC Uniform scheme that does not address age differences but does exploit intergenerational risk sharing can outperform the first best contract without trade between non-overlapping generations (and a fortiori outperforms the second best individual contract) Note that potential differences in individual characteristics have been assumed away Likewise continuity of the contract between non- overlapping generations is assumed A long recovery period is attractive if continuity of the contract is assumed.

34. 34 Extensions of the basic model Final section provides literature reviews on extensions of the basic model +/- indicates additional or less risk taking by young Labor markets and human capital  Risky human capital (-)  Endogenous labor supply (+) Risk factors in financial markets  Interest and inflation risk  Mean reversion in equity returns (+) Preferences:  Minimum consumption (-)  Loss aversion (+)

35. 35 Conclusions Risk taking adds substantial welfare Hybrid restricted collective contracts to be preferred over pure collective DB or DC. Collective contracts have potential to generate welfare through cost reduction, intergenerational solidarity and relaxation of borrowing constraints. Collective contracts can reduce behavioral biases Collective contracts often suffer from in-transparency. Tailor made contracts are valuable if implemented adequately The optimal pension contract might have elements of both worlds: collective as well as individual (guided through adequate defaults)

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