Netspar basic sheets

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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
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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
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
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.

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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

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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)

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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

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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

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Saving and investing over the life cycle in the
basic model
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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

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Benchmark parameters

• Rate of time preference 2
• Risk aversion 5
• Risk free rate 2
• Equity premium 4
• Volatility stock market 20
• Working life (T) 45 yrs
• Retirement (D-T) 15 yrs

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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 ft f (1 Ht / Ft) where
  
• Ht reflects human capital
• Ft reflects financial capital
• Expected asset allocation resembles investment in
  life cycle fund

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Financial, human and total wealth without access
to stock market
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Expected asset allocation financial wealth
Expected share of financial wealth invested in
risky assets
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Asset allocation financial wealth
Expectation, 10 and 90 quantiles and two
simulated scenario paths of the share of
financial wealth invested in risky assets
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Optimal consumption path (contribution level)
Trajectories of the consumption paths of
individuals entering at respectively time t1 and
t 31. Shocks in the asset price are absent
except at time t20 and t40, when a negative
shock is imposed.
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Distribution of future consumption
Expectation, 10 and 90 quantiles and two
simulated scenario paths of the consumption path
over the life cycle
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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

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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

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Welfare loss of sub-optimal contracts

• Specific strategies with constant savings rate
  and asset allocation, relative to optimal
  strategy with constant rates and exposure

• Optimal constant policy r.t. to first best
  without intergenerational risk sharing -7.0

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Borrowing constraints
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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.

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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
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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)

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Risk sharing with non-overlapping generations
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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.

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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

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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

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Welfare analysis of stylized collective schemes
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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 bb) as well as adjustment levels
  towards recovery (?ta and bta)
• ?t ?b ?ta bt bb bta
• ?ta ??1 (1 ft) ? bta ??1 (1 ft)
• The asset allocation is also dependent on the
  coverage ratio ft of the fund xt ?0 ?1(1
  ft)

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Stylized collective schemes

• Model
• ?t ?b ?ta bt bb bta
• ?ta ??1 (1 ft) ? bta ??1 (1 ft)
• xt ?0 ?1(1 ft)
• Note that ??1 gt 0 and ??1 lt 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 gt 0 and ??1 lt
  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

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

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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 ()

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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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