Age-Dependent Investing: Optimal Funding and Investment Strategies in Defined Contribution Pension Plans when Members are Rational Life-Cycle Planners

David Blake, Douglas Wright, and Yumeng Zhang

A defined contribution pension plan allows consumption to be redistributed from the plan
member’s working life to retirement in a manner that is consistent with the member’s personal
preferences. The plan’s optimal funding and investment strategies therefore depend on the
desired profile of consumption over the lifetime of the member. We investigate these strategies
under the assumption that the member is a rational life cycle financial planner and has an
Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity
of intertemporal substitution. We also take into account the member’s human capital during the
accumulation phase of the plan and we allow the annuitisation decision to be endogenously
determined during the decumulation phase.

We show that the optimal funding strategy involves a contribution rate that is not constant over
the life of the plan but is age-dependent and reflects the trade-off between the desire for current
versus future consumption, the desire for stable consumption over time, the member’s attitude to
risk, and changes in the level of human capital over the life cycle. We also show that the optimal
investment strategy during the accumulation phase of the plan is ‘stochastic lifestyling’, with an
initial high weight in equity-type investments and a gradual switch into bond-type investments
as the retirement date approaches in a way that depends on the realised outcomes for the
stochastic processes driving the state variables. The optimal investment strategy during the
decumulation phase of the plan is to exchange the bonds held at retirement for life annuities and
then to gradually sell the remaining equities and buy more annuities, i.e., a strategy known as
‘phased annuitisation’.

Key words:- defined contribution pension plan, funding strategy, investment strategy, Epstein-Zin utility,
stochastic lifestyling, phased annuitisation, dynamic programming.

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