Zvi Bodie, Jérôme Detemple and Marcel Rindisbacher
Volume 10, Number 1, First Quarter 2012
This paper explores the optimal design of personal pensions based on the economic theory of the life cycle. It assumes that individuals derive utility from consumption of goods and leisure and that at some date they retire and stop earning income from labor. The existence of this retirement phase of the life cycle has a profound impact on optimal consumption and portfolio policy. We describe the properties of the optimal pension contract and derive the dynamic trading strategy that hedges the contract. In view of the popularity of age-based strategies like target date funds as default options in 401k and other defined contribution retirement plans, some of our results are particularly noteworthy. All target date funds start with a high proportion in equities at a young age and reduce it as a person ages. We identify conditions where the fraction of wealth optimally invested in equities increases or decreases over time as an individual ages. We also analyze the dynamics of pension plans, wealth and optimal policies. Distributional properties of endogenous variables are examined and the robustness of patterns to variations in parameters such as risk aversion and mortality risk is examined.