From Deterministic to Stochastic Life-Cycle Investing: Implications for the Design of Improved Forms of Target Date Funds

These funds, whose aim is to provide investors with one-stop solutions to their life-cycle investment needs, typically propose a deterministic decrease of equity allocation until a date called the target date of the fund. This approach, however, has been found inconsistent with the prescriptions of standard life-cycle investment models (Viceira and Field 2007). In this paper, we characterise in closed-form the optimal time- and state-dependent allocation strategy for a long-term investor preparing for retirement in the presence of interest-rate and inflation risks and a mean-reverting equity risk premium. We confirm that existing target date fund products are the wrong answer to the right question, and the opportunity cost involved in purely deterministic life-cycle strategies is found to be substantial for reasonable parameter values. Surprisingly, perhaps we also find that even reasonably fine partitions of the set of investors and market conditions, only marginally more complex than current partitions based solely on time horizon, allow substantial welfare gains compared to existing target date funds. Our results have important practical implications since they suggest that a parsimonious set of life-cycle investment benchmarks can be designed, which could serve as relatively accurate proxies for a whole range of retail investors' optimal long-term investment strategies.