Optimal Asset Allocation for Retirement Savings: Deterministic vs. Time Consistent Adaptive Strategies

Abstract

We consider optimal asset allocation for a long-term investor saving for retirement. The investment portfolio consists of a bond index and a stock index. Using multi-period mean variance criteria, we explore two types of strategies: deterministic strategies are based only on the time remaining until the anticipated retirement date, while adaptive strategies also consider the investor's accumulated wealth. The vast majority of financial products designed for retirement saving currently offered in the U.S. market use deterministic strategies, a prominent example being target date funds. The factors used to determine the specific asset allocations for these products are unclear. We develop methods which give the best possible allocations for deterministic strategies, according to mean-variance criteria. We also consider optimal adaptive strategies. For both a synthetic market where the stock index is modeled by a jump diffusion process and bootstrap resampling of long-term historical data, we find that the optimal adaptive strategy significantly outperforms the optimal deterministic strategy. This suggests that investors are not being well-served by the strategies currently dominating the marketplace.

Keywords: mean-variance, dynamic asset allocation, jump diffusion, resampled backtests, deterministic strategy, adaptive strategy

JEL Classification: G11, G22