Optimal Asset Allocation for Retirement Saving: Deterministic Vs. Time Consistent Adaptive Strategies

Abstract

We consider optimal asset allocation for an investor saving for retirement. The portfolio contains a bond index and a stock index. We use multi-period criteria and 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 use deterministic strategies (e.g., target date funds). In the deterministic case, we determine an optimal open loop control using mean-variance criteria. In the adaptive case, we use time consistent mean-variance and quadratic shortfall objectives. Tests based on both a synthetic market where the stock index is modelled by a jump-diffusion process and also on bootstrap resampling of long-term historical data show that the optimal adaptive strategies significantly outperform the optimal deterministic strategy. This suggests that investors are not being well served by the strategies currently dominating the marketplace.

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