Robust stock and bond allocation with end-of-horizon effects

We propose an approach to portfolio management over a finite time horizon that (i) does not require the precise knowledge of the underlying probability distributions, instead relying on range forecasts for the stock returns, and (ii) allows the fund manager to capture the degree of the investor's risk aversion through a single, intuitive parameter called the budget of uncertainty. This budget represents the worst-case number of time periods with poor performance that the investor is willing to plan for. An application of this setting is target-date funds for pension fund management. We describe an efficient procedure to compute the dynamic allocation between (riskless) bonds and (riskier) stocks at each time period, and we illustrate the risk-to-time-horizon tradeoff on optimal allocation tables, which can easily be provided to fund participants to help them select their strategy. The proposed approach refines rules implemented by practitioners and provides an intuitive framework to incorporate risk in applications with end of horizon effects. In contrast with existing literature providing robust fund management approaches to mathematically sophisticated finance professionals, our goal is to provide a simple framework for less quantitative fund participants who seek to understand how stock return uncertainty and planned retirement date affect the optimal stock-vs-bond allocation in their portfolio. We extend our procedure to the case when the investor's wealth is penalized for falling short of performance benchmarks across the time horizon. We also discuss the case where the manager can invest in multiple stocks. Numerical results are provided.