Optimal Asset Allocation for DC Pension Decumulation with a Variable Spending Rule

Abstract

We determine the optimal asset allocation to bonds and stocks using an Annually Recalculated Virtual Annuity (ARVA) spending rule for DC pension plan decumulation. Our objective function minimizes downside withdrawal variability for a given fixed value of total expected withdrawals. The optimal asset allocation is found using optimal stochastic control methods. We formulate the strategy as a solution to a Hamilton Jacobi Bellman (HJB) Partial Integro Differential Equation (PIDE). We impose realistic constraints on the controls (no shorting, no leverage, discrete rebalancing), and solve the HJB PIDEs numerically. Compared to a fixed weight strategy which has the same expected total withdrawals, the optimal strategy has a much smaller average allocation to stocks, and tends to de-risk rapidly over time. This conclusion holds in the case of a parametric model based on historical data, and also in a bootstrapped market based on the historical data.