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

23 Pages Posted: 13 Dec 2019

See all articles by Peter Forsyth

Peter Forsyth

University of Waterloo - David R. Cheriton School of Computer Science

Kenneth R. Vetzal

University of Waterloo

Graham Westmacott

PWL Capital

Date Written: September 30, 2019

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.

Keywords: DC pension plans, decumulation, optimal control, HJB equation, annually recalculated virtual annuity

JEL Classification: G11, G22

Suggested Citation

Forsyth, Peter and Vetzal, Kenneth R. and Westmacott, Graham, Optimal Asset Allocation for DC Pension Decumulation with a Variable Spending Rule (September 30, 2019). Available at SSRN: https://ssrn.com/abstract=3494501 or http://dx.doi.org/10.2139/ssrn.3494501

Peter Forsyth (Contact Author)

University of Waterloo - David R. Cheriton School of Computer Science ( email )

200 University Avenue West
Waterloo, ON
Canada

Kenneth R. Vetzal

University of Waterloo ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1 N2L 3G1
Canada
519-885-1211 (Phone)
519-888-7562 (Fax)

Graham Westmacott

PWL Capital ( email )

20 Erb Street W.
Suite 506
Waterloo, N2L 1T2
Canada

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