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OPTIMAL CONTROL OF THE DECUMULATION OF A RETIREMENT PORTFOLIO WITH VARIABLE SPENDING AND DYNAMIC ASSET ALLOCATION

Part of: Partial differential equations, boundary value problems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  28 July 2021

Peter A. Forsyth Open the ORCID record for Peter A. Forsyth [Opens in a new window] ,
Kenneth R. Vetzal  and
Graham Westmacott
Peter A. Forsyth*
Affiliation:
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada E-Mail: [email protected]
Kenneth R. Vetzal
Affiliation:
School of Accounting and Finance, University of Waterloo, Waterloo, ON N2L 3G1, Canada E-Mail: [email protected]
Graham Westmacott
Affiliation:
PWL Capital, 20 Erb Street W., Suite 506, Waterloo, ON N2L 1T2, Canada, E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

We extend the Annually Recalculated Virtual Annuity (ARVA) spending rule for retirement savings decumulation (Waring and Siegel (2015) Financial Analysts Journal, 71(1), 91–107) to include a cap and a floor on withdrawals. With a minimum withdrawal constraint, the ARVA strategy runs the risk of depleting the investment portfolio. We determine the dynamic asset allocation strategy which maximizes a weighted combination of expected total withdrawals (EW) and expected shortfall (ES), defined as the average of the worst 5% of the outcomes of real terminal wealth. We compare the performance of our dynamic strategy to simpler alternatives which maintain constant asset allocation weights over time accompanied by either our same modified ARVA spending rule or withdrawals that are constant over time in real terms. Tests are carried out using both a parametric model of historical asset returns as well as bootstrap resampling of historical data. Consistent with previous literature that has used different measures of reward and risk than EW and ES, we find that allowing some variability in withdrawals leads to large improvements in efficiency. However, unlike the prior literature, we also demonstrate that further significant enhancements are possible through incorporating a dynamic asset allocation strategy rather than simply keeping asset allocation weights constant throughout retirement.

Keywords

Financerisk managementoptimal asset allocationdecumulationdefined contribution planG11G22

MSC classification

Secondary: 65N06: Finite difference methods 65N12: Stability and convergence of numerical methods 35Q93: PDEs in connection with control and optimization
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 3 , September 2021 , pp. 905 - 938
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The International Actuarial Association

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