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Optimal control of the decumulation of a retirement portfolio with variable spending and dynamic asset allocation

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Listed:
  • Peter A. Forsyth
  • Kenneth R. Vetzal
  • Graham Westmacott

Abstract

We extend the Annually Recalculated Virtual Annuity (ARVA) spending rule for retirement savings decumulation 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 five per cent 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.

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  • Peter A. Forsyth & Kenneth R. Vetzal & Graham Westmacott, 2021. "Optimal control of the decumulation of a retirement portfolio with variable spending and dynamic asset allocation," Papers 2101.02760, arXiv.org.
    • Handle: RePEc:arx:papers:2101.02760
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    References listed on IDEAS

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    1. Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    2. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
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    7. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Optimal Asset Allocation for Retirement Saving: Deterministic Vs. Time Consistent Adaptive Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(1), pages 1-37, January.
    8. Andrew Patton & Dimitris Politis & Halbert White, 2009. "Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 372-375.
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    11. Duy-Minh Dang & P. A. Forsyth & K. R. Vetzal, 2017. "The 4% strategy revisited: a pre-commitment mean-variance optimal approach to wealth management," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 335-351, March.
    12. Forsyth, Peter A. & Vetzal, Kenneth R. & Westmacott, Graham, 2020. "Optimal Asset Allocation For Dc Pension Decumulation With A Variable Spending Rule," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 419-447, May.
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    14. Peter A. Forsyth & Kenneth R. Vetzal, 2017. "Dynamic mean variance asset allocation: Tests for robustness," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.
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