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

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

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: paforsyt@uwaterloo.ca
Kenneth R. Vetzal
Affiliation:
School of Accounting and Finance, University of Waterloo, Waterloo, ON N2L 3G1, Canada E-Mail: kvetzal@uwaterloo.ca
Graham Westmacott
Affiliation:
PWL Capital, 20 Erb Street W., Suite 506, Waterloo, ON N2L 1T2, Canada, E-Mail: gwestmacott@pwlcapital.com
*
E-Mail: paforsyt@uwaterloo.ca
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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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References

Bengen, W. (1994) Determining withdrawal rates using historical data. Journal of Financial Planning, 7, 171–180.Google Scholar
Bengen, W.P. (2001) Conserving client portfolios during retirement, part IV. Journal of Financial Planning, 14(5), 110–119.Google Scholar
Cont, R. and Mancini, C. (2011) Nonparametric tests for pathwise properties of semimartingales. Bernoulli, 17, 781–813.CrossRefGoogle Scholar
Cui, X., Gao, J., Shi, Y. and Zhu, S. (2019) Time-consistent and self-coordination strategies for multi-period mean-conditional-value-at-risk portfolio selection. European Journal of Operational Research, 276, 781–789.CrossRefGoogle Scholar
Dang, D.-M. and 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, 250, 827–841.CrossRefGoogle Scholar
Dang, D.-M., Forsyth, P.A. and Vetzal, K.R. (2017) The 4% strategy revisited: A pre-commitment optimal mean-variance approach to wealth management. Quantitative Finance, 17, 335–351.CrossRefGoogle Scholar
Finke, M., Pfau, W.D. and Blanchett, D.M. (2013) The 4 percent rule is not safe in a low-yield world. Journal of Financial Planning, 26(6), 46–55.Google Scholar
Forsyth, P.A. (2020a) Multi-period mean CVAR asset allocation: Is it advantageous to be time consistent? SIAM Journal on Financial Mathematics, 11(2), 358–384.CrossRefGoogle Scholar
Forsyth, P.A. (2020b) Optimal dynamic asset allocation for DC plan accumulation/decumulation: Ambition-CVAR. Insurance: Mathematics and Economics, 93, 230–245.Google Scholar
Forsyth, P.A. (2021) A stochastic control approach to defined contribution plan decumulation: “The nastiest, hardest problem in finance”. North American Actuarial Journal. doi: 10.1080/10920277.2021.1878043.CrossRefGoogle Scholar
Forsyth, P.A. and Labahn, G. (2019) ϵ–Monotone Fourier methods for optimal stochastic control in finance. Journal of Computational Finance, 22(4), 25–71.CrossRefGoogle Scholar
Forsyth, P.A. and Vetzal, K.R. (2017) Dynamic mean variance asset allocation: Tests for robustness. International Journal of Financial Engineering, 4, 1750021:1–1750021:37. doi: 10.1142/S2424786317500219.CrossRefGoogle Scholar
Forsyth, P.A. and Vetzal, K.R. (2019) Optimal asset allocation for retirement savings: Deterministic vs. time consistent adaptive strategies. Applied Mathematical Finance, 26:1, 1–37.Google Scholar
Forsyth, P.A., Vetzal, K.R. and Westmacott, G. (2020) Optimal asset allocation for DC pension decumulation with a variable spending rule. ASTIN Bulletin, 50, 419–447.CrossRefGoogle Scholar
Gao, J., Xiong, Y. and Li, D. (2016) Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time. European Journal of Operational Research, 249, 647–656.CrossRefGoogle Scholar
Guyton, J.T. and Klinger, W.J. (2006) Decision rules and maximum initial withdrawal rates. Journal of Financial Planning, 19(3), 48–58.Google Scholar
Irlam, G. (2014) Portfolio size matters. Journal of Personal Finance, 13(2), 9–16.Google Scholar
Kou, S.G. and Wang, H. (2004) Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192.CrossRefGoogle Scholar
Lin, Y., MacMinn, R. and Tian, R. (2015) De-risking defined benefit plans. Insurance: Mathematics and Economics, 63, 52–65.CrossRefGoogle Scholar
Ma, K. and Forsyth, P.A. (2016) Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation under stochastic volatility. Journal of Computational Finance, 20(1), 1–37.Google Scholar
MacDonald, B.-J., Jones, B., Morrison, R.J., Brown, R.L. and Hardy, M. (2013) Research and reality: A literature review on drawing down retirement financial savings. North American Actuarial Journal, 17, 181–215.CrossRefGoogle Scholar
MacMinn, R., Brockett, P., Wang, J., Lin, Y. and Tian, R. (2014) The securitization of longevity risk and its implications for retirement security. In Recreating Sustainable Retirement (eds. O.S. Mitchell, R. Maurer and P.B. Hammond), pp. 134–160. Oxford: Oxford University Press.CrossRefGoogle Scholar
Mancini, C. (2009) Non-parametric threshold estimation models with stochastic diffusion coefficient and jumps. Scandinavian Journal of Statistics, 36, 270–296.CrossRefGoogle Scholar
Meeuwis, M. (2020) Wealth fluctations and risk preferences: Evidence from U.S. investor portfolios. Washington University in St. Louis working paper.CrossRefGoogle Scholar
Merton, R.C. (2014) The crisis in retirement planning. Harvard Business Review, 3–10.Google Scholar
Patton, A., Politis, D. and White, H. (2009) Correction to: Automatic block-length selection for the dependent bootstrap. Econometric Reviews, 28, 372–375.CrossRefGoogle Scholar
Pfau, W.D. (2015) Making sense out of variable spending strategies for retirees. Journal of Financial Planning, 28(10), 42–51.Google Scholar
Politis, D. and Romano, J. (1994) The stationary bootstrap. Journal of the American Statistical Association, 89, 1303–1313.CrossRefGoogle Scholar
Politis, D. and White, H. (2004) Automatic block-length selection for the dependent bootstrap. Econometric Reviews, 23, 53–70.CrossRefGoogle Scholar
Rockafellar, R.T. and Uryasev, S. (2000) Optimization of conditional value-at-risk. Journal of Risk, 2, 21–42.CrossRefGoogle Scholar
Shefrin, H.M. and Thaler, R.H. (1988) The behavioral life-cycle hypothesis. Economic Inquiry, 26, 609–643.CrossRefGoogle Scholar
Shimizu, Y. (2013) Threshold estimation for stochastic differential equations with jumps. Proceedings of the 59th ISI World Statistics Conference, Hong Kong.Google Scholar
Strub, M., Li, D. and Cui, X. (2019) An enhanced mean-variance framework for robo-advising applications. SSRN 3302111.Google Scholar
Thaler, R.H. (1990) Anomalies: Savings, fungibility, and mental accounts. Journal of Economic Perspectives, 4(1), 193–205.CrossRefGoogle Scholar
Tretiakova, I. and Yamada, M.S. (2017) Autonomous portfolio: A decumulation investment strategy that will get you there. Journal of Retirement, 5(2), 83–95.CrossRefGoogle Scholar
Van Staden, P., Dang, D.-M. and Forsyth, P. (2018) Time-consistent mean-variance portfolio optimization: A numerical impulse control approach. Insurance: Mathematics and Economics, 83, 9–28.CrossRefGoogle Scholar
Waring, M.B. and Siegel, L.B. (2015) The only spending rule article you will ever need. Financial Analysts Journal, 71(1), 91–107.CrossRefGoogle Scholar
Westmacott, G. (2017) The retiree’s dilemma: The Deckards. PWL Capital White Paper, http://www.pwlcapital.com/retirees-dilemmma-deckards/.Google Scholar