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OPTIMAL ASSET ALLOCATION FOR DC PENSION DECUMULATION WITH A VARIABLE SPENDING RULE

Published online by Cambridge University Press:  15 April 2020

Peter A. Forsyth ,
Kenneth R. Vetzal  and
Graham Westmacott
Peter A. Forsyth*
Affiliation:
David R. Cheriton School of Computer Science, University of Waterloo, WaterlooON, CanadaN2L 3G1, E-Mail: [email protected]
Kenneth R. Vetzal
Affiliation:
School of Accounting and Finance, University of Waterloo, WaterlooON, CanadaN2L 3G1, E-Mail: [email protected]
Graham Westmacott
Affiliation:
PWL Capital, 20 Erb Street W., Suite 506, Waterloo, ON, CanadaN2L 1T2, E-Mail: [email protected]
*
E-Mail: [email protected]
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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 plansdecumulationoptimal controlHJB equationannually recalculated virtual annuity
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 2 , May 2020 , pp. 419 - 447
Copyright
© Astin Bulletin 2020

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