Management of Portfolio Depletion Risk Through Optimal Life Cycle Asset Allocation

29 Pages Posted: 30 May 2018 Last revised: 19 Dec 2018

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 13, 2018

Abstract

Members of defined contribution (DC) pension plans must take on additional responsibilities for their investments, compared to participants in defined benefit (DB) pension plans. The transition from DB to DC plans means that more employees are faced with these responsibilities. We explore the extent to which DC plan members can follow financial strategies that have a high chance of resulting in a retirement scenario that is fairly close to that provided by DB plans. Retirees in DC plans typically must fund spending from accumulated savings. This leads to the risk of depleting these savings, i.e.portfolio depletion risk. We analyze the management of this risk through life cycle optimal dynamic asset allocation, including the accumulation and decumulation phases. We pose the asset allocation strategy as an optimal stochastic control problem. Several objective functions are tested and compared. We focus on the risk of portfolio depletion at the terminal date, using such measures as conditional value at risk (CVAR) and probability of ruin. A secondary consideration is the median terminal portfolio value. The control problem is solved using a Hamilton-Jacobi-Bellman formulation, based on a parametric model of the financial market. Monte Carlo simulations which use the optimal controls are presented to evaluate the performance metrics. These simulations are based on both the parametric model and bootstrap resampling of 91 years of historical data. The resampling tests suggest that target-based approaches which seek to establish a safety margin of wealth at the end of the decumulation period appear to be superior to strategies which directly attempt to minimize risk measures such as the probability of portfolio depletion or CVAR. The target-based approaches result in a reasonably close approximation to the retirement spending available in a DB plan. There is a small risk of depleting the retiree's funds, but there is also a good chance of accumulating a buffer which can be used to manage unplanned longevity risk, or left as a bequest.

Keywords: withdrawal risk, life cycle asset allocation, optimal control, decumulation

JEL Classification: G11, G22

Suggested Citation

Forsyth, Peter and Vetzal, Kenneth R. and Westmacott, Graham, Management of Portfolio Depletion Risk Through Optimal Life Cycle Asset Allocation (September 13, 2018). Available at SSRN: https://ssrn.com/abstract=3180333 or http://dx.doi.org/10.2139/ssrn.3180333

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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