The 4% rule revisited: a pre-commitment optimal mean-variance approach in wealth management

Dang, Duy-Minh, Forsyth, Peter and Vetzal, Ken (2016) The 4% rule revisited: a pre-commitment optimal mean-variance approach in wealth management. Quantitative Finance, 1-17. doi:10.1080/14697688.2016.1205211

Author Dang, Duy-Minh
Forsyth, Peter
Vetzal, Ken
Title The 4% rule revisited: a pre-commitment optimal mean-variance approach in wealth management
Journal name Quantitative Finance   Check publisher's open access policy
ISSN 1469-7688
Publication date 2016
Year available 2016
Sub-type Article (original research)
DOI 10.1080/14697688.2016.1205211
Open Access Status Not Open Access
Start page 1
End page 17
Total pages 17
Place of publication Abingdon, Oxon United Kingdom
Publisher Routledge
Collection year 2017
Language eng
Formatted abstract
In contrast to single-period mean-variance (MV) portfolio allocation, multi-period MV optimal portfolio allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider multi-period MV optimal portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset, the price of which is assumed to follow a jump diffusion process. We consider two wealth management applications: optimal de-accumulation rates for a defined contribution pension plan and sustainable withdrawal rates for an endowment. Several numerical illustrations are provided, with some interesting implications. In the pension de-accumulation context, Bengen (1994)’s [J. Financial Planning, 1994, 7, 171–180], historical analysis indicated that a retiree could safely withdraw 4% of her initial retirement savings annually (in real terms), provided that her portfolio maintained an even balance between diversified equities and U.S. Treasury bonds. Our analysis does support 4% as a sustainable withdrawal rate in the pension de-accumulation context (and a somewhat lower rate for an endowment), but only if the investor follows an MV optimal portfolio allocation, not a fixed proportion strategy. Compared with a constant proportion strategy, the MV optimal policy achieves the same expected wealth at the end of the investment horizon, while significantly reducing the standard deviation of wealth and the probability of shortfall. We also explore the effects of suppressing jumps so as to have a pure diffusion process, but assuming a correspondingly larger volatility for the latter process. Surprisingly, it turns out that the MV optimal strategy is more effective when there are large downward jumps compared to having a high volatility diffusion process. Finally, tests based on historical data demonstrate that the MV optimal policy is quite robust to uncertainty about parameter estimates.
Keyword Multi-period mean-variance optimal
Asset allocation strategy
Sustainable withdrawal rate
Pension de-accumulation
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Fri, 17 Jun 2016, 09:28:11 EST by Duy-minh Dang on behalf of Mathematics