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Optimal Asset Allocation for Retirement Saving: Deterministic Vs. Time Consistent Adaptive Strategies

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  • Peter A. Forsyth
  • Kenneth R. Vetzal

Abstract

We consider optimal asset allocation for an investor saving for retirement. The portfolio contains a bond index and a stock index. We use multi-period criteria and explore two types of strategies: deterministic strategies are based only on the time remaining until the anticipated retirement date, while adaptive strategies also consider the investor’s accumulated wealth. The vast majority of financial products designed for retirement saving use deterministic strategies (e.g., target date funds). In the deterministic case, we determine an optimal open loop control using mean-variance criteria. In the adaptive case, we use time consistent mean-variance and quadratic shortfall objectives. Tests based on both a synthetic market where the stock index is modelled by a jump-diffusion process and also on bootstrap resampling of long-term historical data show that the optimal adaptive strategies significantly outperform the optimal deterministic strategy. This suggests that investors are not being well served by the strategies currently dominating the marketplace.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:26:y:2019:i:1:p:1-37
    DOI: 10.1080/1350486X.2019.1584534
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    Citations

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    Cited by:

    1. Peter A. Forsyth, 2020. "A Stochastic Control Approach to Defined Contribution Plan Decumulation: "The Nastiest, Hardest Problem in Finance"," Papers 2008.06598, arXiv.org.
    2. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    3. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Defined Contribution Pension Plans: Who Has Seen the Risk?," JRFM, MDPI, vol. 12(2), pages 1-27, April.
    4. Kamphol Panyagometh, 2021. "Dynamic Spending and Risk-Based Simulation in Retirement Planning," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 11(4), pages 337-346, April.
    5. Zhang, Hanwen & Dang, Duy-Minh, 2024. "A monotone numerical integration method for mean–variance portfolio optimization under jump-diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 112-140.
    6. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    7. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.
    8. Chendi Ni & Yuying Li & Peter Forsyth & Ray Carroll, 2020. "Optimal Asset Allocation For Outperforming A Stochastic Benchmark Target," Papers 2006.15384, arXiv.org.
    9. 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.
    10. Forsyth, Peter A., 2020. "Optimal dynamic asset allocation for DC plan accumulation/decumulation: Ambition-CVAR," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 230-245.
    11. Marc Chen & Mohammad Shirazi & Peter A. Forsyth & Yuying Li, 2023. "Machine Learning and Hamilton-Jacobi-Bellman Equation for Optimal Decumulation: a Comparison Study," Papers 2306.10582, arXiv.org.
    12. Forsyth, Peter A., 2022. "Short term decumulation strategies for underspending retirees," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 56-74.
    13. van Staden, Pieter M. & Forsyth, Peter A. & Li, Yuying, 2024. "Across-time risk-aware strategies for outperforming a benchmark," European Journal of Operational Research, Elsevier, vol. 313(2), pages 776-800.

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