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Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management

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  • Ali Al-Aradi
  • Sebastian Jaimungal

Abstract

Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the expected growth rate differential between the wealth of the investor’s portfolio and that of a performance benchmark while penalizing risk-weighted deviations from a given tracking portfolio. Using stochastic control techniques, we provide explicit closed-form expressions for the optimal allocation and we show how the optimal strategy can be related to the growth optimal portfolio. The admissible benchmarks encompass the class of functionally generated portfolios (FGPs), which include the market portfolio, as the only requirement is that they depend only on the prevailing asset values. Finally, some numerical experiments are presented to illustrate the risk–reward profile of the optimal allocation.

Suggested Citation

  • Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(3), pages 268-294, May.
    • Handle: RePEc:taf:apmtfi:v:25:y:2018:i:3:p:268-294
    DOI: 10.1080/1350486X.2018.1507751
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    Cited by:

    1. Ali Al-Aradi & Sebastian Jaimungal, 2020. "A Variational Analysis Approach to Solving the Merton Problem," Papers 2003.08450, arXiv.org.
    2. Sebastian Jaimungal & Xiaofei Shi, 2024. "The Price of Information," Papers 2402.11864, arXiv.org, revised Mar 2024.
    3. Steven Campbell & Ting-Kam Leonard Wong, 2021. "Functional portfolio optimization in stochastic portfolio theory," Papers 2103.10925, arXiv.org, revised Oct 2021.
    4. Chendi Ni & Yuying Li & Peter Forsyth & Ray Carroll, 2020. "Optimal Asset Allocation For Outperforming A Stochastic Benchmark Target," Papers 2006.15384, arXiv.org.
    5. Ali Al-Aradi & Sebastian Jaimungal, 2019. "Active and Passive Portfolio Management with Latent Factors," Papers 1903.06928, arXiv.org.
    6. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    7. 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.
    8. T. N. Li & A. Papanicolaou, 2019. "Statistical Arbitrage for Multiple Co-Integrated Stocks," Papers 1908.02164, arXiv.org, revised Feb 2022.

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