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A stochastic control approach to managed futures portfolios

Author

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  • Tim Leung

    (Department of Applied Mathematics, University of Washington, Seattle WA 98195, USA)

  • Raphael Yan

    (#x2020;Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada)

Abstract

We study a stochastic control approach to managed futures portfolios. Building on the (Schwartz, 1997) stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity futures or multiple futures contracts over a finite horizon. By analyzing the associated Hamilton–Jacobi–Bellman (HJB) equation, we solve the investor’s utility maximization problem explicitly and derive the optimal dynamic trading strategies in closed form. We provide numerical examples and illustrate the optimal trading strategies using WTI crude oil futures data.

Suggested Citation

  • Tim Leung & Raphael Yan, 2019. "A stochastic control approach to managed futures portfolios," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-22, March.
    • Handle: RePEc:wsi:ijfexx:v:06:y:2019:i:01:n:s2424786319500051
    DOI: 10.1142/S2424786319500051
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    References listed on IDEAS

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    1. Greg N. Gregoriou & Georges Hübner & Maher Kooli, 2010. "Performance and persistence of Commodity Trading Advisors: Further evidence," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(8), pages 725-752, August.
    2. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
    3. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    4. Tim Leung & Xin Li, 2016. "Futures Trading Under Mean Reversion," World Scientific Book Chapters, in: Optimal Mean Reversion Trading Mathematical Analysis and Practical Applications, chapter 5, pages 105-127, World Scientific Publishing Co. Pte. Ltd..
    5. Tim Leung & Brian Ward, 2018. "Dynamic Index Tracking and Risk Exposure Control Using Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(2), pages 180-212, March.
    6. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 32(3), pages 278-297, August.
    7. Gert Elaut & Péter Erdős & John Sjödin, 2016. "An Analysis of the Risk‐Return Characteristics of Serially Correlated Managed Futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(10), pages 992-1013, October.
    8. Christian-Oliver Ewald & Aihua Zhang & Zhe Zong, 2019. "On the calibration of the Schwartz two-factor model to WTI crude oil options and the extended Kalman Filter," Annals of Operations Research, Springer, vol. 282(1), pages 119-130, November.
    9. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    10. Gonzalo Cortazar & Lorenzo Naranjo, 2006. "An N‐factor Gaussian model of oil futures prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(3), pages 243-268, March.
    11. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
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    Cited by:

    1. Tim Leung & Brian Ward, 2020. "Tracking VIX with VIX Futures: Portfolio Construction and Performance," World Scientific Book Chapters, in: John B Guerard & William T Ziemba (ed.), HANDBOOK OF APPLIED INVESTMENT RESEARCH, chapter 21, pages 557-596, World Scientific Publishing Co. Pte. Ltd..
    2. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    3. Tim Leung & Yang Zhou, 2020. "Optimal dynamic futures portfolio in a regime-switching market framework," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-27, February.
    4. Xiaodong Chen & Tim Leung & Yang Zhou, 2022. "Constrained dynamic futures portfolios with stochastic basis," Annals of Finance, Springer, vol. 18(1), pages 1-33, March.
    5. Bahman Angoshtari & Tim Leung, 2020. "Optimal trading of a basket of futures contracts," Annals of Finance, Springer, vol. 16(2), pages 253-280, June.
    6. Tim Leung & Yang Zhou, 2019. "Optimal dynamic futures portfolio in a regime-switching market framework," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-27, December.

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