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Continuous-time Portfolio Optimization for Absolute Return Funds

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  • Masashi Ieda

Abstract

This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance criterion based on the lower mean square error between the investor's wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton-Jacobi-Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper.

Suggested Citation

  • Masashi Ieda, 2021. "Continuous-time Portfolio Optimization for Absolute Return Funds," Papers 2108.09985, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2108.09985
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    References listed on IDEAS

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    1. Masashi Ieda & Takashi Yamashita & Yumiharu Nakano, 2013. "A liability tracking approach to long term management of pension funds," Papers 1303.3956, arXiv.org.
    2. Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
    3. Hiroaki Hata & Jun Sekine, 2017. "Risk-Sensitive Asset Management in a Wishart-Autoregressive Factor Model with Jumps," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(3), pages 221-252, September.
    4. Guiyuan Ma & Song-Ping Zhu, 2019. "Optimal investment and consumption under a continuous-time cointegration model with exponential utility," Quantitative Finance, Taylor & Francis Journals, vol. 19(7), pages 1135-1149, July.
    5. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    6. Huang, Dashan & Zhu, Shu-Shang & Fabozzi, Frank J. & Fukushima, Masao, 2008. "Portfolio selection with uncertain exit time: A robust CVaR approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 594-623, February.
    7. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    8. J. Wang & P. A. Forsyth, 2012. "Comparison Of Mean Variance Like Strategies For Optimal Asset Allocation Problems," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-32.
    9. Christopher W. Miller & Insoon Yang, 2015. "Optimal Control of Conditional Value-at-Risk in Continuous Time," Papers 1512.05015, arXiv.org, revised Jan 2017.
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