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Continuous-Time Portfolio Optimization for Absolute Return Funds

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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.

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Notes

  1. The computer we use has the following specifications: Intel Core i9-X10900X, 3.5Hz, 12Cores, and 32GB RAM.

  2. We see the histogram of \(E^{(i)}_t\).

  3. Thus, the boundary point is given by \(x^* = (1+\bar{r}T)x_0\).

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Acknowledgements

The author is grateful to the anonymous referees for their valuable comments on the first version of this paper. This work is supported by JSPS Grant-in-Aid for Young Scientists(Start-up) Grant Number JP20K22130.

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  1. Department of Business Economics, School of Management, Tokyo University of Science, 1-11-2 Fujimi, Chiyoda-ku, Tokyo, 102-0071, Japan

    Masashi Ieda

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  1. Masashi Ieda
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Correspondence to Masashi Ieda.

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Ieda, M. Continuous-Time Portfolio Optimization for Absolute Return Funds. Asia-Pac Financ Markets 29, 675–696 (2022). https://doi.org/10.1007/s10690-022-09365-9

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