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Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method

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Listed:
  • Rongju Zhang
  • Nicolas Langren'e
  • Yu Tian
  • Zili Zhu
  • Fima Klebaner
  • Kais Hamza

Abstract

In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investment goal. This strategy favorably shapes the entire probability distribution of returns, as it simultaneously seeks a desired expected return, cuts off downside risk and implicitly caps volatility and higher moments. To illustrate the effectiveness of this investment strategy, we study a multiperiod portfolio optimization problem with transaction costs and develop a two-stage regression approach that improves the classical least squares Monte Carlo (LSMC) algorithm when dealing with difficult payoffs, such as highly concave, abruptly changing or discontinuous functions. Our numerical results show substantial improvements over the classical LSMC algorithm for both the constant relative risk-aversion (CRRA) utility approach and the proposed skewed target range strategy (STRS). Our numerical results illustrate the ability of the STRS to contain the portfolio value within the targeted range. When compared with the CRRA utility approach, the STRS achieves a similar mean-variance efficient frontier while delivering a better downside risk-return trade-off.

Suggested Citation

  • Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2017. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Papers 1704.00416, arXiv.org, revised Jun 2019.
  • Handle: RePEc:arx:papers:1704.00416
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. Morton, David P. & Popova, Elmira & Popova, Ivilina, 2006. "Efficient fund of hedge funds construction under downside risk measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 503-518, February.
    5. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    6. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. Moshe A. Milevsky & Kristen S. Moore & Virginia R. Young, 2006. "Asset Allocation And Annuity‐Purchase Strategies To Minimize The Probability Of Financial Ruin," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 647-671, October.
    8. Dimitris Kugiumtzis & Efthymia Bora-Senta, 2010. "Normal correlation coefficient of non-normal variables using piece-wise linear approximation," Computational Statistics, Springer, vol. 25(4), pages 645-662, December.
    9. Hiroaki Hata & Hideo Nagai & Shuenn-Jyi Sheu, 2010. "Asymptotics of the probability minimizing a "down-side" risk," Papers 1001.2131, arXiv.org.
    10. Lorenzo Garlappi & Georgios Skoulakis, 2009. "Numerical Solutions to Dynamic Portfolio Problems: The Case for Value Function Iteration using Taylor Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 33(2), pages 193-207, March.
    11. Jules Binsbergen & Michael Brandt, 2007. "Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 355-367, May.
    12. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    13. repec:dau:papers:123456789/12195 is not listed on IDEAS
    14. Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
    15. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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