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Goal-based investing based on multi-stage robust portfolio optimization

  • S.I.: Risk Management Decisions and Value under Uncertainty
  • Published:
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Abstract

While portfolio optimization is generally based on the return and risk of a portfolio, goal-based investing primarily focuses on achieving financial goals of individuals, which has become a popular approach in personalized financial planning. While many long-term financial planning models use scenarios for representing uncertainty in future market dynamics, it is subject to the curse of dimensionality. In this study, we propose a goal-based investing model for personalized lifetime financial planning based on robust portfolio optimization, which incorporates multiple goals that occur in different periods with various priorities. Empirical results illustrate how the size of uncertainty sets and risk constraints can be customized for finding the optimal investment and show efficiency in solving a portfolio problem with many stages compared to scenario-based approaches.

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Notes

  1. See Aoun et al. (2012) and Aouni et al. (2014) for surveys on other stochastic models and fuzzy approaches for goal programming.

  2. See Bertsimas and Pachamanova (2008) and Ben-Tal et al. (2000) for further details.

  3. Historical returns of the 10 industries are retrieved from the online data library of Kenneth R. French, which also contain a description on the categorization and construction of the industries.

  4. A simplified investment setting is presented but the model can be applied to lifetime financial planning.

  5. Multi-stage stochastic programming is used for formulating the scenario-tree based model. The objective is to maximize expected spending on predefined goals and the problem is solved incrementally starting with the highest priority goals. A detailed explanation is included in Kim et al. (2020).

References

  • Aouni, B., Ben Abdelaziz, F., & La Torre, D. (2012). The stochastic goal programming model: Theory and applications. Journal of Multi-Criteria Decision Analysis, 19, 185–200.

    Article  Google Scholar 

  • Aouni, B., Ben Abdelaziz, F., & Martel, J.-M. (2005). Decision maker’s preferences modeling in the stochastic goal programming. European Journal of Operational Research, 162, 610–618.

    Article  Google Scholar 

  • Aouni, B., Colapinto, C., & La Torre, D. (2014). Financial portfolio management through the goal programming model: Current state-of-the-art. European Journal of Operational Research, 234(2), 536–545.

    Article  Google Scholar 

  • Ballestero, E. (2001). Stochastic goal programming: A mean–variance approach. European Journal of Operational Research, 131(3), 476–481.

    Article  Google Scholar 

  • Ben Abdelaziz, F., Aouni, B., & El Fayedh, R. (2007). Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research, 177(3), 1811–1823.

    Article  Google Scholar 

  • Ben-Tal, A., Margalit, T., & Nemirovski, A. (2000). Robust modeling of multi-stage portfolio problems. In H. Frenk, K. Roos, T. Terlaky, & S. Zhang (Eds.), High Performance Optimization (pp. 303–328). Boston, MA: Springer.

    Chapter  Google Scholar 

  • Berger, A. J., & Mulvey, J. M. (1998). The Home Account Advisor: Asset and liability management for individual investors. In W. T. Ziemba & J. M. Mulvey (Eds.), Worldwide Asset and Liability Modeling (pp. 634–665). Cambridge University.

    Google Scholar 

  • Bertsimas, D., & Pachamanova, D. (2008). Robust multiperiod portfolio management in the presence of transaction costs. Computers & Operations Research, 35(1), 3–17.

    Article  Google Scholar 

  • Blanchett, D. M. (2015). Revisiting the optimal distribution glide path. Journal of Financial Planning, 28(2), 52–61.

    Google Scholar 

  • Birge, J. R., & Louveaux, F. (2011). Introduction to Stochastic Programming. Springer.

    Book  Google Scholar 

  • Bravo, M., Pla-Santamaria, D., & Garcia-Bernabeu, A. (2010). Portfolio selection from multiple benchmarks: A goal programming approach to an actual case. Journal of Multi-Criteria Decision Analysis, 17, 155–166.

    Article  Google Scholar 

  • Cariño, D. R., Kent, T., Myers, D. H., Stacy, C., Sylvanus, M., Turner, A., Watanabe, K., & Ziemba, W. (1994). The Russell-Yasuda Kasai Model: An asset/liability model for a Japanese insurance company using multistage stochastic programming. Interfaces, 24, 29–49.

    Article  Google Scholar 

  • Chhabra, A. B. (2005). Beyond Markowitz: A comprehensive wealth allocation framework for individual investors. Journal of Wealth Management, 7(4), 8–34.

    Article  Google Scholar 

  • Chopra, V. K., & Ziemba, W. T. (1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management, 19(2), 6–11.

    Article  Google Scholar 

  • Colapinto, C., Jayaraman, R., & Marsiglio, S. (2017). Multi-criteria decision analysis with goal programming in engineering, management and social sciences: A state-of-the art review. Annals of Operations Research, 251(1–2), 7–40.

    Article  Google Scholar 

  • Consigli, G. (2008). Asset-liability management for individual investors. In S. A. Zenios & W. T. Ziemba (Eds.), Handbook of Asset and Liability Management (Vol. 2, pp. 751–827), Chapter 17. North-Holland.

  • Consiglio, A., Cocco, F., & Zenios, S. A. (2007). Scenario optimization asset and liability modelling for individual investors. Annals of Operations Research, 152, 167–191.

    Article  Google Scholar 

  • D’Acunto, F., Prabhala, N., & Rossi, A. G. (2019). The promises and pitfalls of robo-advising. The Review of Financial Studies, 32(5), 1983–2020.

    Article  Google Scholar 

  • Dempster, M. A. H., & Medova, E. A. (2011). Asset liability management for individual households. British Actuarial Journal, 16(2), 405–439.

    Article  Google Scholar 

  • Doumpos, M., & Zopounidis, C. (2020). Multi objective optimization models in finance and investments. Journal of Global Optimization, 76, 243–244.

    Article  Google Scholar 

  • Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics, 75(4), 643–669.

    Article  Google Scholar 

  • Fabozzi, F. J., Gupta, F., & Markowitz, H. M. (2002). The legacy of modern portfolio theory. Journal of Investing, 11(3), 7–22.

    Article  Google Scholar 

  • Fabozzi, F. J., Huang, D., & Zhou, G. (2010). Robust portfolios: Contributions from operations research and finance. Annals of Operations Research, 176, 191–220.

    Article  Google Scholar 

  • Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., & Focardi, S. M. (2007). Robust Portfolio Optimization and Management. Wiley.

    Google Scholar 

  • Ghahtarani, A., & Najafi, A. A. (2013). Robust goal programming for multi-objective portfolio selection problem. Economic Modelling, 33, 588–592.

    Article  Google Scholar 

  • Ji, X., Zhu, S., Wang, S., & Zhang, S. (2005). A stochastic linear goal programming approach to multistage portfolio management based on scenario generation via linear programming. IIE Transactions, 37(10), 957–969.

    Article  Google Scholar 

  • Kim, W. C., Kim, J. H., Ahn, S. H., & Fabozzi, F. J. (2013). What do robust equity portfolio models really do? Annals of Operations Research, 205(1), 141–168.

    Article  Google Scholar 

  • Kim, W. C., Kim, J. H., & Fabozzi, F. J. (2014a). Deciphering robust portfolios. Journal of Banking and Finance, 45, 1–8.

    Article  Google Scholar 

  • Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2014b). Recent developments in robust portfolios with a worst-case approach. Journal of Optimization Theory and Applications, 161(1), 103–121.

    Article  Google Scholar 

  • Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2018a). Recent advancements in robust optimization for investment management. Annals of Operations Research, 266(1–2), 183–198.

    Article  Google Scholar 

  • Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2017). Robust factor-based investing. Journal of Portfolio Management, 43(5), 157–164.

    Article  Google Scholar 

  • Kim, W. C., Kim, J. H., & Fabozzi, F. J. (2016). Robust Equity Portfolio Management + Website: Formulations, Implementations, and Properties using MATLAB. Wiley.

    Google Scholar 

  • Kim, J. H., Kim, W. C., Kwon, D. G., & Fabozzi, F. J. (2018b). Robust equity portfolio performance. Annals of Operations Research, 266(1), 293–312.

    Article  Google Scholar 

  • Kim, W. C., Kwon, D., Lee, Y., Kim, J. H., & Lin, C. (2020). Personalized goal-based investing via multi-stage stochastic goal programming. Quantitative Finance, 20(3), 515–526.

    Article  Google Scholar 

  • Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356–371.

    Article  Google Scholar 

  • Kouwenberg, R., & Zenios, S.A. (2006). Stochastic programming models for asset liability management. In S. A. Zenios, & W. T. Ziemba (Eds.), Handbook of Asset and Liability Management (Vol. 1, pp. 253–303). North-Holland.

  • Lee, S. M., & Chesser, D. L. (1980). Goal programming for portfolio selection. The Journal of Portfolio Management, 6(3), 22–26.

    Article  Google Scholar 

  • Lee, S., & Lerro, A. (1973). Optimizing the portfolio selection for mutual funds. Journal of Finance, 28, 1086–1101.

    Google Scholar 

  • Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.

    Google Scholar 

  • Medova, E. A., Murphy, J. K., Owen, A. P., & Rehman, K. (2008). Individual asset liability management. Quantitative Finance, 8(6), 547–560.

    Article  Google Scholar 

  • Mladina, P. (2014). Dynamic asset allocation with horizon risk: Revisiting glide path construction. The Journal of Wealth Management, 16(4), 18–26.

    Article  Google Scholar 

  • Mulvey, J. M., Gould, G., & Morgan, C. (2000). An asset and liability management system for Towers Perrin-Tillinghast. Interfaces, 30, 96–114.

    Article  Google Scholar 

  • Ogryczak, W. (2000). Multiple criteria linear programming model for portfolio selection. Annals of Operations Research, 97(1), 143–162.

    Article  Google Scholar 

  • Pflug, GCh., Swietanowski, A., Dockner, E., & Moritsch, H. (2000). The AURORA Financial Management System: From model design to parallel implementation. Annals of Operations Research, 99, 189–206.

    Article  Google Scholar 

  • Salas-Molina, F., Rodriguez-Aguilar, J. A., & Pla-Santamaria, D. (2020). A stochastic goal programming model to derive stable cash management policies. Journal of Global Optimization, 76(2), 333–346.

    Article  Google Scholar 

  • Scherer, B. (2007). Can robust portfolio optimisation help to build better portfolios? Journal of Asset Management, 7(6), 374–387.

    Article  Google Scholar 

  • Zopounidis, C., & Doumpos, M. (2002). Multi-criteria decision aid in financial decision making: Methodologies and literature review. Journal of Multi-Criteria Decision Analysis, 11(4–5), 167–186.

    Article  Google Scholar 

  • Zopounidis, C., Galariotis, E., Doumpos, M., Sarri, S., & AndriosopouloS, K. (2015). Multiple criteria decision aiding for finance: An updated bibliographic survey. European Journal of Operational Research, 247(2), 339–348.

    Article  Google Scholar 

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2018R1C1B6004271) and funding provided to Fabozzi by EDHEC Business School.

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Authors and Affiliations

  1. Kyung Hee University, Yongin-si, Gyeonggi-do, South Korea

    Jang Ho Kim

  2. Ulsan National Institute of Science and Technology (UNIST), Ulsan, South Korea

    Yongjae Lee

  3. Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea

    Woo Chang Kim

  4. EDHEC Business School, Nice, France

    Frank J. Fabozzi

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  1. Jang Ho Kim
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  2. Yongjae Lee
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  3. Woo Chang Kim
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  4. Frank J. Fabozzi
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Correspondence to Frank J. Fabozzi.

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Kim, J.H., Lee, Y., Kim, W.C. et al. Goal-based investing based on multi-stage robust portfolio optimization. Ann Oper Res 313, 1141–1158 (2022). https://doi.org/10.1007/s10479-021-04473-7

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