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Foster–Hart optimal portfolios

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  • Anand, Abhinav
  • Li, Tiantian
  • Kurosaki, Tetsuo
  • Kim, Young Shin

Abstract

We reinvestigate the classic portfolio optimization problem where the notion of portfolio risk is captured by the “Foster–Hart risk”—a new, bankruptcy-proof, reserve based measure of risk, extremely sensitive to left tail events (Foster and Hart, 2009). To include financial market frictions induced by market microstructure, we employ a general, ex-ante transaction cost function with fixed, linear and quadratic penalty terms in the objective function. We represent the US equity market by the Dow Jones Industrial Average (DJIA) index and study the performance of the Foster–Hart optimal DJIA portfolio. In order to capture the skewed and leptokurtotic nature of real life stock returns, we model the returns of the DJIA constituents as an ARMA–GARCH process with multivariate “normal tempered stable” innovations. We demonstrate that the Foster–Hart optimal portfolio’s performance is superior to those obtained under several techniques currently in use in academia and industry.

Suggested Citation

  • Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    • Handle: RePEc:eee:jbfina:v:68:y:2016:i:c:p:117-130
    DOI: 10.1016/j.jbankfin.2016.03.011
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    Cited by:

    1. Jaehyung Choi & Hyangju Kim & Young Shin Kim, 2021. "Diversified reward-risk parity in portfolio construction," Papers 2106.09055, arXiv.org, revised Sep 2022.
    2. Antonio Díaz & Carlos Esparcia, 2021. "Dynamic optimal portfolio choice under time-varying risk aversion," International Economics, CEPII research center, issue 166, pages 1-22.
    3. Tetsuo Kurosaki & Young Shin Kim, 2020. "Cryptocurrency portfolio optimization with multivariate normal tempered stable processes and Foster-Hart risk," Papers 2010.08900, arXiv.org.
    4. Yuhao Liu & Petar M. Djurić & Young Shin Kim & Svetlozar T. Rachev & James Glimm, 2021. "Systemic Risk Modeling with Lévy Copulas," JRFM, MDPI, vol. 14(6), pages 1-20, June.
    5. Young Shin Kim & Kum-Hwan Roh & Raphael Douady, 2022. "Tempered stable processes with time-varying exponential tails," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 541-561, March.
    6. Kim, Sung Ik, 2023. "A comparative study of firm value models: Default risk of corporate bonds," Finance Research Letters, Elsevier, vol. 56(C).
    7. Tiantian Li & Young Shin Kim & Qi Fan & Fumin Zhu, 2021. "Aumann–Serrano index of risk in portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 197-217, October.
    8. Abhinav Anand & Tiantian Li & Tetsuo Kurosaki & Young Shin Kim, 2017. "The equity risk posed by the too-big-to-fail banks: a Foster–Hart estimation," Annals of Operations Research, Springer, vol. 253(1), pages 21-41, June.
    9. Cheng Peng & Young Shin Kim & Stefan Mittnik, 2022. "Portfolio Optimization on Multivariate Regime-Switching GARCH Model with Normal Tempered Stable Innovation," JRFM, MDPI, vol. 15(5), pages 1-23, May.
    10. Jiro Hodoshima & Toshiyuki Yamawake, 2021. "Sensitivity of Performance Indexes to Disaster Risk," Risks, MDPI, vol. 9(2), pages 1-22, February.
    11. Heller, Yuval & Schreiber, Amnon, 2020. "Short-term investments and indices of risk," Theoretical Economics, Econometric Society, vol. 15(3), July.
    12. Yao, Haixiang & Huang, Jinbo & Li, Yong & Humphrey, Jacquelyn E., 2021. "A general approach to smooth and convex portfolio optimization using lower partial moments," Journal of Banking & Finance, Elsevier, vol. 129(C).
    13. Leiss, Matthias & Nax, Heinrich H., 2018. "Option-implied objective measures of market risk," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 241-249.
    14. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    15. Gong, Xiao-Li & Xiong, Xiong, 2021. "Multi-objective portfolio optimization under tempered stable Lévy distribution with Copula dependence," Finance Research Letters, Elsevier, vol. 38(C).
    16. Young Shin Kim & Hyangju Kim & Jaehyung Choi, 2023. "Deep Calibration With Artificial Neural Network: A Performance Comparison on Option Pricing Models," Papers 2303.08760, arXiv.org.
    17. Sung Ik Kim & Young Shin Kim, 2018. "Tempered stable structural model in pricing credit spread and credit default swap," Review of Derivatives Research, Springer, vol. 21(1), pages 119-148, April.
    18. Kurosaki, Tetsuo & Kim, Young Shin, 2022. "Cryptocurrency portfolio optimization with multivariate normal tempered stable processes and Foster-Hart risk," Finance Research Letters, Elsevier, vol. 45(C).
    19. Young Shin Kim & Hyun-Gyoon Kim, 2024. "Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence," Papers 2402.17919, arXiv.org, revised Mar 2024.
    20. Yuval Heller & Amnon Schreiber, 2020. "Short-Term Investments and Indices of Risk," Papers 2005.06576, arXiv.org.
    21. Young Shin Kim, 2020. "Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk," Papers 2007.13972, arXiv.org, revised Sep 2020.
    22. Richard Lu & Adrian (Wai Kong) Cheung & Vu T. Hoang & Sardar M. N. Islam, 2021. "Which measure of systematic risk should we use? An empirical study on systematical risk and Treynor measure using the economic index of riskiness and operational measure of riskiness," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 1739-1744, April.
    23. Young Shin Kim, 2023. "Portfolio Optimization with Relative Tail Risk," Papers 2303.12209, arXiv.org, revised Mar 2023.

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    More about this item

    Keywords

    ARMA–GARCH model; Normal tempered stable distribution; Foster–Hart risk; Value-at-Risk (VaR); Average Value-at-Risk (AVaR); Reward risk ratio;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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