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Mean-Value-at-Risk Portfolio Optimization Based on Risk Tolerance Preferences and Asymmetric Volatility

Author

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  • Yuyun Hidayat

    (Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Titi Purwandari

    (Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Sukono

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Igif Gimin Prihanto

    (Research Center for Testing Technology and Standards, National Research and Innovation Agency, Jakarta 10340, Indonesia)

  • Rizki Apriva Hidayana

    (Magister Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Riza Andrian Ibrahim

    (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

Abstract

Investors generally aim to obtain a high return from their stock portfolio. However, investors must realize that a high value-at-risk (VaR) is essential to calculate for this aim. One of the objects in the VaR calculation is the asymmetric return volatility of stocks, which causes an unbalanced decrease and increase in returns. Therefore, this study proposes a mean-value-at-risk (mean-VaR) stock portfolio optimization model based on stocks’ asymmetric return volatility and investors’ risk aversion preferences. The first stage is the determination of the mean of all stocks in the portfolio conducted using the autoregressive moving average Glosten–Jagannathan–Runkle generalized autoregressive conditional heteroscedasticity (ARMA-GJR-GARCH) models. Then, the second stage is weighting the capital of each stock based on the mean-VaR model with the investors’ risk aversion preferences. This is conducted using the Lagrange multiplier method. Then, the model is applied to stock data in Indonesia’s capital market. This application also analyzed the sensitivity between the mean, VaR, both ratios, and risk aversion. This research can be used for investors in the design and weighting of capital in a stock portfolio to ensure its asymmetrical effect is as small as possible.

Suggested Citation

  • Yuyun Hidayat & Titi Purwandari & Sukono & Igif Gimin Prihanto & Rizki Apriva Hidayana & Riza Andrian Ibrahim, 2023. "Mean-Value-at-Risk Portfolio Optimization Based on Risk Tolerance Preferences and Asymmetric Volatility," Mathematics, MDPI, vol. 11(23), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4761-:d:1287447
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    References listed on IDEAS

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    1. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Guo, Yanhong & Zhou, Wenjun & Luo, Chunyu & Liu, Chuanren & Xiong, Hui, 2016. "Instance-based credit risk assessment for investment decisions in P2P lending," European Journal of Operational Research, Elsevier, vol. 249(2), pages 417-426.
    3. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2020. "An optimization–diversification approach to portfolio selection," Journal of Global Optimization, Springer, vol. 76(2), pages 245-265, February.
    4. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    5. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    6. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    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. Yin, Runsheng & Newman, David H. & Siry, Jacek, 2002. "Testing for market integration among southern pine regions," Journal of Forest Economics, Elsevier, vol. 8(2), pages 151-166.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    11. Zhang, Longmei & Zoli, Edda, 2016. "Leaning against the wind: Macroprudential policy in Asia," Journal of Asian Economics, Elsevier, vol. 42(C), pages 33-52.
    12. Titi Purwandari & Riaman & Yuyun Hidayat & Sukono & Riza Andrian Ibrahim & Rizki Apriva Hidayana, 2023. "Selecting and Weighting Mechanisms in Stock Portfolio Design Based on Clustering Algorithm and Price Movement Analysis," Mathematics, MDPI, vol. 11(19), pages 1-22, October.
    13. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    14. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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