IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4761-d1287447.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4761/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4761/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Salo, Ahti & Doumpos, Michalis & Liesiö, Juuso & Zopounidis, Constantin, 2024. "Fifty years of portfolio optimization," European Journal of Operational Research, Elsevier, vol. 318(1), pages 1-18.
    2. 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.
    3. Bernardo K. Pagnoncelli & Domingo Ramírez & Hamed Rahimian & Arturo Cifuentes, 2023. "A Synthetic Data-Plus-Features Driven Approach for Portfolio Optimization," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 187-204, June.
    4. Takano, Yuichi & Gotoh, Jun-ya, 2023. "Dynamic portfolio selection with linear control policies for coherent risk minimization," Operations Research Perspectives, Elsevier, vol. 10(C).
    5. González-Díaz, Julio & González-Rodríguez, Brais & Leal, Marina & Puerto, Justo, 2021. "Global optimization for bilevel portfolio design: Economic insights from the Dow Jones index," Omega, Elsevier, vol. 102(C).
    6. Pieter van der Spek & Chris Verhoef, 2014. "Balancing Time‐to‐Market and Quality in Embedded Systems," Systems Engineering, John Wiley & Sons, vol. 17(2), pages 166-192, June.
    7. Vladimir Rankovic & Mikica Drenovak & Branko Uroševic & Ranko Jelic, 2016. "Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach," CESifo Working Paper Series 5731, CESifo.
    8. Kaehler, Jürgen & Marnet, Volker, 1993. "Markov-switching models for exchange-rate dynamics and the pricing of foreign-currency options," ZEW Discussion Papers 93-03, ZEW - Leibniz Centre for European Economic Research.
    9. Rad, Hossein & Low, Rand Kwong Yew & Miffre, Joëlle & Faff, Robert, 2020. "Does sophistication of the weighting scheme enhance the performance of long-short commodity portfolios?," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 164-180.
    10. Shafiqah Azman & Dharini Pathmanathan & Aerambamoorthy Thavaneswaran, 2022. "Forecasting the Volatility of Cryptocurrencies in the Presence of COVID-19 with the State Space Model and Kalman Filter," Mathematics, MDPI, vol. 10(17), pages 1-15, September.
    11. Yanhong Guo & Shuai Jiang & Wenjun Zhou & Chunyu Luo & Hui Xiong, 2021. "A predictive indicator using lender composition for loan evaluation in P2P lending," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-24, December.
    12. Nguyen, Linh Hoang & Chevapatrakul, Thanaset & Yao, Kai, 2020. "Investigating tail-risk dependence in the cryptocurrency markets: A LASSO quantile regression approach," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 333-355.
    13. Mondher Bellalah & Marc Lavielle, 2002. "A Decomposition of Empirical Distributions with Applications to the Valuation of Derivative Assets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 99-130, June.
    14. Tongyao Wang & Qitong Pan & Weiping Wu & Jianjun Gao & Ke Zhou, 2024. "Dynamic Mean–Variance Portfolio Optimization with Value-at-Risk Constraint in Continuous Time," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    15. Alejandro Bernales & Diether W. Beuermann & Gonzalo Cortazar, 2014. "Thinly traded securities and risk management," Estudios de Economia, University of Chile, Department of Economics, vol. 41(1 Year 20), pages 5-48, June.
    16. João Costa Freitas & Alberto Adrego Pinto & Óscar Felgueiras, 2024. "Game Theory for Predicting Stocks’ Closing Prices," Mathematics, MDPI, vol. 12(17), pages 1-49, August.
    17. Chen, Yan & Wang, Xuancheng, 2015. "A hybrid stock trading system using genetic network programming and mean conditional value-at-risk," European Journal of Operational Research, Elsevier, vol. 240(3), pages 861-871.
    18. Jiro Hodoshima & Toshiyuki Yamawake, 2022. "Comparing Dynamic and Static Performance Indexes in the Stock Market: Evidence From Japan," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 171-193, June.
    19. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, 2016. "Statistical Modeling Of Stock Returns: Explanatory Or Descriptive? A Historical Survey With Some Methodological Reflections," Journal of Economic Surveys, Wiley Blackwell, vol. 30(1), pages 149-164, February.
    20. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 211-250.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4761-:d:1287447. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.