IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_5731.html
   My bibliography  Save this paper

Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach

Author

Listed:
  • Vladimir Rankovic
  • Mikica Drenovak
  • Branko Uroševic
  • Ranko Jelic

Abstract

In accordance with Basel Capital Accords, the Capital Requirements (CR) for market risk exposure of banks is a nonlinear function of Value-at-Risk (VaR). Importantly, the CR is calculated based on a bank’s actual portfolio, i.e. the portfolio represented by its current holdings. To tackle mean-VaR portfolio optimization within the actual portfolio framework (APF), we propose a novel mean-VaR optimization method where VaR is estimated using a univariate Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) volatility model. The optimization was performed by employing a Nondominated Sorting Genetic Algorithm (NSGA-II). On a sample of 40 large US stocks, our procedure provided superior mean-VaR trade-offs compared to those obtained from applying more customary mean-multivariate GARCH and historical VaR models. The results hold true in both low and high volatility samples.

Suggested Citation

  • Vladimir Rankovic & Mikica Drenovak & Branko Uroševic & Ranko Jelic, 2016. "Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach," CESifo Working Paper Series 5731, CESifo.
    • Handle: RePEc:ces:ceswps:_5731
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp5731.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value‐at‐Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    4. Santos, André A.P. & Nogales, Francisco J. & Ruiz, Esther & Dijk, Dick Van, 2012. "Optimal portfolios with minimum capital requirements," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1928-1942.
    5. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Huisman, R. & Koedijik, K.G. & Pownall, R.A.J., 1998. "VaR-x: Fat Tails in Financial Risk Management," Papers 98-54, Southern California - School of Business Administration.
    8. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    9. Konstantinos Anagnostopoulos & Georgios Mamanis, 2011. "Multiobjective evolutionary algorithms for complex portfolio optimization problems," Computational Management Science, Springer, vol. 8(3), pages 259-279, August.
    10. Darryll Hendricks & Beverly Hirtle, 1997. "Bank capital requirements for market risk: the internal models approach," Economic Policy Review, Federal Reserve Bank of New York, vol. 3(Dec), pages 1-12.
    11. Iscoe, Ian & Kreinin, Alexander & Mausser, Helmut & Romanko, Oleksandr, 2012. "Portfolio credit-risk optimization," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1604-1615.
    12. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2008. "Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization," Management Science, INFORMS, vol. 54(3), pages 573-585, March.
    13. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
    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.
    15. Branke, J. & Scheckenbach, B. & Stein, M. & Deb, K. & Schmeck, H., 2009. "Portfolio optimization with an envelope-based multi-objective evolutionary algorithm," European Journal of Operational Research, Elsevier, vol. 199(3), pages 684-693, December.
    16. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    17. Goh, Joel Weiqiang & Lim, Kian Guan & Sim, Melvyn & Zhang, Weina, 2012. "Portfolio value-at-risk optimization for asymmetrically distributed asset returns," European Journal of Operational Research, Elsevier, vol. 221(2), pages 397-406.
    18. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ranković, Vladimir & Ivanović, Miloš & Urošević, Branko & Jelic, Ranko, 2017. "Market risk management in a post-Basel II regulatory environmentAuthor-Name: Drenovak, Mikica," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1030-1044.
    2. Yinpeng Zhang & Zhixin Liu & Xueying Yu, 2017. "The Diversification Benefits of Including Carbon Assets in Financial Portfolios," Sustainability, MDPI, vol. 9(3), pages 1-13, March.
    3. Yiwen Cui & Lei Li & Zijie Tang, 2021. "Risk Analysis of China Stock Market During Economic Downturns–Based on GARCH-VaR and Wavelet Transformation Approaches," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 11(4), pages 322-336, April.
    4. Owusu Junior, Peterson & Tiwari, Aviral Kumar & Tweneboah, George & Asafo-Adjei, Emmanuel, 2022. "GAS and GARCH based value-at-risk modeling of precious metals," Resources Policy, Elsevier, vol. 75(C).
    5. Zexuan Yin & Paolo Barucca, 2022. "Variational Heteroscedastic Volatility Model," Papers 2204.05806, arXiv.org.
    6. Jose Arreola Hernandez & Sang Hoon Kang & Seong‐Min Yoon, 2022. "Nonlinear spillover and portfolio allocation characteristics of energy equity sectors: Evidence from the United States and Canada," Review of International Economics, Wiley Blackwell, vol. 30(1), pages 1-33, February.
    7. Jolanta Tamošaitienė & Vahidreza Yousefi & Hamed Tabasi, 2021. "Project Portfolio Construction Using Extreme Value Theory," Sustainability, MDPI, vol. 13(2), pages 1-13, January.
    8. P. Kumar & Jyotirmayee Behera & A. K. Bhurjee, 2022. "Solving mean-VaR portfolio selection model with interval-typed random parameter using interval analysis," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 41-77, March.
    9. Sukono & Dedi Rosadi & Di Asih I Maruddani & Riza Andrian Ibrahim & Muhamad Deni Johansyah, 2024. "Mechanisms of Stock Selection and Its Capital Weighing in the Portfolio Design Based on the MACD-K-Means-Mean-VaR Model," Mathematics, MDPI, vol. 12(2), pages 1-22, January.
    10. Kresta Aleš & Wang Anlan, 2020. "Portfolio Optimization Efficiency Test Considering Data Snooping Bias," Business Systems Research, Sciendo, vol. 11(2), pages 73-85, October.
    11. Drenovak, Mikica & Ranković, Vladimir & Urošević, Branko & Jelic, Ranko, 2022. "Mean-Maximum Drawdown Optimization of Buy-and-Hold Portfolios Using a Multi-objective Evolutionary Algorithm," Finance Research Letters, Elsevier, vol. 46(PA).
    12. Gianni Filograsso & Giacomo Tollo, 2023. "Adaptive evolutionary algorithms for portfolio selection problems," Computational Management Science, Springer, vol. 20(1), pages 1-38, December.
    13. Mladen Stamenković, 2023. "Where Did All The Papers Go? A Bibliometric Overview Of Publications In Economics From Serbia," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 68(236), pages 29-50, January –.

    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. Harris, Richard D.F. & Stoja, Evarist & Tan, Linzhi, 2017. "The dynamic Black–Litterman approach to asset allocation," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1085-1096.
    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. Ranković, Vladimir & Ivanović, Miloš & Urošević, Branko & Jelic, Ranko, 2017. "Market risk management in a post-Basel II regulatory environmentAuthor-Name: Drenovak, Mikica," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1030-1044.
    4. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2014. "Bank regulation and international financial stability: A case against the 2006 Basel framework for controlling tail risk in trading books," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 107-130.
    5. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    6. Harris, Richard D.F. & Mazibas, Murat, 2013. "Dynamic hedge fund portfolio construction: A semi-parametric approach," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 139-149.
    7. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    8. Lakshina, Valeriya, 2020. "Do portfolio investors need to consider the asymmetry of returns on the Russian stock market?," The Journal of Economic Asymmetries, Elsevier, vol. 21(C).
    9. de Oliveira, Felipe A. & Maia, Sinézio F. & de Jesus, Diego P. & Besarria, Cássio da N., 2018. "Which information matters to market risk spreading in Brazil? Volatility transmission modelling using MGARCH-BEKK, DCC, t-Copulas," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 83-100.
    10. 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.
    11. Takano, Yuichi & Gotoh, Jun-ya, 2023. "Dynamic portfolio selection with linear control policies for coherent risk minimization," Operations Research Perspectives, Elsevier, vol. 10(C).
    12. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    13. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    14. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    15. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    16. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    17. Branko Uroševic & Mikica Drenovak & Vladimir Rankovic & Ranko Jelic & Milos Ivanovic, 2016. "Market Risk Management in a Post-Basel II Regulatory Environment," CESifo Working Paper Series 6293, CESifo.
    18. Kwangmin Jung & Donggyu Kim & Seunghyeon Yu, 2021. "Next Generation Models for Portfolio Risk Management: An Approach Using Financial Big Data," Papers 2102.12783, arXiv.org, revised Feb 2022.
    19. Syriopoulos, Theodore & Roumpis, Efthimios, 2009. "Dynamic correlations and volatility effects in the Balkan equity markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(4), pages 565-587, October.
    20. Sio Chong U & Jacky So & Deng Ding & Lihong Liu, 2016. "An efficient Fourier expansion method for the calculation of value-at-risk: Contributions of extra-ordinary risks," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-27, March.

    More about this item

    Keywords

    portfolio optimization; actual portfolios; value at risk; GARCH; NSGA-II;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    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:ces:ceswps:_5731. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    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.