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Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios

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  • Al Janabi, Mazin A.M.
  • Arreola Hernandez, Jose
  • Berger, Theo
  • Nguyen, Duc Khuong

Abstract

We propose a model for optimizing structured portfolios with liquidity-adjusted Value-at-Risk (LVaR) constraints, whereby linear correlations between assets are replaced by the multivariate nonlinear dependence structure based on Dynamic Conditional Correlation t-copula modeling. Our portfolio optimization algorithm minimizes the LVaR function under adverse market circumstances and multiple operational and financial constraints. When we consider a diversified portfolio of international stock and commodity market indices under multiple realistic portfolio optimization scenarios, the obtained results consistently show the superiority of our approach relative to other competing portfolio strategies including the minimum-variance, risk-parity and equally weighted portfolio allocations.

Suggested Citation

  • Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2016. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," MPRA Paper 84626, University Library of Munich, Germany, revised Nov 2016.
  • Handle: RePEc:pra:mprapa:84626
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    1. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    2. Reboredo, Juan C., 2013. "Is gold a safe haven or a hedge for the US dollar? Implications for risk management," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2665-2676.
    3. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    4. Aloui, Riadh & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2013. "A time-varying copula approach to oil and stock market dependence: The case of transition economies," Energy Economics, Elsevier, vol. 39(C), pages 208-221.
    5. El Hedi Arouri, Mohamed & Jouini, Jamel & Nguyen, Duc Khuong, 2011. "Volatility spillovers between oil prices and stock sector returns: Implications for portfolio management," Journal of International Money and Finance, Elsevier, vol. 30(7), pages 1387-1405.
    6. Markus K. Brunnermeier, 2009. "Deciphering the Liquidity and Credit Crunch 2007-2008," Journal of Economic Perspectives, American Economic Association, vol. 23(1), pages 77-100, Winter.
    7. Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
    8. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Ran Ji & Miguel A. Lejeune, 2018. "Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints," Annals of Operations Research, Springer, vol. 262(2), pages 547-578, March.
    11. Arreola Hernandez, Jose, 2014. "Are oil and gas stocks from the Australian market riskier than coal and uranium stocks? Dependence risk analysis and portfolio optimization," Energy Economics, Elsevier, vol. 45(C), pages 528-536.
    12. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    13. Al Janabi, Mazin A.M., 2012. "Optimal commodity asset allocation with a coherent market risk modeling," Review of Financial Economics, Elsevier, vol. 21(3), pages 131-140.
    14. Kwan, Clarence C. Y. & Yuan, Yufei, 1993. "Optimal portfolio selection without short sales under the full-information covariance structure: A pedagogic consideration," Journal of Economics and Business, Elsevier, vol. 45(1), pages 91-98, February.
    15. Timotheos Angelidis & Alexandros Benos, 2006. "Liquidity adjusted value-at-risk based on the components of the bid-ask spread," Applied Financial Economics, Taylor & Francis Journals, vol. 16(11), pages 835-851.
    16. Alexandre Roch & H. Mete Soner, 2013. "Resilient Price Impact Of Trading And The Cost Of Illiquidity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-27.
    17. Gregor Weiß, 2013. "Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 179-202, August.
    18. Madhavan, Ananth & Richardson, Matthew & Roomans, Mark, 1997. "Why Do Security Prices Change? A Transaction-Level Analysis of NYSE Stocks," The Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 1035-1064.
    19. Cornett, Marcia Millon & McNutt, Jamie John & Strahan, Philip E. & Tehranian, Hassan, 2011. "Liquidity risk management and credit supply in the financial crisis," Journal of Financial Economics, Elsevier, vol. 101(2), pages 297-312, August.
    20. Yu, Jing-Rung & Chiou, Wan-Jiun Paul & Mu, Da-Ren, 2015. "A linearized value-at-risk model with transaction costs and short selling," European Journal of Operational Research, Elsevier, vol. 247(3), pages 872-878.
    21. Laih, Yih-Wenn, 2014. "Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm," European Journal of Operational Research, Elsevier, vol. 232(2), pages 375-382.
    22. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    23. Theo Berger, 2013. "Forecasting value-at-risk using time varying copulas and EVT return distributions," International Economics, CEPII research center, issue 133, pages 93-106.
    24. 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.
    25. Weiß, Gregor N.F. & Supper, Hendrik, 2013. "Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3334-3350.
    26. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    27. Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    28. Bazgour, Tarik & Heuchenne, Cedric & Sougné, Danielle, 2016. "Conditional portfolio allocation: Does aggregate market liquidity matter?," Journal of Empirical Finance, Elsevier, vol. 35(C), pages 110-135.
    29. repec:dau:papers:123456789/4688 is not listed on IDEAS
    30. Bruce I. Jacobs & Kenneth N. Levy & Harry M. Markowitz, 2005. "Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions," Operations Research, INFORMS, vol. 53(4), pages 586-599, August.
    31. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    32. Bekiros, Stelios & Hernandez, Jose Arreola & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2015. "Multivariate dependence risk and portfolio optimization: An application to mining stock portfolios," Resources Policy, Elsevier, vol. 46(P2), pages 1-11.
    33. Sean A. Anthonisz & Talis Putnins, 2017. "Asset Pricing with Downside Liquidity Risks," Published Paper Series 2017-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    34. René Garcia & Éric Renault & Georges Tsafack, 2007. "Proper Conditioning for Coherent VaR in Portfolio Management," Management Science, INFORMS, vol. 53(3), pages 483-494, March.
    35. Aloui, Riadh & Ben Aïssa, Mohamed Safouane & Nguyen, Duc Khuong, 2013. "Conditional dependence structure between oil prices and exchange rates: A copula-GARCH approach," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 719-738.
    36. repec:dau:papers:123456789/14735 is not listed on IDEAS
    37. Low, Rand Kwong Yew & Alcock, Jamie & Faff, Robert & Brailsford, Timothy, 2013. "Canonical vine copulas in the context of modern portfolio management: Are they worth it?," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3085-3099.
    38. 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.
    39. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    40. Gao, Jianjun & Xiong, Yan & Li, Duan, 2016. "Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time," European Journal of Operational Research, Elsevier, vol. 249(2), pages 647-656.
    41. Alexander, Gordon J. & Baptista, Alexandre M., 2008. "Active portfolio management with benchmarking: Adding a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 779-820, March.
    42. Ye, Wuyi & Liu, Xiaoquan & Miao, Baiqi, 2012. "Measuring the subprime crisis contagion: Evidence of change point analysis of copula functions," European Journal of Operational Research, Elsevier, vol. 222(1), pages 96-103.
    43. Bertrand Maillet & Sessi Tokpavi & Benoît Vaucher, 2015. "Global minimum variance portfolio optimisation under some model risk : A robust regression-based approach," Post-Print hal-02312329, HAL.
    44. Liu, Weimin, 2006. "A liquidity-augmented capital asset pricing model," Journal of Financial Economics, Elsevier, vol. 82(3), pages 631-671, December.
    45. Al Janabi, Mazin A.M., 2014. "Optimal and investable portfolios: An empirical analysis with scenario optimization algorithms under crisis market prospects," Economic Modelling, Elsevier, vol. 40(C), pages 369-381.
    46. HEINEN, Andréas & VALDESOGO, Alfonso, 2009. "Asymmetric CAPM dependence for large dimensions: the Canonical Vine Autoregressive Model," LIDAM Discussion Papers CORE 2009069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    47. Mazin Al Janabi, 2013. "Optimal and coherent economic-capital structures: evidence from long and short-sales trading positions under illiquid market perspectives," Annals of Operations Research, Springer, vol. 205(1), pages 109-139, May.
    48. repec:cii:cepiei:2013-q1-133-6 is not listed on IDEAS
    49. 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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    2. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
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    8. Jose Arreola Hernandez & Mazin A.M. Al Janabi, 2020. "Forecasting of dependence, market, and investment risks of a global index portfolio," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(3), pages 512-532, April.
    9. Mazin A.M. Al Janabi, 2021. "Is optimum always optimal? A revisit of the mean‐variance method under nonlinear measures of dependence and non‐normal liquidity constraints," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 387-415, April.
    10. Shahzad, Syed Jawad Hussain & Arreola-Hernandez, Jose & Bekiros, Stelios & Shahbaz, Muhammad & Kayani, Ghulam Mujtaba, 2018. "A systemic risk analysis of Islamic equity markets using vine copula and delta CoVaR modeling," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 56(C), pages 104-127.
    11. Al Janabi, Mazin A.M. & Ferrer, Román & Shahzad, Syed Jawad Hussain, 2019. "Liquidity-adjusted value-at-risk optimization of a multi-asset portfolio using a vine copula approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    12. BenSaïda, Ahmed, 2018. "The contagion effect in European sovereign debt markets: A regime-switching vine copula approach," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 153-165.
    13. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    14. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    15. Grillini, Stefano & Ozkan, Aydin & Sharma, Abhijit & Al Janabi, Mazin A.M., 2019. "Pricing of time-varying illiquidity within the Eurozone: Evidence using a Markov switching liquidity-adjusted capital asset pricing model," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 145-158.
    16. Kim, Jong-Min & Kim, Dong H. & Jung, Hojin, 2020. "Modeling non-normal corporate bond yield spreads by copula," The North American Journal of Economics and Finance, Elsevier, vol. 53(C).
    17. Ahmed BenSaïda & Sabri Boubaker & Duc Khuong Nguyen & Skander Slim, 2018. "Value‐at‐risk under market shifts through highly flexible models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(8), pages 790-804, December.
    18. Yfanti, Stavroula & Karanasos, Menelaos & Zopounidis, Constantin & Christopoulos, Apostolos, 2023. "Corporate credit risk counter-cyclical interdependence: A systematic analysis of cross-border and cross-sector correlation dynamics," European Journal of Operational Research, Elsevier, vol. 304(2), pages 813-831.
    19. Gazi Salah Uddin & Maziar Sahamkhadam & Muhammad Yahya & Ou Tang, 2023. "Investment opportunities in the energy market: What can be learnt from different energy sectors," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(4), pages 3611-3636, October.
    20. Rewat Khanthaporn, 2022. "Analysis of Nonlinear Comovement of Benchmark Thai Government Bond Yields," PIER Discussion Papers 183, Puey Ungphakorn Institute for Economic Research.
    21. Supper, Hendrik & Irresberger, Felix & Weiß, Gregor, 2020. "A comparison of tail dependence estimators," European Journal of Operational Research, Elsevier, vol. 284(2), pages 728-742.

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    More about this item

    Keywords

    Dynamic copulas; LVaR; dependence structure; portfolio optimization algorithm;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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