Skip to main content
SpringerLink
Log in

Robust Portfolio Optimization Based on Semi-Parametric ARMA-TGARCH-EVT Model with Mixed Copula Using WCVaR

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

Portfolio returns generally follow multivariate distribution, whose effectiveness depends not only on the correct estimation of marginal distributions, but also on the accurate capture of the interdependent structure among them. To effectively estimate the marginal distribution and improve the accuracy, we present a hybrid ARMA-TGARCH-EVT model, which considers the leverage effect, thick tail and heteroscedasticity of the financial asset return series. This model utilizes the extreme value theory to process the tail data and uses the kernel regression estimation to process the intermediate data to make the marginal distribution smooth, natural and regular. Furthermore, a novel semi-parametric ARMA-TGARCH-EVT- Copula portfolio model is proposed to achieve the robustness of minimizing worst-case conditional value-at-risk (WCVaR). In the model, a mixed copula set is presented by t-copula and Archimedean copula to cover the wide joint dependence among logarithmic daily returns. To verify the effectiveness and practicality of our proposed model, a static numerical example and a dynamic portfolio based on the historical index data of two stock crash periods are given. The results show that the new model is superior in terms of daily average logarithmic return, cumulative logarithmic return and sharp ratio.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Ang, A., & Chen, J. (2002). Asymmetric correlations of equity portfolios. Journal of Financial Economics, 63(3), 443–494.

    Article  Google Scholar 

  • Bali, T. G., & Neftci, S. N. (2003). Disturbing extremal behavior of spot rate dynamics. Journal of Empirical Finance, 10, 455–477.

    Article  Google Scholar 

  • Ben-Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of Operations Research, 23, 769–805.

    Article  Google Scholar 

  • Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48, 28–43.

    Article  Google Scholar 

  • Chollete, L., Heinen, A., & Valdesogo, A. (2009). Modeling international financial returns with a multivariate regime-switching copula. Journal of Financial Economics, 7(4), 437–480.

    Google Scholar 

  • Dr. Avishek Pal and Dr. PKS Prakash. (2017). Practical Time Series Analysis. Packt Publishing.

  • El, G. L., Oks, M., & Oustry, F. (2003). Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Operations Research, 51(4), 543–556.

    Article  Google Scholar 

  • El Ghaoui, L., & Lebret, H. (1997). Robust solution to least squares problems with uncertain data. SIAM Journal on Matrix Analysis and Applications, 18, 1035–1064.

    Article  Google Scholar 

  • Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779–1801.

    Article  Google Scholar 

  • Goel, A., Sharma, A., & Mehra, A. (2019). Robust optimization of mixed CVaR STARR ratio using copulas. Journal of Computational and Applied Mathematics, 347, 62–83.

    Article  Google Scholar 

  • Han, Y., Li, P., & Xia, Y. (2017). Dynamic robust portfolio selection with copulas. Finance Research Letters, 21, 190–200.

    Article  Google Scholar 

  • Jarque C M. (2011). Jarque-bera test. International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg, 701–702.

  • Joe, H. (1997). Multivariate models and multivariate dependence concepts. CRC Press.

    Book  Google Scholar 

  • Jondeau E. and Rockinger M. (2003). Conditional dependency of financial series: the copula-GARCH model. Social Science Electronic Publishing.

  • Jondeau, E., & Rockinger, M. (2006). The copula-garch model of conditional dependencies: An international stock market application. Journal of International Money Finance, 25(5), 827–853.

    Article  Google Scholar 

  • Kakouris, I., & Rustem, B. (2014). Robust portfolio optimization with copulas. European Journal of Operational Research, 235, 28–37.

    Article  Google Scholar 

  • Ling, Hu. (2006). Dependence patterns across financial markets: A mixed copula approach. Applied Financial Economics, 16(10), 717–729.

    Article  Google Scholar 

  • Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7, 77–91.

    Google Scholar 

  • Münnix, M. C., & Schäfer, R. (2011). A copula approach on the dynamics of statistical dependencies in the us stock market. Physica a: Statist. Mech. Appl., 390(23), 4251–4259.

    Article  Google Scholar 

  • Nelsen R B. (2006). An Introduction to Copulas. Springer Science & Business Media.

  • Pickands, J. (1975). Statistical inference using extreme order statistics. The Annals of Statistics, 2(3), 119–131.

    Google Scholar 

  • Rockafellar, R. T., & Uryasev, S. (2002). Conditional Value-at-risk for general loss distributions. Journal of Banking & Finance, 26, 1443–1471.

    Article  Google Scholar 

  • Sahamkhadam, M., Stephan, A., & Östermark, R. (2018). Portfolio optimization based on GARCH-EVT-Copula forecasting models. International Journal of Forecasting, 34, 497–506.

    Article  Google Scholar 

  • Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71, 599–608.

    Article  Google Scholar 

  • Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publications De L’institut De Statistique De L’université De Paris, 8, 229–231.

    Google Scholar 

  • Soyster, A. L. (1973). Convex programming with set inclusive constraints and applications to inexact linear programming. Operations Research, 21, 1154–1157.

    Article  Google Scholar 

  • Tsay Ruey S. (2010). Analysis of Financial Time Series. Wiley Series in Probability and Statistics.

  • Zakoian J M. (1990). Threshold Heteroskedastic Models. Manuscript, CREST, INSEE, Paris.

  • Zhu, S., & Fukushima, M. (2009). Worst-Case conditional Value-at-Risk with application to robust portfolio management. Operations Research, 57, 1155–1168.

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the “Humanities and Social Sciences Research and Planning Fund of the Ministry of Education of China, No.18YJAZH014-x2lxY9180090”, “Natural Science Foundation of Guangdong Province, No.2019A1515011038”, “Soft Science of Guangdong Province, No.2018A070712006, 2019A101002118” and “Guangdong Graduate Education Innovation Program, 2019SFKC07”. The authors are highly grateful to the referees and editor in-chief for their very helpful comments.

Funding

This research was supported by the “Humanities and Social Sciences Research and Planning Fund of the Ministry of Education of China, No.18YJAZH014-x2lxY9180090”, “Natural Science Foundation of Guangdong Province, No.2019A1515011038”, “Soft Science of Guangdong Province, No.2018A070712006, 2019A101002118” and “Guangdong Graduate Education Innovation Program, 2019SFKC07”.

Author information

Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Xue Deng & Ying Liang

Authors
  1. Xue Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Xue Deng contributed to the conception of the study and helped perform the analysis with constructive discussions. Ying Liang performed the experiment contributed significantly to analysis and manuscript preparation, performed the data analyses and wrote the manuscript.

Corresponding author

Correspondence to Ying Liang.

Ethics declarations

Conflict of interest

We declare that we have no conflict of interest.

Availability of data and material

All data generated or analyzed during this study are included in this paper.

Ethical approval

This paper does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, X., Liang, Y. Robust Portfolio Optimization Based on Semi-Parametric ARMA-TGARCH-EVT Model with Mixed Copula Using WCVaR. Comput Econ 61, 267–294 (2023). https://doi.org/10.1007/s10614-021-10207-5

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-021-10207-5

Keywords

Search

Navigation