Research Article
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Optimal Portfolio Allocation with Elliptical and Mixed Copulas

Year 2023, Volume: 52 Issue: 3, 461 - 480, 30.12.2023

Cemile Özgür Vedat Sarıkovanlık

https://doi.org/10.26650/ibr.2023.52.1038219

Abstract

This research aims to investigate the asset allocation performance of three different optimization methods commonly applied in the literature for a portfolio composed of univariate returns generated from Mixed and Elliptic copulas instead of historical data. As a result, returns of five equities traded at the BIST30 index of the Turkish Stock Market were obtained. Dynamics of the univariate return series are modelled with GARCH processes with Student-t distributed innovations. Following the marginal modelling, a five-dimensional dependence structure between the series is modelled with Elliptical and Mixed copulas. From the fitted Mixed and Elliptical copula functions, daily returns of the equities are simulated which are employed by the specified optimization methods in order to find out methodology specific optimal portfolio allocations. Performance of the constructed optimal portfolios are compared according to varying risk and reward to variability ratios yielding results especially in favor of the Mixed and Student t copulas. The main contribution of this research is to be able to fill the gap in the literature on the out-of-sample portfolio allocation performance of copula functions where there are still fewer papers compared to the dependency modelling or the in-sample portfolio allocation performance of copulas.

Keywords

Portfolio Optimization Copula Functions GARCH Portfolio Performance

Thanks

The authors would like to thank Borsa Istanbul A.Ş. for supplying the raw research data.

References

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  • Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65(1), 141-151. google scholar
  • Demarta, S., & McNeil, A. J. (2005). The t Copula and Related Copulas. International Statistical Review, 73(1), 111-129. doi:10.1111/j.1751-5823.2005.tb00254.x google scholar
  • Elton, E. J., Gruber, M. J., & Padberg, M. W. (1978). Simple Criteria for Optimal Portfolio Selection: Tracing Out the Efficient Frontier. The Journal of Finance, 33(1), 296-302. doi:10.2307/2326368 google scholar
  • Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007. doi:10.2307/1912773 google scholar
  • Fama, E. F. (1970). Multiperiod Consumption and Investment Decisions. American Economic Review, 60, 163-174. google scholar
  • Genest, C., & Neslehova, J. G. (2014). On tests of radial symmetry for bivariate copulas. Statistical Papers, 55(4), 1107-1119. google scholar
  • Gumbel, E. J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55(292), 698-707. google scholar
  • Han, Y., Li, P., & Xia, Y. (2017). Dynamic robust portfolio selection with copulas. Finance Research Letters, 21, 190-200. doi:10.1016/j.frl.2016.12.008 google scholar
  • Hofert, M., Kojadinovic, I., Maechler, M., & Yan, J. (2018). copula: Multivariate Dependence with Copulas. R package version 0.999-19.1. Retrieved from https://cran.r-project.org/package=copula google scholar
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  • Kemaloglu Acik, S., & Kizilok Kara, E. (2015). Modeling dependent financial assets by dynamic copula and portfolio optimization based on CVaR. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 64(1), 1-13. google scholar
  • Kızılok Kara, E., & Acık Kemaloglu, S. (2016). Portfolio Optimization of Dynamic Copula Models for De-pendent Financial Data Using Change Point Approach. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65, 175-188. doi:10.1501/Commua1_0000000768 google scholar
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  • Kresta, A. (2015). Application of GARCH-Copula Model in Portfolio Optimization. Financial Assets and Investing, 6(2), 7-20. doi:10.5817/FAI2015-2-1 google scholar
  • Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13-37. doi:10.2307/1924119 google scholar
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  • Merton, R. C. (1980). On Estimating the Expected Return on the Market: An Exploratory Investigation. google scholar
  • Journal of Financial Economics, 8(4), 323-361. doi:10.1016/0304-405X(80)90007-0 google scholar
  • Merton, R. C., & Samuelson, P. A. (1974). Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods. Journal of Financial Economics, 1(1), 67-94. doi:10.1016/0304-405X(74)90009-9 google scholar
  • Nelsen, R. B. (2006). An Introduction to Copulas. (2 ed.). New York: Springer-Verlag. google scholar
  • Patton, A. J. (2004). On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation. Journal of Financial Econometrics, 2(1), 130-168. doi:10.1093/jjfinec/nbh006 google scholar
  • R Core Team. (2019). R: A Language and Environment for Statistical Computing: R Foundation for Statisti-cal Computing. Retrieved from https://www.r-project.org/ google scholar
  • Riccetti, L. (2013). A copula-GARCH model for macro asset allocation of a portfolio with commodities.Empirical Economics, 44(3), 1315-1336. doi:10.1007/s00181-012-0577-1 google scholar
  • Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of risk, 2, 21-42. google scholar
  • Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/S0378-4266(02)00271-6 google scholar
  • Sahamkhadam, M., Stephan, A., & Östermark, R. (2018). Portfolio optimization based on GARCH-EVT-Copula forecasting models. International Journal of Forecasting, 34(3), 497-506. doi:10.1016/j.ijfore-cast.2018.02.004 google scholar
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk*. The Journal of Finance, 19(3), 425-442. doi:10.1111/j.1540-6261.1964.tb02865.x google scholar
  • Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(1), 119-138. Retrieved from http://www.jstor.org/stable/2351741 google scholar
  • Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), 49-58. doi:10.3905/ jpm.1994.409501 google scholar
  • Sklar, A. (1959). Fonctions de repartition â n dimensions et leurs marges [N-dimensional distribution functi-ons and their margins]. Publ. Inst. Statist. Univ. Paris, 8, 229-231. google scholar
  • Tobin, J. (1958). Liquidity Preference as Behavior Towards Risk. The Review of Economic Studies, 25(2), 65-86. doi:10.2307/2296205 google scholar
  • Trabelsi, N., & Tiwari, A. K. (2019). Market-Risk Optimization among the Developed and Emerging Mar-kets with CVaR Measure and Copula Simulation. Risks, 7(3), 78. Retrieved from https://www.mdpi. com/2227-9091/7/3/78 google scholar
  • Uryasev, S. (2000, 28-28 March 2000). Conditional Value-at-Risk: Optimization Algorithms and Applicati-ons. Paper presented at the Proceedings of the IEEE/IAFE/INFORMS 2000 Conference on Computatio-nal Intelligence for Financial Engineering (CIFEr) (Cat. No.00TH8520). google scholar
  • Yu, C., & Liu, Y. (2021). A Personalized Mean-CVaR Portfolio Optimization Model for Individual Invest-ment. Mathematical Problems in Engineering, 2021, 8863597. doi:10.1155/2021/8863597 google scholar

Year 2023, Volume: 52 Issue: 3, 461 - 480, 30.12.2023

Cemile Özgür Vedat Sarıkovanlık

https://doi.org/10.26650/ibr.2023.52.1038219

Abstract

References

  • Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. doi:10.1016/S0378-4266(02)00283-2 google scholar
  • Bacon, C. R. (2008). Practical Portfolio Performance Measurement and Attribution (Vol. 546): John Wiley & Sons. google scholar
  • Bawa, V. S., & Lindenberg, E. B. (1977). Capital market equilibrium in a mean-lower partial moment frame-work. Journal of Financial Economics, 5(2), 189-200. doi:10.1016/0304-405X(77)90017-4 google scholar
  • Billio, M., Frattarolo, L., & Guegan, D. (2022). High-Dimensional Radial Symmetry of Copula Functions: Multiplier Bootstrap vs. Randomization. Symmetry, 14(1), 97. google scholar
  • Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327. google scholar
  • Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65(1), 141-151. google scholar
  • Demarta, S., & McNeil, A. J. (2005). The t Copula and Related Copulas. International Statistical Review, 73(1), 111-129. doi:10.1111/j.1751-5823.2005.tb00254.x google scholar
  • Elton, E. J., Gruber, M. J., & Padberg, M. W. (1978). Simple Criteria for Optimal Portfolio Selection: Tracing Out the Efficient Frontier. The Journal of Finance, 33(1), 296-302. doi:10.2307/2326368 google scholar
  • Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007. doi:10.2307/1912773 google scholar
  • Fama, E. F. (1970). Multiperiod Consumption and Investment Decisions. American Economic Review, 60, 163-174. google scholar
  • Genest, C., & Neslehova, J. G. (2014). On tests of radial symmetry for bivariate copulas. Statistical Papers, 55(4), 1107-1119. google scholar
  • Gumbel, E. J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55(292), 698-707. google scholar
  • Han, Y., Li, P., & Xia, Y. (2017). Dynamic robust portfolio selection with copulas. Finance Research Letters, 21, 190-200. doi:10.1016/j.frl.2016.12.008 google scholar
  • Hofert, M., Kojadinovic, I., Maechler, M., & Yan, J. (2018). copula: Multivariate Dependence with Copulas. R package version 0.999-19.1. Retrieved from https://cran.r-project.org/package=copula google scholar
  • Jensen, M. C. (1969). Risk, The Pricing of Capital Assets, and The Evaluation of Investment Portfolios. The Journal of Business, 42(2), 167-247. Retrieved from http://www.jstor.org/stable/2351902 google scholar
  • Jin, X., & Lehnert, T. (2018). Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas. Dependence Modeling, 6(1), 19-46. google scholar
  • Joe, H. (1997). Multivariate models and multivariate dependence concepts (Vol. 73). London: Chapman and Hall. google scholar
  • Jorion, P. (2000). Value at Risk: The New Benchmark for Managing Financial Risk. New York: McGraw-Hill. google scholar
  • Kazemi, H., Schneeweis, T., & Gupta, R. (2003). Omega as a Performance Measure. CISDM Research Pa-per, June. google scholar
  • Keating, C., & Shadwick, W. F. (2002). A Universal Performance Measure. Journal of performance measu-rement, 6(3), 59-84. google scholar
  • Kemaloglu Acik, S., & Kizilok Kara, E. (2015). Modeling dependent financial assets by dynamic copula and portfolio optimization based on CVaR. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 64(1), 1-13. google scholar
  • Kızılok Kara, E., & Acık Kemaloglu, S. (2016). Portfolio Optimization of Dynamic Copula Models for De-pendent Financial Data Using Change Point Approach. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65, 175-188. doi:10.1501/Commua1_0000000768 google scholar
  • Kojadinovic, I. (2017). Some copula inference procedures adapted to the presence of ties. Computational Statistics & Data Analysis, 112, 24-41. google scholar
  • Kresta, A. (2015). Application of GARCH-Copula Model in Portfolio Optimization. Financial Assets and Investing, 6(2), 7-20. doi:10.5817/FAI2015-2-1 google scholar
  • Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13-37. doi:10.2307/1924119 google scholar
  • Markowitz, H. (1952). Portfolio Selection*. The Journal ofFinance, 7(1), 77-91. doi:10.1111/j.1540-6261.1952. tb01525.x google scholar
  • Markowitz, H. (1959). Portfolio Selection: Efficient Diversification of Investments. NY: Wiley. google scholar
  • Merton, R. C. (1980). On Estimating the Expected Return on the Market: An Exploratory Investigation. google scholar
  • Journal of Financial Economics, 8(4), 323-361. doi:10.1016/0304-405X(80)90007-0 google scholar
  • Merton, R. C., & Samuelson, P. A. (1974). Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods. Journal of Financial Economics, 1(1), 67-94. doi:10.1016/0304-405X(74)90009-9 google scholar
  • Nelsen, R. B. (2006). An Introduction to Copulas. (2 ed.). New York: Springer-Verlag. google scholar
  • Patton, A. J. (2004). On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation. Journal of Financial Econometrics, 2(1), 130-168. doi:10.1093/jjfinec/nbh006 google scholar
  • R Core Team. (2019). R: A Language and Environment for Statistical Computing: R Foundation for Statisti-cal Computing. Retrieved from https://www.r-project.org/ google scholar
  • Riccetti, L. (2013). A copula-GARCH model for macro asset allocation of a portfolio with commodities.Empirical Economics, 44(3), 1315-1336. doi:10.1007/s00181-012-0577-1 google scholar
  • Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of risk, 2, 21-42. google scholar
  • Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/S0378-4266(02)00271-6 google scholar
  • Sahamkhadam, M., Stephan, A., & Östermark, R. (2018). Portfolio optimization based on GARCH-EVT-Copula forecasting models. International Journal of Forecasting, 34(3), 497-506. doi:10.1016/j.ijfore-cast.2018.02.004 google scholar
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk*. The Journal of Finance, 19(3), 425-442. doi:10.1111/j.1540-6261.1964.tb02865.x google scholar
  • Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(1), 119-138. Retrieved from http://www.jstor.org/stable/2351741 google scholar
  • Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), 49-58. doi:10.3905/ jpm.1994.409501 google scholar
  • Sklar, A. (1959). Fonctions de repartition â n dimensions et leurs marges [N-dimensional distribution functi-ons and their margins]. Publ. Inst. Statist. Univ. Paris, 8, 229-231. google scholar
  • Tobin, J. (1958). Liquidity Preference as Behavior Towards Risk. The Review of Economic Studies, 25(2), 65-86. doi:10.2307/2296205 google scholar
  • Trabelsi, N., & Tiwari, A. K. (2019). Market-Risk Optimization among the Developed and Emerging Mar-kets with CVaR Measure and Copula Simulation. Risks, 7(3), 78. Retrieved from https://www.mdpi. com/2227-9091/7/3/78 google scholar
  • Uryasev, S. (2000, 28-28 March 2000). Conditional Value-at-Risk: Optimization Algorithms and Applicati-ons. Paper presented at the Proceedings of the IEEE/IAFE/INFORMS 2000 Conference on Computatio-nal Intelligence for Financial Engineering (CIFEr) (Cat. No.00TH8520). google scholar
  • Yu, C., & Liu, Y. (2021). A Personalized Mean-CVaR Portfolio Optimization Model for Individual Invest-ment. Mathematical Problems in Engineering, 2021, 8863597. doi:10.1155/2021/8863597 google scholar
There are 45 citations in total.

Details

Primary Language English
Subjects Business Administration
Journal Section Articles
Authors

Cemile Özgür 0000-0001-8366-6745

Vedat Sarıkovanlık 0000-0002-7152-6275

Publication Date December 30, 2023
Submission Date December 18, 2021
Published in Issue Year 2023 Volume: 52 Issue: 3

Cite

APA Özgür, C., & Sarıkovanlık, V. (2023). Optimal Portfolio Allocation with Elliptical and Mixed Copulas. Istanbul Business Research, 52(3), 461-480. https://doi.org/10.26650/ibr.2023.52.1038219
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