Comparison of Markowitz Model and DCC-tCopula-LVaR for Portfolio Optimization in the Tehran Stock Exchange

Document Type : Research Paper


1 Ph.D. Candidate, Department of Finance, Faculty of Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

2 Associate Prof., Department of Finance, Faculty of Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

3 Lecture, Department of Finance, Faculty of Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran.



Objective: Considering that investing in the stock market is associated with risk, therefore, its measurement is one of the most important issues for investors. The focus of the current research is on the calculation of the value at risk of Dynamic Conditional Correlation with the Solvency Approach (DCC t-Cupola LVaR) based on the copula and also the minimization problems of the above model to choose the optimal portfolio. Therefore, the purpose of this research is to compare the performance of the Markowitz models and value-at-risk model with the Liquidity-t Cupola approach and DCC-t Cupola LVaR to optimize the portfolios in Tehran Stock Exchange. While presenting a composite model, the extracted model should be examined to select the most efficient model to optimize the investment portfolio considering the conditions of investment uncertainty and non-linearity of the correlation between asset returns.
Methods: To estimate DCC-tCopula-LVaR, first, the time series of the disturbance distribution of asset returns were estimated and standardized from the ARIMA-GARCH 1,1) model. Then, the marginal distributions of assets were estimated using Student's t-copula function. In the following, DCC-tCopula-LVaR values were calculated using the parametric method. In the last step, using linear programming, the optimal combination of the portfolio and the efficient frontier of the two models were calculated at the confidence levels of 80, 85, 90, 95, and 99 percent for the above two models.
Results: The findings of this research indicate that the Markowitz model performs better as the risk level increases. As the risk level decreases and declines from 99% to 80% (risk level in a sell position), the DCC-LVaR model performs better. Also, as the value at risk increases, the Sharp value of the DCC-tCopula-LVaR model decreases compared to the Markowitz model.
Conclusion: Numerical experiences in the presented empirical analysis, Sharpe ratio, and two loss measures mean absolute value of error (MAE), as well as the root mean square error (RMSE) show that for an arbitrary portfolio, using the DCC t-Cupola LVaR model at a low-risk level is more efficient than the Markowitz model. By reducing the increase and increasing the value at risk, the Markowitz model has better efficiency. Also, using the DCC-tCopula-LVaR model, when the value at risk-adjusted by liquidity is low, brings better performance for stock portfolio optimization compared to the Markowitz model, based on the Sharpe measurement criterion.


Main Subjects

Akkaya, M. (2021). Behavioral Portfolio Theory. In Applying Particle Swarm Optimization (pp. 29-48). Springer, Cham.
Al Janabi, M. A. (2012). Optimal commodity asset allocation with a coherent market risk modeling. Review of Financial Economics, 21(3), 131-140.
Al Janabi, M. A. (2013). Optimal and coherent economic-capital structures: evidence from long and short-sales trading positions under illiquid market perspectives. Annals of Operations Research, 205(1), 109-139.
Al Janabi, M. A., Ferrer, R. & Shahzad, S. J. H. (2019). Liquidity-adjusted value-at-risk optimization of a multi-asset portfolio using a vine copula approach. Physica A: Statistical Mechanics and its Applications, 536, 122579.
Al Janabi, M. A., Hernandez, J. A. Berger, T. & Nguyen, D. K. (2017). Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios. European Journal of Operational Research, 259(3), 1121-1131.
Altay, E. & Çalgıcı, S. (2019). Liquidity adjusted capital asset pricing model in an emerging market: Liquidity risk in Borsa Istanbul. Borsa Istanbul Review, 19(4), 297-309.
Amihud, Y. (2002). Illiquidity and stock returns: cross-section and time-series effects. Journal of financial markets, 5(1), 31-56.
Amihud, Y. & Mendelson, H. (1986). Asset pricing and the bid-ask spread. Journal of Financial Economics, 17, 223–249.
An, H., Wang, H., Delpachitra, S., Cottrell, S. & Yu, X. (2022). Early warning system for risk of external liquidity shock in BRICS countries. Emerging Markets Review, 100878.
Baillie, R. & Bollerslev, T. (1989). The Message in Daily Exchange Rates: A Conditional-Variance Tale, Journal of Business & Economic Statistics, 3(7), 297-305.
Bollerslev, T. (1986). Generalized Autoregressive conditional hetereoscedasticity. Journal of Econometrics, 31(3), 307-327.
Brennan, M.J. & Subrahmanyam, A. (1996). Market microstructure and asset pricing: on the compensation for illiquidity in stock returns. Journal of Financial Economics, 41, 441–464.
Dang, T. L. & Nguyen, T. M. H. (2020). Liquidity risk and stock performance during the financial crisis. Research in International Business and Finance, 52, 101165.
Elton, E. J. & Gruber, M. J. (1997). Modern portfolio theory, 1950 to date. Journal of banking & finance, 21(11-12), 1743-1759.
Engle, R. (2004). Risk and volatility: Econometric models and financial practice. American economic review, 94(3), 405-420.
Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United King dominflation. Econometrica 50(4), 987-1007.
Engle, R.F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroscedasticity models. Journal of Business and Economic Statistics, 20(3), 339-350.
Fabozzi, F. J., Gupta, F. & Markowitz, H. M. (2002). The legacy of modern portfolio theory. The journal of investing, 11(3), 7-22.
Fallahshams, M. & Sadeghi, A. (2021). Portfolio optimization by using the Copula Approach and multivariate conditional value at risk in Tehran Stock Exchange. Journal of Investment Knowledge, 10(40), 205-226. (in Persian)
Gao, J., Xiong, Y., & Li, D. (2016). Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time. European Journal of Operational Research, 249(2), 647-656.
Garcia, R., Renault, É. & Tsafack, G. (2007). Proper conditioning for coherent VaR in portfolio management. Management Science, 53(3), 483-494.
Gleißner, W. (2019). Cost of capital and probability of default in value-based risk management. Management Research Review, 42(11), 1243-1258.
Hassan, S. G. (2020). The funding liquidity risk and bank risk: A review on the Islamic and conventional banks in Pakistan. Hamdard Islamicus, 43(1).
Hatemi-J, A. Roca, E. & Mustafa, A. (2022). Portfolio diversification impact of oil and asymmetric interaction between oil, equity and bonds in the global market: fresh evidence from alternative approaches. Journal of Economic Studies, (ahead-of-print).
Hu, J. (2022, March). Application of Modern Portfolio Theory in Stock Market based on Empirical analysis. In 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022) (pp. 1561-1567). Atlantis Press.
Huang, D. Schlag, C. Shaliastovich, I. & Thimme, J. (2019). Volatility-of-volatility risk. Journal of Financial and Quantitative Analysis, 54(6), 2423-2452.
Jorion, P. (1996). Risk2: Measuring the risk in value at risk. Financial analysts journal, 52(6), 47-56.
Kuttner, K. N. (2018). Outside the box: Unconventional monetary policy in the great recession and beyond. Journal of Economic Perspectives, 32(4), 121-46.
Li, H., Novy-Marx, R., & Velikov, M. (2019). Liquidity risk and asset pricing. Critical Finance Review, 8(1-2), 223-255.
Lintner, J. (1975). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. In Stochastic optimization models in finance (pp. 131-155). Academic Press.
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.
Marozva, G. (2019). Liquidity and stock returns: New evidence from Johannesburg Stock Exchange. The Journal of Developing Areas, 53(2).
Martellini, L. (2008). Toward the design of better equity benchmarks: Rehabilitating the tangency portfolio from modern portfolio theory. The Journal of Portfolio Management, 34(4), 34-41.
Mendonça, G. H., Ferreira, F. G., Cardoso, R. T. & Martins, F. V. (2020). Multi-attribute decision making applied to financial portfolio optimization problem. Expert Systems with Applications, 158, 113527.
Mensi, W., Hammoudeh, S., Vo, X. V., & Kang, S. H. (2021). Volatility spillovers between oil and equity markets and portfolio risk implications in the US and vulnerable EU countries. Journal of International Financial Markets, Institutions, and Money, 75, 101457.
Messaoud, S.B. & Aloui, C. (2015) Measuring Risk of Portfolio: GARCH- Copula Model. Journal of Economic Integration, 30(1), 172-205.
Mirabbasi, Y., Nikoumaram, H., Saeidi, A., Haghshenas, F. (2018). Study of portfolio optimization based on downside risk, upside potential and behavioral variables efficiency. Financial Engineering and Portfolio Management, 9(34), 305-333. (in Persian)
Morgan, J. P. (1997). Creditmetrics-technical document. JP Morgan, New York.
Patton, A. J. (2009). Copula–based models for financial time series. In Handbook of financial time series (pp. 767-785). Springer, Berlin, Heidelberg.
Penza, P., Bansal, V. K., Bansal, V. K., & Bansal, V. K. (2001). Measuring market risk with value at risk (Vol. 17). John Wiley & Sons.
Pishbahar, E., Abedi, S. (2017). Measuring portfolio Value at Risk: The application of copula approach. Financial Engineering and Portfolio Management, 8(30), 55-73. (in Persian)
Prasad, M. A., Elekdag, S., Jeasakul, M. P., Lafarguette, R., Alter, M. A., Feng, A. X., & Wang, C. (2019). Growth at risk: Concept and application in IMF country surveillance. Working Paper No. 2019/036.
Raei, R., Bajalan, S., Ajam, A. (2021). Investigating the Efficiency of the 1/N Model in Portfolio Selection. Financial Research Journal, 23(1), 1-16. (in Persian)
Raghfar, H., Ajorlo, N. (2016). Calculation of Value at Risk of Currency Portfolio for a Typical Bank by GARCH-EVT-Copula Method. Iranian Journal of Economic Research, 21(67), 113-141. (in Persian)
Ruozi, R., & Ferrari, P. (2013). Liquidity risk management in banks: economic and regulatory issues. In Liquidity Risk Management in Banks (pp. 1-54). Springer, Berlin, Heidelberg.
Sahamkhadam, M. & Stephan, A. & Östermark, R. (2018). Portfolio optimization based on GARCH-EVT- Copula forecasting Model. International Journal of Forecasting, 8(4), 497–506.
Shirkavand, S., Fadaei, H. (2022). Robust Portfolio Optimization by Applying Multi-objective and Omega-conditional Value at Risk Models Based on the Mini-max Regret Criterion. Financial Research Journal, 24(1), 1-17. (in Persian)
Sina, A., Fallah, M. (2020). Comparison of Value Risk Models and Coppola-CVaR in Portfolio Optimization in Tehran Stock Exchange. ـJournal of Financial Management Perspective, 10(29), 125-146. (in Persian)
Sklar, A. (1959). Functions de repartition and dimensions et leurs marges. l’Institut de tatistique de L’Universit de Paris, 8, 229–231.
Tran, L. T. H., Hoang, T. T. P., & Tran, H. X. (2018). Stock liquidity and ownership structure during and after the 2008 Global Financial Crisis: Empirical evidence from an emerging market. Emerging Markets Review, 37, 114-133.
Vuković, M., Pivac, S., & Babić, Z. (2020). Comparative analysis of stock selection using a hybrid MCDM approach and modern portfolio theory. Croatian Review of Economic, Business and Social Statistics, 6(2), 58-68.
Wang, Z.R., Chen, X.H., Jin, Y.B. and Zhou, Y.J. (2010) Estimating risk of foreign exchange portfolio: Using VaR and CVaR based on GARCH–EVT- Copula model. Physica A: Statistical Mechanics and its Applications, 389(21), 4918-4928.
Yahiizadefar, M., Khorramdin, J. (2008). The role of liquidity factors and the risk of illiquidity on excess stock returns in Tehran Stock Exchange. Accounting and auditing reviews, 15(4). (in Persian)
Yu, J. R., Chiou, W. J. P., & Mu, D. R. (2015). A linearized value-at-risk model with transaction costs and short selling. European Journal of Operational Research, 247(3), 872-878.