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

Document Type : Research Paper

Authors

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.

10.22059/frj.2022.342896.1007333

Abstract

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.

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References

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Financial Research Journal
Volume 25, Issue 1
2023
Pages 152-179

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