Measuring value at risk using short-term and long-term memory of GARCH models based on switching approach to form an optimal stock portfolio

Document Type : Original Article


1 MSc., Department of Financial Management, Faculty of Management and Economic, University of Alzahra, Tehran, Iran.

2 Associate Prof., Department of Management, Alzahra University, Tehran, Iran.


Value at Risk model based on a switching regime approach was used in this study to optimize portfolios consisting of industry index (petroleum products, investment, chemical products, and metal products). For this purpose, the VaR of returns on index should first be extracted through parametric models of the (GARCH) family in each of the above industries by using regime transitions. After the risk of return on index is obtained for each industry, the optimal portfolio is created in the next step based on VaR minimization, and the optimal value of each industry is determined in the portfolio. According to the results, (MRS-FIEGARCH) model had no superiority in VaR estimation over the other parametric models of the GARCH family. In fact (MS-EGARCH-t) was introduced as the optimal model. Among the designated industries, returns on indices followed regime transitions only in chemical products and investment by showing asymmetric reactions to external shocks. Moreover, the optimal weights were on the rise in the industries where VaR decreased over time, whereas the optimal weight of the portfolio decreased in the industries where VaR increased over time. The higher share of an optimal portfolio belonged to the industries where stock returns had lower rates of VaR. The risk-return-ratio was employed to show that the optimal portfolio with a risk rate was measured by considering the switching regime was superior over the optimal portfolio with a risk rate extracted without considering the switching effects. To create an optimal portfolio, it is then recommended to make investments in the industries characterized by higher stability in prices and lower fluctuations in stock returns in the long run. This approach can be employed to obtain the best results from optimal portfolio preparation in the worst-case scenario of the market fluctuations.


Asgharpour, Hossein; Reza Zadeh, Ali (2015). Optimal Portfolio Preparation through VaR, Applied Theories of Economy, 2 (4), 93-118.
Asgharpour, Hossein; Fallahi, Firouz; Senobar, Naser; Reza Zadeh, Ali (2014). Portfolio Optimization within VaR Framework: Comparative Analysis of MS–GARCH and Bootstrapping, Economic Modeling Research, 17 (3), 87-12.
Asgharpour, Hossein; Rezazadeh, Ali (2015). Determining the optimal stock portfolio using the at-risk value method. Journal of Economic Modeling Research. 2 (4), 118-93. (in Persian)
Asgharpour, Hossein; Fallahi, Firooz; Sanobar, Nasser; Rezazadeh, Ali (2014). Stock portfolio optimization in value at risk framework: Comparison of MS-GARCH and bootstrapping methods. Journal of Economic Modeling Research, 17 (3), 122-87. (in Persian)
Almasi, Mojtaba; Falahati, Ali; Fattahi, Shahram; Rostami, Alireza (2018). Modeling Long-Term Memory and Return Variations in Tehran Stock Exchange and Asymmetric Effects of Oil Market Shocks, Financial Knowledge of Stock Market Analysis, 11 (40), 127-145.
Almasi, Mojtaba; Falahati, Ali; Fattahi, Shahram; Rostami, Alireza (1397). Modeling long-term memory and changes in the returns of the Tehran Stock Exchange and the asymmetric effects of oil market shocks on it. Journal of Financial Knowledge Securities Analysis, 11 (40), 145-127.
Baillie, R.T., Bollerslev, T., Mikkelsen, H.O., 1996. Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 74, 3–30.
Barzegar, Mahdi (2015). A Review of Single-Regime Models in Iran’s Financial Markets and Regime Reactions of Designated Industries, Master’s Thesis in Financial Engineering, Business School of Stevens, US.
Bo, D. (2001). Value at risk. The National University of Singapore, Department of   Mathematical.
cample, R., Huisman, R., Koedijk, K. (2001). Optimal Portfolio in A Value at Risk Framework.  Journal of Banking and Finance 25: 1789-1804.
Jalilian, Omid; Jalilian, Hamid; Ghanbari, Mehrdad (2009). Optimal Portfolio Risk Prediction in Stocks at Companies Listed on Tehran Stock Exchange with no Regard to Investor’s Spirits, Financial Accounting, 2 (2), 123-147.
Zolfaghari, Mahdi; Faghihian, Fatemeh (2018). Extracting and Analyzing Return Risk of Mass Construction Industry and Real Estate (Based on Markov VaR), Urban Management and Economy, 6 (3), 35-53.
Zolfaghari, Mahdi; Sahabi, Bahram (2016). Analyzing Effects of Exchange Rate Fluctuations on Stock Returns in Automotive, Mining, and Cement Industries Based on Markov Regime Transitions, Financial Engineering, and Stock Market Management, 29 (4), 85-106.
Rostami, Mohamad Reza; Naghavi Pour, Maryam; Moghadas Bayat, Maryam (2018). Crude Oil Market Fluctuations Based on Regime Path Adoption Approach, Financial Engineering, and Stock Market Management, 9 (35), 172-196.
Shawalpour, Saeed; Jabar Zadeh, Armin; Khanjarpanah, Hossein (2016). Modeling the Use of VaR in Fluctuation Risk Management for Iran’s Oil Revenue, Iran’s Energy Economy, 5 (19), 113-143.
Faghihian, Fatemeh (2015). Analyzing Regime Transitions in Iran’s Financial Markets in Food Industries, Doctoral Dissertation in Financial Management, University of Izmir, Turkey.
Granger, C.W., Hyung, N., 2004. Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. Journal of Empirical Finance 11 (3), 399–421.
Ho, K.-Y., Shi, Y., Zhang, Z., (2013. How does news sentiment impact asset volatility? evidence from long memory and regime-switching approaches. N. Am. J. Econ. Financ.26, 436–456.
Haas, M., (2009). Value-at-risk via mixture distributions reconsidered. Applied Mathematics and Computation 215 (6), 2103–2119.
Haas, M., Mittnik, S., Paolella, M.S., (2004). A new approach to Markov-switching GARCH models. Journal of Financial Econometrics 2 (4), 493–530.
Keshavarz Hadad, Gholam Reza; Samadi, Baghar (2009). Estimating and Predicting Return Volatility in Tehran Stock Exchange and Comparative Analysis of Accuracies of Methods in VaR Estimation: Use of FIGARCH Models, Economic Research, 44 (1), 193-235.
Keshavarz Hadad, Gholam Reza; Moftakhar Daryayee Nejad, Kobra (2018). Effects of Return Contagion and Volatility On VaR Estimation for Portfolios Consisting of Gold, Foreign Currency, and Stocks, Economic Research, 53 (1), 117-152.
Haas, M., Mittnik, S., Paolella, M. S., 2004. A new approach to Markov-switching GARCH models. J. of Finan. Economics. 2 (4), 493–530.
Klaassen, F., 2002. “Improving GARCH Volatility Forecasts with Regime-Switching GARCH,” Empirical Economics, 27,2002, pp. 363-394.
Marcucci J., 2005. “Forecasting Stock Market Volatility with Regime-Switching GARCH Model,” Working paper, Department of Economics, University of California at San Die ago.
Mahboubi Zadeh, Shaghayegh (2019). Portfolio Optimization through VaR Methods with an Emphasis on Switching, Master’s Thesis, Alzahra University.
Mahdi Zadeh, Saber; Sabet, Parisa (2012). Stock Capital Portfolio Selection of Pension Fund at Oil Company through Markowitz and VaR Approaches, Third Conference on Financial Mathematics and Applications, Semnan University.
Najafi Moghadam, Ali (2016). Optimal Portfolio Selection in VaR Calculation of Investment Funds, Financial Engineering and Stock Securities Management, 8 (31), 237-265.
Gray, S., 1996.  "Modeling the Conditional Distribution of Interest Rates as a Regime Switching Process" Journal of Financial Economics 42, pp. 27-62.
Nikomaram, Hashem; Saeedi, Ali, Anbarestani, Majran (2011). Analysis of Long-Term Memory in Tehran Stock Exchange, 2 (9), 47-63.
Li, J., & Xu, M. (2013). Optimal dynamic portfolio with Mean -CVaR criterion. Risks, 1(3), 119-147.
Nor Azliana Aridi, N., Wen Cheong, Ch., Hooi, T. S.  "An Estimation of Value at Risk using GARCH Models for the Conventional and Islamic Stock Market in Malaysia".
Ranković, V. Drenovak, M. Urosevic, B.  Jelic, R. (2016). Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach. Computers & Operations Research, 72:83-92
Sanzo, S, D, (2018). A Markov Switching Long Memory Model of Crude Oil Price Return Volatility. Journal Of Energy Economics,74:351-359.
Shi, Y., 2015. Can we distinguish regime switching from long memory? A simulation evidence. Applied Economics Letters 22 (4), 318–323.
Yu, X., Sun. H., & Chen, G. (2011). The optimal portfolio model based on Mean-CVaR. Journal of Mathematical Finance, 1, 132-134.
Zolfaghari, M., sahabi, B. (2017). Impact of Foreign Exchange Rate on Oil Companies Risk in Stock Market: A Markov-switching approach. Journal of Computational and Applied Mathematics, 317:274-28.
Zolfaghari, Mehdi, Faghighian, Fatemeh (1397). Extracting and analysis the return on risk of the manufacturing, real estate, and real estate industries (based on the value at risk method based on Markov's approach). Journal of Economics and Urban Management, 6 (3), 53-35. (in presian)
Rostami, Mohammad Reza; Naqvipour, Maryam; Moghaddasbayat, Maryam (1397). A Markov regime-switching model for crude-oil market fluctuations. Journal of Financial Engineering and Securities Management, 9 (35), 196-172. (in Persian)
Zolfaghari, Mehdi; Sahabi, Bahram (2016). The Effect of Exchange Rate Fluctuations on the Stock Return Risk of Mining, Automotive and Cement Index based on the Regime Transmission of Markov. Journal of Financial Engineering and Securities Management, 29 (4), 85-106. (in Persian)
Shavvalpour, Saeed; Jabbarzadeh, Armin; Khanjar Panah, Hossein (2015). Application of Value at Risk in Risk Management of Oil Revenue in Iran. Iranian Journal of Energy Economics, 5 (19), 143-113. (in Persian)
Jalilian, Omid; Jalilian, Hamid; Ghanbari, Mehrdad (2009). forecasting the risk of the optimal portfolio in the stocks of companies listed on the Tehran Stock Exchange. Journal of Financial Accounting, 2 (2), 147-123. (in Persian)
Keshavarz, Gholamreza; Samadi, Baagher (2009). An Appraisal on the Performance of FIGARCH Models in the Estimation of VaR: The Case Study of Tehran Stock Exchange. Journal of Economic Research, 44 (1), 235-193.
Nikomram, Hashem, and Saeedeh, Ali, and Anbarestani, Marjan (2011). Analysis of long-term memory in Tehran Stock Exchange.2 (9), 63-47. (in Persian)
Najafi Moghadam, Ali (2017). Selection of the optimal method in calculating the value at risk of investment fund. Journal of Financial Engineering and Securities Management, 8 (31), 265-237. (in Persian)
Mehdizadeh, Saber; Sabet, Parisa (2012). The choice of the stock portfolio of the company's pension fund using the Markowitz and VaR models. Third Conference of Financial Mathematics and Applications, Semnan University. (in Persian)