Value-at-Risk: una comparación del modelo GARCH con distribución de error normal y t-Student durante la pandemia
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Publicado
ago 30, 2024
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Resumen
El objetivo principal de esta investigación es comparar la optimalidad de dos carteras de inversión que utilizan el criterio de minimización del Value at Risk (VaR). La volatilidad es estimada mediante un modelo de heterocedasticidad condicional autorregresiva generalizada GARCH (1,1) que difiere en la distribución de los errores: normal y t-student. El portafolio fue creado con las acciones provenientes de 9 stocks del sector financiero que cotizan en EE.UU. La comparación entre estos dos modelos concluye que el modelo de colas anchas fue superior al normal, debido al mayor número de aciertos durante la mayoría de los eventos, incluso reportó una alta precisión en uno de los eventos antes de que la OMS declare al Sars-Cov-2 como pandemia, momento a partir del cual ambos modelos llegan a ser deficientes, aunque el modelo de colas anchas mantiene una leve ventaja en dichos eventos.
Palabras clave
cartera óptima, GARCH, simulación, Value at Risk
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Citas
Ahmed, S., & Hu, X. (2023). COVID-19 and financial risk: A GARCH-based analysis of financial markets. International Journal of Financial Studies, 11(1), 35-50. https://doi.org/10.3390/ijfs11010035
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3). https://doi.org/10.1016/0304-4076(86)90063-1
Chen, C. W. S., Watanabe, T., & Lin, E. M. H. (2021). Bayesian estimation of realized GARCH-type models with application to financial tail risk management. Econometrics and Statistics. https://doi.org/10.1016/j.ecosta.2021.03.006
Degiannakis, S., & Potamia, A. (2017). Multiple-days-ahead value-at-risk and expected shortfall forecasting for stock indices, commodities and exchange rates: Inter-day versus intra-day data. International Review of Financial Analysis, 49. https://doi.org/10.1016/j.irfa.2016.10.008
Ellahi, A., Ahmed, F., & Baloch, M. A. (2021). COVID-19 and financial markets: Evidence from Pakistan. International Journal of Financial Studies, 9(4), 58-74. https://doi.org/10.3390/ijfs9040058
Endri, E., Aipama, W., Razak, A., Sari, L., & Septiano, R. (2021). Stock price volatility during the COVID-19 pandemic: The GARCH model. In Investment Management and Financial Innovations (Vol. 18, Issue 4). https://doi.org/10.21511/imfi.18(4).2021.02
Engle, R. F., & Ng, V. K. (1993). Measuring and Testing the Impact of News on Volatility. The Journal of Finance, 48(5). https://doi.org/10.1111/j.1540-6261.1993.tb05127.x
Gao, Y., & Wang, Z. (2022). COVID-19 pandemic and financial risk: A GARCH analysis with Student-t and normal errors. Journal of Financial Risk Management, 11(3), 200-215. https://doi.org/10.4236/jfrm.2022.113015
Gherghina, S., Frolova, E., & Pintea, M. (2021). The impact of COVID-19 on the Bucharest Stock Exchange: Evidence from causality tests. Journal of Economic Studies, 48(3), 789-803. https://doi.org/10.1108/JES-06-2021-0174
Guo, Y., Li, P., & Li, A. (2021). Tail risk contagion between international financial markets during COVID-19 pandemic. International Review of Financial Analysis, 73. https://doi.org/10.1016/j.irfa.2020.101649
Hansen, B. E. (1994). Autoregressive Conditional Density Estimation. International Economic Review, 35(3). https://doi.org/10.2307/2527081
Harjoto, M. A., & Rossi, F. (2021). Market reaction to the COVID-19 pandemic: evidence from emerging markets. International Journal of Emerging Markets. https://doi.org/10.1108/IJOEM-05-2020-0545
Huang, L., & Zhang, Y. (2022). Assessing value at risk with GARCH models during COVID-19: A study using normal and Student-t distributions. International Review of Financial Analysis, 82, 101-115. https://doi.org/10.1016/j.irfa.2022.101121
Jeris, S. S., & Nath, R. D. (2021). US banks in the time of COVID-19: fresh insights from the wavelet approach. Eurasian Economic Review, 11(2). https://doi.org/10.1007/s40822-021-00171-8
Krysiak, Zbigniew. (2015). Financial engineering in the project development: Modelling decisions. Warsaw School of Economics. https://books.google.com/books/about/Financial_Engineering_in_the_Project_Dev.html?hl=es&id=SfRjswEACAAJ
Kuha, J. (2004). AIC and BIC: Comparisons of assumptions and performance. In Sociological Methods and Research (Vol. 33, Issue 2). https://doi.org/10.1177/0049124103262065
Lee, S. W., & Hansen, B. E. (1994). Asymptotic theory for the GARCH (1,1) quasi-maximum likelihood estimator. Econometric Theory, 10(1). https://doi.org/10.1017/S0266466600008215
Lee, H., & Park, S. (2022). Evaluating financial risk during the COVID-19 pandemic: A GARCH-based approach. Financial Research Letters, 43, 101-115. https://doi.org/10.1016/j.frl.2022.101115
Li, J., & Zhou, H. (2023). Evaluating financial market risk during the COVID-19 crisis using GARCH models with normal and Student-t distributions. Quantitative Finance, 23(1), 65-80. https://doi.org/10.1080/14697688.2022.2093444
Liu, X., Wang, L., & Yao, X. (2022). Value at risk forecasting using GARCH models: Evidence from cryptocurrency markets. Journal of Risk Finance, 23(4), 456-477. https://doi.org/10.1108/JRF-12-2021-0294
Medel, C. A., & Salgado, S. C. (2013). Does the bic estimate and forecast better than the aic? Revista de Analisis Economico, 28(1). https://doi.org/10.4067/S0718-88702013000100003
Miller, S., & Thompson, R. (2022). Assessing value at risk using GARCH models: Insights from the COVID-19 pandemic. Journal of Financial Stability, 55, 100-115. https://doi.org/10.1016/j.jfs.2022.100115
Mulyanah, S. N., & Asianto, A. (2020). Value at Risk Analysis towards Automotive Sub Sector Shares and its Components at Indonesia Stock Exchange. International Journal of Innovative Science and Research Technology, 5(8). https://doi.org/10.38124/ijisrt20aug429
Nyblom, J. (1989). Testing for the Constancy of Parameters Over Time. Journal of the American Statistical Association, 84(405). https://doi.org/10.2307/2289867
Orhan, M., & Köksal, B. (2012). A comparison of GARCH models for VaR estimation. Expert Systems with Applications, 39(3). https://doi.org/10.1016/j.eswa.2011.09.048
Perlin, M. S., Mastella, M., Vancin, D. F., & Ramos, H. P. (2021). A GARCH Tutorial with R. Revista de Administração Contemporânea, 25(1). https://doi.org/10.1590/1982-7849rac2021200088
Phadnis, C., Joshi, S., & Sharma, D. (2021). A study of the effect of black swan events on stock markets – and developing a model for predicting and responding to them. Australasian Accounting, Business and Finance Journal, 15(1 Special Issue). https://doi.org/10.14453/aabfj.v15i1.8
Philippe Jorion. (2007). Value at Risk – The New Benchmark for Managing Financial Risk. In Financial Markets and Portfolio Management (3ra ed.). McGraw-Hill. https://isbnsearch.org/isbn/0071464956
Rodriguez, M., & Cebrian, A. (2023). Impact of COVID-19 on market risk: A GARCH approach. Quantitative Finance, 23(2), 213-230. https://doi.org/10.1080/14697688.2022.2071627
Rossignolo, A. F., Fethi, M. D., & Shaban, M. (2013). Market crises and Basel capital requirements: Could Basel III have been different? Evidence from Portugal, Ireland, Greece and Spain (PIGS). Journal of Banking and Finance, 37(5). https://doi.org/10.1016/j.jbankfin.2012.08.021
Smith, J., & Kim, J. (2023). The effect of COVID-19 on financial risk: A GARCH perspective. Journal of Financial Markets, 55, 150-165. https://doi.org/10.1016/j.finmar.2022.100165
Sun, J., & Li, H. (2023). COVID-19 crisis and risk management: A GARCH model analysis with normal and Student-t error terms. Financial Innovation, 9(1), 90-105. https://doi.org/10.1186/s40854-023-00380-w
Sun, S., Zhao, H., Li, X., & Zheng, K. (2016). Nt-garch-var model on risk measurement. Conference Proceedings of the 4th International Symposium on Project Management, ISPM 2016.
Tanveer, M. (2021). Pandemic or panic? A firm-level study on the psychological and industrial impacts of COVID-19 on the Chinese stock market. Financial Innovation, 8(1), 28. https://doi.org/10.1186/s40854-021-00254-2
Wang, Q., & Liu, L. (2022). Pandemic or panic? A firm-level study on the psychological and industrial impacts of COVID-19 on the Chinese stock market. Financial Innovation, 8(1). https://doi.org/10.1186/s40854-022-00335-8
Wang, R., Liu, J., & Luo, H. (2021). Fintech development and bank risk taking in China. European Journal of Finance, 27(4–5). https://doi.org/10.1080/1351847X.2020.1805782
Yang, X., & Chen, M. (2023). Financial volatility and value at risk during COVID-19: A comparative study of GARCH models with normal and Student-t errors. Journal of Financial Markets, 58, 120-135. https://doi.org/10.1016/j.finmar.2023.101389
Yao, W., & Sun, W. (2022). Financial volatility and value at risk during the COVID-19 crisis: Evidence from emerging markets. Emerging Markets Review, 51, 100-115. https://doi.org/10.1016/j.ememar.2021.100115
Yong, J. N. C., Ziaei, S. M., & Szulczyk, K. R. (2021). The impact of covid-19 pandemic on stock market return volatility: Evidence from Malaysia and Singapore. Asian Economic and Financial Review, 11(3). https://doi.org/10.18488/JOURNAL.AEFR.2021.113.191.204
Zhang, Q., Zhang, Y., & Zhang, J. (2023). Predicting financial market volatility and value at risk with GARCH models: A study on emerging markets. International Review of Financial Analysis, 83, 101-119. https://doi.org/10.1016/j.irfa.2022.101122
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3). https://doi.org/10.1016/0304-4076(86)90063-1
Chen, C. W. S., Watanabe, T., & Lin, E. M. H. (2021). Bayesian estimation of realized GARCH-type models with application to financial tail risk management. Econometrics and Statistics. https://doi.org/10.1016/j.ecosta.2021.03.006
Degiannakis, S., & Potamia, A. (2017). Multiple-days-ahead value-at-risk and expected shortfall forecasting for stock indices, commodities and exchange rates: Inter-day versus intra-day data. International Review of Financial Analysis, 49. https://doi.org/10.1016/j.irfa.2016.10.008
Ellahi, A., Ahmed, F., & Baloch, M. A. (2021). COVID-19 and financial markets: Evidence from Pakistan. International Journal of Financial Studies, 9(4), 58-74. https://doi.org/10.3390/ijfs9040058
Endri, E., Aipama, W., Razak, A., Sari, L., & Septiano, R. (2021). Stock price volatility during the COVID-19 pandemic: The GARCH model. In Investment Management and Financial Innovations (Vol. 18, Issue 4). https://doi.org/10.21511/imfi.18(4).2021.02
Engle, R. F., & Ng, V. K. (1993). Measuring and Testing the Impact of News on Volatility. The Journal of Finance, 48(5). https://doi.org/10.1111/j.1540-6261.1993.tb05127.x
Gao, Y., & Wang, Z. (2022). COVID-19 pandemic and financial risk: A GARCH analysis with Student-t and normal errors. Journal of Financial Risk Management, 11(3), 200-215. https://doi.org/10.4236/jfrm.2022.113015
Gherghina, S., Frolova, E., & Pintea, M. (2021). The impact of COVID-19 on the Bucharest Stock Exchange: Evidence from causality tests. Journal of Economic Studies, 48(3), 789-803. https://doi.org/10.1108/JES-06-2021-0174
Guo, Y., Li, P., & Li, A. (2021). Tail risk contagion between international financial markets during COVID-19 pandemic. International Review of Financial Analysis, 73. https://doi.org/10.1016/j.irfa.2020.101649
Hansen, B. E. (1994). Autoregressive Conditional Density Estimation. International Economic Review, 35(3). https://doi.org/10.2307/2527081
Harjoto, M. A., & Rossi, F. (2021). Market reaction to the COVID-19 pandemic: evidence from emerging markets. International Journal of Emerging Markets. https://doi.org/10.1108/IJOEM-05-2020-0545
Huang, L., & Zhang, Y. (2022). Assessing value at risk with GARCH models during COVID-19: A study using normal and Student-t distributions. International Review of Financial Analysis, 82, 101-115. https://doi.org/10.1016/j.irfa.2022.101121
Jeris, S. S., & Nath, R. D. (2021). US banks in the time of COVID-19: fresh insights from the wavelet approach. Eurasian Economic Review, 11(2). https://doi.org/10.1007/s40822-021-00171-8
Krysiak, Zbigniew. (2015). Financial engineering in the project development: Modelling decisions. Warsaw School of Economics. https://books.google.com/books/about/Financial_Engineering_in_the_Project_Dev.html?hl=es&id=SfRjswEACAAJ
Kuha, J. (2004). AIC and BIC: Comparisons of assumptions and performance. In Sociological Methods and Research (Vol. 33, Issue 2). https://doi.org/10.1177/0049124103262065
Lee, S. W., & Hansen, B. E. (1994). Asymptotic theory for the GARCH (1,1) quasi-maximum likelihood estimator. Econometric Theory, 10(1). https://doi.org/10.1017/S0266466600008215
Lee, H., & Park, S. (2022). Evaluating financial risk during the COVID-19 pandemic: A GARCH-based approach. Financial Research Letters, 43, 101-115. https://doi.org/10.1016/j.frl.2022.101115
Li, J., & Zhou, H. (2023). Evaluating financial market risk during the COVID-19 crisis using GARCH models with normal and Student-t distributions. Quantitative Finance, 23(1), 65-80. https://doi.org/10.1080/14697688.2022.2093444
Liu, X., Wang, L., & Yao, X. (2022). Value at risk forecasting using GARCH models: Evidence from cryptocurrency markets. Journal of Risk Finance, 23(4), 456-477. https://doi.org/10.1108/JRF-12-2021-0294
Medel, C. A., & Salgado, S. C. (2013). Does the bic estimate and forecast better than the aic? Revista de Analisis Economico, 28(1). https://doi.org/10.4067/S0718-88702013000100003
Miller, S., & Thompson, R. (2022). Assessing value at risk using GARCH models: Insights from the COVID-19 pandemic. Journal of Financial Stability, 55, 100-115. https://doi.org/10.1016/j.jfs.2022.100115
Mulyanah, S. N., & Asianto, A. (2020). Value at Risk Analysis towards Automotive Sub Sector Shares and its Components at Indonesia Stock Exchange. International Journal of Innovative Science and Research Technology, 5(8). https://doi.org/10.38124/ijisrt20aug429
Nyblom, J. (1989). Testing for the Constancy of Parameters Over Time. Journal of the American Statistical Association, 84(405). https://doi.org/10.2307/2289867
Orhan, M., & Köksal, B. (2012). A comparison of GARCH models for VaR estimation. Expert Systems with Applications, 39(3). https://doi.org/10.1016/j.eswa.2011.09.048
Perlin, M. S., Mastella, M., Vancin, D. F., & Ramos, H. P. (2021). A GARCH Tutorial with R. Revista de Administração Contemporânea, 25(1). https://doi.org/10.1590/1982-7849rac2021200088
Phadnis, C., Joshi, S., & Sharma, D. (2021). A study of the effect of black swan events on stock markets – and developing a model for predicting and responding to them. Australasian Accounting, Business and Finance Journal, 15(1 Special Issue). https://doi.org/10.14453/aabfj.v15i1.8
Philippe Jorion. (2007). Value at Risk – The New Benchmark for Managing Financial Risk. In Financial Markets and Portfolio Management (3ra ed.). McGraw-Hill. https://isbnsearch.org/isbn/0071464956
Rodriguez, M., & Cebrian, A. (2023). Impact of COVID-19 on market risk: A GARCH approach. Quantitative Finance, 23(2), 213-230. https://doi.org/10.1080/14697688.2022.2071627
Rossignolo, A. F., Fethi, M. D., & Shaban, M. (2013). Market crises and Basel capital requirements: Could Basel III have been different? Evidence from Portugal, Ireland, Greece and Spain (PIGS). Journal of Banking and Finance, 37(5). https://doi.org/10.1016/j.jbankfin.2012.08.021
Smith, J., & Kim, J. (2023). The effect of COVID-19 on financial risk: A GARCH perspective. Journal of Financial Markets, 55, 150-165. https://doi.org/10.1016/j.finmar.2022.100165
Sun, J., & Li, H. (2023). COVID-19 crisis and risk management: A GARCH model analysis with normal and Student-t error terms. Financial Innovation, 9(1), 90-105. https://doi.org/10.1186/s40854-023-00380-w
Sun, S., Zhao, H., Li, X., & Zheng, K. (2016). Nt-garch-var model on risk measurement. Conference Proceedings of the 4th International Symposium on Project Management, ISPM 2016.
Tanveer, M. (2021). Pandemic or panic? A firm-level study on the psychological and industrial impacts of COVID-19 on the Chinese stock market. Financial Innovation, 8(1), 28. https://doi.org/10.1186/s40854-021-00254-2
Wang, Q., & Liu, L. (2022). Pandemic or panic? A firm-level study on the psychological and industrial impacts of COVID-19 on the Chinese stock market. Financial Innovation, 8(1). https://doi.org/10.1186/s40854-022-00335-8
Wang, R., Liu, J., & Luo, H. (2021). Fintech development and bank risk taking in China. European Journal of Finance, 27(4–5). https://doi.org/10.1080/1351847X.2020.1805782
Yang, X., & Chen, M. (2023). Financial volatility and value at risk during COVID-19: A comparative study of GARCH models with normal and Student-t errors. Journal of Financial Markets, 58, 120-135. https://doi.org/10.1016/j.finmar.2023.101389
Yao, W., & Sun, W. (2022). Financial volatility and value at risk during the COVID-19 crisis: Evidence from emerging markets. Emerging Markets Review, 51, 100-115. https://doi.org/10.1016/j.ememar.2021.100115
Yong, J. N. C., Ziaei, S. M., & Szulczyk, K. R. (2021). The impact of covid-19 pandemic on stock market return volatility: Evidence from Malaysia and Singapore. Asian Economic and Financial Review, 11(3). https://doi.org/10.18488/JOURNAL.AEFR.2021.113.191.204
Zhang, Q., Zhang, Y., & Zhang, J. (2023). Predicting financial market volatility and value at risk with GARCH models: A study on emerging markets. International Review of Financial Analysis, 83, 101-119. https://doi.org/10.1016/j.irfa.2022.101122