Mitigation of risk in a security-trading environment is one of the strategies that every investor would want. Stock prices keep on changing from time to time and it is difficult for participants to predict share price direction. It is therefore appropriate for any trader to use the risk minimization strategies. One of the strategies is to estimate the amount of money a trader is willing to lose in a given period. This project uses the concept of copula to describe the dependency structure of portfolio returns selected from the Nairobi Securities Exchange. The Copula concept works towards modeling the dependency structure of high volatile data by separating the univariate distribution of their respective marginals. Dependencies in a volatile data enables one to assess the relationship that appears in the extreme values of historically sampled data. The study started with selecting an optimal portfolio from the Nairobi Securities Exchange using the Capital Asset and Pricing Model. The chosen optimal portfolio involved companies from different sectors, thus implying minimization of unsystematic risk. The next step involved estimating the systematic risk based on the historical data of the optimal portfolio selected. Different types of copula-based models were fitted then compared to each other to assess the dependencies measures, the goodness of fit of the model, and backtest of the Value-at-Risk. The main findings were that the Tawn type 1 copula was the best copula-based model for modeling the dependence structure of the portfolio returns. Additionally, the backtesting results also show that this model had the highest coverage of the exceedances.
| Published in | International Journal of Statistical Distributions and Applications (Volume 7, Issue 3) |
| DOI | 10.11648/j.ijsd.20210703.11 |
| Page(s) | 72-77 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
Copula, Dependency, GARCH, Value-at-Risk, Volatility, Heteroscedasticity
| [1] | Agarwal, V., Mullally, K. A., & Naik, N. Y. (2015). The economics and finance of hedge funds: A review of the academic literature. Foundations and Trends® in Finance. 10 (1), 1-111. |
| [2] | Aloui, R., Aïssa, M. S., & Nguyen, D. K. (2013). Conditional dependence structure between oil prices and exchange rates: a copula-GARCH approach. Journal of International Money and Finance, 32, 719-738. |
| [3] | Barnes, P. (2016). Stock market efficiency, insider dealing and market abuse. Gower. |
| [4] | Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. Journal of Business & Economic Statistics, 22, 367-381. |
| [5] | Erel, I., Myers, S. C., & Read Jr, J. A. (2015). A theory of risk capital. Journal of Financial Economics, 118 (3), 620-635. |
| [6] | Evans, W. B. (2016). Effects Of Political Risk And Macroeconomic Factors On Stock Market Returns At Nairobi Securities Exchange. Kenyatta University. |
| [7] | Fama, E. F., & French, K. R. (2017). Long-horizon returns. The Review of Asset Pricing Studies. |
| [8] | Genest, C., Rémillard, B., & Beaudoin, D. (2009). GGoodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and economics,, 44 (2), 199-213. |
| [9] | Koizumi, K., Okamoto, N., & Seo, T. (2009). On Jarque-Bera tests for assessing multivariate normality. Journal of Statistics: Advances in Theory and Applications, 1 (2), 207-220. |
| [10] | Kole, E., Koedijk, K., & Verbeek, M. (2007). Selecting copulas for risk management. Journal of Banking & Finance, 31 (8), 2405-2423. |
| [11] | Omari, C. O., Mwita, P. N., & Gichuhi, A. W. (2018). Currency Portfolio Risk Measurement with Generalized Autoregressive Conditional Heteroscedastic-Extreme Value Theory-Copula Model. Journal of Mathematical Finance. |
| [12] | Pries, H. (2016). Market risk calculations in stock-and bond prices: a garch-copula approach. |
| [13] | Rao, C. a. (2012). Handbook of statistics. Elsevier Science \& Technology. |
| [14] | Wali, B., Greene, D. L., Khattak, A. J., & Liu, J. (2018). Analyzing within garage fuel economy gaps to support vehicle purchasing decisions–A copula-based modeling & forecasting approach. Transportation Research Part D: Transport and Environment, 63-186. |
| [15] | Ye, W., Luo, K., & Liu, X. (2017). Time-varying quantile association regression model with applications to financial contagion and VaR. European Journal of Operational Research, 256 (3), 1015-1028. |
APA Style
Maina Stanley Muchiri, Mung’atu Joseph Kyalo, Wanjoya Antony Kibera. (2021). Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange. International Journal of Statistical Distributions and Applications, 7(3), 72-77. https://doi.org/10.11648/j.ijsd.20210703.11
ACS Style
Maina Stanley Muchiri; Mung’atu Joseph Kyalo; Wanjoya Antony Kibera. Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange. Int. J. Stat. Distrib. Appl. 2021, 7(3), 72-77. doi: 10.11648/j.ijsd.20210703.11
AMA Style
Maina Stanley Muchiri, Mung’atu Joseph Kyalo, Wanjoya Antony Kibera. Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange. Int J Stat Distrib Appl. 2021;7(3):72-77. doi: 10.11648/j.ijsd.20210703.11
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Download@article{10.11648/j.ijsd.20210703.11,
author = {Maina Stanley Muchiri and Mung’atu Joseph Kyalo and Wanjoya Antony Kibera},
title = {Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange},
journal = {International Journal of Statistical Distributions and Applications},
volume = {7},
number = {3},
pages = {72-77},
doi = {10.11648/j.ijsd.20210703.11},
url = {https://doi.org/10.11648/j.ijsd.20210703.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20210703.11},
abstract = {Mitigation of risk in a security-trading environment is one of the strategies that every investor would want. Stock prices keep on changing from time to time and it is difficult for participants to predict share price direction. It is therefore appropriate for any trader to use the risk minimization strategies. One of the strategies is to estimate the amount of money a trader is willing to lose in a given period. This project uses the concept of copula to describe the dependency structure of portfolio returns selected from the Nairobi Securities Exchange. The Copula concept works towards modeling the dependency structure of high volatile data by separating the univariate distribution of their respective marginals. Dependencies in a volatile data enables one to assess the relationship that appears in the extreme values of historically sampled data. The study started with selecting an optimal portfolio from the Nairobi Securities Exchange using the Capital Asset and Pricing Model. The chosen optimal portfolio involved companies from different sectors, thus implying minimization of unsystematic risk. The next step involved estimating the systematic risk based on the historical data of the optimal portfolio selected. Different types of copula-based models were fitted then compared to each other to assess the dependencies measures, the goodness of fit of the model, and backtest of the Value-at-Risk. The main findings were that the Tawn type 1 copula was the best copula-based model for modeling the dependence structure of the portfolio returns. Additionally, the backtesting results also show that this model had the highest coverage of the exceedances.},
year = {2021}
}
TY - JOUR T1 - Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange AU - Maina Stanley Muchiri AU - Mung’atu Joseph Kyalo AU - Wanjoya Antony Kibera Y1 - 2021/08/23 PY - 2021 N1 - https://doi.org/10.11648/j.ijsd.20210703.11 DO - 10.11648/j.ijsd.20210703.11 T2 - International Journal of Statistical Distributions and Applications JF - International Journal of Statistical Distributions and Applications JO - International Journal of Statistical Distributions and Applications SP - 72 EP - 77 PB - Science Publishing Group SN - 2472-3509 UR - https://doi.org/10.11648/j.ijsd.20210703.11 AB - Mitigation of risk in a security-trading environment is one of the strategies that every investor would want. Stock prices keep on changing from time to time and it is difficult for participants to predict share price direction. It is therefore appropriate for any trader to use the risk minimization strategies. One of the strategies is to estimate the amount of money a trader is willing to lose in a given period. This project uses the concept of copula to describe the dependency structure of portfolio returns selected from the Nairobi Securities Exchange. The Copula concept works towards modeling the dependency structure of high volatile data by separating the univariate distribution of their respective marginals. Dependencies in a volatile data enables one to assess the relationship that appears in the extreme values of historically sampled data. The study started with selecting an optimal portfolio from the Nairobi Securities Exchange using the Capital Asset and Pricing Model. The chosen optimal portfolio involved companies from different sectors, thus implying minimization of unsystematic risk. The next step involved estimating the systematic risk based on the historical data of the optimal portfolio selected. Different types of copula-based models were fitted then compared to each other to assess the dependencies measures, the goodness of fit of the model, and backtest of the Value-at-Risk. The main findings were that the Tawn type 1 copula was the best copula-based model for modeling the dependence structure of the portfolio returns. Additionally, the backtesting results also show that this model had the highest coverage of the exceedances. VL - 7 IS - 3 ER -
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