Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange

Maina Stanley Muchiri; Mung’atu Joseph Kyalo; Wanjoya Antony Kibera

doi:doi:10.11648/j.ijsd.20210703.11

| Peer-Reviewed

Copula Models for Equity Portfolio Risk Estimation: A Case Study of Nairobi Securities Exchange

Maina Stanley Muchiri, Mung’atu Joseph Kyalo, Wanjoya Antony Kibera

Published in International Journal of Statistical Distributions and Applications (Volume 7, Issue 3)

Received: 31 July 2021 Accepted: 12 August 2021 Published: 23 August 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

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), 2024. Published by Science Publishing Group

Keywords

Copula, Dependency, GARCH, Value-at-Risk, Volatility, Heteroscedasticity

References

[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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | 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}
}

Copy | Download

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 -

Copy | Download

Author Information

Maina Stanley Muchiri

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mung’atu Joseph Kyalo

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Wanjoya Antony Kibera

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | 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}
}

Copy | Download