American Journal of Theoretical and Applied Statistics

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Application of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study

Received: 28 October 2015    Accepted: 06 November 2015    Published: 22 May 2017
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Abstract

Value at Risk (VaR) became the industry accepted measure for risk by financial institutions and their regulators after the Basel I Accords agreement of 1996. As a result, many methodologies of estimating VaR models used to carry out risk management in finance have been developed. Engle and Manganelli (2004) developed the Conditional Autoregressive Value at Risk (CAViaR) which is a quantile that focuses on estimating and measuring the lower tail risk. The CAViaR quantile measures the quantile directly in an autoregressive framework and applies the quantile regression method to estimate the CAViaR parameters. This research applied the asymmetric CAViaR, symmetric CAViaR and Indirect GARCH (1, 1) specifications to KQ, EABL and KCB stock returns and performed a set of in sample and out of sample tests to determine the relative efficacy of the three different CAViaR specifications. It was found that the asymmetric CAViaR slope specification works well for the Kenyan stock market and is best suited to estimating VaR. Further, more research needs to be carried out to develop e a satisfactory VaR estimation model.

DOI 10.11648/j.ajtas.20170603.13
Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 3, May 2017)
Page(s) 150-155
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

VaR, Asymmetric CAViaR, Symmetric CAViaR, Indirect GARCH (1, 1) CAViaR

References
[1] Allen, D., Singh, A., & Powell, R. “A gourmet’s delight: Caviar and the Australian stock market”. Applied Economics Letters, 19 (15), pp1493–1498, 2012.
[2] Chen, C. W., Gerlach, R., Hwang, B. B., and McAleer, M. “Forecasting value at risk using nonlinear regression quantiles and the intra-day range. International Journal of Forecasting”, 28 (3), pp557 – 574, 2012.
[3] Christoffersen, P. F. “historical simulation, value-at-risk, and expected shortfall”. (Second Edition ed., pp. 21 - 38), 2012. San Diego: Academic Press.
[4] Engle, R., and Manganelli, S. “Caviar: Conditional autoregressive value at risk by regression quantiles”, Journal of Business and economic statistics, 2004.
[5] Gourieroux, C., & Jasiak, J. “Chapter 10 - value at risk” (Vol. 1; Y. A.-S. P. HANSEN, Ed.). San Diego: North-Holland, 2010.
[6] Huang, D., Yu, B., Fabozzi, F. J., & Fukushima, M. “Caviar-based forecast for oil price risk. Energy Economics”, 31 (4), pp511 – 518, 2009.
[7] Koenker, R., & Bassett, G., Jr. “Regression quantiles.” Econometrica: journal of the Econometric Society, pp33–50, 1978.
[8] Taylor, J. W., Generating volatility forecasts from value at risk estimates.Management Science, 51 (5), pp.712–725, 2005.
[9] Thupayagale, P. “Evaluation of garch-based models in value-at-risk estimation: Evidence from emerging equity markets”. Investment Analysts Journal, pp. 13–29, 2010.
[10] Wang, D. L, Huixia Judy “Estimation of high conditional quantiles for heavy-tailed distributions”, 2012.
[11] White, H., Kim, T.-H., & Manganelli, S. “Var for var: measuring systemic risk using multivariate regression quantiles”, 2010.
Author Information
  • Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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

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

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    Winnie Mbusiro Chacha, P. Mwita, B. Muema. (2017). Application of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study. American Journal of Theoretical and Applied Statistics, 6(3), 150-155. https://doi.org/10.11648/j.ajtas.20170603.13

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    Winnie Mbusiro Chacha; P. Mwita; B. Muema. Application of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study. Am. J. Theor. Appl. Stat. 2017, 6(3), 150-155. doi: 10.11648/j.ajtas.20170603.13

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    AMA Style

    Winnie Mbusiro Chacha, P. Mwita, B. Muema. Application of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study. Am J Theor Appl Stat. 2017;6(3):150-155. doi: 10.11648/j.ajtas.20170603.13

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  • @article{10.11648/j.ajtas.20170603.13,
      author = {Winnie Mbusiro Chacha and P. Mwita and B. Muema},
      title = {Application of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {3},
      pages = {150-155},
      doi = {10.11648/j.ajtas.20170603.13},
      url = {https://doi.org/10.11648/j.ajtas.20170603.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20170603.13},
      abstract = {Value at Risk (VaR) became the industry accepted measure for risk by financial institutions and their regulators after the Basel I Accords agreement of 1996. As a result, many methodologies of estimating VaR models used to carry out risk management in finance have been developed. Engle and Manganelli (2004) developed the Conditional Autoregressive Value at Risk (CAViaR) which is a quantile that focuses on estimating and measuring the lower tail risk. The CAViaR quantile measures the quantile directly in an autoregressive framework and applies the quantile regression method to estimate the CAViaR parameters. This research applied the asymmetric CAViaR, symmetric CAViaR and Indirect GARCH (1, 1) specifications to KQ, EABL and KCB stock returns and performed a set of in sample and out of sample tests to determine the relative efficacy of the three different CAViaR specifications. It was found that the asymmetric CAViaR slope specification works well for the Kenyan stock market and is best suited to estimating VaR. Further, more research needs to be carried out to develop e a satisfactory VaR estimation model.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Application of Conditional Autoregressive Value at Risk Model to Kenyan Stocks: A Comparative Study
    AU  - Winnie Mbusiro Chacha
    AU  - P. Mwita
    AU  - B. Muema
    Y1  - 2017/05/22
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    DO  - 10.11648/j.ajtas.20170603.13
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    EP  - 155
    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ajtas.20170603.13
    AB  - Value at Risk (VaR) became the industry accepted measure for risk by financial institutions and their regulators after the Basel I Accords agreement of 1996. As a result, many methodologies of estimating VaR models used to carry out risk management in finance have been developed. Engle and Manganelli (2004) developed the Conditional Autoregressive Value at Risk (CAViaR) which is a quantile that focuses on estimating and measuring the lower tail risk. The CAViaR quantile measures the quantile directly in an autoregressive framework and applies the quantile regression method to estimate the CAViaR parameters. This research applied the asymmetric CAViaR, symmetric CAViaR and Indirect GARCH (1, 1) specifications to KQ, EABL and KCB stock returns and performed a set of in sample and out of sample tests to determine the relative efficacy of the three different CAViaR specifications. It was found that the asymmetric CAViaR slope specification works well for the Kenyan stock market and is best suited to estimating VaR. Further, more research needs to be carried out to develop e a satisfactory VaR estimation model.
    VL  - 6
    IS  - 3
    ER  - 

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