Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange
Science Journal of Applied Mathematics and Statistics
Volume 4, Issue 5, October 2016, Pages: 242-248
Received: Sep. 9, 2016;
Accepted: Sep. 21, 2016;
Published: Oct. 9, 2016
Views 3626 Downloads 129
Kinyua Mark Njega, Applied Statistics, Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Joseph Kyalo Mung’atu, Statistics, Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Quantile regression provides a method of estimating quantiles from a conditional distribution density. It is achieves this by minimizing asymmetrically weighted sum of absolute errors thus partitioning the conditional distribution into quantiles. Lower conditional quantiles are of interest in estimation of Value-at-Risk because they indicate downward movement of financial returns. Current risk measurement methods do not effectively estimate the VaR since they make assumptions in the distribution tails. Financial data is sampled frequently leading to a heavier tailed distribution compared to a normal and student t distribution. A remedy to this is to use a method that does not make assumptions in the tail distribution of financial returns. Little research has been done on the usage of quantile regression in the estimation of portfolio risk in the Nairobi Securities Exchange. The main aim of this study was to model the portfolio risk as a lower conditional quantile, compare the performance of this model to the existing risk measurement methods and to predict the Value-at-Risk. This study presents summary of key findings and conclusion drawn from the study. From the fitted conditional quantile GARCH model 62.4% of VaR can be explained by past standard deviation and absolute residual of NSE 20 share index optimal portfolio returns. The fitted model had less proportion of failure of 7.65% compared to commonly used VaR models.
Kinyua Mark Njega,
Joseph Kyalo Mung’atu,
Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange, Science Journal of Applied Mathematics and Statistics.
Vol. 4, No. 5,
2016, pp. 242-248.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Bassett, G. W., R. Koenker and G. Kordas (2004), ‘Pessimistic portfolio allocation and choquet expected utility’, Journal of financial econometrics 2(4), 477–492.
Bollerslev, T. (1986), ‘Generalized autoregressive conditional heteroskedasticity’, Journal of econometrics 31(3), 307–327.
Chen, X. a. (2009). Copula-based nonlinear quantileautoregression. The Econometrics Journal, 12, S50--S67.
Christofferssen, P. and P. Pelletier (2004), ‘Backtesting value-at-risk: A duration-based approach’, Journal of Empirical Finance 2, 84–108.
Engle, R. F. and S. Manganelli (2004), ‘Caviar: Conditional autoregressive value at risk by regression quantiles’, Journal of Business & Economic Statistics 22(4), 367–381.
Fischer, D.E. and R. J. Jordan (2003), Security Analysis and Portfolio Management,New Delphi, Prentice Hall of India Private Limited.
Grinblatt, Mark and Matti Keloharju (2001), ‘What makes investors trade?’, The Journal of Finance 56(2), 589–616.
Hsu, Ya-Hui (2010), Applications of quantile regression to estimation and detection of some tail characteristics, PhD thesis, University of Illinois at Urbana-Champaign.
Koenker, R. W. and G. Bassett (1978), ‘Regression quantiles’, Econometrica: journal of the Econometric Society 46, 33–50.
Kraus, D. and C. Czado (2015), ‘D-vine copula based quantile regression’, arXiv preprint arXiv:1510.04161.
Machuke, G., P. N. Mwita and J. M. Kihoro (2014), ‘Measuring financial risk in stock returns: A case study of nairobi securities exchange’, International Journal of Sc 3(4).
Kraus, D. a. (2015). D-vine copula based quantile regression. arXiv preprint arXiv:1510.04161.
Kupiec, P., "Techniques for Verifying the Accuracy of Risk Management Models", Journal of Derivatives 3 (1995), pp. 72-84.
Nieppola, O. (2009), ‘Backtesting value-at-risk models’.
R Core Team (2015), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. URL: https://www.R-project.org/.
Rao, CR. and Tata S. R. (2012), Handbook of statistics Time Series Analysis: Methods and Applications, Elsevier Science & Technology, http://elsevier.com/locate/permissions.
Rossi, G. and A. Harvey (2009), ‘Quantiles, expectiles and splines’, Journal of Econometrics 152(2), 179–185.
Taylor, S. (2007), Modelling financial time series, World Scientific Publishing.
Xiao, Z. and R. Koenker (2009), ‘Conditional quantile estimation and inference for garch models’, JASA 104(485), 371–383. URL: http://fmwww.bc.edu/EC-P/wp725.pdf.