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.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5) |
| DOI | 10.11648/j.sjams.20160405.18 |
| Page(s) | 242-248 |
| 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), 2016. Published by Science Publishing Group |
Quantile Regression, GARCH, Value-at-Risk
| [1] | Bassett, G. W., R. Koenker and G. Kordas (2004), ‘Pessimistic portfolio allocation and choquet expected utility’, Journal of financial econometrics 2(4), 477–492. |
| [2] | Bollerslev, T. (1986), ‘Generalized autoregressive conditional heteroskedasticity’, Journal of econometrics 31(3), 307–327. |
| [3] | Chen, X. a. (2009). Copula-based nonlinear quantileautoregression. The Econometrics Journal, 12, S50--S67. |
| [4] | Christofferssen, P. and P. Pelletier (2004), ‘Backtesting value-at-risk: A duration-based approach’, Journal of Empirical Finance 2, 84–108. |
| [5] | 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. |
| [6] | Fischer, D.E. and R. J. Jordan (2003), Security Analysis and Portfolio Management,New Delphi, Prentice Hall of India Private Limited. |
| [7] | Grinblatt, Mark and Matti Keloharju (2001), ‘What makes investors trade?’, The Journal of Finance 56(2), 589–616. |
| [8] | Hsu, Ya-Hui (2010), Applications of quantile regression to estimation and detection of some tail characteristics, PhD thesis, University of Illinois at Urbana-Champaign. |
| [9] | Koenker, R. W. and G. Bassett (1978), ‘Regression quantiles’, Econometrica: journal of the Econometric Society 46, 33–50. |
| [10] | Kraus, D. and C. Czado (2015), ‘D-vine copula based quantile regression’, arXiv preprint arXiv:1510.04161. |
| [11] | 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). |
| [12] | Kraus, D. a. (2015). D-vine copula based quantile regression. arXiv preprint arXiv:1510.04161. |
| [13] | Kupiec, P., "Techniques for Verifying the Accuracy of Risk Management Models", Journal of Derivatives 3 (1995), pp. 72-84. |
| [14] | Nieppola, O. (2009), ‘Backtesting value-at-risk models’. |
| [15] | 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/. |
| [16] | Rao, CR. and Tata S. R. (2012), Handbook of statistics Time Series Analysis: Methods and Applications, Elsevier Science & Technology, http://elsevier.com/locate/permissions. |
| [17] | Rossi, G. and A. Harvey (2009), ‘Quantiles, expectiles and splines’, Journal of Econometrics 152(2), 179–185. |
| [18] | Taylor, S. (2007), Modelling financial time series, World Scientific Publishing. |
| [19] | 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. |
APA Style
Kinyua Mark Njega, Joseph Kyalo Mung’atu. (2016). Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange. Science Journal of Applied Mathematics and Statistics, 4(5), 242-248. https://doi.org/10.11648/j.sjams.20160405.18
ACS Style
Kinyua Mark Njega; Joseph Kyalo Mung’atu. Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange. Sci. J. Appl. Math. Stat. 2016, 4(5), 242-248. doi: 10.11648/j.sjams.20160405.18
AMA Style
Kinyua Mark Njega, Joseph Kyalo Mung’atu. Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange. Sci J Appl Math Stat. 2016;4(5):242-248. doi: 10.11648/j.sjams.20160405.18
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.sjams.20160405.18,
author = {Kinyua Mark Njega and Joseph Kyalo Mung’atu},
title = {Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {4},
number = {5},
pages = {242-248},
doi = {10.11648/j.sjams.20160405.18},
url = {https://doi.org/10.11648/j.sjams.20160405.18},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160405.18},
abstract = {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.},
year = {2016}
}
TY - JOUR T1 - Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange AU - Kinyua Mark Njega AU - Joseph Kyalo Mung’atu Y1 - 2016/10/09 PY - 2016 N1 - https://doi.org/10.11648/j.sjams.20160405.18 DO - 10.11648/j.sjams.20160405.18 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 242 EP - 248 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20160405.18 AB - 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. VL - 4 IS - 5 ER -
Information
Email: