Efficiency and Consistency Assessment of Value at Risk Methods for Selected Banks Data

Main Article Content

Yakubu Musa
Iniabasi Emmanuel Etuk
S. U. Gulumbe

Abstract

The study assesses Value at Risk (VaR) methods with respect to their efficiency and consistency in selected banks of the Nigeria Stock Market. The daily data on share prices of each bank was used from 2006 to 2018. The Value at Risk of each bank was estimated and the predictive performance of each method was assessed using the Failure Ratio and the Confidence Interval. The quality of each method was assessed based on the efficiency and consistency of the estimates. The VaR of each bank was estimated using Historical Simulation, Kernel Estimator, Empirical Estimator and Weighted Mean methods. The weighted mean method had the least estimates while Kernel estimator method had the highest estimates. The Failure Ratio and Confidence Interval show that Historical and Empirical methods had the least number of rejections at both confidence levels. The efficiency and consistency of the various methods shows the Historical Simulation and Weighted mean method had the minimum mean square errors (MSE). The Banks A, D and E gives an efficient and consistent result with Historical Simulation while B and C, is more efficient and consistent with weighted mean method.

Keywords:
VaR, weighted mean, stock market, Nigeria.

Article Details

How to Cite
Musa, Y., Etuk, I. E., & Gulumbe, S. U. (2020). Efficiency and Consistency Assessment of Value at Risk Methods for Selected Banks Data. Journal of Advances in Mathematics and Computer Science, 35(2), 1-11. https://doi.org/10.9734/jamcs/2020/v35i230245
Section
Original Research Article

References

Campbell SD. A review of backtesting and backtesting procedures. Journal of Risk. 2007;9(2):1-18.

Dargiri MN, Shamsabadi HA, Thim CK, Rasiah D, Sayedy B. Value at risk and conditional value at risk assessment and accuracy compliance in dynamic of Malaysian industries. Journal of Applied Sciences. 2013;13(7):974-983.

Jadhav D, Ramanathan TV. Parametric and nonparametric estimation of value at risk. Journal of Risk Model Validation. Spring. 2009;3.

Rodrigues P. Backtesting value-at-risk models. School of Economics and Management University of Minho; 2017.

Guharay S, Chang K, Xu J. Robust estimation of value-at-risk through distribution-free and parametric approaches using the joint severity and frequency model: Applications in financial, actuarial and natural calamities domains. Risks. 2017;5:41.

Cerović J, Lipovina-Božović M, Vujošević S. A comparative analysis of value at risk measurement on emerging stock markets: Case of Montenegro. Business Systems Research. 2015;6(1):36-55.

Vladimir O, Sergey E, Oksana P, Gennady P. Extreme value theory and peaks over threshold model in the Russian stock market. Journal of Siberian Federal University. Engineering & Technologies. 2012;5:111-121.

Ringqvist A. Value at risk on the Swedish stock market. Department of Statistics. Uppsata University; 2014.

Etuk IE, Gulumbe SU, Musa Y. Evaluation of value at risk and expected shortfall models with fat tail data. Nigeria Statistical Association (NSA) Annual Conference; 2018.

Etuk IE, Yakubu M, Gulumbe SU. Estimating and predicting value at risk in selected banks of Nigeria stock market. International Journal of Statistics and Application. 2019;9(4):117-121.

Chen S, Tang Y. Nonparametric inference of value-at-risk for dependent financial returns. Journal of Financial Econometrics. 2005;3(2):227–255.

Van der Vaart AW. Asymptotic statistics. Cambridge Series in Statistical and Probabilistic Mathematics, 3. Cambridge University Press, Cambridge; 1998.

Daníelsson J. Financial risk forecasting: The theory and practice of forecasting market risk, with implementation in R and MATLAB. Chichester: John Wiley; 2011.

Chen Q, Chen R. Method of value at risk and empirical research for Shanghai stock market. Procedia Computer Science. 2013;17:671-677.