Some Stylized Facts of Short-Term Stock Prices of Selected Nigerian Banks — Oak Academic Publishing
Research ArticleOpen AccessGoogle Scholar indexed
Some Stylized Facts of Short-Term Stock Prices of Selected Nigerian Banks
Statistics, Information Modelling, and Financial Mathematics Research Group, Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield, United Kingdom
,
Statistics, Information Modelling, and Financial Mathematics Research Group, Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield, United Kingdom
1 Statistics, Information Modelling, and Financial Mathematics Research Group, Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield, United Kingdom
2 Statistics, Information Modelling, and Financial Mathematics Research Group, Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield, United Kingdom
This paper examines presence of some stylized facts of short-term stock prices in the banking sector of the Nigerian Stock Market (NSM). Non-normality, lack of autocorrelation in the returns at first lag and significant positive autocorrelation in higher magnitude returns, widely studied in other markets, are investigated using daily closing stock prices of the four major Nigerian banks (Access, First, Guaranty Trust and United Bank for Africa (UBA)), from 2001 to 2013; encompassing periods of different financial scenarios. Jarque-Bera (JB), Doonik-Hansen, Kolmogrov-Smirnov and Ljung-Box (Q) test statistics are applied. Our findings reveal that the four banks stocks behave slightly different, but generally possess the stylized facts found in other markets. Observed is that, while the distributions of the returns for two of these banks (First and UBA) are approximately symmetric and leptokurtic; those of Access and Guaranty Trust banks are significantly non-symmetric and leptokurtic, thus non-normally distributed. Also established is that, while autocorrelation functions of daily returns are either negative or zero, those of both absolute returns and the squared returns are mostly positive. The autocorrelations of absolute returns are found to be predominantly positive and more persistent than those of the squared returns; indicating volatility clustering. Consequently, we conclude that the short-term stock prices of these banks behave like those of other markets. Some implications of the results for financial investment and stock market behaviour in the banking sector of NSM are discussed.
Yahaya, A. (2012) On Numerical Solution for Optimal Allocation of Investment Funds in Portfolio Selection Problem. CBN Journal of Applied Statistics, 3, 1-15.
Musa, Y., Asare, B.K. and Gulumbe, S.U. (2013) Effect of Monetary-Fiscal Policies Interaction on Price and Output Growth in Nigeria. CBN Journal of Applied Statistics, 4, 55-74.
African Development Bank (AFDB) (2007) Research Proposal on Financial Services and Economic Development: Case of SANE Countries (South Africa, Algeria, Nigeria and Egypt). ECON Unit, African Development, Tunisia.
Aliyu, S.U.R. (2012) Reactions of Stock Market to Monetary Policy Shocks during the Global Financial Crisis: The Nigerian Case. CBN Journal of Applied Statistics, 3, 1-23.
Alade, S.O. (2012) Quality Statistics in Banking Reforms for National Transformation. CBN Journal of Applied Statistics, 3, 127-142.
Ezeoha, A., Ogamba, E. and Okereke-Onyiuke, N. (2009) Stock Market Development and Private Investment Growth in Nigeria. Journal of Sustainable Development in Africa, 11, 20-35.
Osinubi, T.S. (2004) Does Stock Market Promote Economic Growth in Nigeria? The ICFAI Journal of Applied Finance, 10, 17-35.
Poon, S. and Granger, C.W.J. (2003) Forecasting Volatility in Financial Markets: A Review. Journal of Economic Literature, 41, 478-539. https://doi.org/10.1257/.41.2.478
Ezepue, P.O. and Solarin, A.R.T. (2009) The Meta-Heuristics of Global Financial Crisis in the Eyes of the Credit Squeeze: Any Lessons for Modelling Emerging Financial Markets? In: Ale, S.O., et al., Eds., Proceedings of the 2008 International Conference on Mathematical Modelling of Global Challenging Problems in the 21st Century, National Mathematical Centre, Abuja, Nigeria, 26-30 November 2008 278-288. http://www.afrihero.org.uk/index.php?option=com_content&view=article&id=120&itemid=85
Islam, S.M.N. and Watanapalachaikul, S. (2005) Empirical Finance: Modelling and Analysis of Emerging Financial and Stock Markets. Springer, New York.
Omar, M.A.T. (2012) Stochastic Modelling in Financial Markets: Case Study of the Nigerian Stock Market. Doctoral Thesis, Sheffield Hallam University, Sheffield.
Ezepue, P.O. and Omar, M.A.T. (2012) Weak-Form Market Efficiency of the Nigerian Stock Market in the Context of Financial Reforms and Global Financial Crisis. Journal of African Business, 13, 209-220. https://doi.org/10.1080/15228916.2012.727750
Thompson, S. (2011) The Stylised Facts of Stock Price Movements. New Zealand Review of Economics and Finance, 1, 50.
Taylor, J.W. (2005) Generating Volatility Forecasts from Value at Risk Estimates. Management Science, 51, 712-725. https://doi.org/10.1287/mnsc.1040.0355
Cont, R. (2001) Empirical Properties of Asset Returns: Stylized Facts and Statistical issues. Journal of Quantitative Finance, 1, 223-236. https://doi.org/10.1080/713665670
Mandelbrot, B. (1963) New Methods in Statistical Economics. Journal of Political Economy, 71, 421-440. https://doi.org/10.1086/258792
Fama, E.F. (1965) The Behaviour of Stock Market Prices. Journal of Business, 38, 34-105. https://doi.org/10.1086/294743
Nelson, D.B. (1991) Conditional Heteroscedasticity in Asset Returns: A New Approach. Econometrica: Journal of the Econometric Society, 59, 347-370. https://doi.org/10.2307/2938260
Booth, G.G., Kaen, F.R., Koutmos, G. and Sherman, H.C. (2000) Bundesbank Intervention Effects through Interest Rate Policy. Journal of International Financial Markets, Institutions and Money, 10, 263-274. https://doi.org/10.1016/S1042-4431(00)00032-9
Engle, R.F. (1982) Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation. Econometrica, 50, 987-1008. https://doi.org/10.2307/1912773
Bollerslev, T., Engle, R.F. and Nelson, D.B. (1994) ARCH Models. Handbook of Econometrics, 4, 2959-3038. https://doi.org/10.1016/S1573-4412(05)80018-2
Koutmos, G. and Knif, J. (2002) Estimating Systematic Risk Using Time Varying Distributions. European Financial Management, 8, 59-73. https://doi.org/10.1111/1468-036X.00176
Scruggs, J.T. and Glabadanidis, P. (2003) Risk Premia and the Dynamic Covariance between Stock and Bond Returns. Journal of Financial and Quantitative Analysis, 38, 295-316. https://doi.org/10.2307/4126752
Black, F. (1976) Studies of Stock Price Volatility Changes. In: Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Section, Chicago, IL, 177-181.
Christie, A.A. (1982) The Stochastic Behaviour of Common Stock Variances: Value, Leverage and Interest Rate Effects. Journal of Financial Economics, 10, 407-432. https://doi.org/10.1016/0304-405X(82)90018-6
Bekaert, G. and Wu, G.J. (2000) Asymmetric Volatility and Risk in Equity Markets. Review of Financial Studies, 13, 1-42. https://doi.org/10.1093/rfs/13.1.1
Lebaron, B. (1992) Some Relations between Volatility and Serial Correlations in Stock Market Returns. Journal of Business, 65, 199-219. https://doi.org/10.1086/296565
Campbell, J.Y., Grossman, S.J. and Wang, J. (1993) Trading Volume and Serial Correlation in Stock Returns. The Quarterly Journal of Economics, 108, 905-939. https://doi.org/10.2307/2118454
Sentana, E. and Wadhwani, S. (1992) Feedback Traders and Stock Return Autocorrelations: Evidence from a Century of Daily Data. The Economic Journal, 102, 415-425. https://doi.org/10.2307/2234525
Koutmos, G. (1997) Do Emerging and Developed Markets Behave Alike? Evidence from Six Pacific-Basin Stock Markets. Journal of International Financial Markets Institutions and Money, 7, 221-234. https://doi.org/10.1016/S1042-4431(97)00022-X
Harvey, C.R. (1995) Predictable Risk and Returns in Emerging Markets. The Review of Financial Studies, 8, 773-816. https://doi.org/10.1093/rfs/8.3.773
Harvey, C.R. (1991) The World Price of Covariance Risk. The Journal of Finance, 46, 111-157. https://doi.org/10.1111/j.1540-6261.1991.tb03747.x
Taylor, S.J. (2011) Asset Price Dynamics, Volatility and Prediction. Princeton University Press, Princeton, NJ. https://doi.org/10.1515/9781400839254
Booth, G.G., Hatem, J., Virtanen, I. and Yli-Olli, P. (1992) Stochastic Modelling of Security Returns: Evidence from the Helsinki Stock Exchange. European Journal of Operational Research, 56, 98-106. https://doi.org/10.1016/0377-2217(92)90295-K
Pagan, A. (1996) The Econometrics of Financial Markets. Journal of Empirical Finance, 3, 15-102. https://doi.org/10.1016/0927-5398(95)00020-8
Richardson, M. and Smith, T. (1993) A Test for Multivariate Normality in Stock Returns. Journal of Business, 66, 295-321. https://doi.org/10.1086/296605
Ding, Z.X., Granger, C.W.J and Engle, R.F. (1993) A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance, 1, 83-106. https://doi.org/10.1016/0927-5398(93)90006-D
Aggarwal, R., Inclan, C. and Leal, R. (1999) Volatility in Emerging Stock Markets. Journal of Financial and Quantitative Analysis, 34, 33-55. https://doi.org/10.2307/2676245
Taylor, S.J. (2008) Modelling Financial Time Series. World Scientific, Singapore.
JARQUE, Carlos M. and BERA, Anil K. (1980) Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals. Economics Letters 6, 255-259. https://doi.org/10.1016/0165-1765(80)90024-5
Bera, A.K. and Jarque, C.M. (1981) Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals: Monte Carlo Evidence. Economics Letters, 7, 313-318. https://doi.org/10.1016/0165-1765(81)90035-5
Doornik, J.A. and Hansen, H. (1994) An Omnibus Test for Univariate and Multivariate Normality (No. W4&91). University of Oxford, Nuffield College, Economics Group, Oxford.
Kolmogorov, A.N. (1933) Foundations of Probability. Springer-Verlag, Berlin.
Conover, W.J. (1999) Statistics of the Kolmogorov-Smirnov Type. In: Practical Nonparametric Statistics, John Wiley & Sons, New York, 428-473.
Engle, R. (1995) ARCH: Selected Readings. Oxford University Press, Oxford.
Corhay, A. and Rad, A.T. (1994) Statistical Properties of Daily Returns: Evidence from European Stock Markets. Journal of Business Finance & Accounting, 21, 271-282. https://doi.org/10.1111/j.1468-5957.1994.tb00318.x
Tsay, R. (2010) Analysis of Financial Time Series. 3rd Edition, John Wiley & Sons, New York. https://doi.org/10.1002/9780470644560
Mills, T.C. and Markellos, R.N. (2008) The Econometric Modelling of Financial Time Series. 3rd Edition, Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511817380
Alexander, C. (2008) Quantitative Methods in Finance. John Wiley & Sons, New York.
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011) Statistical Distributions; 4th Edition, John Wiley & Sons, New York.
McNeil, A.J., Frey, R. and Embretchs, P. (2005) Quantitative Risk Management; Princeton University Press, Princeton, NJ.
Koutmos, G., Pericli, A. and Trigeorgis, L. (2006) Short-Term Dynamics in the Cyprus Stock Exchange. European Journal of Finance, 12, 205-216. https://doi.org/10.1080/13518470500146074
Fisher, L. (1966) Some New Stock-Market Indexes. The Journal of Business, 39, 191-225. https://doi.org/10.1086/294848
Fama, E.F. and French, K.R. (1988) Permanent and Transitory Components of Stock Prices. Journal of Political Economy, 96, 246-273. https://doi.org/10.1086/261535
Fama, E.F. and French, K.R. (1993) Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33, 3-56. https://doi.org/10.1016/0304-405X(93)90023-5
Hols, M.C.A.B. and de Vries, C. (1991) The Limiting Distribution of Exchange Rate Returns. Journal of Applied Econometrics, 6, 287-302. https://doi.org/10.1002/jae.3950060306
Koedijk, K. and Kool, C.J.M. (1992) Tail Estimates of East European Exchange Rates. Journal of Business and Economic Statistics, 10, 83-96.
Loretan, M. and Phillips, P. (1994) Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets. Journal of Empirical Finance, 1, 211-248. https://doi.org/10.1016/0927-5398(94)90004-3