keywords: Asset returns, GARCH models, Gaussianity, heteroskedasticity, stylized facts, volatility, Nigeria
This paper models the volatility of asset returns that produces several well-documented stylized facts. The Guinness bottling Company Plc daily closing share prices of the Nigerian stock exchange is used as proxy for Nigerian stock market. The data used for the study covers the period 1/02/1995 to 24/11/2014. The study employed Augmented Dickey-Fuller (ADF) unit root test for stationarity and mean reverting properties of returns while the volatility of asset returns was modeled using symmetric standard GARCH (1,1), asymmetric TGARCH (1,1) and PGARCH (1,1) models with Gaussian errors. Results of the unit root test indicate that the returns are stationary and mean reverting. The standard GARCH (1,1) model showed evidence of volatility clustering and mean reversion in Nigerian stock market. The conditional volatility was found to be quite persistence. The estimated asymmetric TGARCH (1,1) and PGARCH (1,1) models produced supportive evidence to the existence of asymmetry and leverage effects in Nigerian stock market. The study also found that the log returns are non-Gaussian, leptokurtic, fat-tailed and serially uncorrelated. The study therefore concludes that the well-documented stylized facts found in advanced and developed markets are also present in emerging stock markets like Nigeria and recommends that both local and foreign traders and investors should invest heavily in Guinness Plc as it has stable and mean reverting asset returns which are less risky.
Adesina KS 2013. Modelling stock market return volatility: GARCH evidence from Nigerian stock exchange. Int. J. Fin. Mgt., 3: 37 – 46. Akaike H 1974. A new look at statistical model identification, IEEE Trans. on Auto. Contr. AC-19: 716 – 723. Alexander CO 2008. Market risk analysis: Quantitative Methods in Finance. Vol.1, Chichester: John Wiley & Sons Ltd, p. 82. Awogbemi C & Alagbe S 2011. Empirical modeling of Nigerian exchange rate volatility. Math. Theo. &Mdlg., 1(3): 8 – 15. Bollerslev T 1986. Generalised autoregressive conditional heteroskedasticity. J. Econ., 31(3): 307 – 327. Chou R 1988. Volatility persistence and stock valuation: Some empirical evidence using GARCH. J. Appl. Econ., 3(4): 279 – 294. Cont R 2001. Empirical properties of asset returns: stylized facts and statistical issues. Quant. Fin., 1: 223 – 236. Emenike KO & Ani WU 2014. Volatility of the banking sector stock returns in Nigeria. Ruh. J. Mgt Fin., 1(1): 73 – 82. Engle RF 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econ., 50: 987 – 1007. Engle RF & Bollerslev T 1986. Modelling the persistence of conditional variances. Econ. Rev., 5(1): 1 – 50. Ding Z & Granger CWJ 1996. Modeling volatility persistence of speculative returns: A new approach. J. Econs., 73(1): 185 – 215. Du G & Ning X 2008. Multifractal properties of Chinese stock market in Shanghai. Phy. A., 387(1): 261 – 269. Fama EF 1970. Efficient capital markets: A review of theory and empirical work. The J. Fin., 25(2): 383 – 417. Fama EF & French KR 1988. Permanent and temporary components of stock prices. J. Pol. Econ., 96(2): 246 – 273. Gibbons MR & Hess P 1981. Day of the week effects and asset returns. The J. Bus., 54(4): 579 – 596. Glosten L Jaganathan R & Runkle D 1993. Relationship between the expected value and volatility of the nominal excess returns on stocks. J. Fin., 48(5): 1779 – 1802. Granger CWJ & Ding Z 1996. Varieties of long memory models. J. Econs., 73(1): 61 – 77. Granger CWJ & Hyung N 2004. Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. J. Emp. Fin., 11(3): 399 – 421. Greene MT & Fielitz BD 1977. Long-term dependence in common stock returns. J. Fin. Econ., 4(3): 339 – 349. Hamao Y & Hasbrouck J 1995. Securities trading in the absence of dealers: Trades and quotes on the Tokyo stock exchange. Rev. Fin. Studs., 8(3): 849 – 878. Hannan E 1980. The estimation of the Order of ARMA process. Ann. Stat., 8: 1071 – 1081. Hansen PR & Lunde A 2006. Realized variance and market microstructure noise. J. Bus. & Econ. Stat., 24(2): 127 – 161. Harris L 1986. A transaction data study of weekly and intradaily patterns in stock returns. J. Fin. Econs., 16(1): 99 – 117. Jarque CM & Bera AK 1980. Efficient test for normality, heteroskedasticity and serial independence of regression residuals. Econ. Letts., 6: 255 259. Jarque CM & Bera AK 1987. A test for normality of observations and regression residuals. Int. Stat. Rev., 55(2): 163 – 172 MacKinnon J 1996. Numerical distribution functions for unit root and cointegration tests. J. Appl. Econs., 11: 601 – 618. Nelson DB 1991. Conditional heteroskedasticity in asset returns: A new approach. Econ., 59(2): 347 – 370. Okpara GC 2011.Volatility modeling and the Nigerian stock return relationship in EGARCH –in –mean framework. Int. J. Curr. Res., 3(8): 176 – 185. Onakoya AB 2013. Stock market volatility and economic growth in Nigeria. Int. Rev. Mgt. Bus. Res., 2(1): 201 – 209. Olowe RA 2009. Stock return, volatility and the global financial crisis in an emerging market: The Nigerian case. Int. Rev. Bus. Res. Paps., 5(4): 426 447. Olusola O & Opeyemi A 2013. Exchange rate volatility in Nigeria: evidence from a parametric measure. Aust. J. Bus. Mgt. Res., 3(5): 12 – 17. Osazevbaru HO 2014a. Measuring Nigerian stock market volatility. Sing. J. Bus. Econs. Mgt. Stud., 2(8): 1 14 Osazevbaru HO 2014b. Modelling Nigerian stock market news using TGARCH model. Int. J. Dev. Sust., 3: 1894 – 1900. Said SE & Dickey D 1984. Testing for unit roots in autoregressive moving-average models with unknown order. Biom., 71: 599 – 607. Schwert W 1989. Test for unit roots: A montecarlo investigation. J. Bus. Econ. Stat., 7: 147 – 159. Schwarz G 1978. Estimating the dimension of a model. Anns. Stat., 6(2): 461 464 Suliman ZS 2012. Modelling exchange rate volatility using GARCH models: Empirical evidence from Arab countries. Int. J. Econs. Fin., 4(3): 216 – 229. Taylor SJ 1986. Forecasting the volatility of currency exchange rates. Int. J. For.. 3: 159 – 170. Tsay RS 2002. Analysis of Financial Time Series. University of Chicago. John Wiley and Sons. Inc., p. 29 – 35. Uwubanmwen AE & Omorokunwa OG 2015. Oil price volatility and stock price volatility: evidence from Nigeria. Acad. J. Inter. Studs., 4(1): 253 – 260. Zakoian JM 1994. Threshold heteroskedastic models. J. Econ. Dyn. Contr., 18(5): 931 – 955.