Pricing of risk and volatility dynamics on an emerging stock market: evidence from both aggregate and disaggregate data

Figures & data

Table 1. Descriptive statistics and stationarity results. This table reports explanatory statistics consisting of: mean, standard deviation, skewness, kurtosis and Jarque Bera; unit root tests include ADF and PP and results of Ljung Box Q Statistics for both returns and square returns series.

Returns	Mean	S.D	SKU	KU	JB	ADF	PP	LBQ(12)	LBQ^2(12)
KSE 100 Index	0.017	0.091	−0.937	6.924	132.349^*	−12.840^*	−12.840^*	6.510	8.563
Oil & Gas	0.007	0.124	−0.707	6.382	94.087^*	−13.251^*	−13.269^*	10.572	20.803^**
Chemical	0.006	0.070	−0.480	4.323	18.527^*	−11.042^*	−10.977^*	10.110	19.581^**
Tobacco	0.008	0.105	1.277	21.969	2,564.495^*	−17.701^*	−17.943^*	22.737^*	23.586^*
Beverages	0.003	0.121	−0.030	4.342	12.627^*	−15.679^*	−15.814^*	23.572^*	13.454
Forestry	0.003	0.126	−1.084	25.100	3,451.687^*	−16.579^*	−16.543^*	22.714^*	32.520^*
Electricity	−0.002	0.956	0.236	4.209	11.797^*	−12.624^*	−12.643^*	7.661	10.765
Engineering	0.009	0.090	0.439	4.590	23.084^*	−10.875^*	−10.872^*	10.330	8.192
Auto & Parts	0.009	0.092	−0.147	3.682	3.866^*	−11.928^*	−12.002^*	10.821	22.035^*
Gas & Water	0.004	0.192	−0.151	20.753	2,206.878^*	−12.857^*	−18.842^*	27.512^*	39.389^*
Pharma & Bio	0.006	0.069	0.322	3.336	3.687	−10.743^*	−10.749^*	21.845^*	19.173^**
Personal Goods	0.006	0.059	0.065	5.403	40.548^*	−10.180^*	−10.942^*	26.394^*	21.316^*
Life Insurance	0.008	0.122	0.468	4.642	25.012^*	−15.528^*	−15.325^*	12.201	19.817^**
Food Producer	0.009	0.059	0.006	4.170	9.593^*	−12.735^*	−12.735^*	13.958	26.043^*
Travel & Leisure	0.018	0.162	0.880	6.467	105.828^*	−12.249^*	−12.201^*	11.659	23.219^*
Financial Services	−0.007	0.083	−0.535	4.218	18.397^*	−7.345^*	−11.297^*	19.036^**	24.835^*
General Industrial	0.009	0.094	−0.127	14.469	921.266^*	−16.051^*	−16.019^*	18.356^**	37.077^*
Household Goods	0.000	0.106	0.611	5.124	41.537^*	−11.374^*	−11.399^*	6.174	7.578
Non-Life Insurance	−0.002	0.080	−0.578	5.215	43.725^*	−11.903^*	−12.054^*	17.358^**	19.089^**
Fixed Line Telecom	−0.001	0.117	−0.043	4.229	10.629^*	−12.137^*	−12.165^*	19.467^**	21.609^*
Commercial Banking	0.000	0.101	−0.798	5.175	50.908^*	−11.705^*	−11.701^*	11.392	6.564
Electronics & Electricity	0.000	0.120	0.316	4.249	13.722^*	−11.938^*	−11.921^*	10.160	7.936
Industrial Metal and Min.	0.004	0.098	0.387	4.239	14.945^*	−14.196^*	−14.158^*	11.218	25.822^*
Construction & Material	0.008	0.117	0.710	5.287	50.719^*	−10.923^*	−11.013^*	18.929^**	5.534

Note: S.D – Standard Deviation, SKW – Skewness, KU – Kurtosis, JB – Jarque-Bera, Critical value for ADF and PP at 5% and 10% level is –2.87 and –2.57, SIC is used to select the appropriate lag, LBQ (12) and LBQ2 (12) – Ljung Box Q Statistics for returns and square returns series respectively.

^* Represents level of significance at 5% and 10% respectively

^** Represents level of significance at 5% and 10% respectively.

Table 2. Results – GARCH (1, 1), GARCH-M and EGARCH Models. This table shows the results regarding the level of statistically significant and insignificant coefficients of ARCH (α) and GARCH (β) effects together with persistence (α + β) and mean reversion by employing GARCH (1, 1) model at each of the sectoral besides aggregate market level returns. Further, results related to pricing of risk (δ) and asymmetric and leverage effect (γ) by mean of GARCH-M and EGARCH models respectively are also reported therein.

Sectors	ARCH(α)	GARCH(β)	α + β	Half-life	GARCH-M (δ)	EGARCH (γ)
KSE 100 Index	0.68^*	0.02	0.70^a	1.94	−0.49	0.08
Oil & Gas	0.72^*	0.04^*	0.76^a	2.53	−0.95^*	−0.11^*
Chemical	0.03	0.86^*	0.89^b	5.95	0.60^*	−0.04
Tobacco	0.37^*	0.30^*	0.67^a	1.72	−0.34^*	0.07
Beverages	0.21^**	0.42^**	0.63^b	1.54	−1.77^*	0.14
Forestry	0.24^*	0.02	0.26^a	0.51	−23.98	0.16
Electricity	−0.15^*	1.01^*	0.86^b	4.59	0.95^**	−0.21^**
Engineering	0.01	0.47^*	0.48^b	0.94	0.14	0.01
Auto & Parts	0.06	0.42	0.48^b	0.94	1.29^**	−0.02
Gas & Water	1.41^*	0.01	1.42^a	-	0.65^*	−0.39^*
Pharma & Bio	−0.12^*	1.05^*	0.93^b	9.55	0.55	−0.08^*
Personal Goods	0.70^*	0.20^*	0.90^a	6.57	−0.05	−0.20^**
Life Insurance	0.20^*	0.70^*	0.90^b	6.57	0.01	−0.18
Food Producer	0.50^*	0.01	0.51^a	1.02	0.25^*	0.15
Travel & Leisure	0.44^*	0.63^*	1.07^b	-	0.43^*	0.02
Financial Services	0.45^*	0.35^*	0.80^a	3.10	0.57^*	−0.01
General Industrial	0.38^*	0.04	0.42^a	0.79 ^a	0.17	−0.11
Household Goods	0.31^*	0.55^*	0.86^b	4.59	0.31	0.39^*
Non-Life Insurance	0.00	0.88^*	0.88^b	5.42	−0.03	−0.03
Fixed Line Telecom	0.17	0.60^*	0.77^b	2.65	0.65	−0.30^*
Commercial Banking	−0.18^*	1.02^*	0.84^b	3.97	0.32^*	0.01
Electronics & Electricity	0.03	0.61^**	0.64^b	1.55	−2.60	−0.01
Industrial Metal and Min.	0.04^*	0.86^*	0.90^b	6.57	2.27^*	−0.01
Construction & Material	0.52^*	0.06	0.58^a	1.27^a	0.90^*	0.01

^* Represents significance level at 5% and 10% respectively.

^** Represents significance level at 5% and 10% respectively.

^a Represents if volatility is mainly due to ARCH effect.

^b Represents if volatility is mainly due to GARCH effect, ARCH+GARCH.

(α + β) Denotes sum of coefficients of ARCH and GARCH effects representing the persistence.

HL Represents half-life of volatility.

γ coefficient in case of EGARCH model indicates asymmetric and leverage effect.

δ coefficient in case of GARCH-M model represents risk-return trade-off.