Volatility spillover among the sectors of emerging and developed markets: a hedging perspective

Figures & data

Table 1. Sectoral indices.

Sectors	India^1	China^2	UK^2	US^3
Financial Services	Nifty Financial Services	FTSE China A 600 Financials	FTSE 350 Financial Services	Dow Jones US Financials
Auto	Nifty Auto	FTSE China A 600 Automobile & Parts	FTSE 350 Automobiles & Parts	Dow Jones Automobiles
Oil and Gas	Nifty Oil and Gas	FTSE China A 600 Oil & Gas	FTSE 350 Oil & Gas	Dow Jones US Oil & Gas
IT	Nifty IT	FTSE China A 600 Technology	FTSE 350 Technology	Dow Jones US Technology
Healthcare	Nifty Healthcare	FTSE China A 600 Healthcare	FTSE 350 Healthcare	Dow Jones US Healthcare
Real Estate	Nifty Realty	FTSE 350 Real Estate	SSE Real Estate	Dow Jones US Real Estate

Table 2. Descriptive Statistics.

Stat	Sectors	India	China	UK	US
Mean	Financial Services	0.00047	−0.00014	0.00012	0.00027
	Auto	0.00036	0.00012	−0.00072	0.00063
	Oil and Gas	0.00051	−0.00012	0.000083	0.000019
	IT	0.00051	0.000049	0.00031	0.00069
	Healthcare	0.00027	0.00018	0.000052	0.00031
	Real Estate	0.00060	−0.00013	−0.000101	0.000068
Std. Dev	Financial Services	0.01389	0.01455	0.01398	0.01343
	Auto	0.01404	0.01854	0.02731	0.02664
	Oil and Gas	0.01338	0.01588	0.01914	0.01967
	IT	0.01301	0.02192	0.01459	0.01535
	Healthcare	0.01178	0.01182	0.01666	0.01106
	Real Estate	0.01896	0.01814	0.01380	0.01330
Skewness	Financial Services	−1.16253	−0.39597	−0.73037	−0.85424
	Auto	−0.59406	−0.47891	−0.20307	−0.16533
	Oil and Gas	−1.08055	−0.60533	−0.53866	−0.85795
	IT	−0.44766	−0.361899	−0.4914	−0.53846
	Healthcare	−0.26346	−0.18442	−0.44967	−0.57497
	Real Estate	−0.56058	−0.38938	−0.90230	−1.58277
Kurtosis	Financial Services	19.82468	9.45101	13.08661	22.50893
	Auto	13.84184	6.43397	11.15875	9.68953
	Oil and Gas	14.43332	7.53677	19.17624	18.5943
	IT	9.29719	33.3666	36.46319	11.13563
	Healthcare	8.23232	6.15307	6.12806	12.8641
	Real Estate	7.35749	7.98908	17.47829	29.90241
Jarque-Bera	Financial Services	26768.14*	3919.781*	9638.602*	35587.22*
	Auto	11038.23*	1179.348*	6192.011*	4162.562*
	Oil and Gas	12563.18*	2045.872*	24388.56*	22838.5*
	IT	3754.009*	85614.64*	103996.4*	6249.352*
	Healthcare	2566.137*	935.1456*	983.0018*	9151.372*
	Real Estate	1878.547*	2365.949*	19753.25*	68086.82*
ADF	Financial Services	−12.7742*	−10.2971*	−11.2861*	−9.8498*
	Auto	−16.4893*	−16.2684*	−16.0914*	−15.413*
	Oil and Gas	−13.4633*	−35.2345*	−10.436*	−10.46*
	IT	−17.1267*	−18.0584*	−17.277*	−14.8576*
	Healthcare	−31.4777*	−47.9685*	−11.8431*	−28.2707*
	Real Estate	−44.1449*	−9.9482*	−17.3824*	−14.8624*
PP	Financial Services	−45.9991*	−46.7781*	−46.058*	−51.4806*
	Auto	−46.1646*	−45.4519*	−45.7179*	−47.901*
	Oil and Gas	−47.1243*	−47.2039*	−44.6644*	−48.0223*
	IT	−47.8084*	−45.6539*	−46.61*	−53.2197*
	Healthcare	−45.053*	−47.9756*	−45.3351*	−50.9725*
	Real Estate	−44.3118*	−45.227*	−44.2683*	−48.9112*
L-B Q^2 Stat (5)	Financial Services	125.93*	106.95*	186.72*	117.05*
	Auto	108.60*	139.02*	29.01*	256.81*
	Oil and Gas	46.868*	106.21*	86.95*	148.83*
	IT	193.37*	134.78*	40.04*	129.63*
	Healthcare	58.504*	97.76*	142.19*	171.82*
	Real Estate	74.35*	87.93*	63.33*	163.56*
LM Test (5)	Financial Services	116.40*	98.70*	166.87*	108.58*
	Auto	105.53*	126.67*	27.55*	222.79*
	Oil and Gas	42.84*	100.07*	82.60*	149.30*
	IT	173.15*	138.08*	42.814*	116.42*
	Healthcare	54.12*	95.22*	135.11*	153.35*
	Real Estate	66.85*	80.02*	56.42*	152.68*

Notes: (*) indicate the significance at 1%, Unit root test: Augmented Dickey-Fuller (ADF) Phillips–Perron (PP) test, Serial correlation test: Ljung-Box test in squared residual at lag five and ARCH test: Lagrange Multiplier test at lag five.

Source: Author’s calculation.

Table 3. BEKK results.

Descriptive statistics	Financial services	Auto	Oil and gas	IT	Healthcare	Real estate
A(India, India)	0.23478*	0.34529*	0.26939*	0.13332*	0.04612	0.19843*
A(India, China)	0.02758	0.02128	−0.02233	−0.06501	−0.12249*	−0.01072
A(India, UK)	0.01853	−0.04284	−0.00488	−0.33008*	0.00496	0.00586
A(India, US)	0.05192	−0.07141**	0.017826	−0.08796*	−0.02075	0.01045
A(China, India)	0.03876**	0.02197	0.03025	0.03846*	0.05870**	0.06397*
A(China, China)	0.17361*	0.15469*	0.18059*	0.22725*	0.04710**	0.22528*
A(China, UK)	0.05976**	0.02795	0.01897	−0.08608*	−0.03933**	0.03286*
A(China, US)	0.05277**	0.02967*	0.02410	−0.02066	−0.03046	0.04118*
A(UK, India)	0.01846	−0.00698	0.05201*	0.05815*	0.04192*	0.01222
A(UK, China)	−0.01955	0.01853**	0.00031	0.19470*	−0.01889	−0.02282
A(UK, UK)	0.28208*	0.13851*	0.19553*	−0.07967**	0.19140*	0.33809*
A(UK, US)	0.00772	−0.03508**	0.02255	−0.00885	−0.02121	−0.02965*
A(US, India)	−0.0121	0.03238*	0.10444*	−0.04616	0.16096*	0.06215
A(US, China)	−0.00625	0.01109	0.03620*	−0.05361**	0.10776*	0.01527
A(US, UK)	−0.10583	0.08643*	−0.00094	−0.01654	0.07824*	−0.09651*
A(US, US)	0.36012*	0.23407*	0.24221*	0.29084*	0.32299*	0.30240*
B(India, India)	0.95979*	0.90051*	0.71986*	0.74388*	0.79058*	0.90858*
B(India, China)	−0.01333	−0.00717	−0.03267**	0.03465	0.65703*	−0.01217
B(India, UK)	−0.00972	0.03039	0.06742**	0.43163*	−0.02649	0.02253**
B(India, US)	−0.00857	0.02971	−0.00811	−0.05133	0.02939	−0.02765**
B(China, India)	−0.00557	−0.00005	0.01095	−0.02781*	−0.70582*	−0.01208
B(China, China)	0.98121*	0.98644*	0.98360*	0.96174*	0.56911*	0.96566*
B(China, UK)	−0.01368	−0.00294	−0.0092	0.03301*	−0.02822	−0.0152*
B(China, US)	−0.00313	−0.00451	−0.0014	0.00633	−0.08853*	−0.00614
B(UK, India)	0.00732	0.00085	0.01337	0.19975*	0.02799	0.01294
B(UK, China)	0.01344	−0.00869*	0.00529	−0.05664	0.00030	0.00388
B(UK, UK)	0.90059*	0.97601*	0.93270*	0.32088*	0.98443*	0.88755**
B(UK, US)	−0.00361	−0.00167	−0.04601*	−0.2324*	0.01099**	0.03684
B(US, India)	−0.00855	−0.00382	−0.01262	0.09897*	0.19321*	−0.01613
B(US, China)	−0.00494	−0.00015	−0.00852**	0.02650	0.00480	−0.00165
B(US, UK)	0.07808	−0.01476*	0.04547*	0.22862*	−0.01826	0.06839*
B(US, US)	0.89825*	0.97259*	0.99594*	1.01347*	0.95557*	0.92850*

Notes: (*) and (**) indicate the significance at 1% and 5% level.

Source: Author’s calculation.

Table 4. GO-GARCH estimates.

Sectors	Parameter	F1	F2	F3	F4
Financial services	ω	0.02013	0.02241	0.01155	0.07393
	α	0.07364	0.14825	0.07338	0.15363
	β	0.904	0.83091	0.91892	0.77447
	skew	−0.01074	−0.23041	0.09007	−0.01056
	shape	1.37732	1.29433	0.63363	1.75376
Auto	ω	0.00521	0.00329	0.02674	0.00296
	α	0.06699	0.03748	0.08137	0.05526
	β	0.93071	0.96005	0.88887	0.94373
	skew	−0.04784	−0.04923	−0.12747	0.03349
	shape	1.21186	0.85837	1.65184	0.98818
Oil and gas	ω	0.05150	0.00654	0.00460	0.01567
	α	0.06306	0.06643	0.05684	0.07749
	β	0.87823	0.92693	0.94104	0.90699
	skew	−0.18305	−0.0948	0.02646	0.09227
	shape	1.83649	1.61097	0.90450	2.98145
IT	ω	0.01249	0.01631	0.02766	0.16366
	α	0.11943	0.09127	0.05004	0.11609
	β	0.87547	0.89540	0.92003	0.70156
	skew	−0.24954	0.04016	0.04311	0.06732
	shape	1.45798	0.85256	1.40893	0.88577
Healthcare	ω	0.06751	0.00297	0.07889	0.01975
	α	0.07768	0.06014	0.07630	0.09555
	β	0.85252	0.93885	0.84587	0.88305
	skew	−0.0496	−0.0529	0.027853	0.218724
	shape	1.90721	1.80448	1.53660	2.02581
Real estate	ω	0.01152	0.09600	0.01935	0.06710
	α	0.09510	0.08923	0.08293	0.14102
	β	0.89331	0.81329	0.89916	0.78708
	skew	−0.23109	−0.117	0.09506	0.03133
	shape	1.97095	1.41593	0.91220	1.58439

Notes: The GO-GARCH model is computed utilizing a multivariate affine negative inverse Gaussian (MANIG) distribution. Each model incorporates a constant and an AR(1) term in the mean equation. It is customary to display the rotation matrix (U) and the mixing matrix (A); these details are omitted here for space. Nevertheless, they can be made available upon request.

Table 5. Diagnostic tests.

Sectors	Financial Services		Auto		Oil and Gas		IT		Healthcare		Real Estate
Models Markets	BEKK Q(5)	GO-GARCH Q(5)	BEKK Q(5)	GO-GARCH Q(5)	BEKK Q(5)	GO-GARCH Q(5)	BEKK Q(5)	GO-GARCH Q(5)	BEKK Q(5)	GO-GARCH Q(5)	BEKK Q(5)	GO-GARCH Q(5)
India	6.83588	4.10014	0.93260	2.21529	1.77649	3.31128	5.91669	2.14772	0.79881	1.12054	3.6239	5.99495
China	2.65829	1.99359	3.25561	2.82777	2.38698	2.55757	1.26180	1.61151	5.43762	7.89972	1.4155	1.00528
UK	1.92218	8.51321	5.53564	4.28627	4.85646	5.34542	3.43448	4.96228	8.12736	6.46535	9.7719	8.04923
US	6.63209	8.24340	6.17655	4.23971	4.50961	4.82564	2.42760	5.79611	4.63627	3.50131	3.4555	5.98293

Notes: Q(5) is the Ljung-Box test on the residual at lag 5.

Table 6. Hedge ratios.

Pairs	Model	Stat	Financial services	Auto	Oil and Gas	IT	Healthcare	Real Estate
India/China	BEKK	Mean	0.19	0.11	0.07	0.06	0.15	0.11
		HE(%)	7	7	4	3	6	1
	GO-GARCH	Mean	0.22	0.18	0.13	0.11	0.21	0.14
		HE(%)	11	6	2	3	5	2
India/UK	BEKK	Mean	0.31	0.10	0.13	0.15	0.08	0.33
		HE(%)	19	6	7	11	3	10
	GO-GARCH	Mean	0.35	0.14	0.17	0.26	0.11	0.40
		HE(%)	19	6	6	9	3	9
India/US	BEKK	Mean	0.28	0.10	0.08	0.15	0.18	0.24
		HE(%)	10	3	7	4	3	3
	GO-GARCH	Mean	0.29	0.13	0.15	0.25	0.24	0.28
		HE(%)	12	4	6	4	4	4
China/India	BEKK	Mean	0.24	0.17	0.10	0.13	0.16	0.10
		HE(%)	3	4	2	1	6	1
	GO-GARCH	Mean	0.23	0.25	0.15	0.27	0.22	0.12
		HE(%)	5	4	2	0	5	2
China/UK	BEKK	Mean	0.20	0.04	0.12	0.09	0.05	0.14
		HE(%)	2	0	1	1	1	0
	GO-GARCH	Mean	0.21	0.09	0.13	0.17	0.06	0.15
		HE(%)	4	2	2	1	2	2
China/US	BEKK	Mean	0.19	0.09	0.13	0.20	0.42	0.11
		HE(%)	2	3	1	1	14	0
	GO-GARCH	Mean	0.19	0.15	0.14	0.24	0.49	0.14
		HE(%)	3	4	2	1	13	1
UK/India	BEKK	Mean	0.36	0.39	0.27	0.18	0.14	0.16
		HE(%)	16	5	3	8	3	7
	GO-GARCH	Mean	0.38	0.51	0.32	0.30	0.20	0.19
		HE(%)	15	6	6	8	2	9
UK/China	BEKK	Mean	0.17	0.06	0.18	0.04	0.10	0.06
		HE(%)	4	0	2	0	1	3
	GO-GARCH	Mean	0.19	0.15	0.17	0.08	0.16	0.09
		HE(%)	6	1	3	2	2	3
UK/US	BEKK	Mean	0.58	0.28	0.59	0.38	0.16	0.40
		HE(%)	32	8	44	13	0	21
	GO-GARCH	Mean	0.50	0.35	0.57	0.41	0.21	0.48
		HE(%)	29	8	43	14	2	21
US/India	BEKK	Mean	0.24	0.35	0.21	0.21	0.14	0.10
		HE(%)	7	1	5	0	6	9
	GO-GARCH	Mean	0.28	0.42	0.34	0.30	0.20	0.13
		HE(%)	10	3	6	3	4	7
US/China	BEKK	Mean	0.11	0.15	0.19	0.09	0.31	0.05
		HE(%)	4	1	3	1	15	4
	GO-GARCH	Mean	0.17	0.22	0.20	0.11	0.34	0.09
		HE(%)	7	2	4	2	16	5
US/UK	BEKK	Mean	0.42	0.24	0.62	0.37	0.06	0.35
		HE(%)	35	7	45	13	3	26
	GO-GARCH	Mean	0.43	0.28	0.62	0.43	0.10	0.41
		HE(%)	35	8	45	12	4	23

Source: Author’s calculation.

Data availability statement

Data are available on request.