Analysis of industry risk premium with MVS three dimensions vector factor model

Figures & data

Table 1. Volatility of industry risk premium

Industry and code	Mean	Absolute value of variation coefficient	Minimum	Maximum	Std. Deviation
Industry average^1	−0.9780	80.1341	−192.0200	166.4000	78.3712
Energy^2	−5.1687	19.2367	−244.5700	184.6900	99.4279
Materials^3	−1.4213	66.0309	−228.1000	197.9300	93.8519
Capital goods^4	−0.7607	100.2171	−191.3700	146.0300	76.2318
Commercial and special services^5	−2.1267	35.1134	−167.7100	120.8900	74.6745
Transportation^6	−0.8287	93.7053	−197.2200	158.3500	77.6504
Automobiles & components^7	−1.4527	73.2986	−217.8900	249.3400	106.4785
Consumer durables & apparel^8	0.8580	91.9109	−181.0700	173.2300	78.8595
Consumer services^9	−0.9113	93.5004	−198.5100	196.3900	85.2101
Media^10	1.1653	65.9854	−166.9500	170.4700	76.8950
Retailing^11	−0.0400	1989.8453	−196.2000	165.2600	79.5938
Food & staples retailing^12	−1.0333	66.0036	−168.1600	136.6400	68.2037
Food, beverage & tobacco^13	−1.1793	60.0265	−164.8000	156.0800	70.7913
Household & personal products^14	0.4740	181.4536	−229.6800	166.5700	86.0090
Health care equipment & services^15	−1.0727	78.3556	−182.9000	190.2700	84.0495
Pharmaceuticals, biotechnology & life^16 sciences	−1.9520	37.0697	−173.1300	131.2300	72.3600
Banks^17	1.1160	57.2644	−156.4100	117.7800	63.9070
Diversified financials^18	−3.9327	29.7237	−275.8500	196.7700	116.8934
Real estate^19	−0.5353	171.7842	−206.4800	194.6400	91.9618
Software & services^20	−0.1400	546.7267	−148.2300	157.6700	76.5417
Technology hardware & equipment2^1	0.4900	159.1049	−169.9200	163.1800	77.9614
Semiconductors & semiconductor^22 equipment	−0.4880	183.2917	−178.6800	215.4200	89.4464
Telecommunication services^23	−1.4420	54.2562	−178.5000	116.1700	78.2374
Utilities^24	−2.0913	35.8951	−194.1100	122.1700	75.0686

Table 2. M dimension variables volatility

Variable	Mean	Absolute value of variation coefficient	Minimum	Maximum	Std. Deviation
ΔPCDIGR	−0.0733	39.8864	−5.6400	5.1600	2.9250
ΔWMCI	−0.2253	12.2658	−4.4800	6.0500	2.7639
ΔCPI	0.0667	40.6255	−6.6000	4.0000	2.7084
ΔM2GR	0.0720	64.1453	−9.4700	10.6500	4.6185
ΔCGPI	−0.3467	16.9183	−11.8900	11.5600	5.8650

Table 3. V Dimension Variables Volatility (ΔROE&ΔNPM)

Industry	ΔROE					ΔNPM
	Mean	Absolute value of variation coefficient	Minimum	Maximum	Std. Deviation	Mean	Absolute value of variation coefficient	Minimum	Maximum	Std. Deviation
Industry average	0.2367	10.0706	−3.6600	5.9200	2.3834	0.0527	56.0747	−7.1300	3.5500	2.9533
Energy	−0.1787	17.5118	−4.3300	5.6100	3.1288	−0.1420	14.2917	−2.8600	6.0700	2.0294
Materials	−0.1307	29.9102	−8.7900	5.0000	3.9083	−0.2360	8.7238	−4.2800	2.3200	2.0588
Capital goods	0.1393	13.3939	−3.2000	2.8400	1.8662	0.0593	14.7727	−1.6600	1.4500	0.8765
Commercial and special services	0.0407	588.4544	−32.5500	52.8100	23.9305	−0.0013	27,335.0719	−112.7500	56.2200	36.4468
Transportation	0.1200	40.5973	−11.2900	9.1300	4.8717	−0.0487	115.8236	−10.4400	10.6000	5.6367
Automobiles & components	0.5373	10.7517	−7.0000	14.4200	5.7773	0.2967	9.1510	−3.3400	7.0000	2.7148
Consumer durables & apparel	0.2867	15.0150	−10.0300	6.4400	4.3043	0.2067	13.4159	−7.6400	4.6500	2.7726
Consumer services	0.4220	4.9308	−3.1700	6.2800	2.0808	−0.0640	49.2533	−4.8500	7.4800	3.1522
Media	−0.1347	23.7686	−8.1700	5.7800	3.2008	−0.9060	8.2816	−18.0800	9.2700	7.5032
Retailing	0.4480	7.3738	−3.6500	6.6700	3.3034	0.1327	9.5749	−1.4800	3.3400	1.2703
Food & staples retailing	0.1607	19.8908	−6.0400	8.3200	3.1958	−0.0033	211.3051	−1.2100	1.3500	0.7044
Food, beverage & tobacco	0.1453	19.7157	−4.0600	4.7900	2.8653	0.0360	63.6657	−4.9700	3.4700	2.2920
Household & personal products	2.2493	3.4210	−9.5300	24.2800	7.6950	1.6173	4.0249	−8.6200	18.9500	6.5096
Health care equipment & services	0.0067	345.9786	−5.1600	3.8900	2.3065	0.7300	3.6351	−2.1000	6.8000	2.6536
Pharmaceuticals, biotechnology & life sciences	0.2713	8.7946	−3.1200	5.8100	2.3863	0.1907	10.8986	−3.3600	4.5900	2.0780
Banks	0.2080	9.3135	−3.5000	2.9600	1.9372	−0.3147	17.6997	−15.0300	11.0200	5.5695
Diversified financials	0.6687	11.5855	−12.6500	13.7200	7.7469	1.1740	23.9784	−61.3700	73.8800	28.1506
Real estate	0.3280	6.8060	−4.1300	4.4900	2.2324	−0.0147	176.7918	−6.0500	4.7700	2.5929
Software & services	0.4487	18.0422	−15.9700	16.4200	8.0950	0.2320	26.8999	−10.5700	10.5400	6.2408
Technology hardware & equipment	−0.0053	920.2894	−10.3500	9.4900	4.9082	0.2247	13.9765	−5.4100	5.5700	3.1401
Semiconductors & semiconductor equipment	−0.1600	77.6691	−30.1100	18.4100	12.4271	−0.3040	34.0485	−23.6300	15.3200	10.3507
Telecommunication services	−0.0467	165.5913	−22.3400	16.7400	7.7276	−0.7867	7.5098	−15.8500	12.5600	5.9077
Utilities	−0.3960	10.6103	−10.7700	8.3800	4.2017	−0.8927	5.7769	−14.2300	9.0100	5.1569

Table 4. S Dimension Variables Volatility (ΔTR&ΔIAGR)

Industry			ΔTR					ΔIAGR
	Mean	Absolute value of variation coefficient	Minimum	Maximum	Std. Deviation	Mean	Absolute value of variation coefficient	Minimum	Maximum	Std. Deviation
Industry average	0.0613	13.6440	−1.1600	1.3800	0.8368	0.9240	51.9466	−114.5000	92.9200	47.9986
Energy	−0.0360	26.0159	−1.8900	1.6400	0.9366	−1.9253	46.0982	−225.0200	234.9200	88.7544
Materials	0.0373	23.8383	−1.1100	1.9700	0.8900	−0.5560	64.8933	−72.7100	101.0300	36.0807
Capital goods	0.0053	207.0749	−1.4700	2.2200	1.1044	1.4880	22.6463	−75.4100	70.8400	33.6978
Commercial and special services	0.1233	10.7281	−2.6000	2.9200	1.3231	2.8700	11.1078	−43.4200	58.1900	31.8794
Transportation	−0.0293	46.1156	−2.9000	3.3400	1.3527	−0.3860	74.8223	−69.4800	66.4500	28.8814
Automobiles & components	0.0620	9.8278	−1.1900	1.0600	0.6093	2.1440	11.3141	−34.4200	51.4300	24.2574
Consumer durables & apparel	0.1187	10.5496	−1.9400	2.5300	1.2519	2.0527	12.1354	−34.9400	57.6500	24.9099
Consumer services	0.0253	51.5132	−2.3200	3.1800	1.3050	1.0287	27.7805	−52.9200	82.7000	28.5769
Media	0.0753	8.1280	−1.5000	0.9400	0.6123	−3.1087	12.9689	−73.8100	101.1100	40.3161
Retailing	0.0893	9.4257	−1.4100	1.6500	0.8420	2.3707	12.0964	−33.1500	79.5000	28.6766
Food & staples retailing	0.0680	14.6315	−1.2400	2.5200	0.9949	0.1900	141.4345	−42.4500	66.4600	26.8726
Food, beverage & tobacco	0.0593	16.4437	−1.2400	2.7500	0.9757	−0.8573	27.4705	−41.7300	60.9200	23.5514
Household & personal products	0.1033	11.4536	−1.6400	3.2100	1.1835	2.7860	10.1644	−32.8700	75.7100	28.3181
Health care equipment & services	0.0740	15.1940	−1.5800	1.9700	1.1244	−2.3133	17.1028	−81.5200	78.1800	39.5645
Pharmaceuticals, biotechnology & life sciences	0.0573	16.3116	−1.2700	2.5900	0.9352	0.4060	64.8615	−55.6300	68.7500	26.3338
Banks	0.0067	214.1893	−2.2400	3.1600	1.4279	−3.4453	20.9832	−199.2200	132.0300	72.2941
Diversified financials	0.0360	78.7927	−5.4700	5.2700	2.8365	−1.1827	31.4023	−45.9000	90.9800	37.1384
Real estate	0.0653	19.9812	−1.7300	2.5500	1.3054	1.8607	12.5034	−29.8800	57.4100	23.2647
Software & services	0.2120	4.8201	−1.3400	2.6700	1.0219	5.9907	5.6040	−42.4800	101.7000	33.5715
Technology hardware & equipment	0.1140	6.5314	−1.0700	1.2800	0.7446	0.7427	32.1823	−32.2300	58.7600	23.9007
Semiconductors & semiconductor equipment	0.2007	8.7760	−3.1900	3.5200	1.7611	5.2367	5.0568	−25.6700	59.4500	26.4808
Telecommunication services	−0.0573	41.4467	−4.7700	6.3100	2.3763	3.5720	282.3683	−2,679.9300	2,650.8900	1,008.6197
Utilities	−0.0007	1893.4192	−2.2200	2.5600	1.2623	2.2807	13.7556	−64.2800	73.4900	31.3719

Table 5. Correlation matrix of M dimension variables

Correlation matrix
Variable		ΔPCDIGR	ΔWMCI	ΔCPI	ΔM2GR	ΔCGPI
Correlation	ΔPCDIGR	1.000	0.550	0.609	−0.464	0.533
	ΔWMCI	0.550	1.000	0.769	−0.586	0.908
	ΔCPI	0.609	0.769	1.000	−0.619	0.936
	ΔM2GR	−0.464	−0.586	−0.619	1.000	−0.630
	ΔCGPI	0.533	0.908	0.936	−0.630	1.000

Table 6. Component matrix of M dimension variables

Component matrix
Variable	Component
	1
ΔPCDIGR	0.717
ΔWMCI	0.903
ΔCPI	0.930
ΔM2GR	−0.760
ΔCGPI	0.952

Table 7. Component matrix of V dimension variables

Component matrix
Variable	Component
	1	2	3
ΔROE	0.060	0.183	0.729
ΔNPM	0.060	−0.841	0.033
ΔTEGR	−0.113	0.706	−0.330
ΔTATR	0.031	−0.145	0.707
ΔRLA	0.210	0.719	0.322
ΔTAGR	0.984	0.034	−0.084
ΔORGR	0.986	0.024	−0.066
ΔTPGR	0.952	−0.089	−0.026

Table 8. Component matrix of S dimension variables

Component matrix
Variable	Component
	1	2
ΔTR	0.15	0.99
ΔIAGR	0.96	−0.19
ΔTVGR	0.97	0.04

Figure 1. Time tendency figure of different industries’ ΔIRP.

Table 9. Random-coefficients regression of MVS three dimensions vector factor model

Random-coefficients regression					Number of obs = 360
Group variable: Industry					Number of groups = 24
					Obs per group: min = 15
					avg = 15.0
					max = 15
					Wald χ^2(6) = 226.19
					Prob > χ^2 = 0.0000
ΔIRP	Coef.	Std. Err.	z	P>|z|	[95% CI]
$f_{X_1}$	−16.66244	4.73547	−3.52000	0.00000	−25.94379	−7.38109
$f_{Y_1}$	126.49850	104.62680	1.21000	0.22700	−78.56630	331.56340
$f_{Y_2}$	0.24869	21.75617	0.01000	0.99100	−42.39261	42.89000
$f_{Y_3}$	9.81417	11.53764	0.85000	0.39500	−12.79919	32.42752
$f_{Z_1}$	170.81630	16.85810	10.13000	0.00000	137.77500	203.85760
$f_{Z_2}$	2.45629	5.79160	0.42000	0.67100	−8.89502	13.80761
_cons	0.59886	2.58457	0.23000	0.81700	−4.46680	5.66452

Notes: Test of parameter constancy: χ²(161) = 385.77 Prob > χ² = 0.0000.

Table 10. Random-coefficients regression on industry average level

Group variable: Industry average
ΔIRP	Coef.	Std. Err.	z	P > |z|	[95% CI]
$f_{X_1}$	−20.97019	7.97395	−2.63000	0.00900	−36.59884	−5.34154
$f_{Y_1}$	−149.14160	73.11899	−2.04000	0.04100	−292.45220	−5.83100
$f_{Y_2}$	−6.60444	36.85904	−0.18000	0.85800	−78.84682	65.63795
$f_{Y_3}$	54.42608	17.23106	3.16000	0.00200	20.65383	88.19833
$f_{Z_1}$	176.66950	30.25549	5.84000	0.00000	117.36980	235.96920
$f_{Z_2}$	10.87883	10.68739	1.02000	0.30900	−10.06808	31.82573
_cons	1.21460	3.25224	0.37000	0.70900	−5.15967	7.58887

Table 11. Coefficients of MVS variable factors

Industry	$f_{X_1}$	$f_{Y_1}$	$f_{Y_2}$	$f_{Y_3}$	$f_{Z_1}$	$f_{Z_2}$	_cons
Industry average	−20.97019	−149.14160	−6.60444	54.42608	176.66950	10.87883	1.21460
Energy	−15.73251	60.56367	64.17254	3.09665	231.80260	−8.81249	0.39770
Materials	−15.65044	431.08900	43.10264	−15.50516	227.54170	−6.04884	−2.66665
Capital goods	−10.70527	−125.05640	−13.01150	25.42028	172.93470	10.81857	1.74005
Commercial and special services	−10.90145	−46.78872	0.02810	6.31184	107.24610	22.81812	0.87568
Transportation	−31.10155	−109.75430	2.63305	50.12944	197.16240	−28.56211	2.54764
Automobiles & components	−24.78544	327.20480	17.31860	5.63323	215.30720	−5.63081	−0.99250
Consumer durables & apparel	−31.30670	−31.17036	−5.65125	25.00085	183.25770	−6.24954	2.08077
Consumer services	−22.84086	293.30860	12.75066	3.05782	205.26190	1.70984	−1.24938
Media	−21.34773	191.44980	26.61033	11.23670	211.99350	−3.51904	0.26980
Retailing	−6.71475	382.03740	85.37997	−9.47978	183.27040	17.09488	−3.65944
Food & staples retailing	−5.99654	333.41500	−6.36958	−15.55171	159.02040	0.98413	0.11584
Food, beverage & tobacco	−23.49480	460.83150	−28.24828	−2.21079	159.22910	1.07187	−0.40581
Household & personal products	−20.54661	340.92590	−28.07301	−23.53138	181.97080	1.00498	0.36036
Health care equipment & services	−15.24876	119.77240	−20.45014	18.08223	137.83210	−6.43722	3.43879
Pharmaceuticals, biotechnology & life sciences	−12.64302	408.21800	−41.41587	−21.02281	173.73480	−1.64450	−0.19983
Banks	−6.40596	−100.85190	−12.03998	23.62605	85.71844	25.67161	1.50555
Diversified financials	−16.16937	132.37620	28.84768	32.58611	173.04530	0.91216	−0.71854
Real estate	−17.46303	−78.17347	−27.68537	32.71354	157.60140	19.59680	1.61309
Software & services	−18.55480	218.58330	−65.56739	−24.44426	167.38400	−9.29273	1.98267
Technology hardware & equipment	−21.81561	77.43596	18.85807	16.26157	151.53840	6.91168	0.94685
Semiconductors & semiconductor equipment	−10.59395	46.49481	−24.45235	11.79327	125.45530	12.83924	0.95444
Telecommunication services	−9.17557	−150.77960	−22.40764	−9.41680	147.98410	−6.31382	3.79971
Utilities	−9.73364	3.97459	8.24379	37.32704	166.62930	9.14939	0.42135