Empirical measures of symmetry of market sentiments

Figures & data

Table 1. The daily domestic company indices and log returns

Day t:	1	2	3	…	t	…	n − 1	n
DCI Pt:	P1	P2	P3	…	Pt	…	Pn−1	Pn
Log return index $r_t=\ell ln\left(\frac{P_t}{P_{t-1}}\right)$	–	$\ell ln\left(\frac{P_2}{P_1}\right)$	$\ell ln\left(\frac{P_3}{P_2}\right)$	…	$\ell ln\left(\frac{P_t}{P_{t-1}}\right)$	…	$\ell ln\left(\frac{P_{n-1}}{P_{n-2}}\right)$	$\ell ln\left(\frac{P_n}{P_{n-1}}\right)$

Table 2. Table of states and observed frequencies

States	S1	·	·	·	Si	·	·	·	Sk	Total
Observed frequency	f1	·	·	·	fi	·	·	·	fk	$W=\sum _{i=1}^k{f}_i$

Table 3. Simulated values of bias, MAD and S.D of measures of equi-symmetry for equi-symmetric market sentiments

No. of weeks (W)		50			100			150
Measure	Criteria	Simulation run (N)
		1,000	2,000	5,000	1,000	2,000	5,000		1,000	2,000	5,000
ESDME (0)	BIAS	8.0	7.9	8.0	15.6	15.9	15.8		24.3	23.6	24.3
	MAD	8.0	7.9	8.0	15.6	15.9	15.8		24.3	23.6	24.3
	S.D	5.24	5.50	5.64	11.21	11.12	11.19		17.53	16.59	17.28
ESADME (0)	BIAS	2.24	2.23	2.23	3.14	3.17	3.16		3.91	3.86	3.93
	MAD	2.24	2.23	2.23	3.14	3.17	3.16		3.91	3.86	3.93
	S.D	0.82	0.85	0.86	1.20	1.20	1.19		1.47	1.45	1.47
ESNME (0)	BIAS	0.22	0.22	0.22	0.16	0.16	0.16		0.13	0.13	0.13
	MAD	0.22	0.22	0.22	0.16	0.16	0.16		0.13	0.13	0.13
	S.D	0.08	0.08	0.09	0.06	0.06	0.06		0.05	0.05	0.05
ESSAME (0)	BIAS	−0.02	−0.03	−0.03	−0.023	−0.020	−0.020		−0.011	−0.008	−0.018
	MAD	0.02	0.03	0.03	0.023	0.020	0.020		0.011	0.008	0.018
	S.D	0.23	0.23	0.21	0.23	0.23	0.23		0.23	0.23	0.24
ESSDME (0)	BIAS	0.37	0.45	0.44	0.71	0.59	0.68		0.75	0.60	0.72
	MAD	0.37	0.45	0.44	0.71	0.59	0.68		0.75	0.60	0.72
	S.D	2.30	2.40	2.39	4.86	4.85	4.71		7.14	6.88	7.01

Table 4. Simulated values of bias, MAD and S.D of measures of equi-symmetry for non-equi-symmetry market sentiments

No. of weeks		50			100			150
Measure	Criteria	Simulation run
		1,000	2,000	5,000	1,000	2,000	5,000	1,000	2,000	5,000
ESDME (67.2, 120, 50)	BIAS	6.63	6.65	6.52	16.72	13.67	14.35	24.65	24.75	23.42
	MAD	73.83	73.85	73.72	136.72	133.67	134.35	74.65	74.75	73.42
	S.D	18.72	19.69	19.13	48.49	47.43	48.49	39.14	37.04	37.70
ESADME (8, 8, 6)	BIAS	0	0	0	1.33	1.26	1.24	1.19	1.19	1.11
	MAD	8.00	7.99	7.99	9.33	9.25	9.24	7.19	7.19	7.11
	S.D	1.09	1.14	1.12	1.65	1.63	1.63	2.04	1.96	2.01
ESNME (0.8, 0.4, 0.2)	BIAS	0	0	0	0.07	0.06	0.06	0.04	0.04	0.04
	MAD	0.80	0.80	0.80	0.47	0.46	0.46	0.24	0.24	0.24
	S.D	0.11	0.11	0.11	0.08	0.08	0.08	0.06	0.06	0.06
ESSNME (0, 0, 0)	BIAS	−0.20	−0.20	−0.20	−0.21	−0.20	−0.21	−0.02	−0.02	−0.02
	MAD	0.20	0.20	0.20	0.21	0.20	0.21	0.02	0.02	0.02
	S.D	0.040	0.034	0.034	0.241	0.237	0.244	0.224	0.231	0.230
ESSDME (128.8, 0.5, 0)	BIAS	15.5	15.8	15.6	42.1	40.4	41.7	3.50	3.22	3.42
	MAD	15.67	15.88	15.75	42.21	40.52	41.80	3.49	3.22	3.42
	S.D	7.60	7.84	7.46	30.74	30.09	31.57	17.62	16.85	17.20

Table 5. Simulated values of Bias, MAD and S.D of measures of complete symmetry for complete symmetric market sentiments

No. of weeks (W)		50			100			150
Measure	Criteria	Simulation run (N)
		1,000	2,000	5,000	1,000	2,000	5,000	1,000	2,000	5,000
CSDMC (0)	BIAS	9.00	8.95	8.82	18.77	18.31	17.76	26.28	27.02	26.38
	MAD	9.00	8.95	8.82	18.77	18.31	17.76	26.28	27.02	26.38
	S.D	8.77	8.91	8.48	20.0	18.79	18.72	26.53	26.14	26.66
CSADMC (0)	BIAS	1.52	1.51	1.50	2.16	2.13	2.10	2.60	2.64	2.58
	MAD	1.52	1.51	1.50	2.16	2.13	2.10	2.60	2.64	2.58
	S.D	0.80	0.81	0.80	1.16	1.14	1.13	1.36	1.39	1.38
CSNMC (0)	BIAS	0.16	0.16	0.16	0.11	0.11	0.11	0.08	0.08	0.08
	MAD	0.16	0.16	0.16	0.11	0.11	0.11	0.08	0.08	0.08
	S.D	0.11	0.13	0.12	0.08	0.07	0.07	0.05	0.05	0.05
CSSAMC (0)	BIAS	0.05	0.05	0.05	0.02	0.02	0.02	0.01	0.01	0.01
	MAD	0.05	0.05	0.05	0.02	0.02	0.02	0.01	0.01	0.01
	S.D	0.19	0.17	0.17	0.10	0.10	0.10	0.08	0.07	0.07
CSSDMC (0)	BIAS	0	−0.24	−0.03	0.18	0.53	−0.37	−0.64	−0.38	−0.25
	MAD	0	0.24	0.03	0.18	0.53	−0.37	0.64	0.38	0.25
	S.D	10.92	10.92	10.4	24.14	23.35	22.99	32.78	32.18	32.21

Table 6. Simulated values of Bias, MAD and S.D of measures of complete symmetry for asymmetric market sentiments

No. of weeks		50			100			150
Measure	Criteria	Simulation run
		1,000	2,000	5,000	1,000	2,000	5,000	1,000	2,000	5,000
CSDMC (155.6, 1,640, 3,445)	BIAS	5.9	6.3	5.6	16.9	12.6	12.6	−3.5	−13.9	−0.6
	MAD	161.5	161.9	161.2	441.9	437.6	437.6	1,636.5	1,626.2	1,639.35
	S.D	44.7	45.1	45.2	105.2	106.3	106.2	269.9	260.0	270.9
CSADMC (6.8, 20, 33)	BIAS	0	0	0	0.1	0	0	2.7	2.7	2.7
	MAD	6.9	6.8	6.8	11.1	11.0	11.0	18.7	18.7	18.7
	S.D	1.0	1.4	1.0	1.4	1.5	1.5	1.6	1.5	1.6
CSNMC (0.32, 0.38, 0.352)	BIAS	0	0	−0.1	0	0	0	0.24	0.24	0.24
	MAD	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3
	S.D	0.1	0.1	0.1	0.04	0.04	0.04	0.1	0.1	0.1
CSSNMC (−0.32, −0.002, −0.352)	BIAS	−0.62	−0.63	−0.63	−0.55	−0.55	−0.55	−0.27	−0.27	−0.27
	MAD	0.30	0.30	0.30	0.27	0.27	0.27	0.15	0.15	0.15
	S.D	0.07	0.06	0.06	0.04	0.04	0.04	0.11	0.14	0.12
CSSDMC (155.6, −1,600, 3,445)	BIAS	5.9	6.3	5.6	16.8	12.4	12.5	32.6	21.9	35.31
	MAD	161.5	161.9	161.1	441.8	437.4	437.4	1,632.6	1,621.8	1,635.3
	S.D	44.8	45.1	45.2	105.3	106.4	106.2	270.1	260.5	271.2

Table 7. Summary statistics for domestic company weekly return indices

Statistics	NAP	STANCHART
Mean	0.0001828	−0.0006268
Maximum	0.0039420	0.0000
Minimum	0.00000	−0.012350
Std. Dev.	0.000602	0.001952
Skewness	4.891232	−4.559608
Kurtosis	26.58265	22.92539
Jarque-Bera (JB)	1,888.7	1,434
Probability	0.0000	0.0000
ADF-test statistics	−3.3792	−3.3665
Probability	0.06874	0.07073
No. of observations	51	51

Figure 1. Weekly and daily returns for NAP from January 2016 to December 2016.

Figure 2. Weekly and daily returns for STANCHART from January 2016 to December 2016.

Table 8. Empirical measures of market symmetry

Measures	NAP	STANCHART
CSDMC	0.4	0.4
CSADMC	0.4	0.4
CSNMC	0.09	0.14
CSSNMC	0.01	0.14
CSSDMC	0	0.4
ESDME	606	146
ESADME	44	9.6
ESNME	4.4	0.96
ESSNME	4.4	0.96
ESSDME	606	146

Figure 3. Plot of NAP and STANCHART absolute market sentiment states for year 2016.

Table

Week	State	Week	State	Week	State	Week	State
2	S1	17	S3	32	S2	47	S3
3	S3	18	S3	33	S3	48	S3
4	S5	19	S3	34	S3	49	S3
5	S1	20	S5	35	S3	50	S3
6	S4	21	S1	36	S3	51	S3
7	S2	22	S4	37	S3	52	S3
8	S4	23	S5	38	S3
9	S2	24	S1	39	S3
10	S3	25	S3	40	S3
11	S4	26	S3	41	S3
12	S2	27	S3	42	S3
13	S5	28	S3	43	S3
14	S1	29	S3	44	S3
15	S3	30	S4	45	S3
16	S3	31	S2	46	S3

Table

Week	State	Week	State	Week	State	Week	State
2	S4	16	S3	30	S3	44	S3
3	S3	17	S3	31	S3	45	S3
4	S3	18	S3	32	S1	46	S3
5	S3	19	S1	33	S5	47	S3
6	S3	20	S5	34	S2	48	S3
7	S2	21	S5	35	S4	49	S3
8	S3	22	S3	36	S3	50	S3
9	S4	23	S3	37	S3	51	S3
10	S1	24	S1	38	S3	52	S3
11	S5	25	S5	39	S3
12	S3	26	S1	40	S3
13	S3	27	S5	41	S3
14	S3	28	S3	42	S3
15	S3	29	S3	43	S3