IS COMMONALITY IN LIQUIDITY A PRICED RISK FACTOR?

SILVA JÚNIOR, CLÁUDIO P.; MACHADO, MÁRCIO A. V.

doi:10.1590/1678-6971/eRAMF200158

CLÁUDIO P. SILVA JÚNIOR

Universidade Federal da Paraíba (UFPB), João Pessoa, PB, Brazil.

Cláudio P. Silva Júnior, doctor in Administration by the Graduate Program in Administration, Federal University of Paraíba (UFPB); Márcio A. V. Machado, doctor in Administration by the Graduate Program in Administration, University of Brasília (UnB). Cláudio P. Silva Júnior is now assistant professor at the Management Department of Federal University of Paraíba (UFPB); Márcio A. V. Machado is now associate professor at the Management Department of Federal University of Paraíba (UFPB).

http://orcid.org/0000-0002-3665-7077

MÁRCIO A. V. MACHADO Correspondence concerning this article should be addressed to Márcio A. V. Machado, Cidade Universitária, campus I, Castelo Branco, João Pessoa, Paraíba, Brazil, CEP 58.051-900. E-mail: mavmachado@hotmail.com

Universidade Federal da Paraíba (UFPB), João Pessoa, PB, Brazil.

Cláudio P. Silva Júnior, doctor in Administration by the Graduate Program in Administration, Federal University of Paraíba (UFPB); Márcio A. V. Machado, doctor in Administration by the Graduate Program in Administration, University of Brasília (UnB). Cláudio P. Silva Júnior is now assistant professor at the Management Department of Federal University of Paraíba (UFPB); Márcio A. V. Machado is now associate professor at the Management Department of Federal University of Paraíba (UFPB).

http://orcid.org/0000-0003-2635-5240

Correspondence concerning this article should be addressed to Márcio A. V. Machado, Cidade Universitária, campus I, Castelo Branco, João Pessoa, Paraíba, Brazil, CEP 58.051-900. E-mail: mavmachado@hotmail.com

Cláudio P. Silva Júnior, doctor in Administration by the Graduate Program in Administration, Federal University of Paraíba (UFPB); Márcio A. V. Machado, doctor in Administration by the Graduate Program in Administration, University of Brasília (UnB).

Cláudio P. Silva Júnior is now assistant professor at the Management Department of Federal University of Paraíba (UFPB); Márcio A. V. Machado is now associate professor at the Management Department of Federal University of Paraíba (UFPB).

Year	Population	Sample	% of population
2007	404	89	22.03
2008	393	129	32.82
2009	385	123	31.95
2010	381	147	38.58
2011	373	157	42.09
2012	364	162	44.50
2013	363	168	46.28
2014	363	171	47.11
2015	359	169	47.07
Average	376	146	39.22

Year	Number of stocks	Average	Minimum	Maximum	Standard deviation
2007	89	0.200	0.003	0.998	0.172
2008	129	0.189	0.001	0.910	0.151
2009	123	0.194	0.001	0.998	0.185
2010	147	0.197	0.000	0.894	0.151
2011	157	0.174	0.002	0.997	0.148
2012	162	0.167	0.000	0.998	0.152
2013	168	0.177	0.001	0.999	0.156
2014	171	0.204	0.000	0.996	0.159
2015	169	0.176	0.001	0.997	0.143
General average	146	0.186	0.001	0.976	0.157

Year	Commonality
Year	First quartile	Second quartile	Third quartile
2007	0.193	0.195	0.202
2008	0.194	0.193	0.188
2009	0.195	0.193	0.189
2010	0.193	0.192	0.193
2011	0.184	0.177	0.172
2012	0.161	0.159	0.162
2013	0.170	0.168	0.171
2014	0.191	0.192	0.200
2015	0.178	0.175	0.172

Portfolio/year	2007	2008	2009	2010	2011	2012	2013	2014	2015
LL/LC	8	10	12	14	15	18	19	17	19
LL/2C	8	10	13	15	15	14	17	17	15
LL/3C	7	9	11	14	13	16	16	17	17
LL/4C	8	10	11	13	14	14	15	16	17
LL/HC	7	11	12	15	18	15	16	17	18
HL/LC	7	10	12	15	15	14	14	16	15
HL/2C	8	11	10	13	16	16	16	17	19
HL/3C	8	10	13	15	16	14	17	17	17
HL/4C	7	10	13	15	16	16	18	17	17
HL/HC	8	10	12	14	13	16	17	16	16

Portfolio/ year	2007	2008	2009	2010	2011	2012	2013	2014	2015
LL/LC	33,259	15,629	21,800	21,264	23,087	34,134	32,552	18,579	20,891
LL/2C	30,122	18,559	24,580	47,522	20,292	23,293	30,711	23,678	13,835
LL/3C	36,867	18,545	15,963	21,620	34,260	32,256	28,239	30,273	21,947
LL/4C	35,498	16,030	11,955	17,326	27,076	27,485	25,381	21,273	22,719
LL/HC	23,083	48,596	16,573	177,731	108,572	71,973	64,255	80,175	83,601
HL/LC	324,793	274,654	218,426	266,856	305,653	274,208	208,286	360,404	371,428
HL/2C	276,651	300,932	232,031	322,741	389,622	373,858	356,403	415,802	413,304
HL/3C	220,605	303,227	284,314	380,836	295,874	358,611	385,735	300,974	479,054
HL/4C	177,661	255,741	237,459	395,533	409,728	332,639	428,312	397,112	295,139
HL/HC	342,043	200,165	284,863	257,291	266,023	384,801	407,208	393,519	348,836
Average return of portfolios per year
Portfolio/ year	2007	2008	2009	2010	2011	2012	2013	2014	2015
LL/LC	-0.362	-0.080	-0.333	0.028	-0.011	0.028	-0.012	-0.040	0.004
LL/2C	-0.051	-0.075	0.086	0.025	0.001	0.013	-0.004	-0.036	-0.052
LL/3C	-0.042	-0.081	0.095	0.029	0.016	0.040	-0.016	0.000	-0.037
LL/4C	0.015	-0.049	0.079	0.025	0.026	0.018	-0.014	-0.021	-0.031
LL/HC	-0.010	-0.063	0.089	0.007	-0.008	0.015	-0.006	-0.005	0.031
HL/LC	0.025	-0.026	0.052	-0.003	-0.010	0.011	0.003	-0.001	0.007
HL/2C	0.021	-0.057	0.040	-0.004	-0.020	0.005	-0.004	0.005	0.005
HL/3C	0.019	-0.043	0.049	-0.004	-0.018	0.024	0.015	-0.004	-0.001
HL/4C	0.037	-0.028	0.035	0.004	-0.003	0.020	0.001	-0.004	0.012
HL/HC	0.027	-0.032	0.028	0.037	0.005	0.015	-0.007	-0.001	0.018

Factors	Average (%)	Standard deviation	t-Test	P-value	Minimum	Maximum
Market	0.397	0.059	0.658	0.512	-0.255	0.121
Size	-0.227	0.041	-0.538	0.592	-0.065	0.266
Book-to-market	-2.087	0.053	-3.817	0.000	-0.111	0.272
Momentum	1.240	0.054	2.241	0.027	-0.279	0.300
Liquidity	-1.220	0.045	-2.606	0.011	-0.170	0.120
Commonality	4.165	0.282	1.448	0.151	-0.108	2.541

	Market	Size	BM	Momentum	Liquidity	Commonality
Market	1
Size	-0.239^ ,* significant at 1% and 5% respectively.	1
BM	-0.001	0.511^* ,* significant at 1% and 5% respectively.	1
Momentum	-0.297^* ,* significant at 1% and 5% respectively.	0.049	0.011	1
Liquidity	0.546^* ,* significant at 1% and 5% respectively.	0.279^* ,* significant at 1% and 5% respectively.	0.075	-0.116	1
Commonality	-0.068	0.045	0.058	-0.069	-0.184	1

Panel A: Stage 1			Panel B: Stage 2
	Coef.	t-statistics		Coef.	Shanken t-statistics
Intercept	-0.002	-1.782	Intercept	-0.003	-0.652
β _i,mkt	1.084	26.622	λ₁	0.014	1.906
β _i,smb	0.286	7.249	λ₂	-0.081	-12.544
β _,hml	-0.052	-1.612	λ₃	-0.009	-1.112
β _i,mom	0.222	7.803	λ₄	0.008	0.835
β _i,liq	0.127	1.064	λ₅	-0.011	-5.937
β _i,pcom	-0.182	-0.951	λ₆	0.043	8.705

$P \underset{─}{} Com = α + β_{i} [Market] + s_{i} (SMB) + h_{i} (HML) + m_{i} (Mom) + l_{i} (LIQ) + ε_{i}$
Model	Intercept	β _i	*s_i*	*h_i*	*m_i*	*l_i*	F statistic	Adj. R²
5 factors	0.029	0.497	1.048	0.012	-0.412	-1.803^* ***** significant at 1%.	1.134	0.007

{\hat{u}}_{i, d, t} = β_{0 i, t} + β_{1 i, t} {\hat{u}}_{m, d, t} + β_{2 i, t} {\hat{u}}_{m, d + 1, t} + β_{3 i, t} {\hat{u}}_{m, d - 1, t} + e_{i, d, t}

\begin{matrix} (R_{i, t}) - R_{f, t} = α_{i} + β_{i, mkt} [(R_{m, t}) - R_{f, t}] + β_{i, SMB} ({SMB}_{t}) + β_{i, HML} ({HML}_{t}) + \\ β_{i, MOM} ({MOM}_{t}) + β_{i, LIQ} ({LIQ}_{t}) + β_{i, COM} ({PCOM}_{t}) + ε_{i, t} \end{matrix}

({\bar{R}}_{i}) - {\bar{R}}_{f} = λ_{0} + λ_{1} {\hat{β}}_{i, mkt} + λ_{2} {\hat{β}}_{i, smb} + λ_{3} {\hat{β}}_{i, hml} + λ_{4} {\hat{β}}_{i, mom} + λ_{5} {\hat{β}}_{i, liq} + λ_{6} {\hat{β}}_{i, pcom} + ε_{i}

[1] Correspondence concerning this article should be addressed to Márcio A. V. Machado, Cidade Universitária, campus I, Castelo Branco, João Pessoa, Paraíba, Brazil, CEP 58.051-900. E-mail: mavmachado@hotmail.com

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IS COMMONALITY IN LIQUIDITY A PRICED RISK FACTOR?

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