Applicability of Investment and Profitability Effects in Asset Pricing Models

Machado, Márcio André Veras; Faff, Robert; Silva, Suelle Cariele de Souza e

doi:10.1590/1982-7849rac2017170027

Márcio André Veras Machado

Universidade Federal da Paraíba

Robert Faff

University of Queensland

Suelle Cariele de Souza e Silva

Universidade Federal da Paraíba

Authors’ Profiles

Márcio André Veras Machado

Cidade Universitária, s/nº, Campus I, 58051-900, Joao Pessoa, PB, Brasil. E-mail address: mavmachado@hotmail.com

Robert Faff

Room 343, Colin Clark Building, St. Lucia Campus, 4072, Brisbane, Queensland. E-mail address: r.faff@business.uq.edu.au

Suelle Cariele de Souza e Silva

Cidade Universitária, s/nº, Campus I, 58051-900, Joao Pessoa, PB, Brasil. E-mail address: su.cariele@gmail.com

Variable	ME	B/M	RET11	LIQ	E/A	INV
Average	4,123	1.24	0.11	205	0.10	1.98
SD	14,320	1.68	0.53	920	0.27	94.15
25^th	126	0.41	- 0.17	1	0.03	0.01
Median	645	0.80	0.12	9	0.09	0.09
75^th	3,054	1.43	0.38	93	0.17	0.21
CV	3.47	1.36	4.82	4.49	2.7	47.55

	Low	2	3	4	High	H-L
	Panel A: Student’s t-test
Size-based portfolios	0.012^ p-value <0.05,	0.019^* ***** p-value <0.01,	0.014^ p-value <0.05,	0.017^* ***** p-value <0.01,	0.014^ p-value <0.05,	0.002
B/M-based portfolios	0.023^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.009	0.005	-0.002	-0.025^* ***** p-value <0.01,
Momentum-based portfolios	-0.006	0.010	0.015^ p-value <0.05,	0.021^* ***** p-value <0.01,	0.031^* ***** p-value <0.01,	0.037^* ***** p-value <0.01,
Liquidity-based portfolios	0.033^* ***** p-value <0.01,	0.020^* ***** p-value <0.01,	0.021^* ***** p-value <0.01,	0.014^ p-value <0.05,	0.012^ p-value <0.05,	-0.021^ p-value <0.05,
Profitability-based portfolios	0.015^ p-value <0.05,	0.009	0.015^ p-value <0.05,	0.015^ p-value <0.05,	0.018^* ***** p-value <0.01,	0.003
Investment-based portfolios	0.017^* ***** p-value <0.01,	0.007	0.010	0.017^* ***** p-value <0.01,	0.014^ p-value <0.05,	-0.003
	Panel C: Wilcoxon test
Size-based portfolios	0.012^* ***** p-value <0.01,	0.019^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	0.002
B/M-based portfolios	0.023^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.009^ p-value <0.05,	0.005^* * p-value<0.10.	-0.002	-0.025^* ***** p-value <0.01,
Momentum-based portfolios	-0.006	0.010^ p-value <0.05,	0.015^* ***** p-value <0.01,	0.021^* ***** p-value <0.01,	0.031^* ***** p-value <0.01,	0.037^* ***** p-value <0.01,
Liquidity-based portfolios	0.033^* ***** p-value <0.01,	0.020^* ***** p-value <0.01,	0.021^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	0.012^* ***** p-value <0.01,	-0.021
Profitability-based portfolios	0.015^* ***** p-value <0.01,	0.009^ p-value <0.05,	0.015^* ***** p-value <0.01,	0.015^* ***** p-value <0.01,	0.018^* ***** p-value <0.01,	0.003
Investment-based portfolios	0.017^* ***** p-value <0.01,	0.007^ p-value <0.05,	0.010^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	-0.003

Panel A: 5 x 5 portfolios formed on size and B/M
			Low	2	3	4	High
		Small	0.026	0.017	0.011	0.006	-0.008
		2	0.026	0.029	0.015	0.012	-0.003
		3	0.018	0.025	0.015	0.004	-0.006
		4	0.031	0.020	0.014	0.012	0.003
		Big	0.020	0.022	0.011	0.011	-0.001
Panel B: 2 x 4 x 4 portfolios formed on size, B/M and profitability
Small					Big
B/M →	Low	2	3	High	B/M →	Low	2	3	High
Low E/A	0.034	0.020	0.008	-0.005	Low E/A	0.016	0.015	0.014	-0.001
2	0.028	0.022	0.006	-0.006	2	0.024	0.020	0.004	-0.004
3	0.028	0.020	0.008	0.000	3	0.020	0.018	0.005	0.001
High E/A	0.026	0.017	0.001	-0.003	High E/A	0.020	0.020	0.003	0.002
Panel C: 2 x 4 x 4 portfolios formed on size, B/M and investment
Small					Big
B/M →	Low	2	3	High	B/M →	Low	2	3	High
Low Inv	0.028	0.016	0.000	-0.002	Low Inv	0.026	0.023	0.015	-0.001
2	0.028	0.028	0.013	0.001	2	0.019	0.026	0.006	-0.003
3	0.030	0.017	0.012	0.001	3	0.021	0.016	0.012	0.000
High Inv	0.022	0.012	0.003	-0.016	High Inv	0.025	0.009	0.004	-0.003

	Intercept	ME	B/M	RET11	LIQ	RENT	INV	F stat
All	0.335^ p-value <0.05,	0.002	-0.065^* ***** p-value <0.01,	0.348^* ***** p-value <0.01,	-0.021^ p-value <0.05,	0.085	-0.039	20.46^* ***** p-value <0.01,
Small	0.579^* ***** p-value <0.01,	-0.016	-0.067^* ***** p-value <0.01,	0.368^* ***** p-value <0.01,	-0.024^ p-value <0.05,	0.101	-0.074	16,48^* ***** p-value <0.01,
Big	0.224	0.007	-0.088^* ***** p-value <0.01,	0.345^* ***** p-value <0.01,	-0.016	-0.042	-0.061	25,63^* ***** p-value <0.01,

Sort	Breakpoints	Factors and their components
Construction of models 6, 5, 4 and 1
2 x 3 combination of ME and B/M, ME and E/A, ME and INV	ME: median	SMB_B/M = (SH + SN + SL)/3 – (BH + BN + BL)/3 SMB_E/A = (SR + SN + SW)/3 – (BR + BN + BW)/3 SMB_INV = (SC + SN + SA)/3 – (BC + BN + BA)/3 SMB = (SMB_B/M + SMB_E/A + SMB_INV)/3
2 x 3 combination of ME and B/M, ME and E/A, ME and INV	B/M: percentiles E/A: 30^th and 70^th percentiles INV: 30^th and 70^th percentiles	HML = (SH + BH)/2 – (SL+ BL)/2 RMW = (SR + BR)/2 – (SW + BW)/2 CMA = (SC + BC)/2 – (SA + BA)/2
Construction of models 3 and 2
2 x 3 combination of ME and B/M, ME and MOM, ME and LIQ	ME: median	SMB_B/M = (SH + SN + SL)/3 – (BH + BN + BL)/3 SMB_Mom = (SW + SN + SL)/3 – (BW + BN + BL)/3 SMB_LIQ = (SH + SN + SL)/3 – (BH + BN + BL)/3 SMB = (SMB_B/M + SMB_Mom+ SMB_LIQ)/3
2 x 3 combination of ME and B/M, ME and MOM, ME and LIQ	B/M: 30^th and 70^th percentiles MOM: 30^th and 70^th percentiles LIQ: 30^th and 70^th percentiles	HML = (SH + BH)/2 – (SL + BL)/2 WML = (SW + BW)/2 – (SL + BL)/2 LMH = (SL + BL)/2 – (SH + BH)/2
Construction of model 7
2 x 3 combination of ME and E/A, ME and INV, ME and LIQ	ME: median	SMB_E/A = (SR + SN + SW)/3 – (BR + BN + BW)/3 SMB_INV = (SC + SN + SA)/3 – (BC + BN + BA)/3 SMB_LIQ = (SH + SN + SL)/3 – (BH + BN + BL)/3 SMB = (SMB_E/A + SMB_INV + SMB_LIQ)/3
2 x 3 combination of ME and E/A, ME and INV, ME and LIQ	E/A: 30th and 70th percentiles INV: 30th and 70th percentiles LIQ: 30th and 70th percentiles	RMW = (SR + BR)/2 – (SW + BW)/2 CMA = (SC + BC)/2 – (SA + BA)/2 LMH = (SL + BL)/2 – (SH + BH)/2

	Models 6, 5, 4 and 1				Models 3 and 2
	2 x 3 Factors	2 x 2 Factors	2 x 2 x 2 x 2 Factors		2 x 3 Factors	2 x 2 Factors	2 x 2 x 2 x 2 Factors
R_m - R_f	0.002	0.002	0.002	R_m - R_f	0.002	0.002	0.002
SMB	0.003	0.003	0.003	SMB	0.001	0.002	0.000
HML	-0.028^* ***** p-value <0.01,	-0.020^* ***** p-value <0.01,	-0.018^* ***** p-value <0.01,	HML	-0.028^* ***** p-value <0.01,	-0.020^* ***** p-value <0.01,	-0.019^* ***** p-value <0.01,
RMW	0.007^ p-value <0.05,	0.004	-0.018	WML	0.029^* ***** p-value <0.01,	0.019^* ***** p-value <0.01,	0.015^* ***** p-value <0.01,
CMA	0.000	-0.003	0.001	LMH	0.010^ p-value <0.05,	0.006^ p-value <0.05,	0.005^* * p-value<0.10.
			Model 7
			2 x 3 Factors	2 x 2 Factors	2 x 2 x 2 x 2 Factors
		R_m - R_f	0.002	0.002	0.002
		SMB	0.003	0.003	0.001
		RMW	0.007^ p-value <0.05,	0.004	0.004^* * p-value<0.10.
		CMA	0.000	-0.003	-0.001
		LMH	0.010^ p-value <0.05,	0.006^ p-value <0.05,	0.005^* * p-value<0.10.

	GRS	$\bar{\| α_{i} \|}$	R²	GRS	$\bar{\| α_{i} \|}$	R²	GRS	$\bar{\| α_{i} \|}$	R²
	2 x 3 Factors			2 x 2 Factors			2 x 2 x 2 x 2 Factors
Panel A: 25 portfolios constructed from Size and B/M
MKT SMB HML	2.144^* ***** p-value <0.01,	0.006	0.534	2.434^* ***** p-value <0.01,	0.007	0.538	2.599^* ***** p-value <0.01,	0.008	0.531
MKT SMB HML WML	2.092^* ***** p-value <0.01,	0.006	0.561	2.267^* ***** p-value <0.01,	0.006	0.561	1.799	0.005	0.539
MKT SMB HML WML LMH	1.969^* ***** p-value <0.01,	0.005	0.567	2.362^* ***** p-value <0.01,	0.006	0.574	1.797	0.005	0.553
MKT RMW CMA	3.741^* ***** p-value <0.01,	0.008	0.437	3.893^* ***** p-value <0.01,	0.008	0.445	4.072^* ***** p-value <0.01,	0.008	0.444
MKT SMB RMW CMA	3.726^* ***** p-value <0.01,	0.008	0.528	3.941^* ***** p-value <0.01,	0.008	0.540	4.202^* ***** p-value <0.01,	0.009	0.523
MKT SMB HML RMW CMA	2.139^* ***** p-value <0.01,	0.006	0.553	2.455^* ***** p-value <0.01,	0.007	0.567	2.503^* ***** p-value <0.01,	0.007	0.549
MKT SMB RMW	3.770^* ***** p-value <0.01,	0.008	0.514	3.959^* ***** p-value <0.01,	0.008	0.518	4.245^* ***** p-value <0.01,	0.009	0.497
MKT SMB CMA	3.978^* ***** p-value <0.01,	0.009	0.520	4.000^* ***** p-value <0.01,	0.009	0.533	4.168^* ***** p-value <0.01,	0.009	0.522
MKT SMB HML RMW	2.143^* ***** p-value <0.01,	0.006	0.540	2.544^* ***** p-value <0.01,	0.007	0.551	2.614^* ***** p-value <0.01,	0.008	0.534
MKT SMB HML CMA	2.150^* ***** p-value <0.01,	0.006	0.548	2.376^* ***** p-value <0.01,	0.007	0.562	2.497^* ***** p-value <0.01,	0.007	0.549
MKT SMB RMW CMA LMH	3.325^* ***** p-value <0.01,	0.008	0.530	3.865^* ***** p-value <0.01,	0.009	0.549	3.802^* ***** p-value <0.01,	0.008	0.522
MKT SMB RMW LMH	3.372^* ***** p-value <0.01,	0.008	0.516	3.949^* ***** p-value <0.01,	0.009	0.536	3.837^* ***** p-value <0.01,	0.008	0.511
MKT SMB CMA LMH	3.573^* ***** p-value <0.01,	0.009	0.522	3.851^* ***** p-value <0.01,	0.009	0.542	3.913^* ***** p-value <0.01,	0.009	0.517
Panel B: 32 portfolios constructed from Size, B/M and Profitability
MKT SMB HML	1.239	0.005	0.494	1.542^ p-value <0.05,	0.006	0.501	1.438^* * p-value<0.10	0.006	0.503
MKT SMB HML WML	1.382	0.005	0.518	1.573^ p-value <0.05,	0.005	0.514	1.032	0.005	0.494
MKT SMB HML WML LMH	1.603^* ***** p-value <0.01,	0.005	0.524	1.805^* ***** p-value <0.01,	0.005	0.523	1.146	0.005	0.503
MKT RMW CMA	2.483^* ***** p-value <0.01,	0.009	0.427	2.569^* ***** p-value <0.01,	0.010	0.437	2.657^* ***** p-value <0.01,	0.010	0.431
MKT SMB RMW CMA	2.446^* ***** p-value <0.01,	0.009	0.496	2.569^* ***** p-value <0.01,	0.010	0.506	2.633^* ***** p-value <0.01,	0.010	0.498
MKT SMB HML RMW CMA	1.217	0.005	0.522	1.477^* * p-value<0.10	0.005	0.532	1.361	0.005	0.528
MKT SMB RMW	2.477^* ***** p-value <0.01,	0.009	0.485	2.581^* ***** p-value <0.01,	0.010	0.485	2.663^* ***** p-value <0.01,	0.010	0.482
MKT SMB CMA	2.636^* ***** p-value <0.01,	0.010	0.477	2.652^* ***** p-value <0.01,	0.010	0.486	2.652^* ***** p-value <0.01,	0.010	0.485
MKT SMB HML RMW	1.226	0.005	0.511	1.539^ p-value <0.05,	0.006	0.517	1.433^* * p-value<0.10	0.006	0.518
MKT SMB HML CMA	1.231	0.005	0.506	1.490^* * p-value<0.10	0.005	0.518	1.373	0.005	0.516
MKT SMB RMW CMA LMH	2.413^* ***** p-value <0.01,	0.009	0.500	2.476^* ***** p-value <0.01,	0.009	0.512	2.528^* ***** p-value <0.01,	0.009	0.491
MKT SMB RMW LMH	2.448^* ***** p-value <0.01,	0.009	0.489	2.536^* ***** p-value <0.01,	0.009	0.498	2.553^* ***** p-value <0.01,	0.009	0.480
MKT SMB CMA LMH	2.606^* ***** p-value <0.01,	0.010	0.481	2.539^* ***** p-value <0.01,	0.010	0.493	2.644^* ***** p-value <0.01,	0.009	0.474
Panel C: 32 portfolios constructed from Size, B/M and Investment
MKT SMB HML	1.766^ p-value <0.05,	0.007	0.474	2.018^* ***** p-value <0.01,	0.007	0.483	2.003^* ***** p-value <0.01,	0.008	0.485
MKT SMB HML WML	1.743^ p-value <0.05,	0.006	0.501	1.905^* ***** p-value <0.01,	0.006	0.504	1.335	0.006	0.486
MKT SMB HML WML LMH	1.652^ p-value <0.05,	0.006	0.503	1.838^* ***** p-value <0.01,	0.007	0.512	1.278	0.006	0.495
MKT RMW CMA	3.158^* ***** p-value <0.01,	0.009	0.409	3.290^* ***** p-value <0.01,	0.010	0.421	3.290^* ***** p-value <0.01,	0.010	0.415
MKT SMB RMW CMA	3.134^* ***** p-value <0.01,	0.009	0.482	3.322^* ***** p-value <0.01,	0.010	0.493	3.354^* ***** p-value <0.01,	0.010	0.484
MKT SMB HML RMW CMA	1.789^* ***** p-value <0.01,	0.006	0.507	2.034^* ***** p-value <0.01,	0.007	0.521	1.904^* ***** p-value <0.01,	0.007	0.515
MKT SMB RMW	3.147^* ***** p-value <0.01,	0.010	0.456	3.229^* ***** p-value <0.01,	0.010	0.460	3.394^* ***** p-value <0.01,	0.011	0.452
MKT SMB CMA	3.315^* ***** p-value <0.01,	0.010	0.470	3.405^* ***** p-value <0.01,	0.011	0.481	3.376^* ***** p-value <0.01,	0.010	0.480
MKT SMB HML RMW	1.778^* ***** p-value <0.01,	0.006	0.482	2.009^* ***** p-value <0.01,	0.007	0.495	1.993^* ***** p-value <0.01,	0.008	0.492
MKT SMB HML CMA	1.781^* ***** p-value <0.01,	0.007	0.499	2.034^* ***** p-value <0.01,	0.007	0.513	1.918^* ***** p-value <0.01,	0.007	0.511
MKT SMB RMW CMA LMH	2.748^* ***** p-value <0.01,	0.009	0.483	2.997^* ***** p-value <0.01,	0.010	0.498	3.034^* ***** p-value <0.01,	0.009	0.476
MKT SMB RMW LMH	2.776^* ***** p-value <0.01,	0.009	0.457	2.927^* ***** p-value <0.01,	0.009	0.473	3.049^* ***** p-value <0.01,	0.009	0.451
MKT SMB CMA LMH	2.922^* ***** p-value <0.01,	0.010	0.472	3.054^* ***** p-value <0.01,	0.010	0.487	3.163^* ***** p-value <0.01,	0.010	0.467

	Intercept	R_m-R_f	SMB	HML	RMW	CMA	R²
	2 x 3 Factors
R_m-R_f	0.008		-0.601^* ***** p-value <0.01,	0.110	-0.195	-0.118	0.172
SMB	0.002	-0.267^* ***** p-value <0.01,		-0.066	-0.068	-0.153	0.170
HML	-0.025^* ***** p-value <0.01,	0.063	-0.085		-0.316^ p-value <0.05,	-0.072	0.068
RMW	0.002	-0.068	-0.053	-0.191^* * p-value<0.10.		-0.253^* ***** p-value <0.01,	0.126
CMA	0.001	-0.048	-0.139	-0.051	-0.295^* ***** p-value <0.01,		0.074
	2 x 2 Factors
R_m-R_f	0.003		-0.621^* ***** p-value <0.01,	-0.137	-0.550^* ***** p-value <0.01,	-0.267	0.239
SMB	0.004	-0.299^* ***** p-value <0.01,		0.036	-0.054	-0.323^* ***** p-value <0.01,	0.260
HML	-0.019^* ***** p-value <0.01,	-0.051	0.028		-0.404^* ***** p-value <0.01,	-0.263	0.103
RMW	-0.001	-0.123^ p-value <0.05,	-0.025	-0.242^* ***** p-value <0.01,		-0.378^* ***** p-value <0.01,	0.310
CMA	-0.004	-0.094^* * p-value<0.10.	-0.235^ p-value <0.05,	-0.248	-0.595^* ***** p-value <0.01,		0.301
	2 x 2 x 2 x 2 Factors
R_m-R_f	0.004		-0.728^* ***** p-value <0.01,	-0.009	-0.843^* ***** p-value <0.01,	-0.241	0.317
SMB	0.006	-0.302^* ***** p-value <0.01,		0.078	-0.135	-0.372^* ***** p-value <0.01,	0.306
HML	-0.018^* ***** p-value <0.01,	-0.003	0.063		-0.159	-0.409^ p-value <0.05,	0.143
RMW	-0.001	-0.151^* ***** p-value <0.01,	-0.058	-0.085		-0.210^* ***** p-value <0.01,	0.177
CMA	-0.004	-0.061	-0.225^ p-value <0.05,	-0.305^* * p-value<0.10.	-0.294^* ***** p-value <0.01,		0.252

	Intercept	R_m-R_f	SMB	HML	WML	LMH	R²
	2 x 3 Factors
R_m-R_f	0.014^* ***** p-value <0.01,		-0.251^ p-value <0.05,	-0.018	-0.143^* * p-value<0.10	-0.814^* ***** p-value <0.01,	0.516
SMB	-0.001	-0.152^* * p-value<0.10		-0.068	-0.048	0.184	0.183
HML	-0.023^* ***** p-value <0.01,	-0.019	-0.113		-0.109	-0.128	0.048
WML	0.023^ p-value <0.05,	-0.303	-0.169	-0.230		0.071	0.104
LMH	0.008^ p-value <0.05,	-0.462^* ***** p-value <0.01,	0.172	-0.072	0.019		0.501
	2 x 2 Factors
R_m-R_f	0.011^ p-value <0.05,		-0.287^ p-value <0.05,	-0.244^ p-value <0.05,	-0.367^* ***** p-value <0.01,	-1.023^* ***** p-value <0.01,	0.515
SMB	0.002	-0.192^ p-value <0.05,		0.105	0.016	0.235	0.200
HML	-0.015^* ***** p-value <0.01,	-0.148^* * p-value<0.10	0.095		-0.131	-0.349^* * p-value<0.10	0.068
WML	0.018^* * p-value<0.10	-0.372^ p-value <0.05,	0.024	-0.220		-0.361	0.145
LMH	0.005^* * p-value<0.10	-0.341^* ***** p-value <0.01,	0.117	-0.192^* * p-value<0.10	-0.119		0.450
	2 x 2 x 2 x 2 Factors
R_m-R_f	0.012^ p-value <0.05,		-0.459^* ***** p-value <0.01,	-0.106	-0.446^* ***** p-value <0.01,	-1.072^* ***** p-value <0.01,	0.503
SMB	0.000	-0.207^* ***** p-value <0.01,		0.045	0.088	0.055	0.210
HML	-0.020^* ***** p-value <0.01,	-0.041	0.038		0.126^* * p-value<0.10	-0.190^* * p-value<0.10	0.073
WML	0.023^* ***** p-value <0.01,	-0.340^* ***** p-value <0.01,	0.148	0.251		-0.484^* * p-value<0.10	0.249
LMH	0.005^ p-value <0.05,	-0.306^* ***** p-value <0.01,	0.035	-0.142^ p-value <0.05,	-0.182^ p-value <0.05,		0.385

Category	Anomalous Variable	Measurement
Value-versus growth	Book-to-market (B/M)	The book value of equity in December of year t-1 divided by the market value of equity in December of year t-1
	Price to earnings (P/E)	The stock price in December divided by the profit per stock in December of year t-1.
	Operational cash flow to price (OCF/P)	Obtained by dividing Earnings Before Interest, Taxes, Depreciation and Amortisation (EBITDA) by the companies’ market equity (stock price times shares outstanding); both refer to December of year t-1.
	Indebtedness (D/E)	The gross debt in December of year t-1 divided by the equity in December of year t-1.
Investment	Total Asset Variation (TAV)	The change of total asset between t-2 and t-1 divided by total asset of year t-2
	Change of investment (CI)	Annual changes in inventories between years t-2 and t-1 plus the annual changes of fixed assets of t-2 and t-1 divided by the total asset of year t-2.
	Capital expenditures growth rate (CEGR)	The value of capital expenditures of year t-1 divided by the value of capital expenditures of year t-2 minus one.
Profitability	Return on Equity (ROE)	The net profit of year t-1 divided by equity of year t-1..
	Return on asset (ROA)	Calculated as Earnings Before Interest and Taxes (EBIT) of year t-1 divided by operational asset of year t-1.
Trading frictions	Market Equity (ME)	Calculated as Earnings Before Interest and Taxes (EBIT) of year t-1 divided by operational asset of year t-1.
	Total volatility (Tvol)	The standard deviation of daily stock returns for the last 12 months before the construction of the portfolio, that is, starting July of year t-1 and finishing June of year t.
	Liquidity (LIQ)	The negotiated volume, represented by the annual average volume negotiated, in Reais, for the stock in the period of July of year t-1 to June of year t.
Momentum	Accumulated return in the last 11 months (RET11)	Comprehends the accumulated return of the 11 months before the construction of the portfolio; excluding the month immediately before the month of portfolio construction; that is, the accumulated return in the 11-month period, starting July of year t-1 and finishing in May of year t.

	B/M	P/E	OCF/P	D/E	TAV	CI	CEGR	ROE	ROA	ME	Tvol	LIQ	RET11
m	-0.025^* ***** p-value <0.01,	0.002	-0.005	0.001	-0.003	-0.004	0.006	0.005	0.003	0.002	-0.018^ p-value <0.05,	-0.021^ p-value <0.05,	0.037^* ***** p-value <0.01,
α₁	-0.012^* * p-value<0.10.	-0.003	-0.015^* ***** p-value <0.01,	-0.014^ p-value <0.05,	-0.019^* ***** p-value <0.01,	-0.017^* ***** p-value <0.01,	-0.014^ p-value <0.05,	0.001	-0.006	-0.009^* * p-value<0.10.	-0.034^* ***** p-value <0.01,	-0.036^* ***** p-value <0.01,	0.037^* * p-value<0.10.
α₂	-0.002	-0.014^ p-value <0.05,	-0.015^ p-value <0.05,	-0.011	-0.027^* ***** p-value <0.01,	-0.022^* ***** p-value <0.01,	-0.014^* * p-value<0.10.	-0.012^* * p-value<0.10.	-0.013^ p-value <0.05,	-0.019^* ***** p-value <0.01,	-0.026^* ***** p-value <0.01,	-0.028^* ***** p-value <0.01,	-0.014^ p-value <0.05,
α₃	-0.002	-0.014^ p-value <0.05,	-0.017^* ***** p-value <0.01,	-0.012	-0.026^* ***** p-value <0.01,	-0.022^* ***** p-value <0.01,	-0.014^* * p-value<0.10.	-0.011	-0.012^ p-value <0.05,	-0.017^* ***** p-value <0.01,	-0.022^* ***** p-value <0.01,	-0.022^* ***** p-value <0.01,	-0.012^ p-value <0.05,
α₄	-0.038^* ***** p-value <0.01,	-0.010^ p-value <0.05,	-0.018^* ***** p-value <0.01,	-0.011^ p-value <0.05,	-0.015^* ***** p-value <0.01,	-0.017^* ***** p-value <0.01,	-0.006	-0.006	-0.009^ p-value <0.05,	-0.011^ p-value <0.05,	-0.032^* ***** p-value <0.01,	-0.036^* ***** p-value <0.01,	0.027^* ***** p-value <0.01,
α₅	-0.038^* ***** p-value <0.01,	-0.010^ p-value <0.05,	-0.018^* ***** p-value <0.01,	-0.012^ p-value <0.05,	-0.016^* ***** p-value <0.01,	-0.017^* ***** p-value <0.01,	-0.006	-0.007	-0.010^ p-value <0.05,	-0.008^ p-value <0.05,	-0.029^* ***** p-value <0.01,	-0.033^* ***** p-value <0.01,	0.027^* ***** p-value <0.01,
α₆	-0.009^* * p-value<0.10.	-0.005	-0.014^ p-value <0.05,	-0.013^* * p-value<0.10.	-0.022^* ***** p-value <0.01,	-0.019^* ***** p-value <0.01,	-0.015^ p-value <0.05,	-0.002	-0.008^* * p-value<0.10.	-0.010^ p-value <0.05,	-0.033^* ***** p-value <0.01,	-0.036^* ***** p-value <0.01,	0.029^ p-value <0.05,
α₇	-0.032^* ***** p-value <0.01,	-0.010^* * p-value<0.10.	-0.020^* ***** p-value <0.01,	-0.012^ p-value <0.05,	-0.019^* ***** p-value <0.01,	-0.020^* ***** p-value <0.01,	-0.007	-0.010^* * p-value<0.10.	-0.012^* ***** p-value <0.01,	-0.007^ p-value <0.05,	-0.030^* ***** p-value <0.01,	-0.032^* ***** p-value <0.01,	0.026^* ***** p-value <0.01,
$\bar{\| α_{1} \|}$	0.003	0.002	0.006	0.004	0.007	0.006	0.005	0.006	0.003	0.004	0.013	0.014	0.017
$\bar{\| α_{2} \|}$	0.004	0.005	0.004	0.002	0.009	0.006	0.004	0.005	0.005	0.006	0.009	0.009	0.006
$\bar{\| α_{3} \|}$	0.003	0.005	0.005	0.003	0.009	0.006	0.005	0.006	0.005	0.005	0.007	0.007	0.006
$\bar{\| α_{4} \|}$	0.014	0.003	0.008	0.003	0.006	0.004	0.003	0.003	0.003	0.004	0.011	0.012	0.013
$\bar{\| α_{5} \|}$	0.014	0.003	0.009	0.003	0.005	0.005	0.003	0.003	0.004	0.003	0.009	0.011	0.013
$\bar{\| α_{6} \|}$	0.003	0.003	0.006	0.004	0.007	0.007	0.005	0.005	0.004	0.004	0.012	0.013	0.014
$\bar{\| α_{7} \|}$	0.011	0.003	0.009	0.004	0.006	0.005	0.004	0.003	0.003	0.004	0.009	0.011	0.013

[1] Authors’ Profiles

Márcio André Veras Machado

Cidade Universitária, s/nº, Campus I, 58051-900, Joao Pessoa, PB, Brasil. E-mail address: mavmachado@hotmail.com

Robert Faff

Room 343, Colin Clark Building, St. Lucia Campus, 4072, Brisbane, Queensland. E-mail address: r.faff@business.uq.edu.au

Suelle Cariele de Souza e Silva

Cidade Universitária, s/nº, Campus I, 58051-900, Joao Pessoa, PB, Brasil. E-mail address: su.cariele@gmail.com

	Low	2	3	4	High	H-L
	Panel A: Student’s t-test
Size-based portfolios	0.012^ p-value <0.05,	0.019^* ***** p-value <0.01,	0.014^ p-value <0.05,	0.017^* ***** p-value <0.01,	0.014^ p-value <0.05,	0.002
B/M-based portfolios	0.023^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.009	0.005	-0.002	-0.025^* ***** p-value <0.01,
Momentum-based portfolios	-0.006	0.010	0.015^ p-value <0.05,	0.021^* ***** p-value <0.01,	0.031^* ***** p-value <0.01,	0.037^* ***** p-value <0.01,
Liquidity-based portfolios	0.033^* ***** p-value <0.01,	0.020^* ***** p-value <0.01,	0.021^* ***** p-value <0.01,	0.014^ p-value <0.05,	0.012^ p-value <0.05,	-0.021^ p-value <0.05,
Profitability-based portfolios	0.015^ p-value <0.05,	0.009	0.015^ p-value <0.05,	0.015^ p-value <0.05,	0.018^* ***** p-value <0.01,	0.003
Investment-based portfolios	0.017^* ***** p-value <0.01,	0.007	0.010	0.017^* ***** p-value <0.01,	0.014^ p-value <0.05,	-0.003
	Panel C: Wilcoxon test
Size-based portfolios	0.012^* ***** p-value <0.01,	0.019^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	0.002
B/M-based portfolios	0.023^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.009^ p-value <0.05,	0.005^* * p-value<0.10.	-0.002	-0.025^* ***** p-value <0.01,
Momentum-based portfolios	-0.006	0.010^ p-value <0.05,	0.015^* ***** p-value <0.01,	0.021^* ***** p-value <0.01,	0.031^* ***** p-value <0.01,	0.037^* ***** p-value <0.01,
Liquidity-based portfolios	0.033^* ***** p-value <0.01,	0.020^* ***** p-value <0.01,	0.021^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	0.012^* ***** p-value <0.01,	-0.021
Profitability-based portfolios	0.015^* ***** p-value <0.01,	0.009^ p-value <0.05,	0.015^* ***** p-value <0.01,	0.015^* ***** p-value <0.01,	0.018^* ***** p-value <0.01,	0.003
Investment-based portfolios	0.017^* ***** p-value <0.01,	0.007^ p-value <0.05,	0.010^* ***** p-value <0.01,	0.017^* ***** p-value <0.01,	0.014^* ***** p-value <0.01,	-0.003

Brasil

Brasil

Applicability of Investment and Profitability Effects in Asset Pricing Models

Abstract