The pricing of anomalies using factor models: a test in Latin American markets

Carvalho, Gabriel Augusto de; Amaral, Hudson Fernandes; Pinheiro, Juliano Lima; Correia, Laíse Ferraz

doi:10.1590/1808-057x202111640

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Original Article • Rev. contab. finanç. 32 (87) • Sep-Dec 2021 • https://doi.org/10.1590/1808-057x202111640 copy

The pricing of anomalies using factor models: a test in Latin American markets^* * The authors would like to thank the Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG) for the financial support provided to this study.

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This article aimed to test the five-factor model in Latin American emerging markets. In order to verify which set of factors best fits the data, the three- and four-factor models were also estimated. Asset pricing models have been proposed within the context of developed markets, with few empirical tests of these models performed based on emerging markets’ data. This study is based on the differences between the markets of developed and emerging countries, which affect the models’ predictive power and, thus, the investors’ decision-making process. The study also provides evidence that contributes to a more assertive decision-making by all financial market players. In addition, the study results suggest an opportunity to carry out tests with the inclusion of new factors in the models. The study sample included assets listed on stock exchanges in Brazil, Chile, Colombia, Mexico and Peru between June 1999 and June 2017. The building of the factors was based on the return differential between portfolios formed based on the characteristics of the assets, and the models were estimated using the two-step regression methodology. The results for the first- and second-step regressions indicated that the five-factor model had the best predictive power. However, in the second-step estimation, none of the models was able to fully explain the returns on the portfolios. Our conclusion is that the five-factor model showed the best performance for the sample, although there may be other relevant factors that could be incorporated into it. The main contribution of this article lies in the better knowledge it provides of the relevant factors for the asset pricing in emerging markets.

Keywords:
asset pricing; factor models; pricing factors; emerging markets; Latin America

Authors	Sample	Factors included	Main findings
Cakici et al. (2013Cakici, N., Fabozzi, F. J., & Tan, S. (2013). Size, value, and momentum in emerging market stock returns. Emerging Markets Review, 16, 46-65.)	18 emerging markets	Market; size; value; and momentum	Local factors showed a better predictive power compared with American and global factors.
Hanauer and Linhart (2015Hanauer, M. X., & Linhart, M. (2015). Size, value, and momentum in emerging market stock returns: integrated or segmented pricing? Asia-Pacific Journal of Financial Studies, 44, 175-214.)	21 emerging markets	Market; size; value; and momentum	The model with the greater predictive power was based on Carhart (1997Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-81.) and used local factors.
Cakici et al. (2016Cakici, N., Tang, Y., & Yan, A. (2016). Do the size, value, and momentum factors drive stock returns in emerging markets? Journal of International Money and Finance, 69, 179-204.)	18 emerging markets	Market; size; value; and momentum	The value and momentum factors fail to explain asset returns.
Xie and Qu (2016Xie, S., & Qu, Q. (2016). The three-factor model and size and value premiums in China’s stock market. Emerging Markets Finance & Trade, 52(5), 1092-1105.)	Shanghai Stock Exchange (SSE)	Market; size; and value	The model of Fama and French (1993Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.) performed well, being able to increase the predictive power compared with CAPM.
Siqueira, Amaral and Correia (2017Siqueira, L. S., Amaral, H. F., & Correia, L. F. (2017). O efeito do risco de informação assimétrica sobre o retorno de ações negociadas na BM&FBOVESPA. Revista Contabilidade & Finanças, 28(75), 425-444.)	Brazilian Market (B3)	Market; size; value; momentum; investment; profitability; and volume-synchronized probability of informed trading (VPIN)	The VPIN factor increased the models' explanatory power. The model that performed better was composed of market, size, investment, profitability and VPIN factors.
Zaremba and Czapkiewicz (2017Zaremba, A., & Czapkiewicz, A. (2017). Digesting anomalies in emerging European markets: a comparison of factor pricing models. Emerging Markets Review, 31, 1-15.)	5 Eastern-European emerging markets	Market; size; value; momentum; investment; and profitability	The model of Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.) best explains the returns of anomaly portfolios.
Foye (2018Foye, J. (2018). A comprehensive test of the Fama-French five-factor model in emerging markets. Emerging Markets Review, 37, 199-222.)	18 emerging markets	Market; size; value; investment; and profitability	The factors used by Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.) offered a better description of returns in Eastern Europe and Latin America, whereas for Asia this model failed to increase the explanatory power of the model of Fama and French (1993Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.).
Leite et al. (2018Leite, A. L., Klotzle, M. C., Pinto, A. C. F., & Silva, A. F. (2018). Size, value, profitability, and investment: evidence from emerging markets. Emerging Markets Review, 36, 45-59.)	12 emerging markets	Market; size; value; investment; and profitability	The models of Carhart (1997Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-81.) and Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.) performed better, the value factor showed to be redundant in the model of Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.).
Ali, Khurram and Jiang (2019Ali, F., Khurram, M. U. & Jiang, Y. (2019). The five-factor asset pricing model tests and profitability and investment premiums: evidence from Pakistan. Emerging Markets Finance & Trade, 1-23.)	Pakistan’s Market	Market; size; value; momentum; investment; and profitability	The model using the factors of Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.) showed the greater predictive power. An important point is that the momentum and value factors were redundant.
Ganz, Schlotefeldt and Rodrigues Junior (2020Ganz, A. C. S., Schlotefeldt, J. O., & Rodrigues Junior, M. M. (2020). Modelos de precificação de ativos financeiros e governança corporativa. Revista de Administração Mackenzie, 21(2), 1-27.)	Brazilian Market (B3)	Market; size; value; investment; profitability; and corporate governance	Results showed that the market risk factor was the only significant one, regardless of the combination of factors tested.

	Brazil	Chile	Colombia	Mexico	Peru	Total
2000	109	70	8	65	21	273
2001	119	63	8	69	25	284
2002	123	61	9	61	29	283
2003	128	65	9	58	31	291
2004	141	64	9	58	35	307
2005	144	68	7	60	40	319
2006	161	78	6	60	47	352
2007	178	88	6	58	48	378
2008	211	81	5	58	51	406
2009	229	76	7	66	49	427
2010	231	84	7	67	47	436
2011	223	92	8	71	44	438
2012	233	84	9	69	37	432
2013	224	84	12	67	35	422
2014	215	86	19	66	31	417
2015	201	82	17	70	26	396
2016	192	78	20	73	27	390
2017	197	80	21	71	28	397

Model	Equation	Empirical basis
Three-factor	$R_{i} - R_{f} = α_{i} + β_{i} (R_{m} - R_{f}) + s_{i} S M B + h_{i} H M L + ε_{i}$	Fama and French (1993Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.)
Four-factor	$R_{i} - R_{f} = α_{i} + β_{i} (R_{m} - R_{f}) + s_{i} S M B + h_{i} H M L + w_{i} W M L + ε_{i}$	Carhart (1997Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-81.)
Five-factor	$R_{i} - R_{f} = α_{i} + β_{i} (R_{m} - R_{f}) + s_{i} S M B + h_{i} H M L + r_{i} R M W + c_{i} C M A + ε_{i}$	Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.)

Model	Equation	Empirical basis
Three-factor	$\bar{R} = γ_{0} + γ_{1} β + γ_{2} s + γ_{3} h + ε_{i}$	Fama and French (1993Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.)
Four-factor	$\bar{R} = γ_{0} + γ_{1} β + γ_{2} s + γ_{3} h + γ_{4} w + ε_{i}$	Carhart (1997Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-81.)
Five-factor	$\bar{R} = γ_{0} + γ_{1} β + γ_{2} s + γ_{3} h + γ_{5} r + γ_{6} c + ε_{i}$	Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.)

Variable	Classification	Factor
Size	Median	SMB_B/M = ${S M B}_{B ∕ M} = (S H + S N + S L) / 3 - (B H + B N + B L) / 3$
		${S M B}_{L u c} = (S R + S N + S W) / 3 - (B R + B N + B W) / 3$
		${S M B}_{I n v} = (S C + S N + S A) / 3 - (B C + B N + B A) 3$
		$S M B = ({S M B}_{B / M} + {S M B}_{L u c} + {S M B}_{I n v}) / 3$
Book-to-market	30th and 70th percentiles	$H M L = (S H + B H) / 2 - (S L + B L) / 2$
Momentum	30th and 70th percentiles	$W M L = ({S W}_{i n} + {B W}_{i n}) / 2 - (S_{L o s} + B_{L o s}) / 2$
Profitability	30th and 70th percentiles	$R M W = (S R + B R) / 2 - (S W + B W) / 2$
Investment	30th and 70th percentiles	$C M A = (S C + B C) / 2 - (S A + B A) / 2$

Panel (a): Portfolios formed by size - book-to-market
	Size					Book-to-market
	Low	2	3	4	High	Low	2	3	4	High
Small	37.16	31.92	35.06	32.36	20.64	0.94	2.24	3.91	6.85	26.14
2	202.19	190.58	195.20	181.38	174.20	0.56	1.08	1.71	2.88	9.48
3	595.75	545.91	552.13	546.51	549.39	0.41	0.83	1.29	2.15	7.15
4	1498.66	1441.27	1412.36	1333.77	1376.17	0.31	0.65	1.03	1.72	5.76
Big	10532.17	8392.76	7629.42	7509.62	7404.11	0.24	0.47	0.73	1.21	3.12
Panel (b): Portfolios formed by size - investment
	Size					Investment
	Low	2	3	4	High	Low	2	3	4	High
Small	31.17	31.70	32.14	28.76	33.24	-0.21	-0.06	0.02	0.12	0.48
2	182.68	182.43	194.30	196.38	188.30	-0.16	-0.02	0.05	0.14	0.49
3	551.20	556.07	550.61	564.68	570.09	-0.12	-0.01	0.07	0.16	0.56
4	1373.81	1418.07	1433.96	1404.19	1437.23	-0.12	0.00	0.08	0.17	0.62
Big	6286.97	8604.36	9039.85	9241.75	8381.72	-0.10	0.01	0.09	0.18	0.55
Panel (c): Portfolios formed by size - profitability
	Size					Profitability
	Low	2	3	4	High	Low	2	3	4	High
Small	27.97	30.23	35.01	34.76	29.30	-0.76	0.01	0.10	0.18	0.96
2	174.62	190.35	192.15	189.65	197.58	-0.13	0.08	0.14	0.22	0.44
3	528.38	571.35	562.52	545.58	584.12	0.00	0.11	0.17	0.25	0.57
4	1391.35	1392.12	1395.13	1435.58	1454.04	0.03	0.13	0.19	0.28	0.68
Big	5560.85	7312.36	7555.83	10434.41	10700.42	0.00	0.14	0.21	0.31	0.61

Panel (a): Portfolios formed by size - book-to-market
	Average					Standard deviation
	Low	2	3	4	High	Low	2	3	4	High
Small	0.8436	1.6775	1.8581	2.0105	2.2637	9.0437	8.3484	9.6646	9.0696	8.4727
2	1.2731	1.2952	1.7941	2.7619	1.8136	8.8339	7.4174	7.8206	8.5000	9.3274
3	0.5159	1.3284	0.9358	1.5069	1.5458	8.1598	7.1883	8.0903	7.8140	8.6186
4	0.9368	0.8417	1.1315	1.0921	1.1476	6.8290	6.6835	6.6623	7.3880	8.3322
Big	0.4209	0.3880	0.4499	0.9325	0.7213	7.1090	6.6723	7.0559	7.9369	9.6569
Panel (b): Portfolios formed by size - investment
	Average					Standard deviation
	Low	2	3	4	High	Low	2	3	4	High
Small	1.6851	1.5126	1.6140	2.1141	1.6395	10.1082	8.7661	9.2969	8.2701	9.1962
2	2.0772	1.7192	2.1014	1.7472	1.1454	9.0066	7.9045	9.0331	7.7572	8.8953
3	1.1125	1.3214	1.4360	1.0629	0.7175	7.4009	7.6881	7.7626	7.8410	9.9135
4	0.8620	1.0621	1.1183	1.0570	1.0488	7.3286	7.1012	6.5647	7.2185	8.2037
Big	0.2964	0.8184	0.4306	0.7031	0.4818	7.5539	7.3562	7.9723	7.8180	8.4644
Panel (c): Portfolios formed by size - profitability
	Average					Standard deviation
	Low	2	3	4	High	Low	2	3	4	High
Small	1.5424	1.9536	1.3257	1.8692	1.9659	10.7182	8.8083	8.3039	7.7938	10.1249
2	1.9084	1.2445	1.4908	1.6217	2.4318	9.7890	7.6491	7.4476	8.0016	8.9191
3	0.7834	1.1481	1.4690	1.1965	1.1571	8.5374	7.7659	7.4743	7.2863	8.8785
4	0.8954	0.7066	0.9109	1.2370	1.3156	7.0042	7.9307	6.4517	6.6165	7.8578
Big	0.3354	0.4861	0.3406	0.9200	0.5517	8.9496	7.0948	7.0585	7.9690	7.4829

Panel (a): Descriptive statistics for the three-factor of Fama and French (1993Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.) and for the momentum factor of Carhart (1997Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-81.)
	Rm-Rf		SMB	HML	WML
Average	0.7750		0.8783	0.4460	0.5629
Standard deviation	6.9756		2.7187	3.9544	4.8929
Skewness	-0.9295		0.0852	-0.0215	-0.3034
Kurtosis	3.2129		-0.0090	1.1484	1.6118
t-statistics	1.6328		4.7480	1.6577	1.6909
P-value	0.1040		0.0000	0.0988	0.0923
Panel (b): Descriptive statistics for the five-factor of Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.)
	Rm-Rf	SMB	HML	CMA	RMW
Average	0.7750	0.9076	0.4460	0.1586	0.2749
Standard deviation	6.9756	2.7721	3.9544	4.1325	3.3548
Skewness	-0.9295	0.1468	-0.0215	0.0445	-0.9242
Kurtosis	3.2129	-0.0359	1.1484	1.3586	3.3941
t-statistics	1.6328	4.8117	1.6577	0.5640	1.2044
P-value	0.1040	0.0000	0.0988	0.5733	0.2297

Panel (a): Correlation between the three-factor of Fama and French (1993Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.) and the momentum factor of Carhart (1997Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-81.)
	Rm-Rf		SMB	HML	WML
Rm-Rf	1
SMB	-0.1525		1
HML	0.4043		0.0306	1
WML	-0.1411		-0.1187	-0.3166	1
Panel (b): Correlation between the five-factor of Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.)
	Rm-Rf	SMB	HML	RMW	CMA
Rm-Rf	1
SMB	-0.1111	1
HML	0.4043	0.0359	1
RMW	-0.1346	-0.2194	-0.2699	1
CMA	-0.2108	0.0428	0.1773	-0.2243	1

Panel (a): Portfolios formed by size - book-to-market
	GRS	*p-value*	A\|α_i\|	s(α)	A\|α_i\|/A\|r_i\|	R²
Three factors	1.7815	0.0165	0.2731	0.3803	0.5676	0.7657
Four factors	1.6918	0.0265	0.2600	0.3769	0.5402	0.7684
Five factors	1.5884	0.0447	0.2547	0.3574	0.5292	0.7715
Panel (b): Portfolios formed by size - investment
	GRS	*p-value*	A\|α_i\|	s(α)	A\|α_i\|/A\|r_i\|	R²
Three factors	1.1879	0.2548	0.2229	0.2996	0.5180	0.7265
Four factors	1.5134	0.0641	0.2610	0.3565	0.6066	0.7315
Five factors	1.1164	0.3277	0.2496	0.3140	0.5801	0.7574
Panel (c): Portfolios formed by size - profitability
	GRS	*p-value*	A\|α_i\|	s(α)	A\|α_i\|/A\|r_i\|	R²
Three factors	1.4103	0.1029	0.2533	0.3359	0.5911	0.7441
Four factors	1.3569	0.1300	0.2305	0.3288	0.5379	0.7475
Five factors	1.1291	0.3139	0.2085	0.2515	0.4866	0.7600

Panel (a): Portfolios formed by size - book-to-market
	Pre-2009			Post-2009
	GRS	p-value	A\|α_i\|	GRS	p-value	A\|α_i\|
Three factors	1.8508	0.0207	0.4563	1.8030	0.0255	0.25840
Four factors	1.7970	0.0264	0.4422	1.5870	0.0636	0.28518
Five factors	1.7163	0.0375	0.4412	1.5711	0.0683	0.23002
Panel (b): Portfolios formed by size - investment
	Pre-2009			Post -2009
	GRS	p-value	A\|α_i\|	GRS	p-value	A\|α_i\|
Three factors	1.1960	0.2694	0.3737	0.8840	0.6246	0.27889
Four factors	1.1897	0.2754	0.3900	0.8505	0.6674	0.28041
Five factors	1.1400	0.3223	0.3704	0.6742	0.8662	0.25086
Panel (c): Portfolios formed by size - profitability
	Pre-2009			Post -2009
	GRS	p-value	A\|α_i\|	GRS	p-value	A\|α_i\|
Three factors	1.8827	0.0180	0.5128	1.4471	0.1101	0.40548
Four factors	1.8353	0.0224	0.5084	1.2600	0.2182	0.40767
Five factors	1.6781	0.0440	0.4974	1.2960	0.1932	0.32200

Variable	Three factors	Four factors	Five factors
β	1.0235	1.0216	1.0246
s	1.0303	1.0678	1.0452
h	1.0105	1.0055	1.0378
w	-	1.0475	-
r	-	-	1.0544
c	-	-	1.0299

Model	DW	p-value	BP	p-value	Hausman	p-value
Three factors	2.0480	0.5743	5.3742	0.1464	2.4555	0.4834
Four factors	2.0686	0.6200	9.1008	0.0586	2.8188	0.5886
Five factors	2.1301	0.7375	11.3020	0.0457	3.4976	0.6237

Panel (a): Three-factor Fama and French (1993Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.)
	γ₀	γ₁	γ₂	γ₃			Adjusted R^²
Coef	1.6041	-0.9308	0.9527	0.3226			0.6555
p-val	0.0000	0.0002	0.0000	0.0082			0.6555
Panel (b): Four-factor Carhart (1997Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-81.)
	γ₀	γ₁	γ₂	γ₃	γ₄		Adjusted R^²
Coef	1.5997	-0.9217	0.9784	0.3582	0.2020		0.6606
p-val	0.0000	0.0003	0.0000	0.0037	0.5001		0.6606
Panel (c): Five-factor Fama and French (2015Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.)
	γ₀	γ₁	γ₂	γ₃	γ₅	γ₆	Adjusted R^²
Coef	1.7301	-1.0481	0.9246	0.3988	0.2946	-0.0410	0.6958
p-val	0.0000	0.0002	0.0000	0.0018	0.0774	0.7821	0.6958

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The pricing of anomalies using factor models: a test in Latin American markets* * The authors would like to thank the Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG) for the financial support provided to this study.

ABSTRACT

The pricing of anomalies using factor models: a test in Latin American markets^* * The authors would like to thank the Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG) for the financial support provided to this study.