Book-to-Market Ratio, return on equity and Brazilian Stock Returns

Araújo, Rebeca Cordeiro da Cunha; Machado, Márcio André Veras

doi:10.1108/RAUSP-04-2018-001

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Research Paper • RAUSP 53 (3) • Sept 2018 • https://doi.org/10.1108/RAUSP-04-2018-001 copy

Book-to-Market Ratio, return on equity and Brazilian Stock Returns

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Purpose

This study aims to analyze the influence of future expectations of the book-to-market ratio (B/M) and return on equity (ROE) in explaining the Brazilian capital market returns.

Design/methodology/approach

The study analyzed the explanatory power of risk-factor approach variables such as beta, size, B/M ratio, momentum and liquidity.

Findings

The results show that future expectations of the B/M ratio and ROE, when combined with proxies for risk factors, were able to explain part of the variations of Brazilian stock returns. With respect to risk factors approach variables, the authors verified the existence of size and B/M effects and a liquidity premium in the Brazilian capital market, during the period analyzed.

Research limitations/implications

This research was limited to the non-financial companies with shares traded at Brasil, Bolsa and Balcão, from January 1, 1995 to June 30, 2015. This way, the conclusions reached are limited to the sample used herein.

Practical implications

The evidences herein presented can also contribute to establishing investment strategies, considering that the B/M ratio may be calculated through accounting information announced by companies. Besides, using historical data enable investors, in a specific year, to calculate the predictor variables for the B/M ratio and ROE in the next year, which enhance the explanatory power of the current B/M, when combined in the form of an aggregate predictor variable for stock returns.

Originality/value

The main contribution of this study to the literature is to demonstrate how the expected future B/M ratio and ROE may improve the explanatory capacity of the stock return, when compared with the variables traditionally studied in the literature.

Keywords
Anomalies; Risk factors; Return on equity; Fundamental valuation; Book-to-market ratio

		Variables
Empirical evidence	Country	B/M	ROE	Method
Fairfield (1994)Fairfield, P.M. (1994), “P/E, P/B and the present value of future dividends”, Financial Analysts Journal, Vol. 50 No. 4, pp. 23-31.	USA	X	X	Accounting valuation model
Ryan (1995)Ryan, S.G. (1995), “A model of accrual measurement with implications for the evolution of the book-to-market ratio”, Journal of Accounting Research, Vol. 33 No. 1, pp. 95-128.	USA	X		B/M decomposition
Berk (1995)Berk, J. (1995), “A critique of size-related anomalies”, Review of Financial Studies, Vol. 8 No. 2, pp. 275-286.	USA	X		Market value decomposition
Berk (1997)Berk, J. (1997), “Does size really matter?”, Financial Analyst Journal, Vol. 53 No. 5, pp. 12-18.	USA	X		Portfolio analysis/regression
Frankel and Lee (1998)Frankel, R. and Lee, C.M.C. (1998), “Accounting valuation, market expectation, and cross-sectional stock returns”, Journal of Accounting and Economics, Vol. 25 No. 3, pp. 283-319.	USA	X	X	Accounting valuation model
Pontiff and Schall (1998)Pontiff, J. and Schall, L.D. (1998), “Book-to-market ratios as predictors of market returns”, Journal of Financial Economics, Vol. 49 No. 2, pp. 141-160.	USA	X		Regression analysis
Lev and Sougiannis (1999)Lev, B. and Sougiannis, T. (1999), “Penetrating the book-to-market black box: the R&D effect”, Journal of Business Finance and Accounting, Vol. 26 Nos 3/4, pp. 419-449.	USA	X	X	Portfolio analysis/regression
Beaver and Ryan (2000)Beaver, W.H. and Ryan, S.G. (2000), “Biases and lags in book value and their effects on the ability of the book-to-market ratio to predict book return on equity”, Journal of Accounting Research, Vol. 38 No. 1, pp. 127-148.	USA	X	X	B/M decomposition
Billings and Morton (2001)Billings, B.K. and Morton, R.M. (2001), “Book-to-market components, future security returns, and errors in expected future earnings”, Journal of Accounting Research, Vol. 39 No. 2, pp. 197-219.	USA	X		B/M decomposition
Vuolteenaho (2002)Vuolteenaho, T. (2002), “What drives frim-level stock returns?”, Journal of Finance, Vol. 57 No. 1, pp. 233-264.	USA	X	X	VAR model
Chen and Zhao (2006)Chen, L. and Zhao, X. (2006), “On the relation between the market-to-book ratio, growth opportunity, and leverage ratio”, Finance Research Letters, Vol. 3 No. 4, pp. 253-266.	USA	X		Portfolio analysis/regression
Clubb and Naffi (2007)Clubb, C. and Naffi, M. (2007), “The usefulness of book-to-market and ROE expectations for explaining UK stock returns”, Journal of Business Finance & Accounting, Vol. 34 Nos 1/2, pp. 1-32.	UK	X	X	Regression analysis
Fama and French (2008)Fama, E.F. and French, K.R. (2008), “Average returns, BM, and share issues”, The Journal of Finance, Vol. 63 No. 6, pp. 2971-2995.	USA	X		B/M decomposition
Almeida and Eid (2010)Almeida, J.R. and Eid, W. Jr (2010), “Estimando o retorno das ações com decomposição do índice book-to-market: Evidências na bovespa”, Revista Brasileira de Finanças, Vol. 8 No. 4, pp. 417-441.	Brazil	X		B/M decomposition
Skogsvik and Skogsvik (2010)Skogsvik, S. and Skogsvik, K. (2010), “Accounting-based probabilistic prediction of ROE, the residual income valuation model and the assessment of mispricing in the Swedish stock market”, Abacus, Vol. 46 No. 4, pp. 387-418.	Sweden		X	Accounting valuation model
Dorantes (2013)Dorantes, C.D. (2013), “The relevance of using accounting fundamentals in the Mexican stock market”, Journal of Economics, Finance and Administrative Science, Vol. 18, pp. 2-10.	Mexico	X		Portfolio analysis/regression
Lee and Zhang (2014)Lee, W.J. and Zhang, Y. (2014), “Accounting valuation and cross sectional stock returns in China”, China Accounting and Finance Review, Vol. 16 No. 2, pp. 155-169.	USA and China	X		Portfolio analysis/regression
*Evrard et al.* (2015)**Evrard, H.S., Cruz, J.A.W. and Da Silva, W.V. (2015), “Multifatorialidade e o retorno de ações brasileiras entre o período de 2003 e 2013”, Revista de Gestão, Finanças e Contabilidade, Vol. 5 No. 3, pp. 42-60.	Brazil	X	X	Forward selection regression/event study

Equation	Description
$R_{t} = \ln (\frac{P_{i t}}{P_{i t - 1}})$	P_it = Nominal closing price of stock i in year t (adjusted to gain);	P_it₋₁ = Nominal closing price of stock i in year t−1 (adjusted to gain)
${B M}_{t} = \frac{{B V}_{t - 1}}{{M V}_{t - 1}}$	BV_t₋₁ = book value on December 31 of year t − 1;	VM_t₋₁ = market value on December 31 of year t−1
${R O E}_{t} = \frac{{N P}_{t - 1}}{{B V}_{t - 1}}$	NP_t₋₁ = company's net profit on December 31 of year t−1;	BV_t₋₁ = book value on December 31 of year t − 1
FBM_{t +1} = γ₀ + γ₁BM_t	γ₀ = intercept of a model to predict the B/M, estimated through a linear dynamic panel, using data from all sample companies, from 1995 to 2010;	γ₁ = slope coefficient of a model to predict the B/M, estimated through a linear dynamic panel, using data from all sample companies, from 1995 to 2010
FROE_t+1 = λ₀ + λ₁ROE_t	λ₀ = intercept of a model to predict the ROE, estimated through a linear dynamic panel, using data from all sample companies, from 1995 to 2010;	λ₁ = slope coefficient of a model to predict the ROE, estimated through a linear dynamic panel, using data from all sample companies, from 1995 to 2010
β_t	Calculated on the 60 months immediately prior the beginning of year t, in July
SIZE_t = lnMV_t	VM_t = Market value on June 30 of year t
MOM_t	Calculated by summing up the return of the 12 months immediately prior to the beginning of year t, in July
Trading quantity	Quantity of annual trading of a stock
Traded volume	Volume of annual trading of a stock, in Brazilian Reais
Negotiability index	$N e g o t i a b i l i t y = 100 \times \frac{p}{P} \times \sqrt{\frac{n}{N} \times \frac{v}{V}}$

Variable	No. of observations	Average	SD	Minimum	Maximum
BM	1,691	3.4787	9.04	−92.67	81.30
BM forecast	1,602	3.3170	2.94	−23.24	30.08
ROE forecast	1,602	0.0957	0.02	−0.25	0.36
Aggregate forecast (FRM)	1,691	0.4269	7.32	−80.43	64.36
Beta	1,339	0.7730	0.25	−0.07	2.10
Size (in thousand R$)	1,688	5,592,396.33	20,413,196.54	376	286,390,438
Momentum	1,691	0.1125	0.47	−2.10	2.76
Liquidity
Negotiability	1,691	0.4045	1.13	0.03	12.56
Trading quantity	1,691	146.748.55	615.960.03	6	8.114.196
Traded volume (R$)	1,691	2,922,968	14,937,630.12	14	218,327,039

	BM	FBM	FROE	FRM	BETA	SIZE	MOM	LIQ¹	LIQ²	LIQ³
BM	1.000	0.751^ significant at 5%	0.038	0.957^ significant at 5%	0.007	−0.062^* * significant at 1%;	0.006	−0.035	−0.034	−0.004
FBM		1.000	0.068^ significant at 5%	0.542^ significant at 5%	0.008	−0.072^ significant at 5%	0.054^* * significant at 1%;	−0.048	−0.044	−0.020
FROE			1.000	0.302^ significant at 5%	0.027	0.054^* * significant at 1%;	−0.047	0.027	0.032	0.044
FRM					0.001	−0.054^* * significant at 1%;	−0.018	−0.030	−0.029	0.003
BETA					1.000	0.128^ significant at 5%	−0.188^ significant at 5%	0.195^ significant at 5%	0.180^ significant at 5%	0.338^ significant at 5%
SIZE						1.000	0.025	0.493^ significant at 5%	0.585^ significant at 5%	0.507^ significant at 5%
MOM							1.000	−0.066^ significant at 5%	−0.037	0.013
LIQ¹								1.000	0.843^ significant at 5%	0.566^ significant at 5%
LIQ²									1.000	0.734^ significant at 5%
LIQ³										1.000

Model	BM	FBM	FROE	FRM	Beta	Size	Momentum	Quant.	Volume	Negot.
1	2.291	2.299	1.005
4	1.005				1.017	1.022
5	1.005				1.057	1.025	1.040
6	1.006				1.219	1.543	1.061	3.585	3.705	2.569
7	2.567	2.581	1.010		1.001
8	2.567	2.586	1.013		1.019	1.028
9	2.579	2.608	1.014		1.061	1.032	1.052
10	2.580	2.609	1.016		1.223	1.550	1.070	3.597	3.994	2.814
11	3.063			3.065	1.001
12	3.082			3.068	1.017	1.022
13	3.230			3.076	1.057	1.026	1.053
14	3.238			3.246	1.219	1.544	1.075	3.583	3.707	2.572

Variable	t-statistic	p-value
Return	14.09^* Notes: *Significant at 1%;	0.0000
BM	7.84^* Notes: *Significant at 1%;	0.0000
BM forecast	4.53^* Notes: *Significant at 1%;	0.0000
ROE forecast	7.81^* Notes: *Significant at 1%;	0.0000
Aggregate forecast (FRM)	46.70^* Notes: *Significant at 1%;	0.0000
Beta	2.50^* Notes: *Significant at 1%;	0.0000
Size	1.80^ significant at 5%	0.0353
Momentum	17.64^* Notes: *Significant at 1%;	0.0000
Liquidity
Negotiability	10.56^* Notes: *Significant at 1%;	0.0000
Trading quantity	17.29^* Notes: *Significant at 1%;	0.0000
Traded volume	6.86^* Notes: *Significant at 1%;	0.0000

	Part 1-Coefficients
Model	Constant	BM	FBM	FROE	FRM
(1)	0.0400531^* * significant at 1%	0.07376^* * significant at 1%	−0.035035	0.111385
(2)	0.0678418^* * significant at 1%				0.0180011^* * significant at 1%
			Part 2-Tests
	Adjusted R²	F-Test	Wald	LM	Hausman
(1)	0.0287	3.88^* * significant at 1%	4.40^* * significant at 1%	6.66^* * significant at 1%	30.51^* * significant at 1%
(2)	0.0452	1.47^* * significant at 1%	3.13^* * significant at 1%	2.1900	10.99^* * significant at 1%

Part 1-Coefficients
Model	Size	Constant	Beta	BM	Momentum	Liquidity
(3)	0.14159^* * significant at 1%;	−0.11223^* * significant at 1%;
(4)	0.14632^* * significant at 1%;	−0.13303^* * significant at 1%;	−0.09829^* * significant at 1%;	0.025361^* * significant at 1%;
(5)	0.14738^* * significant at 1%;	−0.11559^ significant at 5%; and ***significant at 10%	−0.10037^* * significant at 1%;	0.02553^* * significant at 1%;	0.03223^* * significant at 1%;
(6.1)	0.14902^* * significant at 1%;	−0.12124^* * significant at 1%;	−0.10166^* * significant at 1%;	0.02568^* * significant at 1%;	0.03264^ significant at 5%; and ***significant at 10%	−0.09694
(6.2)	0.01294^* * significant at 1%;	−0.83002^* * significant at 1%;	−0.06897^* * significant at 1%;	0.02671^* * significant at 1%;	0.00879^ significant at 5%; and ***significant at 10%	−0.02975^ significant at 5%; and ***significant at 10%
(6.3)	0.13274^* * significant at 1%;	−0.06710^* * significant at 1%;	−0.05950^* * significant at 1%;	0.02820^* * significant at 1%;	0.00373^* * significant at 1%;	−0.03780^* * significant at 1%;
Part 2-Tests
	Adjusted R²	F-test	Wald	LM	Hausman
(3)	0.0235	1.21^* * significant at 1%;	1.637^* * significant at 1%;	12.815^* * significant at 1%;	4,49^ significant at 5%; and ***significant at 10%
(4)	0.0623	18.05^* * significant at 1%;	8.629^* * significant at 1%;	52.680^* * significant at 1%;	114,73^* * significant at 1%;
(5)	0.0636	21.08^* * significant at 1%;	1.230^* * significant at 1%;	57.436^* * significant at 1%;	49.62^* * significant at 1%;
(6.1)	0.0637	11.76^* * significant at 1%;	1.113^* * significant at 1%;	56.218^* * significant at 1%;	46.99^* * significant at 1%;
(6.2)	0.0703	12.11^* * significant at 1%;	1.905^* * significant at 1%;	56.610^* * significant at 1%;	49.69^* * significant at 1%;
(6.3)	0.0723	13.19^* * significant at 1%;	6.429^* * significant at 1%;	57.73^* * significant at 1%;	88.37^* * significant at 1%;

	Constant	BM	FBM	FROE	FRM	Beta	Size	Momentum	Liquidity	Adjust. R²	F-Test	Wald	LM	Hausman
(7)	0.02960^* * significant at 1%;	0.08493^* * significant at 1%;	−0.00435	0.13289^* ***** significant at 10%		−0.12699^* * significant at 1%;				0.0710	1.52^* * significant at 1%;	7.330^* * significant at 1%;	14.931^* * significant at 1%;	18.40^* * significant at 1%;
(8)	0.14009^ significant at 5% and	0.06029 ^* * significant at 1%;	−0.01210^* * significant at 1%;	0.16633^ significant at 5% and		−0.14314^* ***** significant at 10%	−0.10259^* * significant at 1%;			0.0682	12.19^* * significant at 1%;	6.229^* * significant at 1%;	44.771^* * significant at 1%;	99.56^* * significant at 1%;
(9)	0.14088^* * significant at 1%;	0.04047^ significant at 5% and	−0.01330^* ***** significant at 10%	0.17683^ significant at 5% and		−0.12031	−0.10536^* * significant at 1%;	0.04009		0.0701	10.58^* * significant at 1%;	3.329^* * significant at 1%;	47.399^* * significant at 1%;	185.17^* * significant at 1%;
(10.1)	0.14097^* * significant at 1%;	0.04051^ significant at 5% and	−0.01331^* ***** significant at 10%	0.17682^ significant at 5% and		−0.12600	−0.10543^* * significant at 1%;	0.04012	−0.00052¹	0.0725	12.17^* * significant at 1%;	3.005^* * significant at 1%;	47.016^* * significant at 1%;	182.44^* * significant at 1%;
(10.2)	0.12293^* * significant at 1%;	0.03173^ significant at 5% and	−0.14549^* ***** significant at 10%	0.17929^ significant at 5% and		−0.08645	−0.07301^* * significant at 1%;	0.01555	−0.03113²^ significant at 5% and	0.0774	10.39^* * significant at 1%;	7.929^* * significant at 1%;	46.554^* * significant at 1%;	207.28^* * significant at 1%;
(10.3)	0.12668^* * significant at 1%;	0.03409^ significant at 5% and	−0.15325^ significant at 5% and	0.18273^* * significant at 1%;		−0.06754	−0.062163^* * significant at 1%;	0.00945	−0.04118³^* * significant at 1%;	0.0804	11.04^* * significant at 1%;	2.305^* * significant at 1%;	45.098^* * significant at 1%;	104.19^* * significant at 1%;
(11)	0.17215^ significant at 5% and	0.09632^* ***** significant at 10%			0.01248^ significant at 5% and	−0.11491				0.0717	2.31^* ***** significant at 10%	2.130^* * significant at 1%;	14.121^* * significant at 1%;	17.19^* * significant at 1%;
(12)	0.20093^ significant at 5% and	0.09719^ significant at 5% and			0.01233^ significant at 5% and	−0.12204	−0.33109^* * significant at 1%;			0.0716	7.09^* * significant at 1%;	1.138^* * significant at 1%;	14.814^* * significant at 1%;	16.20^* * significant at 1%;
(13)	0.19992^ significant at 5% and	0.09788^ significant at 5% and			0.01242^ significant at 5% and	−0.12015	−0.11208^* * significant at 1%;	0.00342		0.0957	5.67^* * significant at 1%;	2.937^* * significant at 1%;	64.439^* * significant at 1%;	43.61^* * significant at 1%;
(14.1)	0.19928^ significant at 5% and	0.09805^ significant at 5% and			0.01244^ significant at 5% and	−0.19942	−0.32909^* * significant at 1%;	0.00345	−0.0018¹	0.0964	5.54^* * significant at 1%;	4.005^* * significant at 1%;	64.154^* * significant at 1%;	37.23^* * significant at 1%;
(14.2)	0.63497^* * significant at 1%;	0.01416^ significant at 5% and			0.01529^ significant at 5% and	−0.05131	−0.11309^* * significant at 1%;	−0.01780	−0.05667²^* * significant at 1%;	0.0980	9.14^* * significant at 1%;	2.028^* * significant at 1%;	54.598^* * significant at 1%;	56.26^* * significant at 1%;
(14.3)	0.85466^* * significant at 1%;	0.01534^ significant at 5% and			0.01610^ significant at 5% and	−0.03159	−0.12309^* * significant at 1%;	−0.01781	−0.06398³^* * significant at 1%;	0.0630	12.13^* * significant at 1%;	1.235^* * significant at 1%;	43.512^* * significant at 1%;	46.36^* * significant at 1%;

Company	Sector	Share	Share class
Alfa Consórcio	Other	BRGE11	PNE
Alfa Consórcio	Other	BRGE12	PNF
Alfa Consórcio	Other	BRGE3	ON
Alfa Holding	Other	RPAD3	ON
Alfa Holding	Other	RPAD5	PNA
Alfa Holding	Other	RPAD6	PNB
Alpargatas	Textile	ALPA3	ON
Alpargatas	Textile	ALPA4	PN
Ambev	Food and Beverage	AMBV3	ON
Ambev	Food and Beverage	AMBV4	PN
Ampla Energia	Electricity	CBEE3	ON
Bardella	Industrial machinery	BDLL4	PN
Bombril	Chemical industry	BOBR4	PN
Brasil Telecom	Telecommunications	BRTO3	ON
Brasil Telecom	Telecommunications	BRTO4	PN
Braskem	Chemical industry	BRKM5	PNA
Brasmotor	Electronics	BMTO4	PN
CELESC	Electricity	CLSC6	PNB
CEMIG	Electricity	CMIG3	ON
CEMIG	Electricity	CMIG4	PN
CESP	Electricity	CESP3	ON
CESP	Electricity	CESP5	PNA
CONFAB	Steelmaking and Metallurgy	CNFB4	PN
COPERL	Electricity	CPLE3	ON
Coteminas	Textile	CTNM3	ON
Coteminas	Textile	CTNM4	PN
Panvel Farmácias	Commerce	PNVL3	ON
Panvel Farmácias	Commerce	PNVL4	PN
Eletrobrás	Electricity	ELET3	ON
Eletrobrás	Electricity	ELET6	PNB
Estrela	Other	ESTR4	PN
Eternit	Non-Metallic Minerals	ETER3	ON
Ferbasa	Steelmaking and Metallurgy	FESA4	PN
Forjas Taurus	Steelmaking and Metallurgy	FJTA4	PN
Fras-Le	Vehicles and parts	FRAS4	PN
Gerdau	Steelmaking and Metallurgy	GGBR3	ON
Gerdau	Steelmaking and Metallurgy	GGBR4	PN
Gerdau Metalúrgica	Steelmaking and Metallurgy	GOAU4	PN
Inepar	Other	INEP4	PN
Itaúsa	Other	ITSA3	ON
Itaúsa	Other	ITSA4	PN
Itautec Philco	Electronics	ITEC3	ON
Klabin S/A	Paper and Cellulose	KLBN4	PN
Light S/A	Electricity	LIGT3	ON
Lojas Americanas	Commerce	LAME4	PN
M G Poliest	Chemical industry	RHDS3	ON
Mangels Indl	Steelmaking and Metallurgy	MGEL4	PN
Marcopolo	Vehicles and parts	POMO4	PN
Metisa	Steelmaking and Metallurgy	MTSA4	PN
Petrobras	Petrol and Gas	PETR3	ON
Petrobras	Petrol and Gas	PETR4	PN
Pettenati	Textile	PTNT4	PN
Pro Metalurg	Vehicles and parts	PMET6	PNB
Randon Participações	Vehicles and parts	RAPT4	PN
Recrusul	Vehicles and parts	RCSL4	PN
Sansuy Indústria de Plásticos	Other	SNSY5	PNA
Companhia Siderúrgica Nacional	Steelmaking and Metallurgy	CSNA3	ON
Souza Cruz	Other	CRUZ3	ON
Construtora Sultepa	Construction	SULT4	PN
Suzano Papel	Paper and Cellulose	SUZB5	PNA
Teka	Textile	TEKA4	PN
Telemar	Telecommunications	TMAR3	ON
Telesp	Telecommunications	TLPP3	ON
Telesp	Telecommunications	TLPP4	PN
Unipar Participações	Chemical industry	UNIP6	PNB
Usiminas	Steelmaking and Metallurgy	USIM3	ON
Usiminas	Steelmaking and Metallurgy	USIM5	PNA
Vale	Mining	VALE3	ON
Vale	Mining	VALE5	PNA
Valefert	Chemical industry	FFTL4	PN
Wetzel S/A	Vehicles and parts	MWET4	PN
Whirlpool	Electronics	WHRL4	PN
Wlm Indústria e Comércio	Commerce	SGAS4	PN
Yara Brasil Fertilizantes	Chemical industry	ILMD4	PN

Universidade de São Paulo Avenida Professor Luciano Gualberto, 908, sala F184, CEP: 05508-900, São Paulo , SP - Brasil, Telefone: (11) 3818-4002 - São Paulo - SP - Brazil
E-mail: rausp@usp.br

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[1] *Corresponding author Rebeca Cordeiro da Cunha Araújo can be contacted at: rebecacordeiro1@gmail.com