SCALAR AND VECTOR GAMES IN THE EVALUATION OF SOCIAL AND ENVIRONMENTAL DISCLOSURE AND THEIR RELATIONSHIP WITH MARKET VALUE

Kroenke, Adriana; Caballero, Victoriana Rubiales; Cecon, Bianca; Hein, Nelson

doi:10.1590/0101-7438.2018.038.02.0215

Adriana Kroenke ^**Corresponding author.

Universidade Regional de Blumenau, Rua Antônio da Veiga, 140 - Itoupava Seca, 89030-903 Blumenau, SC, Brasil. Tel.: (47) 3321-0565 - E-mails: akroenke@furb.br; hein@furb.br

Victoriana Rubiales Caballero

Universidad de Sevilla, Departamento de Economia Aplicada III, C/S. Fernando, 4, C.P. 41004 - Sevilla, España. E-mail: vrubiales@us.es

Bianca Cecon

Universidade Federal do Paraná, Centro Politécnico, 81531-980 Curitiba, PR, Brasil. E-mail: bcecon@outlook.com

Nelson Hein

Universidade Regional de Blumenau, Rua Antônio da Veiga, 140 - Itoupava Seca, 89030-903 Blumenau, SC, Brasil. Tel.: (47) 3321-0565 - E-mails: akroenke@furb.br; hein@furb.br

*Corresponding author.

Categories	Subcategories
Community (s ₁)	Volunteering programs
	Sponsoring public health projects
	Relations with indigenous peoples / Relations with quilombola peoples
	Sponsoring conferences or seminars or exhibitions or campaigns
	Donations of resources to public entities or OSCIP (Civil Society Organization for Public Interest)
	Supporting education
	Giving housing support / food support
	Supporting culture
	Supporting sports activities
	Relationship with stakeholders
	Decisions or fines related to the community in which it operates
	Investments of a social character
Diversity (s ₂)	Number of women or minorities in the workforce
	Occupation of women or minorities in management positions
	Proportion of salary between men and women
	Hiring people with disabilities
	Non-discrimination policies against minorities
Product, services and consumers (s ₃)	Quality Program - ISO 9000 / Quality Program - ISO 9.001
	Product Innovation (Research & Development)
	Products in accordance with safety standards
	Consumer satisfaction or dissatisfaction
	Unfair competition or trust practices
Relations with employees (s ₄)	Number of employees / Employees’ length of service / Age group of employees
	Payment of employees (average or total)
	Trade union relations or with class agencies
	Programs to encourage culture
	Development of recreational or sports activities
	Employee Education / Employee Training
	Health in the workplace / Hygiene in the workplace / Safety in the workplace
	Accidents at work / Occupational diseases / Absenteeism / Deaths
	Retirement or supplementary pension plans
	Childcare aid for children of employees / Scholarship for children of employees
	Maternity Support / Paternity Support
	Profit sharing
	Turnover rate / Resignation policy
	Employee participation in managerial decisions
	Job satisfaction / Employee motivation
	Child labor or forced labor or analogous to slavery
	Investments in managerial development
	Value added per employee

Categories	Subcategories
Environmental policies (a ₁)	Statement of current policies / Statement of current practices or actions
	Setting goals / Establishing environmental objectives
	Environmental certification /Compliance with environmental laws and regulations
	Partnerships, councils, environmental forums
	Environmental awards /Participation in environmental indexes
	Participation in environmental organizations
	Environmental relationship with stakeholders
Environmental management and auditing (a ₂)	Environmental risk management
	ISO 14.000
	Environmental Performance Indicators
	Environmental review or environmental audits
	Evaluation including independent opinion
Environmental impacts (a ₃)	Waste / Residue
	Leaks / Spills / Land used
	Repairs to environmental damage
	Emission of Greenhouse Gases (GHG)
	Emission of substances that deplete the ozone layer
Ecological products (a ₄)	Development of ecological products
	Recycling
	Packaging process (reuse of packaging)
	Efficient use or reuse of water
Energetic resources (a ₅)	Development or exploitation of new energy sources
	Use of material waste for the production of energy
	Consumption of energy from renewable sources
	Company’s efforts to reduce energy consumption
Environmental education and research (a ₆)	Environmental education (internally or community)
Environmental education and research (a ₆)	Support for research related to the environment
Carbon credits market (a ₇)	Clean Development Mechanism Projects (CDM)
	Reduced Emissions Certificates (RECs)
	Carbon credits or carbon offsets
Sustainability and biodiversity (a ₈)	Mention related to sustainable development
	Forest management or reforestation
	Preservation of biodiversity / Preservation of natural resources
Environmental financial information (a ₉)	Environmental investments
	Environmental revenues
	Environmental costs / Environmental expenditures
	Liabilities or environmental contingencies
	Accounting practices of environmental items - measurement criteria
	Environmental insurance
	Intangible environmental assets

Criteria	Linear
No disclosure	0
Qualitative disclosures	1
Non-monetary quantitative disclosures	2
Monetary quantitative disclosures	3

Companies	Social Restrictions				Environmental Restrictions
Companies	s ₁	s ₂	s ₃	s ₄	a ₁	a ₂	a ₃	a ₄	a ₅	a ₆	a ₇	a ₈	a ₉
PARANAPANEMA (x ₁)	0.15	0.55	0.20	0.48	0.42	0.50	0.13	0.80	0.22	0.00	0.00	0.29	0.30
PANATLANTICA (x ₂)	0.00	0.00	0.00	0.02	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
COSAN (x ₃)	0.56	1.00	1.00	0.86	0.84	0.63	0.53	1.00	0.78	0.50	0.00	0.57	0.90
PETRORIO (x ₄)	0.00	0.00	0.00	0.05	0.11	0.13	0.00	0.00	0.00	0.17	0.00	0.14	0.00
PETROBRAS (x ₅)	0.74	0.73	0.30	0.98	0.89	0.75	1.00	0.80	0.44	0.50	0.00	0.29	0.60
QGEP PART (x ₆)	0.78	0.91	0.80	0.98	0.84	0.50	0.67	0.40	0.00	1.00	0,00	0.57	0.70
ULTRAPAR (x ₇)	0.33	0.00	0.40	0.31	0.42	0.50	0.33	0.40	0.11	00.0	0.33	0.00	0.70
FER HERINGER (x ₈)	0.33	0.73	0.40	0.67	0.42	0.13	0.53	0.80	0.67	0.17	0.00	0.86	0.30
BR PHARMA (x ₉)	0.11	0.00	0.00	0.12	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
CREMER (x ₁₀)	0.00	0.00	0.00	0.21	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
DIMED (x ₁₁)	0.04	0.00	0.00	0.07	0.11	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
PROFARMA (x ₁₂)	0.41	0.00	0.10	0.17	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
RAIADROGASIL (x ₁₃)	0.22	0.18	0.00	0.12	0.00	0.00	0.13	0.00	0.00	0.00	0.00	0.00	0.00
BRADESPAR (x ₁₄)	0.04	0.00	0.00	0.00	0.11	0.00	0.00	0.00	0.11	0.00	0.00	0.14	0.00
VALE (x ₁₅)	1.00	0.73	0.50	0.88	1.00	0.88	1.00	0.40	1.00	0.67	0.33	0.86	0.40
CELUL IRANI (x ₁₆)	0.56	0.82	0.90	0.81	0.58	1.00	0.87	0.60	0.67	1.00	1.00	0.86	0.90
FIBRIA (x ₁₇)	0.63	0.36	0.50	0.67	1.00	0.63	0.47	0.20	0.22	0.83	0.00	1.00	0.10
KLABIN (x ₁₈)	0.41	0.45	0.30	0.31	0.89	0.63	0.33	0.20	0.33	0.33	0.00	0.71	0.40
BRASKEM (x ₁₉)	0.67	0.55	0.60	0.67	0.79	0.75	0.93	0.80	0.56	0.67	0.00	0.57	1.00
ELEKEIROZ (x ₂₀)	0.48	0.45	0.30	0.86	0.32	0.63	0.53	0.00	0.11	0.67	0.00	0.29	0.60
NATURA (x ₂₁)	0.78	0.82	1.00	1.00	0.89	0.38	0.53	0.60	0.44	0.33	1.00	0.43	0.40
VITALYZE.ME (x ₂₂)	0.11	0.00	0.00	0.00	0.00	0.00	0.13	0.00	0.00	0.00	0.00	0.00	0.00
UNIPAR (x ₂₃)	0.00	0.00	0.30	0.19	0.00	0.13	0.00	0.00	0.00	0.00	0.00	0.00	0.30
GERDAU (x ₂₄)	0.44	0.00	0.40	0.55	0.53	0.13	0.07	0.40	0.33	0.50	0.00	0.57	1.00

Companies	Social Restrictions				Environmental Restrictions
Companies	s ₁	s ₂	s ₃	s ₄	a ₁	a ₂	a ₃	a ₄	a ₅	a ₆	a ₇	a ₈	a ₉
PARANAPANEMA (x ₁)	0.13	0.55	0.33	0.44	0.35	0.67	0.13	0.50	0.33	0.00	0.00	0.29	0.23
PANATLANTICA (x ₂)	0.00	0.00	0.00	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
COSAN (x ₃)	0.65	0.55	0.67	0.56	0.71	0.50	0.53	1.00	0.00	0.75	0.00	0.43	0.23
PETRORIO (x ₄)	0.09	0.00	0.00	0.19	0.12	0.33	0.00	0.00	0.00	0.5	0.00	0.14	0.23
PETROBRAS (x ₅)	0.74	1.00	0.78	1.00	0.76	1.00	0.93	0.83	0.67	1.00	0.33	0.57	0.38
QGEP PART (x ₆)	0.39	0.73	0.78	0.77	0.59	0.50	0.33	0.50	0.50	0.50	0.00	0.14	0.31
ULTRAPAR (x ₇)	0.52	0.00	0.56	0.40	0.47	0.83	0.33	0.67	0.17	0.50	0.33	0.14	0.54
FER HERINGER (x ₈)	0.35	0.18	0.56	0.60	0.47	0.33	0.47	0.67	0.33	0.50	0.00	0.29	0.08
BR PHARMA (x ₉)	0.13	0.00	0.00	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
CREMER (x ₁₀)	0.09	0.00	0.00	0.21	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
DIMED (x ₁₁)	0.00	0.00	0.00	0.10	0.12	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
PROFARMA (x ₁₂)	0.52	0.00	0.11	0.19	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
RAIADROGASIL (x ₁₃)	0.04	0.00	0.11	0.15	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
BRADESPAR (x ₁₄)	0.04	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.14	0.00
VALE (x ₁₅)	1.00	0.91	0.56	0.79	1.00	0.83	1.00	0.33	0.83	1.00	0.00	0.86	0.23
CELUL IRANI (x ₁₆)	0.48	0.55	0.67	0.65	0.76	0.67	0.87	0.33	1.00	0.75	0.33	0.86	0.23
FIBRIA (x ₁₇)	0.61	0.45	0.67	0.67	0.76	0.67	0.27	0.33	0.67	0.50	0.00	1.00	0.31
KLABIN (x ₁₈)	0.57	0.09	0.22	0.42	0.88	0.50	0.47	0.33	0.50	0.50	0.00	0.86	0.77
BRASKEM (x ₁₉)	0.65	0.55	0.89	0.63	0.94	0.83	0.73	0.67	0.67	1.00	0.67	0.57	1.00
ELEKEIROZ (x ₂₀)	0.43	0.27	0.44	0.44	0.47	0.50	0.40	0.00	1.00	0.50	0.00	0.29	0.23
NATURA (x ₂₁)	0.70	0.73	1.00	0.79	0.76	0.67	0.60	0.33	0.67	0.25	1.00	0.43	0.23
VITALYZE.ME (x ₂₂)	0.13	0.00	0.11	0.04	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
UNIPAR (x ₂₃)	0.22	0.00	0.11	0.25	0.18	0.00	0.00	0.00	0.00	0.25	0.00	0.00	0.46
GERDAU (x ₂₄)	0.57	0.00	0.44	0.48	0.47	0.17	0.00	0.33	0.17	0.25	0.00	0.43	0.77

Market Value		2014	2015
Unit share price (R$)	Minimum	0.79	0.48
	Maximum	212.14	290.00
	Mean	27.21	25.29
	Standard deviation	47.33	58.41
Number of shares (UN)	Minimum	4.560	4.559
	Maximum	13,044.497	13,044.497
	Mean	1,253.602	1,209.223
	Standard deviation	2,841.363	2,854.873
Market value = unit share price × number of shares (R$)	Minimum	64,087.00	35,941.95
	Maximum	125,096,726.23	111,791,339.29
	Mean	16,825,591.80	13,964,524.64
	Standard deviation	32,558,422.84	26,520,894.49

Trading Floor	Result - 2013				Result - 2014
Trading Floor	Position	Value	Z*	STR	Position	Value	Z*	STR
NATURA	1^st	x₂₁ = 0.47	0.83	Mixed	1^st	x₂₁ = 0.52	0.81	Mixed
QGEP PART	2^nd	x₆ = 0.31	0.83	Mixed	5^th	x₆ = 0.23	0.59	Mixed
VALE	3rd	x₁₅ = 0.22	0.83	Mixed	2^nd	x₁₅ = 0.37	0.81	Mixed
BRASKEM	4^th	x₁₉ = 0.72	0.65	Mixed	4^th	x₁₉ = 0.77	0.59	Mixed
COSAN	5^th	x₃ = 0.20	0.65	Mixed	6^th	x₃ = 1.00	0.55	Pura
PETROBRAS	6^th	x₅ = 0.08	0.65	Mixed	3rd	x₅ = 0.11	0.81	Mixed
CELUL IRANI	7^th	x₁₆ = 0.51	0.59	Mixed	7^th	x₁₆ = 0.70	0.52	Mixed
FIBRIA	8^th	x₁₇ = 0.49	0.59	Mixed	8^th	x₁₇ = 0.30	0.52	Mixed
FER HERINGER	9^th	x₈ = 0.48	0.39	Mixed	11^th	x₈ = 1.00	0.18	Pure
GERDAU	10^th	x₂₄ = 0.43	0.39	Mixed	13^th	x₂₄ = 0.80	0.46	Mixed
ELEKEIROZ	11^th	x₂₀ = 0.09	0.39	Mixed	9^th	x₂₀ = 0.72	0.35	Mixed
KLABIN	12^th	x₁₈ = 0.63	0.32	Mixed	12^th	x₁₈ = 1.00	0.09	Pure
ULTRAPAR	13^th	x₇ = 0.30	0.32	Mixed	14^th	x₇ = 0.20	0.46	Mixed
PARANAPANEMA	14^th	x₁ = 0.07	0.32	Mixed	10^th	x₁ = 0.28	0.35	Mixed
RAIADROGASIL	15^th	x₁₃ = 0.62	0.11	Mixed	18^th	x₁₃ = 0.32	0.10	Mixed
UNIPAR	16^th	x₂₃ = 0.38	0.11	Mixed	16^th	x₂₃ = 1.00	0.11	Pure
PROFARMA	17^th	x₁₂ = 1.00	0.10	Pure	15^th	x₁₂ = 1.00	0.11	Pure
BR PHARMA	18^th	x₉ = 1.00	0.11	Pure	20^th	x₉ = 0.59	0.11	Mixed
VITALYZE.ME	19^th	x₂₂ = 0.66	0.07	Mixed	17^th	x₂₂ = 0.56	0.10	Mixed
CREMER	20^th	x₁₀ = 0.34	0.07	Mixed	19^th	x₁₀ = 0.12	0.10	Mixed
DIMED	21st	x₁₁ = 1.00	0.04	Pure	23^rd	x₁₁ = 0.29	0.03	Mixed
BRADESPAR	22^nd	x₁₄ = 0.56	0.02	Mixed	22^nd	x₁₄ = 0.71	0.03	Mixed
PETRORIO	23^rd	x₄ = 0.44	0.02	Mixed	21^st	x₄ = 0.41	0.11	Mixed
PANATLANTICA	24^th	-	-	Pure	24^th	-	-	Pure

Trading Floor	Result - 2013				Result - 2014
Trading Floor	Position	Value	Z*	STR	Position	Value	Z*	STR
CELUL IRANI	1^st	x₁₆ = 0.60	0.70	Mixed	2^nd	x₁₆ = 0.16	0.62	Mixed
COSAN	2^nd	x₃ = 0.27	0.70	Mixed	9^th	x₃ = 0.16	0.44	Mixed
NATURA	3^rd	x₂₁ = 0.08	0.70	Mixed	3^rd	x₂₁ = 0.35	0.47	Mixed
VALE	4^th	x₁₅ = 0.05	0.70	Mixed	7^th	x₁₅ = 0.45	0.44	Mixed
ULTRAPAR	5^th	x₇ = 0.68	0.22	Mixed	5^th	x₇ = 0.24	0.47	Mixed
BRASKEM	6^th	x₁₉ = 0.22	0.22	Mixed	1st	x₁₉ = 0.84	0.62	Mixed
FIBRIA	7^th	x₁₇ = 0.09	0.22	Mixed	11^th	x₁₇ = 0.20	0.31	Mixed
FER HERINGER	8^th	x₈ = 0.01	0.22	Mixed	16^th	x₈ = 0.48	0.16	Mixed
PETROBRAS	9^th	x₅ = 0.72	0.41	Mixed	6^th	x₅ = 0.13	0.47	Mixed
KLABIN	10^th	x₁₈ = 0.28	0.41	Mixed	4^th	x₁₈ = 0.28	0.47	Mixed
GERDAU	11^th	x₂₄ = 0.62	0.25	Mixed	8^th	x₂₄ = 0.39	0.44	Mixed
ELEKEIROZ	12^th	x₂₀ = 0.38	0.25	Mixed	13^th	x₂₀ = 0.54	0.23	Mixed
PARANAPANEMA	13^th	x₁ = 0.82	0.18	Mixed	14^th	x₁ = 0.46	0.23	Mixed
QGEP PART	14^th	x₆ = 0.18	0.18	Mixed	10^th	x₆ = 0.78	0.31	Mixed
BRADESPAR	15^th	x₁₄ = 0.35	0.04	Mixed	18^th	x₁₄ = 0.46	0.06	Mixed
RAIADROGASIL	16^th	x₁₃ = 0.30	0.04	Mixed	21st	-	-	Mixed
PETRORIO	17^th	x₄ = 0.23	0.04	Mixed	15^th	x₄ = 0.52	0.16	Mixed
UNIPAR	18^th	x₂₃ = 0.13	0.04	Mixed	12^th	x₂₃ = 0.02	0.31	Mixed
DIMED	19^th	x₁₁ = 0.54	0.06	Mixed	17^th	x₁₁ = 0.54	0.06	Mixed
VITALYZE.ME	20^th	x₂₂ = 0.46	0.06	Mixed	23^rd	-	-	Mixed
PROFARMA	21st	-	-	Mixed	19^th	-	-	Mixed
BR PHARMA	22^nd	-	-	Mixed	20^th	-	-	Mixed
CREMER	23^rd	-	-	Mixed	22^nd	-	-	Mixed
PANATLANTICA	24^th	-	-	Mixed	24^th	-	-	Mixed

Trading Floor	Result - 2013				Result - 2014
Trading Floor	Position	Value	Z*	STR	Position	Value	Z*	STR
NATURA	1^st	x₂₁ = 0.33	1.80	Mixed	2^nd	x₂₁ = 0.22	1.84	Mixed
VALE	2^nd	x₁₅ = 0.29	1.80	Mixed	4^th	x₁₅ = 0.14	1.84	Mixed
CELUL IRANI	3^rd	x₁₆ = 0.17	1.80	Mixed	5^th	x₁₆ = 0.87	1.08	Mixed
BRASKEM	4^th	x₁₉ = 0.12	1.80	Mixed	1^st	x₁₉ = 0.45	1.84	Mixed
COSAN	5^th	x₃ = 0.08	1.80	Mixed	9^th	x₃ = 0.31	1.21	Mixed
QGEP PART	6^th	x₆ = 1.00	0.94	Pure	8^th	x₆ = 0.38	1.21	Mixed
ULTRAPAR	7^th	x₇ = 0.45	0.69	Mixed	7^th	x₇ = 0.02	1.08	Mixed
FER HERINGER	8^th	x₈ = 0.39	0.69	Mixed	15^th	x₈ = 0.14	0.76	Mixed
PETROBRAS	9^th	x₅ = 0.13	0.69	Mixed	3^rd	x₅ = 0.20	1.84	Mixed
FIBRIA	10^th	x₁₇ = 0.02	0.69	Mixed	10^th	x₁₇ = 0.19	1.21	Mixed
KLABIN	11^th	x₁₈ = 0.39	0.78	Mixed	6^th	x₁₈ = 0.11	1.08	Mixed
GERDAU	12^th	x₂₄ = 0.31	0.78	Mixed	11^th	x₂₄ = 0.12	1.21	Mixed
ELEKEIROZ	13^th	x₂₀ = 0.21	0.78	Mixed	12^th	x₂₀ = 0.40	0.76	Mixed
PARANAPANEMA	14^th	x₁ = 0.09	0.78	Mixed	13^th	x₁ = 0.29	0.76	Mixed
RAIADROGASIL	15^th	x₁₃ = 0.62	0.14	Mixed	19^th	x₁₃ = 0.22	0.12	Mixed
UNIPAR	16^th	x₂₃ = 0.38	0.14	Mixed	14^th	x₂₃ = 0.16	0.76	Mixed
PROFARMA	17^th	x₁₂ = 1.00	0.12	Pure	17^th	x₁₂ = 1.00	0.14	Pure
BR PHARMA	18^th	x₉ = 1.00	0.13	Pure	22^nd	-	-	Mixed
BRADESPAR	19^th	x₁₄ = 0.32	0.10	Mixed	21^st	x₁₄ = 0.17	0.12	Mixed
PETRORIO	20^th	x₄ = 0.27	0.10	Mixed	16^th	x₄ = 1.00	0.19	Pure
VITALYZE.ME	21^st	x₂₂ = 0.27	0.10	Mixed	18^th	x₂₂ = 0.41	0.12	Mixed
CREMER	22^nd	x₁₀ = 0.14	0.10	Mixed	23^rd	-	-	Mixed
DIMED	23^rd	x₁₁ = 1.00	0.21	Pure	20^th	x₁₁ = 0.20	0.12	Mixed
PANATLANTICA	24^th	-	-	Pure	24^th	-	-	Mixed

Trading floor	Position (2013)	Market Value* (2013)	Position (2014)	Market Value* (2014)
PETROBRAS	1^st	125,096,726.23	1^st	111,791,339.30
VALE	2^nd	107,134,332.37	2^nd	67,148,476.25
BR PHARMA	3^rd	47,015,104.50	24^th	35,941.95
ULTRAPAR	4^th	27,232,293.97	4^th	32,407,997.40
FIBRIA	5^th	16,453,877.25	5^th	28,208,714.11
KLABIN	6^th	14,635,202.58	3^rd	38,622,897.04
GERDAU	7^th	13,182,534.29	10^th	5,869,625.52
NATURA	8^th	12,752,406.87	8^th	10,000,601.71
COSAN	9^th	10,807,194.45	9^th	9,726,141.32
RAIADROGASIL	10^th	8,172,109.41	7^th	11,622,076.63
BRASKEM	11^th	7,536,652.72	6^th	11,884,634.68
UNIPAR	12^th	3,925,304.75	17h	455,222.02
BRADESPAR	13^th	3,708,486.79	11^th	1,545,270.96
QGEP PART	14^th	1,756,646.65	12^th	1,452,029.07
DIMED	15^th	967,370.40	13^th	1,322,110.00
PARANAPANEMA	16^th	754,744.89	15^th	672,242.41
PETRORIO	17^th	687,178.80	14^th	807,765.00
CELUL IRANI	18^th	519,192.78	16^th	494,675.44
PROFARMA	19^th	346,729.67	19^th	195,155.96
CREMER	20^th	318,643.14	18^th	412,334.45
PANATLANTICA	21^st	271,546.53	20^th	187,969.37
FER HERINGER	22^nd	255,442.17	22^nd	72,706.95
ELEKEIROZ	23^rd	220,395.00	21^st	173,482.35
VITALYZE.ME	24^th	64,087.00	23^rd	39,181.56

Period	Kendall Correlation	Values
2013 Social Disclosure - 2014 Market Value	Correlation coefficient	0.290
2013 Social Disclosure - 2014 Market Value	Sig.	0.047
2014 Social Disclosure - 2015 Market Value	Correlation coefficient	0.348
2014 Social Disclosure - 2015 Market Value	Sig.	0.017

Period	Kendall Correlation	Values
2013 Environmental Disclosure - 2014 Market Value	Correlation coefficient	0.319
2013 Environmental Disclosure - 2014 Market Value	Sig.	0.029
2014 Environmental Disclosure - 2015 Market Value	Correlation coefficient	0.471
2014 Environmental Disclosure - 2015 Market Value	Sig.	0.001

Year	Kendall Correlation	Values
2013 Socio-environmental - 2014 Market Value	Correlation coefficient	0.341
2013 Socio-environmental - 2014 Market Value	Sig.	0.020
2013 Socio-environmental - 2014 Market Value	Correlation coefficient	0.500
2013 Socio-environmental - 2014 Market Value	Sig.	0.001

min [\frac{v_{1}^{*} - v_{1} (x)}{v_{1}^{*}}] + [\frac{v_{2}^{*} - v_{2} (x)}{v_{2}^{*}}] + \dots + [\frac{v_{k}^{*} - v_{k} (x)}{v_{k}^{*}}] s.t. x^{t} P (p) \geq (v_{p}, . . ., v_{p}); p = 1, . . ., k \sum_{i = 1}^{n} x_{i} = 1; x_{i} \geq 0

P_{S} = (\begin{matrix} s_{1, 1} & s_{1, 2} & \dots & s_{1, 4} \\ s_{2, 1} & s_{2, 2} & \dots & s_{2, 4} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ s_{24, 1} & s_{24, 2} & \dots & s_{24, 4} \end{matrix}); P_{A} = (\begin{matrix} a_{1, 1} & a_{1, 2} & \dots & a_{1, 9} \\ a_{2, 1} & a_{2, 2} & ⋮ & ⋮ \\ \dots & a_{2, 9} & ⋱ & ⋮ \\ a_{24, 1} & a_{24, 2} & \dots & a_{24, 9} \end{matrix})

max v_{s} s.t. s_{1, 1} x_{1} + s_{2, 1} x_{2} + \dots + s_{24, 1} x_{24} \geq v_{s} s_{1, 2} x_{1} + s_{2, 2} x_{2} + \dots + s_{24, 2} x_{24} \geq v_{s} ⋮ ⋮ + \dots + ⋮ \geq ⋮ s_{1, 4} x_{1} + s_{2, 4} x_{2} + \dots + s_{24, 4} x_{24} \geq v_{s} x_{1} + x_{2} + \dots + x_{24} = 1 x_{1}, x_{2}, \dots, x_{24} \geq 0

max v_{A} s.t. a_{1, 1} x_{1} + a_{2, 1} x_{2} + \dots + a_{24, 1} x_{24} \geq v_{a} a_{1, 2} x_{1} + a_{2, 2} x_{2} + \dots + a_{24, 2} x_{24} \geq v_{a} ⋮ ⋮ + \dots + ⋮ \geq ⋮ a_{1, 9} x_{1} + a_{2, 9} x_{2} + \dots + a_{24, 9} x_{24} \geq v_{a} x_{1} + x_{2} + \dots + x_{24} = 1 x_{1}, x_{2}, \dots, x_{24} \geq 0

P = (\begin{matrix} (s_{1, 1}, s_{1, 2}, \dots, s_{1, 4}) & (a_{1, 1}, a_{1, 2}, \dots, a_{1, 9}) \\ (s_{2, 1}, s_{2, 2}, \dots, s_{2, 4}) & (a_{2, 1}, a_{2, 2}, \dots, a_{2, 9}) \\ ⋮ & ⋮ \\ s_{24, 1}, s_{24, 2}, \dots, s_{24, 4} & (a_{24, 1}, a_{24, 2}, \dots, a_{24, 9}) \end{matrix})

max v_{S}, v_{A} s.t. s_{1, 1} x_{1} + s_{2, 1} x_{2} + \dots + s_{24, 1} x_{24} \geq v_{S} s_{1, 2} x_{1} + s_{2, 2} x_{2} + \dots + s_{24, 2} x_{24} \geq v_{S} ⋮ ⋮ + \dots + ⋮ \geq ⋮ s_{1, 4} x_{1} + s_{2, 4} x_{2} + \dots + s_{24, 4} x_{24} \geq v_{S} a_{1, 1} x_{1} + a_{2, 1} x_{2} + \dots + a_{24, 1} x_{24} \geq v_{A} a_{1, 2} x_{1} + a_{2, 2} x_{2} + \dots + a_{24, 2} x_{24} \geq v_{A} ⋮ ⋮ + \dots + ⋮ \geq ⋮ a_{1, 9} x_{1} + a_{2, 9} x_{2} + \dots + a_{24, 9} x_{24} \geq v_{A} x_{1} + x_{2} + \dots + x_{24} = 1 x_{1}, x_{2}, \dots, x_{24} \geq 0

\begin{array}{l} \min [\frac{v_{S}^{*} - v_{S} (x)}{v_{S}^{*}}] + [\frac{v_{A}^{*} - v_{A} (x)}{v_{A}^{*}}] \\ s .t . \\ \begin{matrix}  \end{matrix} s_{1,1} x_{1} + s_{2,1} x_{2} + ... + s_{24,1} x_{24} \geq v_{S} \\ \begin{matrix}  \end{matrix} s_{1,2} x_{1} + s_{2,2} x_{2} + ... + s_{24,2} x_{24} \geq v_{S} \\ \begin{matrix} ⋮ \end{matrix} \begin{matrix} ⋮ \begin{matrix}  \end{matrix} \end{matrix} + ... + \begin{matrix} ⋮ \begin{matrix} \geq \end{matrix} \end{matrix} \begin{matrix}  \end{matrix} ⋮ \\ \begin{matrix}  \end{matrix} s_{1,4} x_{1} + s_{2,4} x_{2} + ... + s_{24,4} x_{24} \geq v_{S} \\ \begin{matrix}  \end{matrix} a_{1,1} x_{1} + a_{2,1} x_{2} + ... + a_{24,1} x_{24} \geq v_{A} \\ \begin{matrix}  \end{matrix} a_{1,2} x_{1} + a_{2,2} x_{2} + ... + a_{24,2} x_{24} \geq v_{A} \\ \begin{matrix} ⋮ \end{matrix} \begin{matrix} ⋮ \begin{matrix}  \end{matrix} \end{matrix} + ... + \begin{matrix} ⋮ \begin{matrix} \geq \end{matrix} \end{matrix} \begin{matrix}  \end{matrix} ⋮ \\ \begin{matrix}  \end{matrix} a_{1,9} x_{1} + a_{2,9} x_{2} + ... + a_{24,9} x_{24} \geq v_{A} \\ \begin{matrix}  \end{matrix} x_{1} + x_{2} + ... + x_{24} = 1 \\ \begin{matrix}  \end{matrix} x_{1}, x_{2},..., x_{24} \geq 0 \end{array}

[1] *Corresponding author.

Brasil

Brasil

SCALAR AND VECTOR GAMES IN THE EVALUATION OF SOCIAL AND ENVIRONMENTAL DISCLOSURE AND THEIR RELATIONSHIP WITH MARKET VALUE

ABSTRACT