Study on the relationship between the IVol-BR and the future returns of the Brazilian stock market<sup>,</sup>

Cainelli, Paloma Vanni; Pinto, Antonio Carlos Figueiredo; Klötzle, Marcelo Cabús

doi:10.1590/1808-057x202009890

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Revista Contabilidade & Finanças

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Original Article • Rev. contab. finanç. 32 (86) • May-Aug 2021 • https://doi.org/10.1590/1808-057x202009890 copy

Study on the relationship between the IVol-BR and the future returns of the Brazilian stock market^* * Article presented at the XLII ANPAD Conference, Curitiba, PR, Brazil, October of 2018. ^,^ This study was conducted with the financial support of the Coordination for the Improvement of Higher Education Personnel (CAPES), the National Council for Scientific and Technological Development (CNPq) (305641/2019-0 and 408470/2016-0), and the Carlos Chagas Filho Research Support Foundation of the State of Rio de Janeiro (FAPERJ) (E-26/202.824/2018).

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In 2015, the Financial Economics Research Center (NEFIN) of the University of São Paulo proposed an implicit volatility index for the Brazilian stock market based on the daily prices of options for the Bovespa index (Ibovespa) and that measures the expected volatility of the Ibovespa in the next two months. The aim of this study is to determine whether this implicit volatility index can be considered an antecedent indicator of future returns of the Brazilian stock market, given that it represents the expected volatility of the Ibovespa two months into the future. This study contributes to the literature on the implicit volatility index for the Brazilian stock market, which has been scarce until now. This happens due to the recent establishment of the index and due to the fact that there is not an official one published by the B3 S.A. - Brasil, Bolsa, Balcão (B3). Given the relationship found between the Brazilian implicit volatility index and the future returns of the Ibovespa, investors could anticipate instabilities in the Brazilian market by putting together strategies to protect their investment portfolios, as well as identifying opportunities to enter and exit the market. This research corroborates in disclosing the Brazilian implicit volatility index in order for it to become more widely used in academia and in the Brazilian financial market. The increase in studies on this index may also incentivize the launch of an official implicit volatility index by the B3. The relationship between the Brazilian implicit volatility index and the future returns of the Ibovespa is examined using least squares and quantile regressions. The implicit volatility index for the Brazilian stock market could help in predicting the future returns of the Ibovespa, especially for 20-, 60-, 120-, and 250-day future returns.

Keywords
Ibovespa; IVol-BR; future returns

	Bear period	Bull period	Full series
Mean	23.789	23.227	23.567
Median	22.928	22.320	22.702
Maximum	47.053	40.004	47.053
Minimum	13.878	13.109	13.109
Standard deviation	4.498	4.650	4.566
Asymmetry	1.410	0.925	1.195
Kurtosis	6.038	3.766	5.101
Jarque-Bera	768.302	117.098	748.596
Probability	0.000	0.000	0.000

Future returns	Statistic	p-value
1 day	1.997	0.136
5 days	11.258***	0.000
20 days	46.195***	0.000
60 days	87.353***	0.000
120 days	243.182***	0.000
250 days	540.327***	0.000

		Bear period	Bull period	Full series
1 day	$β$	-	-	0.001
	$σ$	-	-	0.009
	p-value	-	-	0.941
	R²	-	-	0.000
5 days	$β$	0.054	0.062	0.048
	$σ$	0.049	0.051	0.037
	p-value	0.265	0.225	0.188
	R²	0.006	0.009	0.005
20 days	$β$	0.199**	0.345***	0.218***
	$σ$	0.093	0.121	0.082
	p-value	0.033	0.005	0.008
	R²	0.022	0.060	0.025
60 days	$β$	0.647***	0.498**	0.491***
	$σ$	0.202	0.206	0.161
	p-value	0.001	0.016	0.002
	R²	0.071	0.059	0.043
120 days	$β$	1.145***	0.850***	0.870***
	$σ$	0.198	0.216	0.182
	p-value	0.000	0.000	0.000
	R²	0.161	0.132	0.089
250 days	$β$	1.214***	0.816***	0.962***
	$σ$	0.288	0.218	0.271
	p-value	0.000	0.000	0.000
	R²	0.131	0.200	0.066

	Percentile (IVol-BR)
		1%	5%	10%	90%	95%	99%
1 day	$β$	-0.141	-0.115	-0.061	-0.029	-0.011	-0.256
	$σ$	0.264	0.091	0.074	0.049	0.084	0.254
	p-value	0.599	0.207	0.409	0.552	0.895	0.328
	R²	0.015	0.012	0.004	0.002	0.000	0.081
5 days	$β$	0.701	0.413**	0.139	-0.037	0.000	0.208
	$σ$	0.507	0.201	0.138	0.090	0.149	0.543
	p-value	0.183	0.043	0.313	0.677	0.999	0.706
	R²	0.059	0.037	0.005	0.001	0.000	0.010
20 days	$β$	1.375	0.778	0.106	0.235	0.215	0.692
	$σ$	1.922	0.573	0.436	0.152	0.197	0.573
	p-value	0.484	0.178	0.809	0.125	0.278	0.244
	R²	0.037	0.022	0.000	0.013	0.012	0.060
60 days	$β$	3.982	1.429*	-0.113	-0.704**	-0.289	0.938
	$σ$	2.381	0.827	0.781	0.275	0.349	1.030
	p-value	0.112	0.088	0.885	0.012	0.411	0.376
	R²	0.124	0.027	0.000	0.049	0.010	0.051
120 days	$β$	4.963	1.880	-0.782	0.136	0.025	1.004
	$σ$	3.530	1.185	1.030	0.283	0.345	0.948
	p-value	0.182	0.116	0.449	0.632	0.943	0.305
	R²	0.091	0.019	0.003	0.002	0.000	0.046
250 days	$β$	1.547	-0.759	-3.717***	-1.147***	-1.665***	0.122
	$σ$	8.417	1.741	1.212	0.388	0.525	1.434
	p-value	0.858	0.664	0.003	0.004	0.002	0.933
	R²	0.003	0.002	0.058	0.051	0.096	0.000

	Percentile (future returns)
		1%	5%	10%	90%	95%	99%
1 day	$β$	-0.139**	-0.078***	-0.082***	0.062***	0.098***	0.112***
	$σ$	0.056	0.015	0.013	0.014	0.015	0.019
	p-value	0.013	0.000	0.000	0.000	0.000	0.000
	R²	0.031	0.037	0.029	0.025	0.047	0.069
5 days	$β$	-0.002	-0.116***	-0.098***	0.156***	0.256***	0.343***
	$σ$	0.031	0.024	0.024	0.029	0.030	0.043
	p-value	0.957	0.000	0.000	0.000	0.000	0.000
	R²	0.000	0.017	0.013	0.037	0.077	0.140
20 days	$β$	0.081	0.073	0.137***	0.357***	0.364***	0.767***
	$σ$	0.126	0.070	0.050	0.069	0.104	0.075
	p-value	0.522	0.299	0.007	0.000	0.001	0.000
	R²	0.004	0.001	0.004	0.029	0.041	0.176
60 days	$β$	0.014	0.123*	0.312***	0.564***	0.557***	1.234***
	$σ$	0.091	0.073	0.117	0.109	0.143	0.119
	p-value	0.878	0.091	0.008	0.000	0.000	0.000
	R²	0.000	0.002	0.007	0.028	0.031	0.183
120 days	$β$	1.168***	0.763***	0.778***	0.482***	0.785***	1.114***
	$σ$	0.066	0.090	0.069	0.091	0.200	0.086
	p-value	0.000	0.000	0.000	0.000	0.000	0.000
	R²	0.069	0.042	0.043	0.026	0.040	0.154
250 days	$β$	0.161**	0.146	0.195**	0.818***	1.678***	2.034***
	$σ$	0.080	0.091	0.097	0.204	0.255	0.116
	p-value	0.045	0.109	0.044	0.000	0.000	0.000
	R²	0.007	0.002	0.004	0.029	0.078	0.201

Series of future returns	1 day	5 days	20 days	60 days	120 days	250 days
$φ$	-0.012	0.801***	0.948***	0.981***	0.987***	0.992***
$σ$	0.021	0.010	0.007	0.005	0.004	0.003
p-value	0.565	0.000	0.000	0.000	0.000	0.000
R²	0.000	0.630	0.897	0.963	0.975	0.986

Series of future returns		Percentile (IVol-BR)
Series of future returns		1%	5%	10%	90%	95%	99%
1 day	$φ$	0.261	-0.130	-0.046	-0.081	-0.039	0.528**
	$σ$	0.234	0.092	0.064	0.082	0.112	0.214
	p-value	0.279	0.159	0.467	0.326	0.727	0.026
	R²	0.073	0.017	0.002	0.007	0.002	0.283
5 days	$φ$	-0.111	0.139	0.095	-0.128*	-0.069	0.124
	$σ$	0.269	0.116	0.080	0.076	0.116	0.270
	p-value	0.685	0.235	0.238	0.092	0.552	0.651
	R²	0.011	0.019	0.009	0.016	0.005	0.014
20 days	$φ$	0.000	-0.069	-0.008	0.012	0.139	0.155
	$σ$	0.281	0.108	0.074	0.082	0.112	0.306
	p-value	1.000	0.526	0.914	0.885	0.216	0.620
	R²	0.000	0.005	0.000	0.000	0.019	0.021
60 days	$φ$	0.120	-0.180	-0.102	-0.092	-0.036	0.225
	$σ$	0.269	0.109	0.074	0.086	0.130	0.329
	p-value	0.661	0.103	0.172	0.284	0.785	0.503
	R²	0.015	0.033	0.010	0.009	0.001	0.041
120 days	$φ$	0.127	-0.213	-0.122	0.116	-0.025	0.117
	$σ$	0.268	0.132	0.081	0.094	0.136	0.283
	p-value	0.643	0.110	0.132	0.217	0.853	0.685
	R²	0.014	0.037	0.014	0.014	0.001	0.013
250 days	$φ$	-0.165	-0.199	-0.096	0.144*	0.148	0.069
	$σ$	0.421	0.143	0.094	0.083	0.116	0.273
	p-value	0.705	0.168	0.311	0.084	0.208	0.804
	R²	0.029	0.041	0.009	0.021	0.024	0.005

		Bear period	Bull period	Full series
5 days	$β$	0.011	0.043	0.016
	$σ$	0.038	0.042	0.030
	p-value	0.767	0.307	0.587
	R²	0.355	0.364	0.356
20 days	$β$	0.152*	0.294***	0.170**
	$σ$	0.090	0.112	0.078
	p-value	0.092	0.009	0.030
	R²	0.116	0.146	0.118
60 days	$β$	0.600***	0.481**	0.455***
	$σ$	0.197	0.202	0.159
	p-value	0.002	0.018	0.004
	R²	0.105	0.084	0.075
120 days	$β$	1.105***	0.846***	0.841***
	$σ$	0.197	0.214	0.181
	p-value	0.000	0.000	0.000
	R²	0.181	0.151	0.108
250 days	$β$	1.175***	0.825***	0.938***
	$σ$	0.285	0.217	0.270
	p-value	0.000	0.000	0.001
	R²	0.146	0.217	0.077

		Percentile (IVol-BR)
		1%	5%	10%	90%	95%	99%
1 day	$β$	-	-	-	-	-	-0.157
	$σ$	-	-	-	-	-	0.129
	p-value	-	-	-	-	-	0.245
	R²	-	-	-	-	-	0.750
5 days	$β$	-	-	-	0.010	-	-
	$σ$	-	-	-	0.010	-	-
	p-value	-	-	-	0.321	-	-
	R²	-	-	-	0.984	-	-
250 days	$β$	-	-	-	-0.167***	-	-
	$σ$	-	-	-	0.055	-	-
	p-value	-	-	-	0.003	-	-
	R²	-	-	-	0.983	-	-

	Percentile (future returns)
		1%	5%	10%	90%	95%	99%
5 days	$β$	-0.144*	-0.106***	-0.111***	0.117***	0.211***	0.318***
	$σ$	0.087	0.018	0.019	0.020	0.022	0.066
	p-value	0.099	0.000	0.000	0.000	0.000	0.000
	R²	0.195	0.217	0.214	0.224	0.256	0.304
20 days	$β$	0.058	0.029	0.085**	0.318***	0.345***	0.689***
	$σ$	0.127	0.071	0.040	0.076	0.092	0.077
	p-value	0.649	0.687	0.033	0.000	0.000	0.000
	R²	0.056	0.053	0.055	0.072	0.085	0.215
60 days	$β$	0.044	0.105*	0.251	0.484***	0.427***	1.060***
	$σ$	0.084	0.061	0.159	0.110	0.125	0.115
	p-value	0.600	0.084	0.114	0.000	0.001	0.000
	R²	0.023	0.023	0.025	0.043	0.046	0.196
120 days	$β$	0.994***	0.761***	0.714***	0.445***	0.622***	1.162***
	$σ$	0.097	0.076	0.069	0.094	0.169	0.077
	p-value	0.000	0.000	0.000	0.000	0.000	0.000
	R²	0.080	0.052	0.053	0.039	0.051	0.171
250 days	$β$	0.161**	0.157*	0.163*	0.914***	1.729***	1.988***
	$σ$	0.074	0.082	0.094	0.232	0.234	0.111
	p-value	0.028	0.055	0.082	0.000	0.000	0.000
	R²	0.016	0.011	0.012	0.036	0.088	0.208

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