The main limitation of studies that have proposed to apply the PIN or, in this case, the VPIN, is related to misclassification of purchase and sales orders.
Thus, the probability of having privileged transactions is, in theory, lower for these shares, resulting in lower VPIN than that found for shares from small companies, as also verified by Abad and Yagiie (2012) and Wei, Gerace and Frino (2013).
Hypothesis 2: The BM&FBOVESPA listing segments have different VPIN values.
It was expected that the companies constituting the various segments of the BM&FBOVESPA have lower VPIN, as verified by Barbedo et al.
Hypothesis 3: A factor related to the VPIN helps explaining portfolio returns.
It was expected that the addition of a VPIN factor in the 3- and 5-factor models proposed by Fama and French (1993,2015) and the 4-factor model proposed by Carhart (1997) had a reduced general intercept in the portfolios analyzed by the GRS and Average F-test proposed by Hwang and Satchell (2014).
For creating the portfolios, the main variable 'size' was retained and the second component was exchanged between the other variables: book-to-market, profitability, investment, and VPIN. Following Sanvicente and Bellato (2004), portfolios with less than 6 stocks were excluded from the tests, because they were not sufficiently diversified.
At the same time, the stocks were divided into 2 groups: low and high VPIN. Finally, we calculated the weighed return on each intersection (Table 3).
In this study, we observed that the correlation between VPIN and return was 0.0141 with p = 0.0003.
The result for VPIN calculation is displayed in Table 4.
Regarding the different BM&FBOVESPA listing segments, it was expected that companies in the New Market (NM) segment, which have, in theory, greater transparency than those in the segments Level 1 (LI), Level 2 (L2), and Traditional (Trad), had lower VPIN. To analyze this hypothesis, daily VPIN was calculated for each segment (Table 5).
We observe that the Level 2 VPIN was the highest among the BM&FBOVESPA listing segments, followed by the New Market, Traditional, and finally Level 1.