For calculating the VPIN, the sample was restricted to those stocks that had at least one transaction per day between May 1, 2014, and May 31, 2016, period in which information was available on the BM&FBOVESPA market data.
In this study, however, no emphasis was assigned to the difference of VPIN for the different classes of shares.
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.
Thus, the hypothesis established was that the VPIN for the NM segment is the lowest, followed by N2, Nl, and, finally, the traditional.
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.
At the same time, the stocks were divided into 2 groups: low and high VPIN.
In this study, we observed that the correlation between VPIN and return was 0.
The result for VPIN calculation is displayed in Table 4.