4. Results

The mean and standard deviation were initially calculated and the significance was verified for return and liquidity measures. Table 1 refers to the behavior of the asset return and Tables 2, 3, 4, 5, 6 and 7 show the behavior of the various liquidity measures in the 5 minute interval. Each table is divided into three blocks. The first, named Total, presents the results for the entire study period, that is, data from 10:00 a.m. to 4:55 p.m., and the two following blocks have the results for the morning and afternoon period, respectively.

Table 1 – Daily returns average in the 5 minute interval

Analyzing the Total period (Table 1), it can be seen that, on average, there is negative return only on Tuesday. This result may be associated with the Brasilia effect, which is highlighted in the study of Bone and Ribeiro (2002). The only day that the return is not significantly different from zero is Wednesday. The highest significant average returns are 0.000076 on Monday, followed by 0.000042 on Thursday and 0.000025 on Friday. The morning period had positive returns for Mondays and Wednesdays and negative returns for Tuesdays and Fridays. There were not negative returns in the afternoon. The division in two periods shows that the negative average return on Tuesday is predominantly derived from the morning period, since the average return is negative in this period and not significantly different from zero in the afternoon. On Friday, it is seen a negative return in the morning and a positive return in the afternoon.

There is no consensus in the literature about the proper way to measure liquidity. Therefore, this study used the following measures: spread1, spread2, variation in trading volume, measured in Reais, variation in the weighted trading volume, measured in Reais, variation in the amount of traded securities and variation in the amount of weighted securities traded. Tables 2 and 3 analyze daily averages of spread1 and spread2.

Table 2 – Daily averages for spread1 in the 5 minute interval

Table 3 - Daily averages for spread2 in the 5 minute interval

Analyzing Tables 2 and 3, the coefficients of spread1 spread2 are, on average, all significantly different from zero, except for Wednesday (total and the afternoon) and Friday (total). Note in Table 2 that, on average, Mondays in spread1, in the morning and afternoon, are lower than the other averages, corroborating the results seen in Table 3, where Monday stands out as the day with highest return.

It can be observed in Table 3 that the highest average coefficient (0.00010) is on Tuesday in the morning and this result is consistent with the negative average return on the same day (Tuesday) in Table 1. Positive differences in relative prices in the 5 minute interval mean that the opening prices are higher than the closing prices of the assets. Tuesday in the morning has the highest spread in Table 3 (open-close), that is, asset prices presented, on average, closing prices lower than opening prices for the 5 minute interval. Table 4 analyzes the daily averages for the variation in trading volume in the 5 minute interval.

Table 4 - Daily averages for variation in volume in the 5 minute interval

The variation in volume in Table 4, measured in Reais, shows values near 1 in the 5 minute interval. It is noticed that Monday has the largest variation in volume (1.165), corroborating with Table 1, where the average returns are higher and positive on Monday. This verification shows that there are more investors trading in the market this day, thus having a higher trading volume on Monday followed by Friday. It is observed that, in the afternoon throughout the week, the variation in volume is, on average, higher than in the morning. Table 5 analyzes the variation in trading volume, weighted by Ibovespa.

Table 5 - Daily averages for variation in volume weighed by Ibovespa

Table 5 shows the variation in volume in the 5 minute interval, measured in Reais and weighted by Ibovespa. It is noticed that Friday has the largest variation in volume (1.152), followed by Monday (1.091). Comparing the average values for the total period of Tables 4 and 5, it is observed that the average values from Table 4, variation in volume, are larger than the average values weighted by Ibovespa (Table 5), indicating that, on average, the variation in the companies volume is less than the variation of Ibovespa volume. The daily average variation in the amount of securities traded will be examined in Table 6 and the variation averages in the amount of traded securities, weighted by Ibovespa, in Table 7.

Table 6 - Daily averages for variation in the amount of traded securities

Table 7 - Daily averages for variation in the amount of traded securities weighed by Ibovespa

Evaluating liquidity in Tables 6 and 7 under the size of the traded securities in the 5 minute interval, it was considered variation in the amount of traded securities and variation in the amount of securities weighted by Bovespa index. Table 6 presents the coefficients around 1 in the 5 minute interval, all significantly different from zero. Only the morning period on Monday and Wednesday and the afternoon on Tuesday, in Table 7, are not significantly different from zero. The average values in Table 6 are very close to those presented in Table 4. These results show that the behavior of the variation in the amount of securities and trading volume are very similar, that is, the two variables tend to evaluate the same liquidity dimension. On the other hand, the comparison between coefficients in Tables 6 and 7 shows that the weighted variable has larger average than the variable without weighting, indicating that variation in the amount of traded securities for companies is greater than variation in the total amount of securities at Bovespa index. Noteworthy, the analysis of the weighted variations in relation to those without weighting suggests that the greatest differences are found for the variable amount of securities.

To evaluate the weekday effect, as proposed in the method, the equation model [1] with dummy variables was applied. Based on the observation that average returns were higher on Monday, the differences in relation to Monday were obtained from the liquidity variable. (variables identified with the code Dif_). The results for the return are presented in Table 8. The results for liquidity variables are presented in Tables 9, 10, 11, 12, 13 and 14.

Table 8 - Differences in relation to Monday average

For total block on Table 8, all mean differences of the shares return in relation to Monday are negative, indicating that returns are, on average, lower than those obtained on Monday during the week. In the morning, except on Wednesday, coefficients are negative and larger than those presented in the entire period, indicating that returns during the day tend to be lower in the morning than in the afternoon. So, in the total of the week (morning and afternoon) in the afternoon period differences, the differences in returns remained negative on Tuesday and Wednesday, but they are not different from zero, on average, for other days (Wednesday and Friday). The mean differences in spread1 in relation to Monday are presented in Table 9.

Table 9 - Differences in relation to the spread1 average on Monday

Table 9 presents all coefficients, on average significant, for differences between the days of the week in relation to Monday for spread1 (maximum price, minimum price) within the 5 minute interval. All coefficients are positive, with the largest spread on Wednesday afternoon and lower spread on Wednesday morning. The mean differences of spread2 in relation to Monday are presented in Table 10.

Table 10 - Differences in relation to the spread2 average on Monday

Table 10 shows that, on average, all coefficients are significant for differences between the days of the week in relation to Monday for spread2 (maximum price-minimum price) within the 5 minute interval. The largest spread is found on Tuesday in the morning and the lowest spread on Thursday for the total week. The average differences of the variation in the amount of securities in relation to Monday are presented in Table 11.

Table 11 – Differences in relation to the average of the variation in the amount of securities on Monday

Table 11 presents, on average, coefficients of the variation in the amount of securities in relation to Monday, showing that there are not significant differences from zero for every day of the week, morning and afternoon, therefore there are no significant differences in the amount of traded securities over the week. Table 12 presents the average differences in the variation of the amount of securities, weighted by Ibovespa, in relation to Monday.

Table 12 – Difference in relation to the average of the variation in the amount of weighed securities on Monday

With respect to Table 12, it can be observed that weighing the variation in the amount of securities by Bovespa index has certain significant differences for the total of the week (Thursday and Friday), morning (Tuesday, Thursday and Friday) and afternoon (only Friday). Note that the average values of coefficients increased considerably compared to the variation in the quantity of securities. Table 13 presents the average differences of the variation in trading volume relative to Monday.

Table 13 – Difference in relation to the average of the variation in the volume on Monday

Table 13 presents the average of the coefficients of variation in volume in relation to Monday. It can be said that none of the differences is significant, that is, there is, on average, no differences in trading volume within the 5 minute interval. Table 14 presents the average differences of the variation in trading volume, weighted by Ibovespa, in relation to Monday.

Table 14 – Difference in relation to the average of the variation in the weighed volume on Monday

Table 14 shows the variation in trading volume, measured in Reais and weighted by Bovespa index, for the differences in the days of the week in relation to Monday. There was significant difference only on Friday morning, while there were no differences within the 5 minute analysis for other days.

Finally, to evaluate intraday seasonality, the differences in the afternoon compared to morning were calculated in Table 15 for return and liquidity variables.

Table 15 – Daily averages for intraday seasonality

Table 15 is compound by the average coefficients in the morning and their differences for the afternoon period (Dif_aftern). Almost every afternoon are, on average, different from morning, confirming the existence of differences for periods within the same day. Regarding the return, the afternoon period (0.000042) was higher than morning. With respect to illiquidity, it was observed that both measures have negative coefficients in the afternoon. For the liquidity measures, the coefficients in the afternoon are positive (except for variation in the amount of weighted securities) indicating that, on average, afternoon period has a higher amount of securities and trading volume.

5. Conclusions

The aim of this study was to investigate the weekday effect and intraday seasonality in the Brazilian stock market using stock belonging to Sao Paulo Stock Exchange index with high frequency data in terms of return and liquidity.

For the weekday effect, the results indicate that Monday is the day of higher average return over the analyzed period. Some authors suggest that such behavior arises from the fact that Monday brings together the weekend results. Tuesday result is also noteworthy since it is the only negative return in the total block. The behavior on that day may be associated with the Brasilia effect, since this is the first day of effective operation in the Brazilian Congress. It is noteworthy that these results are different from those presented by Bone and Ribeiro (2002), who noted that Tuesday showed positive returns in a different sample period. Adding the evidence of the two studies, one can presume that Tuesday is a day with quite expectation for the arrival of new information. Thus, the average returns, positive or negative, will be obtained depending on the agents’ interpretation of this information. With respect to liquidity levels, there are no significant variations throughout the week.

In general, the results for the intraday seasonality effect show that, on average, the return in the morning between five minute intervals is virtually zero and liquidity is lower than in the afternoon. There is an increase in return in the afternoon, followed by an improvement in liquidity. It is noteworthy that the lower liquidity level in the morning may be linked to the fact that the USA market is still not working due to time difference. It is possible that the Brazilian market presents a lower movement in the early morning due to expectations on the arrival of new information.

This study stands out for handling the high frequency data and the effort to examine the weekday effects and intraday seasonality in terms of returns and liquidity. However, researches in this subject can still move in several directions: (1) analysis of other sampling periods; (2) construction of a large sample, including less liquid shares; (3) comparative analysis of the returns with the vote on the Congress agenda; (4) analysis of the opening hours effect of the USA market on the Brazilian market liquidity; and (5) evaluation of the intraday seasonality effect with a major division of time periods.

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