The Evolution and Cross Section of the Day-of-The-Week Effect

We study the day of the week effect across size deciles and in three 18-year subperiods. The results show a decline in the magnitude of the day-of-the-week effect, but the effect did not vanish. We find that the decline in the magnitude of the effect is larger in the larger market capitalization deciles. We also find substantial evidence that the day-of-the-week effect is characterized by a pattern of monotonically improving returns during the week, but the pattern is interrupted as market capitalization increases. The behavioral explanation for the day of the week effect, based on monotonically improving mood throughout the week, is therefore a stronger candidate in smaller market capitalization deciles.


Introduction and literature review
The day-of-the-week effectthe observation that returns vary across days of the week in a persistent wayis one of the intriguing anomalies in finance. The first documented evidence of the day-of-the-week effect (henceforth the effect) is provided by Kelly (1930), who reports that returns on Mondays are lower than returns on other days of the week. Several other practitioners have confirmed the existence of a dayof-the-week effect, including Fields (1931), Hirsch (1968), andCross (1973).
Interest in the effect within academic circles begins with French (1980), who documents negative returns on Mondays and positive returns on other days of the week. Subsequent research verified the existence of the effect 1 and identified that its magnitude is larger in small market capitalization stocks. 2 This paper makes two contributions to the literature on the day-of-the-week effect.
The first contribution is to describe the development of the effect over time and across size deciles. Analysis of the effect in three subperiods suggests that the magnitude of the effect has declined over time. The decline in the magnitude of the effect is not uniform, but inversely related to size. This is to the degree that, in the last subperiod, the largest market capitalization decile and the value-weighted portfolio, display no signs of a day-of-the-week effect.
The second contribution of the paper is the documentation of a pattern of improving returns during the week. These results are consistent with the behavioral hypothesis of the day of the week effect, which relates the pattern of improving returns to the pattern of improving mood during the week. Farber (1953) and Golder and Macy (2011), among others, document a pattern of improving mood during the week. Cole et al. (1998) and Bader (2005) document a relation between mood and increased prudence. Increased prudence during periods of low mood may explain the findings of Pettengill (1993) who shows higher tendency for investors to take financial risks before the weekend and lower tendency to take risks after the weekend. Higher levels of prudence may also explain the increased tendency of individual investors to sell stocks on Monday (see for example, Abraham and Ikenberry (1994), Brockman and Michayluk (1998), Brooks and Kim (1997) and Lakonishok and Maberly (1990). Rystrom and Benson (1989), Jacobs and Levy (1988) and Markese (1989) were the first to propose the behavioral hypothesis as a possible explanation for the day of the week effect. Some empirical support for the behavioral explanation is provided by Gondhalekar and Mehdian (2003), who show that the negative returns on Mondays are intensified during periods of investor pessimism. More recently, Hirshleifer et al. (2017) study the effect of mood on the cross section of returns by using moodmimicking returns and find that mood is a valid explanation of the day of the week effect. Further support for the behavioral explanation of the day of the week effect is recently provided by Birru (2017).
Alternative explanations of the day of the week effect Several theories attempt to explain the day-of-the-week effect. Three of the prominent theories are, information-timing, short-sellers activity around the weekend, and the behavioral hypothesis already discussed above.
The information-timing hypothesis suggests that bad news is more likely to reach the markets during the weekend or on Mondays. Defusco et al. (1993) and Dyl and Maberly (1988) find support for this theory in studies of announcements at the firm level. Pettengill and Buster (1994), however, reach conclusions that are at odds with the information-timing hypothesis. Other researchers concentrating upon a limited universe of dividend and earnings announcements find weak support for the theory at best (see for example, Fishe et al., 1993;Schatzberg and Datta, 1992;Damodaran, 1989). Chang and Pinegar (1998) examine the effect of macroeconomic news on the Monday effect and find that macroeconomic news is an important factor in explaining the Monday returns of small stocks. Chen and Singal (2003) propose the short sellers hypothesis. This theory suggests that the positive abnormal return on Friday and negative on Monday are generated by short sellers who close their position before the weekend and re-establish them on Monday. This creates excess demand on Friday and excess supply on Monday, leading to positive and negative abnormal returns on these days, respectively. Full period analysis of the effect,  The sample used in this paper includes all stocks listed on the NYSE, AMEX and NASDAQ exchanges in the CRSP daily data file. In 2005, CRSP extended the daily data file from 1965 back to 1926. Due to the fact that exchanges in the U.S. moved from a six-day to a five-day trading week in the middle of 1952, we analyze data from 1953 to 2006. Using continuously compounded returns, we analyze the day-of-theweek effect in the equally-weighted (EW) portfolio, value-weighted (VW) portfolio, and 10 deciles sorted by market capitalization (with one being the smallest capitalization decile and 10 the largest).  Figure 1 shows a pattern of improving returns in the EW portfolio. However, the pattern is disrupted by the fact that Wednesday's average abnormal return is larger than Thursday's. In the VW portfolio the disruption is even larger since Wednesday's return is larger than both Thursday's and Friday's.

Figure 1 about here
Before we turn to analyzing the average abnormal returns, it is important to determine whether returns across days of the week are homoscedastic. The existing evidence suggests that return variances across days of the week are not homoscedastic (see for example, Aggrawal and Schatzberg, 1997;Connolly, 1994). Panel A of Table 1 provides information on the standard deviations of daily returns from Monday to Friday across the various deciles and portfolios. The evidence in Panel A suggests substantial variation in the standard deviations across days of the week, with Mondays exhibiting the highest standard deviations and Fridays the lowest.
Using a chi-square distribution Panel A of Table 1 also reports p-values for the null   hypothesis   2  2 i ij    , where 2 ij  is the variance of portfolio i on day j and 2 i  is the variance of portfolio i across all days. The evidence in Panel A strongly rejects the null hypothesis that the variance of a particular day is equal to the variance of all week days, except for two casesdeciles 1 and 10 on Tuesday (where the p-values are 7.2% and 10.4%, respectively).  (1960) and Brown-Forsythe (1974) tests for the joint null hypothesis that variances across days of the week are all equal.
The results of these tests strongly reject the hypothesis of homoscedasticity, as pvalues are practically zero in all cases. Following the evidence provided in Table 1, our analysis proceeds under the assumption of heteroscedasticity.
The results in Panel A show a pattern of improving returns during the week in deciles 1 through 4. In deciles 5 through 9 and in the EW portfolio the pattern of improving returns is disturbed, however, by the fact that Wednesday's average abnormal return is higher than Thursday's. In decile 10 and in the VW portfolio, the violation of the pattern is even larger since Wednesday's average abnormal return is larger than that of Thursday and Friday. The results in Panel A of Table 1 also show that the significance of the single-day average abnormal daily return is impressive. The average abnormal return is statistically significant in all cases but two (decile 10 on Tuesday and Thursday).  Table 2 provides results for the joint hypothesis that average abnormal returns are equal across all days of the week. The tests that are used for this purpose are standard ANOVA and ANOVA adjusted for heteroscedasticity (Welch, 1951).
The results show that the null hypothesisthat average abnormal returns are equal across all days of the weekis strongly rejected. All p-values in Panel B of Table 2 (both the homoscedasticity and heteroscedasticity cases) are close to zero.
The evolution of the day-of-the-week effect In this section, we analyze the evolution of the day-of-the-week effect in three 18-year subperiods: 1953-1970, 1971-1988, and 1989-2006. The purpose of this analysis is to examine the evolution of the day-of-the-week effect over time. Figure   We begin the subperiod analysis by testing for heteroscedasticity in the three subperiods. The results of the heteroscedasticity tests are reported in Table 3. Table 3 about here The results in Table 3 indicate that heteroscedasticity is present in the large majority of the cases. The sizes of the F-statistics suggest, however, a decline in the magnitude of heteroscedasticity to the degree that, in terms of statistical significance, heteroscedasticity has disappeared in some of the largest capitalization deciles during the recent 1989-2006 period. Nevertheless, the bulk of the evidence in Table 3 rejects the null hypothesis of homoscedasticity, and therefore the subperiod analysis below proceeds under the assumption of heteroscedasticity.   Table 4 suggests that the pattern of improving returns throughout the week is also present in the subperiods. However, as in the full-period analysis, Wednesday's return seems too high and violates the pattern in many cases.
The results in Table 4 also suggest that the magnitude of the day of the week effect has declined over time. This can be observed in the size of the F-statistics in the EW and VW portfolio. In the VW portfolio, the F-statistic is 26.92 in the first subperiod, 6.51 in the second subperiod, and 0.3 in the third subperiod. In the EW portfolio the F-statistics are 34.72, 37.25, and 15.00, respectively. Hence, although not entirely smooth in the EW portfolio, there is a general tendency of decline in the magnitude of the day-of-the-week effect. Note also that, as part of this decline, the effect disappeared in the last subperiod in the largest capitalization decile (decile 10) and in the VW portfolio. In decile 9, the effect became boarder line significant. The effect remains, however, statistically significant in all other 8 deciles and in the EW portfolio in the last subperiod. Consistent with other studies, we conclude that the results show a decline in the magnitude of the effect over time (see, for example, Brusa et al., 2000;Gu, 2004;Kohers et al., 2004;Mehdian and Perry, 2001;Kamara, 1997, for similar evidence). However, the evidence does not suggest that the effect has vanished.

Summary and Conclusions
We study the day-of-the-week effect across size deciles and over time. Full period analysis  of the day of the week effect shows that returns are monotonically increasing during the week in the four smallest capitalization deciles.
However, the pattern of increasing returns is interrupted in the EW and size deciles 5 through 9 by the fact that Wednesday average abnormal return is higher than Thursday's. In decile 10 and in the VW portfolio, the interruption of the pattern is even larger since Wednesday's average abnormal return is larger than that of Thursday's and Friday's.
The behavioral explanation of the day-of-the-week effect is based on empirical findings that mood tends to improve throughout the week. Thus, if the behavioral explanation is true, we should expect returns to improve throughout the week. Our evidence suggests that the behavioral hypothesis is a stronger candidate in the smaller capitalization deciles.
We also examine the evolution of the day of the week effect in three subperiods, 1953-1970, 1971-1988, and 1989-2006. We find that the day of the week effect has contracted with the decline inversely related to market capitalization. As part of this   , where ij  is the average abnormal return of portfolio/decile i on day j. The results in Panel A show a pattern of improving returns throughout the week in size deciles 1 through 4, but the pattern is less monotonic in the larger capitalization deciles. Panel B provides results for the more general null hypothesis of equal averages across all days of the week. The results in Panel B reject the null hypotheses, using both standard ANOVA and ANOVA adjusted for heteroscedasticity. 1  2  3  4  5  6  7  8  9  10 Monday

EW VW
Tuesday -0.071% -0.008% -0.142% -0.119% -0.102% -0.093% -0.075% -0.066% -0.054% -0.042% -0.036% 0.   Table 3 provides information on standard deviations of returns across days of the week for the EW, VW, and 10 size decile portfolios in three subperiods : 1953-1970(Panel A), 1971-1988(Panel B), and 1989-2006. We use the Levene and Brown-Forsythe tests to examine the joint null hypothesis that variances are equal across days of the week. The null hypothesis is rejected in all cases in the first two subperiods. In the third subperiod, the null hypothesis is rejected in deciles 1 through 6 and 9.   Table 4 provides information on the statistical significance of the day-of-the-week effect on a day-by-day basis and jointly across days of the week in three subperiods: 1953-1970 (panel A), 1971-1988 (panel B), and 1989-2006 (panel C). The sizes of the F statistics of the Welch ANOVA in the VW and EW portfolios suggest that the magnitude of the effect has declined over time. The results also show tendency for returns to improve during the week in many cases, although in some cases this pattern is interrupted by a high abnormal return on Wednesday.  However, in the EW portfolio the pattern is interrupted by the fact that Wednesday's return is higher than Thursdays. In the VW portfolio Wednesday's return is higher than Thursday's and Friday's. The figure also suggests that the day-of-the-week effect is more pronounced in the EW portfolio.  1953-1970, 1971-1988 and 1989-2006. Average abnormal return is defined as the average return for the relevant day, portfolio and subperiod minus the average daily return across all days for the relevant portfolio and subperiod.