The evolution and cross-section of the day-of-the-week effect

Financial Innovation

Table 1 Are variances equal across days of the week?

	Portfolio/Decile
	EW	VW	1	2	3	4	5	6	7	8	9	10
Panel A: Standard deviation of daily returns and their p-values
All days	0.71%	0.85%	0.71%	0.71%	0.73%	0.74%	0.77%	0.80%	0.82%	0.82%	0.82%	0.88%
Monday	0.83%	1.16%	0.89%	0.82%	0.85%	0.86%	0.90%	0.93%	0.94%	0.95%	0.96%	1.03%
p-value	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Tuesday	0.67%	0.83%	0.76%	0.69%	0.70%	0.71%	0.74%	0.77%	0.79%	0.79%	0.79%	0.87%
p-value	0.0%	2.3%	7.2%	1.2%	0.3%	0.3%	0.2%	0.4%	1.1%	0.6%	0.7%	10.4%
Wednesday	0.68%	0.87%	0.75%	0.68%	0.69%	0.69%	0.74%	0.77%	0.79%	0.78%	0.78%	0.84%
p-value	0.2%	0.1%	0.2%	0.0%	0.0%	0.0%	0.1%	0.2%	0.5%	0.1%	0.1%	0.1%
Thursday	0.67%	0.82%	0.72%	0.67%	0.68%	0.69%	0.73%	0.75%	0.78%	0.78%	0.77%	0.83%
p-value	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Friday	0.63%	0.81%	0.71%	0.63%	0.64%	0.66%	0.69%	0.72%	0.75%	0.75%	0.75%	0.82%
p-value	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Panel B: Joint tests of equality of variances across days of the week
Levene
Test statistic	18.6	10.1	15.7	17.5	15.9	20.1	19.1	18.4	15.9	18.0	16.8	9.0
p-value	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Brown-Forsythe
Test statistic	17.0	9.7	15.6	16.6	14.8	18.8	17.2	16.7	14.6	16.0	15.4	8.8
p-value	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%

Table 1 provides information on standard deviations of returns across days of the week for the EW, VW, and size decile portfolios in the 1953–2006 period. Panel A provides the standard deviation for the relevant day and portfolio/decile, and the corresponding p-value for the null hypothesis \( {\sigma}_{ij}^2={\sigma}_i^2 \), where \( {\sigma}_{ij}^2 \) is the variance of portfolio i on day j and \( {\sigma}_i^2 \) is the variance of portfolio i across all days of the week. The results in Panel A suggest substantial variation in the variances across days of the week, with Monday displaying the highest variance and Friday the lowest. Panel B provides the results of two statistical tests, the Levene and Brown-Forsythe tests, for the more general null hypothesis \( {\sigma}_{i, Mon}^2={\sigma}_{i, Tue}^2={\sigma}_{i, Wed}^2={\sigma}_{i, Thu}^2={\sigma}_{i, Fri}^2={\sigma}_i^2 \). The results in Panel B suggest that the null hypothesis of homoscedasticity is rejected for all portfolios/deciles