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Table 1 Are variances equal across days of the week?

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

  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%
  1. 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