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Financial Innovation

Table 3 Are variances equal across days of the week? Subperiod analysis

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 tests of variance equality 1953–1970

Monday

0.81%

0.78%

0.94%

0.88%

0.89%

0.87%

0.89%

0.87%

0.82%

0.80%

0.77%

0.79%

Tuesday

0.62%

0.65%

0.75%

0.72%

0.71%

0.68%

0.70%

0.67%

0.65%

0.61%

0.60%

0.68%

Wednesday

0.65%

0.65%

0.75%

0.69%

0.71%

0.70%

0.73%

0.71%

0.68%

0.64%

0.62%

0.68%

Thursday

0.64%

0.59%

0.75%

0.71%

0.72%

0.71%

0.72%

0.69%

0.66%

0.62%

0.59%

0.60%

Friday

0.57%

0.55%

0.75%

0.65%

0.66%

0.63%

0.65%

0.61%

0.59%

0.55%

0.53%

0.56%

Levene

Test statistic

11.4

11.8

6.3

10.6

9.7

10.1

10.8

11.1

10.7

12.9

12.4

11.0

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

9.5

10.7

6.2

10.2

8.5

8.7

9.0

9.3

9.3

10.6

11.0

10.4

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: Standard deviation of daily returns and tests of variance equality 1971–1988

Monday

0.87%

1.16%

0.81%

0.86%

0.90%

0.93%

0.95%

0.97%

0.99%

1.01%

1.04%

1.22%

Tuesday

0.68%

0.83%

0.69%

0.70%

0.73%

0.76%

0.77%

0.79%

0.79%

0.78%

0.78%

0.89%

Wednesday

0.68%

0.87%

0.64%

0.67%

0.69%

0.71%

0.75%

0.76%

0.79%

0.77%

0.80%

0.92%

Thursday

0.64%

0.82%

0.64%

0.65%

0.68%

0.69%

0.72%

0.73%

0.75%

0.74%

0.75%

0.87%

Friday

0.63%

0.81%

0.60%

0.63%

0.65%

0.68%

0.69%

0.71%

0.73%

0.72%

0.74%

0.85%

Levene

Test statistic

7.1

5.4

6.1

5.7

4.8

6.6

6.8

7.3

6.5

8.9

6.6

5.1

p-value

0.0%

0.0%

0.0%

0.0%

0.1%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

Brown-Forsythe

Test statistic

6.8

5.3

6.1

5.5

4.5

6.4

6.3

6.7

6.2

8.3

6.3

4.9

p-value

0.0%

0.0%

0.0%

0.0%

0.1%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.1%

Panel C: Standard deviation of daily returns and tests of variance equality 1989–2006

Monday

0.79%

1.01%

0.91%

0.72%

0.74%

0.78%

0.85%

0.93%

1.01%

1.03%

1.04%

1.04%

Tuesday

0.70%

0.97%

0.84%

0.65%

0.65%

0.68%

0.75%

0.83%

0.91%

0.94%

0.94%

1.00%

Wednesday

0.70%

0.89%

0.85%

0.66%

0.65%

0.67%

0.75%

0.83%

0.89%

0.91%

0.90%

0.91%

Thursday

0.72%

0.94%

0.75%

0.65%

0.65%

0.67%

0.76%

0.83%

0.91%

0.93%

0.93%

0.96%

Friday

0.69%

0.96%

0.77%

0.61%

0.62%

0.66%

0.73%

0.83%

0.90%

0.92%

0.92%

0.99%

Levene

Test statistic

2.5

1.1

4.5

2.9

2.8

4.3

3.1

2.7

2.4

2.2

2.9

1.2

p-value

4.4%

35.2%

0.1%

2.0%

2.3%

0.2%

1.5%

3.1%

4.9%

6.7%

2.1%

31.4%

Brown-Forsythe

Test statistic

2.3

1.1

4.6

2.7

2.8

4.3

2.9

2.6

2.2

2.0

2.7

1.2

p-value

5.4%

35.1%

0.1%

2.7%

2.6%

0.2%

2.3%

3.7%

6.3%

8.8%

3.0%

31.8%

  1. 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 (Panel C). 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
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