The fading day-of-the-week effect in developed equity markets.

Kohers, Gerald ; Pandey, Vivek ; Kohers, Ninon 等

ABSTRACT

The day-of-the-week effect, one of the most widely documented anomalies, has revealed that security returns tend to be significantly higher on some days of the week relative to other days. If the efficiency of markets improves over time, then the day-of-the-week effect may have faded away in recent time periods. This paper investigates the existence of this anomaly in the world's 23 developed equity markets over the last 22 years. The findings show that the day-of-the-week effect clearly was evident in the vast majority of developed markets during the 1980s, but it appears to have faded away in the 1990s. These results imply that increases in market efficiency over long time periods may have dissipated the effects of certain anomalies in more recent years.

INTRODUCTION

A substantial volume of research on security price behavior has identified a number of persistent seasonal patterns commonly known as calendar anomalies. According to these seasonal anomalies, the tendency exists for securities to display systematic patterns at certain times like days, weeks or months. One of the most widely documented anomalies is the day-of-the-week effect, according to which the security returns are significantly higher on some days of the week relative to other days (see e.g., Aggarwal & Tandon, 1994; Barone, 1990; Cross, 1973; Lakonishok & Smidt, 1988). Some studies showed that the average return for Monday is significantly negative for countries like the United States, the United Kingdom, and Canada (see e.g., Aggarwal & Schatzberg, 1997; Balaban et al., 2001; Flannery & Protopapadakis, 1988; French, 1980; Gibbons & Hess, 1981; Keim & Stambauch, 1984; Kohers & Kohers, 1995; Pena, 1995; Pettengill, 1985; Rogalski, 1984; Schwert, 1983; Smirlock & Starks, 1986; Solnik & Bousquet,1990). In contrast, for several Pacific Rim countries, the lowest rate of return tends to occur on Tuesdays (see Brooks & Persand, 2001; Davidson & Faff, 1999; Dubois & Louvet, 1996; Jaffe & Westerfield, 1985).

The literature offers a number of possible explanations for the existence of the day-of-the-week effect, (see e.g., Keim & Stambauch, 1984; Miller, 1988; Wilson & Jones, 1993). However, most of the evidence centers around negative news releases over the weekend (e.g., Berument & Kiymaz, 2001; Penman, 1988). While most research supports the existence of a day-of-the-week effect, some offer contradictory evidence. For example, Connolly (1989) and Chang et. al. (1992) submitted evidence to suggest that sample size and/or error term adjustments render U.S. day-of-the-week effects statistically insignificant.

These day-of-the-week findings appear to conflict with the Efficient Market Hypothesis since they imply that investors could develop a trading strategy that takes advantage of these seasonal regularities. However, once transaction costs and time-varying stock market risk premiums are taken into account, it is not clear that the predictability of stock returns translate into market inefficiencies.

Focusing on the returns in Korea and the United Kingdom, two recent studies have suggested that starting in the 1990s, the day-of-the-week effect has disappeared in these countries (e.g., see Kamath & Chusanachoti, 2002; Steeley, 2001). If markets have become more efficient over time, seasonal anomalies such as the day-of-the-week effect may have gradually faded away in more recent periods. Given the possible evolution of this seasonal over time, renewed attention to this topic seems warranted. Thus, the purpose of this paper is to test for the existence of this anomaly in the world's developed equity markets over the last two decades. Specifically, the daily returns for the indices of the 23 MSCI-designated developed markets for the period from January 1980 through June 2002 are examined for the continuous presence of this regularity. Furthermore, to generate information on the consistency of this anomaly over time, the overall period 1980--2002 is broken down into several sub-periods.

METHODOLOGY AND DATA

In this study, first the daily rates of return for the (Morgan Stanley Capital International) MSCI Developed Markets Indices from January 1980 through June 2002 are calculated and then examined for the persistent existence of the day-of-the-week effect. As of 2002, this index consisted of the following 23 developed market indices: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the United Kingdom, and the United States. The MSCI data was retrieved from Datastream. Those country indices for which information was not available on a consistent basis in the 1980s were excluded from the first sub-period (1980-1990). The combined market capitalization of the companies that comprise the indices is equal to at least 60 percent of the aggregate market value of the respective national stock exchanges which each index represents. Each one of the country indices is composed of stocks that broadly represent the stock compositions in the different countries.

The model employed in this study tests the hypothesis of equal mean returns for each trading day of the week. The specific hypothesis tested is:

[H.sub.o]: [R.sub.i] (Monday) = [R.sub.i] (Tuesday) = [R.sub.i] (Wednesday) = [R.sub.i] (Thursday) = [R.sub.i] (Friday),

where:

[R.sub.i] = the rate of return, by the day of the week (i.e., Monday, Tuesday, ..., Friday) for country index i (i.e., the index for Australia, Austria, ..., the MSCI World Index).

Rejection of the hypothesis implies that at least one of the five daily rates of return is not equal to the others. The vast majority of seasonal anomaly studies have relied on parametric tests such as ANOVA, which is known to be quite robust to mild violations of its assumptions of normal distributions and equal variances. No such assumptions are required by the Kruskal-Wallis test, a non-parametric procedure. Many anomaly studies concluded that the returns are either near-normal or that they can be considered normal due to the large number of observations used in their analyses. In this study, both ANOVA and Kruskal-Wallis tests are utilized to examine the existence of the day-of-the-week effect in the world's developed equity markets. (Where the assumptions of a normal distribution and equal variances could not be met, a non-parametric test was utilized.) In cases of rejection of the hypothesis, both ANOVA and Kruskal-Wallis do not reveal which specific daily returns differ from each other. In order to identify days with significantly different returns, Duncan's Test Statistics (a parametric multiple comparison test) and, when necessary, the Mann-Whitney U test (a non-parametric multiple comparison test) are utilized.

The methodology employed in this paper overcomes many of the shortcomings found in previous research dealing with seasonal anomalies. For example, the models used to test for the day-of-the-week effect incorporate both parametric as well as non-parametric approaches. Also, examining these indices over various sub-periods makes it possible to generate valuable information on the consistency of this anomaly over time.

RESULTS

To investigate the consistent presence of the day-of-the-week effect in the developed markets, the overall period under examination (i.e., 1980 through June 2002) was broken down into several smaller sub-periods from four through eleven years. A relatively clear picture emerged from the results. For example, for the 6-year periods 1980-1985, 1986-1991, 1992-1997, and 1998-6/2002, the findings are shown in Table 1: (NOTE: Due to space constraints, details of other sub-periods are not reported.)

Clearly, the hypothesis of equal rates of return by the day of the week is rejected in the majority of indices during the first two sub-periods (i.e., 1980-1985 and 1986-1991), while the opposite is true for the subsequent two sub-periods (i.e., 1992-1997 and 1998-6/2002).

More specifically, for the 22 country indices as well as the MSCI World Index, the results of the ANOVA test and the Kruskal-Wallis test to detect differences in the rates of return by the day of the week and by the two 11-year periods (i.e., 1980-1990 and 1991-2002) are reported in Table 2. This table shows the mean rates of return by the day of the week, the corresponding standard deviations and the number of observation on which the values were based. Also, the ANOVA (or in cases where the statistical assumptions of ANOVA could not be met, the Kruskal-Wallis) F- and corresponding p-values to test the hypothesis Ho: [R.sub.i] (Monday) = [R.sub.i] (Tuesday) = [R.sub.i] (Wednesday) = [R.sub.i] (Thursday) = [R.sub.i] (Friday) are shown.

For example, in the case of the Australian Index, for the first 11-year period from 1980-1990, the hypothesis of no differences in the rates of return by the day of the week is rejected at the .005 level. In contrast, for the second 11-year period from 1991-6/2002, relying on Kruskal-Wallis (due to non-compliance with the ANOVA assumptions), the same hypothesis cannot be rejected. Thus, over this latter period, no day-of-the-week effect was detected in the Australian Index.

An examination of the 18 indices for which daily returns were available for the entire first 11-year period (1980-1990) reveals that the hypothesis of equal returns can be rejected for 15. For only three indices (i.e., Austria, Denmark, and Hong Kong) could the hypothesis not be rejected. Testing the same hypothesis for the second 11-year period shows the opposite picture. Of the 23 indices for which returns were available for the period from 1991 -6/2002, the hypothesis could be rejected at the .05 level in only three cases (i.e., Japan, New Zealand, and Singapore), while for the remaining 20 indices it could not be rejected.

While the results reported in Table 2 are useful in that they reveal the possible existence of differences in daily rates of return by the two 11-year periods examined, additional information is needed. Specifically, Table 2 reveals that, for many of the indices during the two time periods, the rate of return for at least one day is different from the returns on the other days. For the cases in which rejection of the hypothesis occurs, it is of primary interest to identify the specific days that differ from other days. To conduct a more complete test for differences in returns by the day of the week, ten comparisons would be needed for each possible combination (i.e., M-Tu, M-W, M-Th, M-F, Tu-W, Tu-Th, Tu-F, W-Th, W-F, and Th-F). Duncan's test statistic and, where necessary, the Mann-Whitney U test identify the days of the week where the rates of return are significantly different from other days. We perform these tests over the same two time periods discussed in Table 2 to capture gradual changes in market efficiency that may have caused the day-of-the-week effect to dissipate over time. We also examined alternative shorter subperiods and the results were consistent with the large two period time frames reported. The results of these tests for the 23 indices examined over the two 11-year periods are reported in Table 3.

For the period from 1980-1990, a day-of-the-week effect was evident in 14 of the 18 indices for which daily returns were available for the entire period. For nine of the 14 markets with a day-of-the-week effect, (i.e., Canada, France, Italy, Norway, Singapore, Switzerland, the United Kingdom, the United States, and the MSCI World Index), Monday returns were significantly lower and negative compared to most other days of the week. For France, Italy, and Switzerland, Tuesday returns were also negative and significantly lower than Wednesday, Thursday, and Friday returns. Singapore's index return also was lowest and negative on Tuesdays, but it was significantly lower only relative to Wednesday returns. For the U.S. Index, aside from Monday returns being significantly lower than Tuesday, Wednesday, and Friday returns, Wednesday returns were also significantly higher than Tuesday and Thursday returns. The MSCI World Index also showed negative Monday returns being significantly lower than Friday returns.

An examination of the second 11-year period (1991-2002) clearly reveals the fading away of the day-of-the-week effect in developed markets. Of the 23 indices for which daily rates of return could be generated on a consistent basis, only three still retained this anomaly. Japan, Norway, and Singapore continued to display the pattern of a traditional day-of-the-week effect, all with negative Monday returns which are statistically significantly smaller than the returns on most of the other days of the week.

SUMMARY AND CONCLUSION

The day-of-the-week effect remains one of the most heavily researched seasonal anomalies. The seasonality has shown that for many countries, Monday returns tended to be the lowest of any day of the week, while for some countries (e.g., Japan, Australia), it was Tuesday. A few recent studies (e.g., Kamath & Chusanachoti, 2002; Steeley, 2001) have suggested that the day-of-the-week effect has vanished in the two countries examined.

If markets have become more efficient over time, then the day-of-the--week effect may have disappeared in more recent years. Relying on both parametric and nonparametric statistical tests, this study examines the evolution of the day-of-the-week seasonality for all 23 developed equity markets over the last 22 years. The results indicate that while the day-of-the-week effect clearly was prevalent in the vast majority of developed markets during the 1980s, it appears to have faded away starting in the 1990s. These findings imply that increases in market efficiency over long time periods may act to erode the effects of certain anomalies such as the day of the week effect.

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Gerald Kohers, Sam Houston State University

Vivek Pandey, The University of Texas at Tyler

Ninon Kohers, University of South Florida

Theodor Kohers, Mississippi State University

Table 1: Summary Statistics of Tests of Equality in the Rates of
Returns by the Day-of-the-Week by Sub-Periods

[H.sub.o]: [R,sub.i] (Monday) = [R.sub.i] (Tuesday) = [R.sub.i]
(Thursday) = [R.sub.i] (Friday)

Number of Country 1980-1985 1986-1991 1992-1997 1998-
Indices where: 6/2002

[H.sub.o] of equal 13 (a) 14 (c) 7 (e) 2 (g)
returns is rejected:

[H.sub.o] of equal 6 (b) 8 (d) 16 (f) 21 (h)
returns is not rejected:

Total Number of Indices: 19 22 23 23

(NOTE: Due to space constraints, details of other sub-periods are not
reported.)

(a) The following indices are included in this group: Australia,
Belgium, Canada, France, Italy, Japan, the Netherlands, Singapore,
Spain, Sweden, Switzerland, the United Kingdom, and the World Index.

(b) The following indices are included in this group: Austria, Denmark,
Germany, Hong Kong, Norway, and the U.S.

(c) The following indices are included in this group: Belgium, Canada,
Finland, France, Hong Kong, Italy, the Netherlands, New Zealand,
Norway, Spain, Sweden, Switzerland, the United Kingdom, and the World
Index.

(d) The following indices are included in this group: Australia,
Austria, Denmark, Germany, Ireland, Japan, Singapore, and the U.S.

(e) The following indices are included in this group: Germany,
Hong Kong, Japan, the Netherlands, New Zealand, Singapore, and the
U.S.

(f) The following indices are included in this group: Australia,
Austria, Belgium, Canada, Denmark, Finland, France, Ireland, Italy,
Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and
the World Index.

(g) The following indices are included in this group: Finland and New
Zealand.

(h) The following indices are included in this group: Australia,
Austria, Belgium, Canada, Denmark, France, Germany, Hong Kong,
Ireland, Italy, Japan, the Netherlands, Norway, Portugal, Singapore,
Spain, Sweden, Switzerland, the United Kingdom, the U.S. and the World
Index.

Table 2: Testing for Differences in Developed Market Indices' Rates
of Return by the Day-of-the Week:
ANOVA and Kruskal-Wallace Results for 1/1980--12/1990 and
1/1991--6/2002

[H.sub.o]: [R.sub.i] (Monday) = [R.sub.i] (Tuesday) = [R.sub.i]
(Wednesday) = [R.sub.i] (Thursday) = [R.sub.i] (Friday)

Index: Period: Monday Tuesday Wednesday Thursday

Australia '80-'90 .0310 -.1187 .0845 .1115
 Std. Dev. 1.2502 1.3912 1.0357 1.1121
 Observ. 532 566 566 567
 '91-'02 .0147 .0495 .0487 .0438
 Std. Dev. .9958 .8586 .9201 .8003
 Observ. 557 589 592 593

Austria '80-'90 .0953 .0498 .0203 .0256

 Std. Dev. 1.1212 1.0040 0.7861 0.8377
 Observ. 530 553 552 533
 '91-'02 -.0086 .0317 -.0054 -.0248
 Std. Dev. 1.1742 1.0517 .9519 1.0107
 Observ. 559 582 582 559

Belgium '80-'90 .0395 -.0853 .0757 .1159
 Std. Dev. 1.1000 0.8415 0.8678 0.8252
 Observ. 519 556 560 547
 '91-'02 .0223 .0517 .0203 .0400
 Std. Dev. 1.0311 .9095 .8984 1.0163
 Observ. 555 587 587 578

Canada '80-'90 -.1562 .0458 .1123 .0305
 Std. Dev. 1.1002 .9463 .9221 .9521
 Observ. 540 569 567 568
 '91-'02 .0987 .0120 .0069 .0046
 Std. Dev. .9685 1.0433 1.0457 .9508
 Observ. 541 591 593 593

Denmark '80-'90 .0472 .0637 .0575 .0947
 Std. Dev. .9636 9975 .9307 .8719
 Observ. 547 566 562 544
 '91-'02 -.0112 .0494 .0399 .0542
 Std. Dev. 1.2092 1.0884 1.0677 1.0893
 Observ. 567 590 590 567

Finland '80-'90 (not available)
 '91-'02 .0650 .0312 -.0500 .1827
 Dev. 2.0997 2.3060 2.1978 2.7089
 Observ. 574 588 586 566

France '80-'90 -.1234 -.0149 .1299 .1571
 Std. Dev. 1.2688 1.0553 1.1162 1.1096
 Observ. 528 560 562 553
 '91-'02 .0228 .1061 .0140 .0434
 Std. Dev. 1.2899 1.2172 1.1816 1.2456
 Observ. 555 591 585 583

Germany '80-'90 -.0394 -.0187 .1221 .0789
 Std. Dev. 1.3775 1.1507 1.1154 1.0544
 Observ. 543 563 550 547
 '91-'02 .1084 .0496 .0199 .0196
 Std. Dev. 1.4060 1.2487 1.2013 1.2655
 Observ. 568 588 585 573

Hong Kong '80-'90 -.1902 .0654 .1996 .0964
 Std. Dev. 2.8467 1.7051 1.4744 1.8098
 Observ. 571 559 558 561
 '91-'02 -.0312 .0178 .1687 -.0906
 Std. Dev. 2.0461 1.5070 1.9103 1.6830
 Observ. 545 579 575 577

Ireland '80-'90 (not available)
 '91-'02 -.0034 .1072 .0215 .0216
 Std. Dev. 1.2567 1.1637 1.1929 1.0900
 Observ. 526 586 590 593

Italy '80-'90 -.0546 -.0374 .1407 .1315
 Std. Dev. 1.5673 1.3346 1.2981 1.4006
 Observ. 554 556 559 558
 '91-'02 -.0150 .0807 -.0155 .0854
 Std. Dev. 1.6807 1.3895 1.3485 1.3323
 Observ. 567 584 585 587

Japan '80-'90 .0707 -.0609 .1522 .0492
 Std. Dev. 1.2016 1.2049 1.0286 .9556
 Observ. 539 548 551 552
 '91-'02 -.1535 .0360 -.0251 .0889
 Std. Dev. 1.4651 1.1574 1.3331 1.2508
 Observ. 548 573 571 570

Netherlands '80-'90 -.1307 .0482 .1657 .1146
 Std. Dev. 1.3313 1.0777 1.1645 1.2007
 Observ. 542 567 563 555
 '91-'02 .1407 .0969 .0144 -.0286
 Std. Dev. 1.2193 1.1358 1.0072 1.1046
 Observ. 569 591 592 582

New Zealand '80-'90 (not available)
 '91-'02 -.1307 .0379 .0466 .0881
 Std. Dev. 1.2462 1.3741 1.3345 1.1950
 Observ. 547 582 591 589

Norway '80-'90 -.0033 -.0923 .1125 .1450
 Std. Dev. 1.5004 1.6613 1.4650 1.4078
 Observ. 541 564 563 541
 '91-'02 -.0600 .0830 -.0497 .0700
 Std. Dev. 1.4874 1.2653 1.2641 1.4181
 Observ. 564 589 589 566

Portugal '80-'90 (not available)
 '93-'02 .0340 .0755 .0011 .0509
 Std. Dev. 1.0940 1.0499 1.0569 1.0691
 Observ. 465 467 480 469

Singapore '80-'90 -.0779 -.0613 .1407 .0705
 Std. Dev. 1.5679 1.4791 1.1475 1.3012
 Observ. 556 556 561 559
 '91-'02 -.1696 .0114 .0674 .0698
 Std. Dev. 1.5963 1.1622 1.2415 1.2508
 Observ. 568 584 579 585

Spain '80-'90 (not available)
 '91-'02 .0008 .1375 -.0222 .0426
 Std. Dev. 1.3893 1.2671 1.3131 1.3775
 Observ. 574 585 581 575

Sweden '80-'90 .0401 .0061 .1167 .1526
 Std. Dev. 1.3723 1.2485 1.0846 1.1527
 Observ. 539 563 560 549
 '91-'02 .1487 .0358 -.0280 .0310
 Std. Dev. 1.6728 1.4327 1.5639 1.6111
 Observ. 564 589 588 577

Switzerland '80-'90 -.1106 -.0441 .1089 .0654
 Std. Dev. 1.2063 .8891 .8217 .8184
 Observ. 533 562 561 551
 '91-'02 .0691 .0584 .0651 .0374
 Std. Dev. 1.2013 1.0576 .9710 1.1085
 Observ. 555 589 592 576

U. K. '80-'90 -.1247 .0681 .1634 .0369
 Std. Dev. 1.1374 1.0854 .9599 .9257
 Observ. 535 566 567 568
 '91-'02 .0347 .0493 .0048 .0440
 Std. Dev. .9961 .9796 .8993 .9522
 Observ. 541 591 595 595

U. S. '80-'90 -.0715 .0998 .1181 -.0034
 Std. Dev. 1.4068 .9695 .9478 .9588
 Observ. 534 569 569 562
 '91-'02 .0947 .0525 .0396 .0322
 Std. Dev. 1.0393 1.0264 .9161 .9775
 Observ. 551 594 593 584

World Index * '80-'90 -.0510 .0282 .1238 .0350
 Std. Dev. .8960 .6992 .6801 .6307
 Observ. 570 569 569 570
 '91-'02 .0177 .0470 .0106 .0387
 Std. Dev. .8193 .7338 .7098 .7799
 Observ. 596 598 596 598

Index: Period: Friday F-value P-value

Australia '80-'90 .0999 3.71 .005
 Std. Dev. 1.0164
 Observ. 555
 '91-'02 .0135 *0.15 *.997
 Std. Dev. .8801
 Observ. 579

Austria '80-'90 .0466 *5.75 *.219
 Std. Dev. 0.7786
 Observ. 532
 '91-'02 .0300 *2.22 *.695
 Std. Dev. 1.0381
 Observ. 565

Belgium '80-'90 .0930 4.28 .002
 Std. Dev. 0.8642
 Observ. 530
 '91-'02 .0426 0.12 .977
 Std. Dev. .9411
 Observ. 567

Canada '80-'90 .0855 6.96 .000
 Std. Dev. .8376
 Observ. 556
 '91-'02 .0619 0.97 .421
 Std. Dev. 1.0263
 Observ. 581

Denmark '80-'90 .0654 0.19 .942
 Std. Dev. .9468
 Observ. 546
 '91-'02 .0730 0.48 .751
 Std. Dev. .9692
 Observ. 565

Finland '80-'90 (not available)
 '91-'02 .3094 2.09 .079
 Dev. 2.2345
 Observ. 560

France '80-'90 .1217 6.20 .000
 Std. Dev. 1.0243
 Observ. 549
 '91-'02 .0445 0.51 .727
 Std. Dev. 1.1528
 Observ. 569

Germany '80-'90 .0718 1.93 .010
 Std. Dev. 1.0693
 Observ. 547
 '91-'02 .0003 0.63 .640
 Std. Dev. 1.2396
 Observ. 576

Hong Kong '80-'90 .1532 *6.74 *.150
 Std. Dev. 1.5172
 Observ. 543
 '91-'02 .1823 *7.29 *.121
 Std. Dev. 1.7154
 Observ. 564

Ireland '80-'90 (not available)
 '91-'02 .0454 0.78 .541
 Std. Dev. 1.0031
 Observ. 576

Italy '80-'90 .1624 *25.02 .000
 Std. Dev. 1.2306
 Observ. 547
 '91-'02 .0838 *7.32 *.120
 Std. Dev. 1.2915
 Observ. 579

Japan '80-'90 .0709 *20.91 *.000
 Std. Dev. .9354
 Observ. 544
 '91-'02 .0123 *10.86 *.028
 Std. Dev. 1.2624
 Observ. 570

Netherlands '80-'90 .0454 5.22 .000
 Std. Dev. 1.0289
 Observ. 551
 '91-'02 .0359 2.05 .084
 Std. Dev. 1.1611
 Observ. 577

New Zealand '80-'90 (not available)
 '91-'02 .0665 2.64 .032
 Std. Dev. 1.1672
 Observ. 577

Norway '80-'90 .0838 2.40 .048
 Std. Dev. 1.2673
 Observ. 552
 '91-'02 .0750 1.70 .148
 Std. Dev. 1.1951
 Observ. 574

Portugal '80-'90 (not available)
 '93-'02 .0691 0.38 .822
 Std. Dev. 1.0031
 Observ. 467

Singapore '80-'90 .0917 *17.87 *.001
 Std. Dev. 1.1185
 Observ. 547
 '91-'02 .1138 *20.66 *.000
 Std. Dev. 1.2401
 Observ. 575

Spain '80-'90 (not available)
 '91-'02 .1064 1.54 .188
 Std. Dev. 1.2455
 Observ. 570

Sweden '80-'90 .1442 *11.17 *.025
 Std. Dev. 1.0033
 Observ. 539
 '91-'02 .1381 1.35 .248
 Std. Dev. 1.5303
 Observ. 565

Switzerland '80-'90 .1056 6.27 .000
 Std. Dev. .7733
 Observ. 546
 '91-'02 .0606 0.08 .989
 Std. Dev. .9656
 Observ. 572

U. K. '80-'90 .1444 7.01 .000
 Std. Dev. .9317
 Observ. 556
 '91-'02 .0265 0.19 .942
 Std. Dev. 1.0040
 Observ. 582

U. S. '80-'90 .0761 3.05 .016
 Std. Dev. .9929
 Observ. 553
 '91-'02 -.0016 0.70 .592
 Std. Dev. .9943
 Observ. 577

World Index # '80-'90 .0802 *17.02 *.002
 Std. Dev. .6343
 Observ. 560
 '91-'02 .0221 0.24 .919
 Std. Dev. .7674
 Observ. 596

The reported F-values and associated P-values correspond to the null
hypothesis of equal mean daily percentage return by the day of the
week. An asterisk (*) signifies that due to violations of the ANOVA
assumptions, a nonparametric test (Kruskal-Wallis) was employed.

# The MSCI World Index, based on market capitalization, is designed
to measure global developed market equity performance. As of 2002, this
index consisted of the following 23 developed market country indices:
Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany,
Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand,
Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the United
Kingdom, and the United States.

NOTE: Those country indices for which daily information was not
available on a consistent basis in the early 1980s were excluded from
the first sub-period (1980-1990). They included Finland, Ireland, New
Zealand, Portugal, and Spain.

Table 3: Summary Test Statistics for Comparisons in the Daily Returns
of Developed Market Indices: Results of Duncan's or Mann-Whitney U Tests
Comparison of Days With Significantly Different Returns at the .05 Level

Country Index: Period Jan. 1980- Period Jan. 1991-
 Dec. 1990: June/2002:

Australia Tues < Mon, Wed,
 Thurs, Friday
Austria
Belgium Tues < Mon, Wed,
 Thurs, Friday
Canada Mon < Tues, Wed,
 Thurs, Friday
Denmark
Finland n/a
France Mon, Tues < Wed,
 Thurs, Friday
Germany
Hong Kong
Ireland n/a
Italy * Mon, Tues < Wed,
 Thurs, Friday
Japan * Tues < Wed * Mon < Tues,
 Thurs, Friday
Netherlands Mon < Tues, Wed,
 Thurs, Friday
New Zealand n/a Mon < Tues, Wed,
 Thurs, Friday
Norway Tues < Wed, Thurs
Portugal n/a
Singapore * Mon, Tues < Wed * Mon < Tues, Wed,
 Thurs, Friday
Spain n/a
Sweden * Tues < Wed,
 Thurs, Friday
Switzerland Mon, Tues < Wed,
 Thurs, Friday
U. K. Mon < Tues, Wed,
 Thurs, Friday
U. S. Mon < Tues, Wed,
 Friday
 Wed > Mon, Tues,
 Thurs
World Index Mon < Friday

An asterisk (*) signifies that due to violations of the ANOVA
assumptions, a nonparametric test (Mann-Whitney U) was
employed.