- Email: [email protected]
The day-of-the-week effect: The international evidence
Journalof BANKING & ELSEVIER
Journal of Banking& Finance 20 (1996) 1463-1484
FINANCE
The day-of-the-week effect: The international evidence M. Dubois a,*, p. Louvet b a The Universi~ ofNeuchgttel, Groupe de Gestion d'Entreprise, Pierre-h-Mazel 7, Neuchhtel, CH 2000 Switzerland Pzerre Mendbs-France University Grenoble, France b
.
•
Received 12 April 1994; accepted 5 July 1995
Abstract We re-examine the day-of-the-week effect for eleven indexes from nine countries during the 1969-1992 period. The standard methodology as well as the moving average methodology are used and we find returns to be lower at the beginning of the week (but not necessarily on Monday) for the full period. As in Chang et al. (International evidence on the robustness of the day-of-the-week effect, Journal of Financial and Quantitative Analysis 28 (1993), 497-514), the anomaly disappears for the most recent period in the USA. However, the effect is still strong for European countries, Hong-Kong and Toronto. JEL classification: G 12 Keywords." Day-of-the-weekeffect; Seasonal component;Internationalstock indexes
1. Introduction Since the results provided by Cross (1973) attesting that returns on the Standard and Poors index are significantly negative on Mondays, many researchers have detected a day effect on stock returns. French (1980), Keim and Stambaugh (1984), examining longer periods, or Rogalski (1984) choosing the DJIA index, confirmed the phenomenon which changes over time (see Smirlock and Starks,
* Correspondingauthor. Tel.: 41 38 21 28 71; fax: 41 38 21 29 40. This paper was presented at the EFA meeting(1994). 0378-4266/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. SSDI 0378-4266(95)00054-2
1464
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
1986). Harris (1986), Lakonishok and Smidt (1988) and Keim (1987) studied interactions with both size and month effects. Gibbons and Hess (1981), Lakonishok and Levi (1982) noted abnormal high returns at the end of the week, and Cadsby (1989) identified a Monday effect for the Canadian stock market. On Asian markets, Japanese indexes show negative returns on Tuesday. This was proved by Jaffe and Westerfield (1985) and Lee et al. (1990) respectively. However, no significant day anomalies affect the Stock Exchanges in Hong-Kong, Korea, Taiwan or Singapore. In Europe, seasonal patterns vary across countries and time periods. Spanish (Santesmeses, 1986) and Danish markets (Jennergren and Sorensen, 1989) do not experience a day effect; a negative return is observed on Monday on the London Stock Exchange (Theobald and Price, 1984) and the Paris Bourse (Hamon and Jacquillat, 1990; Louvet and Taramasco, 1990; Solnik and Bousquet, 1990). Returns are found to be negative on Tuesday and Wednesday on the Greek Stock Exchange (see Condoyanni et al., 1989), and on Monday and Tuesday on the Milan Stock Exchange (Barone, 1990). Merton (1990) and Levi (1988), among others, wondered about statistical methods used to detect such anomalies and they cast some doubt on approaches relying exclusively on empirical evidence. Using more sophisticated methodologies, Connolly (1989) showed that the magnitude of Monday returns is weak in the USA. Moreover, after correcting the critical t-value for sample size with a Bayesian approach, Monday returns are no longer negative at conventional levels (see Connolly, 1991). For the most recent period, the day-of-the-week effect has disappeared in most countries (see Chang et al., 1993). However, five European markets are still negative on Monday. 1 On the other hand, Jaffe et al. (1989) found that the negative effect occurred when the market return was negative the previous week, 2 the effect being insignificant when the market return was positive. Different economic rationales were hypothesized. Settlement delays vary among countries and could explain part of the previous findings (see Gibbons and Hess, 1981; Baillie and DeGennaro, 1989). Admati and Pfleiderer (1989) and Porter (1990) demonstrated that the market-making process could induce intraweek patterns. But this explanation does not fully account for day-of-the-week effects because market-makers do not exist in continental Europe. Penman (1987) suggested that bad earnings announcements may be responsible for the seasonality but this was not confirmed by Peterson (1990) and Connolly (1991). Chang et al. (1993) examined the pattern of macroeconomics new releases but the evidence is weak. Lakonishok and Maberly (1990), Theobald and Price (1984) and Louvet and
i These results contradict those of Sentesmeses' study, who does not find a day-of-the-week for Spain before 1984. 2 This effect is possibly due to positive first-order autocorrelation.
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
1465
Taramasco (1991) hypothesized: (a) a cyclical behaviour of shareholders and (b) seasonal fluctuations in transaction volumes. In this paper we address the issue in a different way by focusing on the mean value of the seasonal component of each day-of-the-week return. We test the equality of these components with a parametric as well as a non-parametric approach. The rationale for the last type of test is the presence of 'outliers' in our sample. 3 The paper is organised as follows. Section 2 outlines the methodology. Seasonal components are computed for each day of the week and in this way, we test the stability of the day-of-the-week effect. Section 3 presents evidence based on the most important capital markets of America, the Pacific Basin and Europe. Commonly used indexes are employed for each country. Section 4 concludes.
2. The moving average approach Previous researches generally detected daily abnormal returns by using an analysis of variance. This method is not fully satisfactory because returns are required to be (a) normal, (b) independent and (c) stationary. To avoid hypothesis (a), Gibbons and Hess (1981) used the standard procedure and a non-parametric test (Kruskal-Wallis' analysis of variance) but conclusions remain unchanged. Employing robust to non-normality and heteroskedasticity techniques, Connolly (1989), 4 Connolly (1991) and Chang et al. (1993) showed that the day-of-the-week effect is weak. In this paper, daily returns are analysed as time series and not as independent observations of a given sample. The existence of systematic daily fluctuations (seasonal components) is tested as it is usually done in time series analyses. The trend and seasonal effects are computed. 2.1. T h e d a i l y return p r o c e s s
Let Rj,~ be the logarithmic return of an index the day j of the week s. We assume that Rj., is generated by the following process: Rj.. = Sj + F,. j + o'jEj..~
(1)
where t = 5s + j , j = Monday, Tuesday . . . . . Friday, and s ~ {1 . . . . . p}, . . . Ft = F.i , random trend with o-~ << cri? ' ~rj' variance of daily returns, e, = ei..~ are independent variables N(0, 1), (rj = the standard deviation of day j, S/ = additive daily seasonal component.
In our opinion, outliers cannot be removed from the sample. However, the influence of extreme values must be reduced to put forth the regularities of the seasonal components. 4 Different estimators of returns dispersion giving less weight to outliers are used. A GARCH ( 1,1 ) model is presented too, but Bollerslev et al. (1992 p. 22) pointed out that "a failure to take proper account of such deterministic influences might lead to a spurious seasonal ARCH effect".
M. Dubois, P. Louvet/ Journal of Banking & Finance 20 (1996) 1463-1484
1466
Seasonal components are normalised so that the sum of the components for a given week is zero. This model extends the random walk model where F t is assumed to be constant over time. First, the model allows expected returns to change over time with both information flow and modifications in the investors' preferences, the presupposed sources o f randomness. Changes in the shape of the returns density function are weak at the day level. This hypothesis is compatible with previous researches by F a m a and French (1988) and Poterba and Summers (1988) who found that the permanent component of returns decreases slowly over time. However, these results were obtained with monthly or annual returns. Second, a seasonal component can affect the risk. There is no rationale to assume that the trend alone is affected by seasonal fluctuations: F a m a (1965) was the first to show that the variance is abnormally low on Monday. 5 The tests presented here only concern mean returns and mean seasonal components.
2.2. The moving average approach The moving average operator is calculated using five days windows and is centred on the current day. 6 The moving average characterizes the trend of current daily returns which are no more supposed to be constant over time. Removing the trend from the current return, we find the seasonal component plus a white noise. Let M t, be the moving average for day t:
lk=+2 M j ' s = M t = 5 k Y "R 2t+k==-
lk=+2 5k y'=.z[Ft+k+Sj(t+k)
+~(t+k)et+k]"
(2) It was assumed above that ~rF2, << cry,
-
lk=+2 ~ F ( t + k ) = F t, 5k= 2 -
e t are independent and N ( 0 , 1),
lk=+2 5k=_2 1-1 k=+2 and el, t N ( 0 , 1 ) w i t h
]1/2
o-,,j = /-~k=~ 2tTj2[ .
(3)
Because ~1E kk= = -+2 2 S = 0, we find M t-=- F t + (rl,jel, j
5 Fama (1965) finds a 20% decrease in variance. French and Roll (1986) show that the variance of common equities exhibits a seasonality. 6 Until 1989, Tokyo was open on Saturday mornings. Thus, from 1969 to 1989, the moving average is computed with six days; since 1989, a standard five days moving average operator has been used.
M. Dubois, P. LouL, et / Journal o[Banking & Finance 20 (1996) 1463-1484
1467
Let A i., = A r be the difference between Rj. ~ and Mj.~, A i,., = Rj..~ - Mj,.~ = Fj, s + Sj.., + o)ej,~ - (Fj..~ + o ' l . j e , . j . s )
= Si.., + °2.Je2.J.,
and A the covariance matrix of hi. Note that cov(et, e , j ) = 0 for t i s~ tj does not imply that c o y ( e 2 . , / e 2 , , j ) = 0, because E2, t is a linear function of e,_ 2, et 1, e,, e, + 1, ~, + 2- Because the variance is possibly seasonal, we used a Hotelling-T 2 test, the distribution of which does not depend on the correlation matrix. 2.3. T h e d a t a
A daily record of values for eleven stock market indexes was collected from 7 The period under study is from January 2, 1969 to December 30, 1992 except for the Sydney and Hong-Kong Stock Exchange and the Nikkei Indexes (see Appendix A). The indexes used in this study are representative of each market and account for approximately 85% of the world market value of listed securities at the end of 1992. 8 Employing different sub-periods, we also test seasonal stability. Weeks with incomplete data, less than five returns per week or six for Japan when the market was open on Saturday, are eliminated to concentrate the study on the Monday effect. By eliminating incomplete weeks, we avoid the interaction between day-of-the-week and Holiday effects. Daily returns are computed as tollows: DataStream.
It
R,= 100×InIt-
j
I t is the value of the index at time t. Indexes are computed with closing prices except for the SBF 240 Index (France)9 where opening prices are used. A question arises in deciding to which day the return is affected. Solnik and Bousquet (1990) chose to compute Monday returns as the difference in Log prices between Monday opening and Friday opening arguing that 90% of the transactions take place at this time. Hamon and Jacquillat (1990) compute Monday returns as the difference in Log prices between Tuesday opening and Monday opening. But negative returns on Mondays are related to the low volume that day. The last
7 As it was underlined by Board and Sutcliffe (1988), the omission of dividends induces a downward bias in computing returns. When dividends are taken into account, the pattern of returns does not change significantly(see also Theobald and Price (1984)). This is the reason why dividends are neglected in this research. Topix and Nikkei indexeswere provided to us by Yamaichi Securitiesin Geneva because Saturday figures are omitted in DataStream. We are grateful to CED1F-Universit6de Lausanne and Yamaichi Securities in Geneva for providingus the data. 8 Source: Frdrration Internationaledes Bourses de Valeurs (FIBV), Geneva, Annual Report 1993. 9 The SBF 240 Index is computed with opening prices, see Solnik and Bousquet (1990, p. 463).
M. Dubois, P. Loucet / Journal of Banking & Finance 20 (1996) 1463-1484
1468
convention was retained in this paper because the correspondence between return and trading volume seasonalities (see Louvet and Taramasco, 1991) suggests the last convention to be more accurate. As far as we are concerned, one of the most important differences across markets is the settlement procedure. Two main systems exist in the world (see Appendix A). The first one is characterized by fixed delays and the second by fixed settlement dates. In both situations, observed prices include the cost of carry which is computed using calendar days:
V=
1 + rt × ~-,/360
where: IIP~, It rt
rt
= = = =
price at time t of a stock (or an index) settled at time t + "rt, spot price at time t considering an instantaneous cash settlement, spot interest rate on day t ending at t + r t, length of the interval of time between transaction and payment.
Cash returns are not exactly equal to returns computed from observed prices except in special cases: It c
1 + r t × ~t/360
Ie
RC = ln-7~-- = l n - ~ lt l It-l,'rt_l
(4)
Ln l + rt_l X rt_J360
1 + r t X ~-t/360 R c = R, - In 1 + r t _ J × ~',_ 1 / 3 6 0 '
'
(5)
Assuming r t ..~ r t_ 1 = r for consecutive days, 1 + r × 7"t/360 e c = e t - In
1 + r × ~'t- 1/360
-- e t -
r(o't-
"/'t- 1) '
(6)
the difference between R c and R t results from r t :g -r,_ j for certain days of the week. 2.3.1. Fixed
settlement
d e l a y io
Delivery of securities and receipt of payment occur a fixed number of business days (one in Hong-Kong to five in Canada and USA) after the transaction. The cost of carry does not bias the return measure when the delay and the number of business days in the week are equal (i.e. r t = "rt 1 Vt). Otherwise, the cost of carry has a negative effect on Mondays (equal to - h r / 3 6 0 where h is the number of closing days during a week 11), recovered another day of the week. It is
10 The bank float problems in U.S. stock transactionsmentionedby Lakonishok and Levi (1982) are ignored. 11 h = 1 for Japan and h = 2 for other countries in the sample.
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
1469
Friday, Thursday or Wednesday when the settlement is at T + l, T + 2 or T + 3. Because delays of payment do not affect weekly returns, seasonal components reflect the same pattern as crude returns. 2.3.2. F i x e d s e t t l e m e n t d a t e 12
This situation corresponds to the settlement procedure for stocks registered on the Official List of the London Stock Exchange (LSE) and the March6 ~ R~glement Mensuel in the Paris Bourse where the most important firms are listed. These procedures are discussed in Yadav and Pope (1992, p. 235) for the LSE and by Solnik and Bousquet (1990) for the Paris Bourse. The main difference between them is that the settlement period begins the same day of the week (Friday 3.30 p.m.) and lasts for two weeks (sometimes three weeks) for the LSE, while the day varies and the period is approximately one month in the French system. Supposing t - 1 and t belong to two different account periods, let t - 1 ~ [ Pt ] and t ¢ [ P2] we have % = % I + 8 (where 8 is the number of days in the current account period). Other things being equal, the price increases the first day of a new settlement period by an amount of 8 r / 3 6 0 . During the period, one day of credit is lost every day ( r / 3 6 0 ) , except around the weekend where three days are lost (3 r/360).
3. Empirical results First, the day-of-the-week effect is tested using an analysis of variance and it is shown that standard hypotheses do not hold any longer. Second, seasonal components are computed and the stability of these estimates is examined. Third, a non-parametric test is performed. 3.1. S t a n d a r d m e t h o d o l o g y
Assuming that daily returns are normal, independent and identically distributed, the day-of-the-week effect is tested via an analysis of variance. In this case, the estimated covariance matrix of daily returns must be o~21, where ~r 2 is the constant variance of the series, equal for each day of the week, and I is a 5 × 5 identity matrix. Using the sphericity-test (see Anderson, 1984, p. 427), we strongly reject independence and homoskedasticity for almost all indexes and sub-periods at 1%. ~3
12 We have no information on how this problem is solved by Chang et al. (1993). 13 At 5%, homoskedasticitywas not rejected for the FAZ index during the 85-88 subperiod.
1470
M . D u b o i s , P. L o u v e t / J o u r n a l o f B a n k i n g & F i n a n c e 2 0 ( 1 9 9 6 ) 1 4 6 3 - 1 4 8 4
Table 1 Daily return over the period a Index
Monday
CAN US-SP US-DJ
0.123
-
- 0.105 - 0.087
JAP-TSE(69-88) JAP-TSE (89-92) JAP-NIK (71-88) JAP-NIK(89-92) HK (73-89) AUS (80-92) GER FRA
-0.006 -0.128 -0.20
-0.021 0.034 0.033 0.071
0.082 0.1}93 0.076 0.154
0.042 -0.161 0.052 0.083
- 0.099
- 0.081
-0.021 0.064 0.080 -0.065
0.064 0.120 0.093 0.074
- 0.107 -
0.123
0.079 0.125 56.19"* 998 0.051 3.40 197 0.080 0.132 67.02 * * 900 0.075 3.64 197 0.189 24.01 * * 1003 0.107 12.42 * 666
- 0.098
0.025 0.118
0.039 - 0.139
- 0.227
No. of obs.
0.082 0.063 0.052
-0.044
0.2110 -0.029 0.186 0.053
Satur- T 2 day
0.061 0.028 0.023
-0.066 -0.035 -0.033
- 0.172
-
UK SWI
Tuesday Wednes- Thursday Friday day
0.047 0.101 0.024 0.063
0.073 -0.022 0.069 0.105
49.79 * * 1224 19.41 * * 1229 11.83 * 1226
18.30 55.06 26.95 53.93
** ** ** **
1202 1206 1239 1154
a Bold (italic) characters indicate the highest (lowest) return of the week. * H 0 (daily returns are equal) rejected at the 5% level. * * H 0 rejected at the 1% level.
T h e equality o f daily m e a n returns is tested with the H o t e l l i n g T2-statistic w h e r e [ix] is the multivariate normal v e c t o r o f daily returns. The main difference with the standard m e t h o d o l o g y is that heteroskedasticity and linear d e p e n d e n c i e s a m o n g c o m p o n e n t s are allowed. H0 :
/xl = ~2 =/-~3 = ~lz4 =/-L5 w h e r e / z i is the e x p e c t e d return on day i.
Hi:
3(i,j)el,2
.....
5, i : ~ j a n d / x i v ~ / x ;.
The d a y - o f - t h e - w e e k effect is always significant at the 5% level and in almost all cases at the 1% level (see T a b l e 1). A m e r i c a n , E u r o p e a n and H o n g - K o n g markets exhibit daily returns w h i c h h a v e a close profile: n e g a t i v e returns on M o n d a y and positive returns on W e d n e s d a y and Friday. W e obtain negative returns on T u e s d a y for Australian ( 1 9 8 0 - 1 9 9 2 ) and Japanese Markets ( 1 9 6 9 1988). N o n - s y n c h r o n o u s trading m a y be an explanation for the one-day lag as was h y p o t h e s i z e d by Jaffe and W e s t e r f i e l d (1985). As elsewhere, returns are higher on W e d n e s d a y and Friday. T h e s e findings support the hypothesis o f a universal effect spreading all around the w o r l d and leave u n a n s w e r e d the M o n d a y effect on the H o n g - K o n g market. If the T u e s d a y effect on Australian and Japanese markets results f r o m the M o n d a y effect o b s e r v e d on other markets, correlations a m o n g daily returns with a o n e - d a y lag b e t w e e n W e s t e r n and Eastern countries m u s t be h i g h e r than instantaneous correlations. S y n c h r o n o u s and one-day lag pairwise correlations b e t w e e n
1471
M. Dubois, P. Louvet / Journal o f Banking & Finance 20 (1996) 1 4 6 3 - 1 4 8 4
Table 2 Daily return 85-92 a Index
Monday
Tuesday
CAN US-SP US-DJ
- 0.072 - 0.022 - 0.003
- 0.007 0.096 0.111
0.079 0.110 0.117
0.025 0.013 0.013
0.054 0.1145 0.015
JAP-TSE (89-92) JAP-NIK (89-92) HK AUS
- 0.128 - 0.172 - 0.277
- 0.066 -0.035 0.137
-0.010
- 0.053
- 0.044 0.029 0.199 0.075
- 0.139 -0.161 0.096 0.074
0.051 0.075 0.193 0.1199
3.40 3.64 10.40 * 4.73
197 197 4(/3 41 I
GER FRA UK SWI
-
- 0.012 0.005 0.066 -0.045
0.072 0.169 0.1 0.105
0.092 0.142 0.061 0.114
0.065 0.022 0.106 0.116
4.95 16.12 * * 16.66 ' * 21.28 ' *
404 402 411 393
O.103 0.089 0.138 0.167
Wednesday
Thursday
Friday
T2 6.01 2.61 3.48
No. of obs. 41 I 408 410
a Bold (italic) characters indicate the highest (lowest) return of the week. * H 0 (daily returns are equal) rejected at the 5% level. * * H 0 rejected at the 1% level.
i n d e x e s w e r e first c o m p u t e d . 14 C o n t e m p o r a n e o u s c o r r e l a t i o n s across i n d e x r e t u r n s w i t h i n a g e o g r a p h i c a l z o n e are b i g g e r t h a n c o r r e l a t i o n s w i t h a o n e - d a y lag. A s e x p e c t e d , this r e l a t i o n is r e v e r s e d w h e n w e c o n s i d e r c o r r e l a t i o n s w i t h U S i n d e x e s : p(US-SP,;
JAP-TSEt)=O.095
and p(US-SP,;
AUS t) = 0.019
while Q(US-SPt;
1) = 0 . 2 8 9 a n d Q ( U ~ S - S P t ; A U S t _ 1) = 0.511. M o r e o v e r , t h e c o r r e l a t i o n b e t w e e n M o n d a y r e t u r n s o f the U S - S P a n d T u e s d a y r e t u r n s o f the J A P - T S E is 0 . 4 0 8 ( 0 . 7 3 7 for J A P - N I K ) , w h i l e it is 0 . 2 9 0 ( 0 . 2 8 9 for J A P - N I K ) for t h e o t h e r d a y s o f the week. C o r r e l a t i o n s b e t w e e n E u r o p e a n c o u n tries a n d J a p a n are s i g n i f i c a n t l y p o s i t i v e o n M o n d a y a n d nil the rest o f the week. No significant differences appear between US-DJ and AUS. S y n c h r o n o u s a n d o n e - d a y lag c o r r e l a t i o n s b e t w e e n the H K a n d the U S i n d e x e s or J a p a n e s e i n d e x e s are l o w ( m a x i m u m e q u a l to 0 . 1 6 ) a n d the H o n g - K o n g S t o c k E x c h a n g e s e e m s to b e w e a k l y i n t e g r a t e d . T h e s e f i n d i n g s m a y e x p l a i n the fact that H K d o e s n o t e x h i b i t n e g a t i v e r e t u r n s o n T u e s d a y . I n f o r m a t i o n d o e s n o t s e e m to b e solely the o r i g i n o f the d a y - o f - t h e - w e e k effect. T h e last s u b - p e r i o d ( 1 9 8 5 - 1 9 9 2 ) is q u i t e p u z z l i n g (see T a b l e 2). R e s u l t s are d i f f e r e n t a n d the d a y - o f - t h e - w e e k e f f e c t is n o l o n g e r s i g n i f i c a n t in A m e r i c a n o r in the Pacific B a s i n c o u n t r i e s w i t h t h e e x c e p t i o n o f H o n g - K o n g . T h e s e results are s i m i l a r to t h o s e o f C h a n g et al. ( 1 9 9 3 ) w i t h o u t c o r r e c t i o n for s a m p l e size.
JAP-TSEt
14 Correlations are calculated using weeks with five returns only. Contemporaneous pairwise correlations, correlations with one-day lag and correlations between Monday and Tuesday are available upon request from the authors.
1472
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
However, Monday returns have the lowest return of the week and are negative in each country under consideration.
3.2. Seasonal components, stability and settlement effects The aim of the method is to remove market trends because they prevent us from measuring the permanency and the stability of seasonal components. If negative returns on Mondays are due to negative trends as noticed by Jaffe et al. (1989), we avoid this problem by eliminating the trend. Monday seasonal components indicate how much lower the return is on that day compared to the rest of the week. Table 3 presents empirical values of seasonal components for each index and the whole period. The main conclusions of Section 3.1 are still valid. Eight countries out of nine have a significant negative Monday component (see Table 3). Magnitudes are close for American and European markets ( - 0.10% and - 0 . 1 6 % ) and twice as much for Hong-Kong ( - 0 . 2 5 2 % ) . The negative Monday component is a well established fact in most countries including Japan (at the 5% level). As it was found by other researchers, seasonality is strong for each country in the sample from 1969 to 1989. The Wednesday component is also significantly positive in eight countries out of nine, Australia being an exception.
3.2.1. Seasonal component stability The sample is divided into six four-year sub-periods. Daily components are found to be different from zero in most countries: Monday or Tuesday is negative and Wednesday is positive (see Table 4). Thursday and Friday are not presented here because we do not find any significant pattern for these days. Monday seasonal components are almost always negative for American, European and Hong-Kong markets, and as a consequence the day-of-the-week may not be the result of a statistic pitfall. As daily returns are strongly volatile over short periods of time (four years), estimated components are not significant for each sub-period. However, only five coefficients out of 60 are positive, confirming the persistence of low returns on Monday. However, the Monday component is no longer significant for the most recent period in America; Japan and Australia exhibit a negative (not significant at the usual levels) component on Monday, and Tuesday is now positive. When computed over four-years sub-periods, seasonal components are unstable. 3.2.2. Correcting settlement effects As shown above (see Section 2.3.2), the London Stock Market as well as the Paris Bourse are affected by intricate settlement procedures. Correct seasonal components are obtained by eliminating the cost of carry. Returns spanning two settlement periods are adjusted by deducting the interest component from the first return of a settlement period. The one month London Euro-currency rate was used as proxy for the risk free rate for both GBP and FFR. The tests were conducted for the 1975-1992 period. Data were collected from Datastream.
M. Dubois, P. Lout~et/ Journal of Banking & Finance 20 (1996) 1463-1484
©
~
~ ~
~
~
~ i ~
o ~ = ~
I
~-~
I
I
~N
o .
©
III
I l l l l l
.fi o I
~
I
I
I
<<<<~<
I,II
~£
1473
M. Dubois, P. Louver/Journal of Banking & Finance 20 (1996) 1463-1484
1474
Table 4 Seasonal components analysis a
Monday
Index
69-72
73-76
CAN
- 0 . 1 2 8 **
-0.152
US-SP
-0.243 * *
-0.135 *
US-DJ HK
-0.240 * * n.a.
-0.118 - 0.309
GER FRA
-0.123 * -0.203 * *
UK SWI JAP-NIK JAP-TSE AUS Tuesday SWI JAP-NIK JAP-TSE
77-80
81-84
85-89
89-92
- 0 . 2 0 3 **
- 0 . 2 4 4 **
- 0 . 1 7 3 **
-0.004
-0.124
-0.189
0.074
-0.122 * 0.080
-0.073 - 0.383 *
-0.153 - 0.289
0.079 - 0.368 *
-0.087 -0.160 * *
-0.040 -0.217 * *
-0.078 -0.051
-0.159 -0.242 * *
-0.106 -0.089
-0.091 -0.076
-0.178 -0.154 * *
-0.082 -0.094 * *
-0.114" -0.113 *
-0.214"* -0.193 *
- 0 . 1 5 7 ** -0.227 * *
n.a. -0.007 n.a.
n.a. -0.035 n.a.
-0.042 -0.025 n.a.
-0.007 0.087 * - 0.031
0.141 * * -0.274 * * - 0.066
-0.096 -0.051 - 0.038
-0.129 *
-0.007
-0.147 * *
-0.075
-0.104
-0.050
n.a. -0.096
-0.133 * -0.110 *
-0.195 * * -0.155 * *
-0.202 * * -0.201 * *
-0.211 -0.195 *
0.034 0.010
-0.283 *
0.076 0.020 0.021 0.026 0.154 0.014 0.089 0.026 0.067
AUS Wednes- C A N US-SP day US-DJ HK GER FRA UK SWI JAP-NIK JAP-TSE
**
-0.120 *
n.a.
n.a.
n.a.
-0.175 * *
0.063 0.186 * * 0.144 * * n.a. 0.064 0.219 * * 0.031 0.125
0.109 * 0.030 0.043 0.320 0.025 0.061 0.123 0.025
0.091 * 0.097 * 0.080 0.008 0.049 0.122 * 0.098 0.061
0.090 * 0.026 0.007 0.302 * 0.087 0.071 0.052 0.079 *
0.137 0.125 0.128 0.161 0.147 0.133 * 0.143 * 0.156 *
0.109 0.076
0.070 * 0.049
0.074 0.069
0.075 0.048
0.013 - 0.004
n.a.
0.034
0.092
0.003
n.a. - 0.017
AUS
n.a.
n.a.
a H0: Sj = 0 the corresponding seasonal component is nil. n.a. not available. * H 0 rejected at the 5% level (Student t-test). * * H 0 rejected at the 1% level (Student t-test).
After correction in London, seasonal
for settlement
nor in Paris
component
difference
is l a r g e r
is o b t a i n e d
c i e n t is n o l o n g e r
procedures,
for the full period after
correction
for the last period
significant
fundamental (see Table for
1989-1992,
the
patterns
do not change
5). The
magnitude
cost
carry.
of
where
of the
The
the Monday
main coeffi-
in Paris.
3.3. N o n - p a r a m e t r i c tests The but
this
Hotelling-T hypothesis
2 statistic
assumes
is q u e s t i o n a b l e .
that daily To
avoid
returns
are multivariate
misleading
conclusions
normal due
to
a
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (19961 1463-1484
1475
Table 5 Daily returns and seasonal components after settlement-effect correction Period
Monday
Tuesday
Wednesday
Thursday
Friday
T2
FRA index Return 75-76
0.055
0.135
0.088
-0.059
77-80
-0.191 0.132
*
0.077
0. 132 *
0.087
0.094
81-84
- 0.008
0.092
0.087
0.007
0.023
85-89
-0.152
0.115
0.159 *
0.106
(I. 187 ~
89-92
- 0.084
0.062
I/. 103
0.022
75-92
-0.108
0.110 * *
0.079 *
0.056
- 0.075 **
0.056
9.51 12.02 * 4.23 14.54 * 5.96 30.78 * *
Seasonal component 75-76
-0.208
**
0.038
0.115
0.105
77-80
-0.202
**
0.009
0.078
0.038
0.061
0.017
0.088
14.35
0.061
-0.040
85-89
-0.227
89-92
- 0.086
0.075
0.103
0.022
75 92
- 0.150 * *
0.004
0.078 * *
(I.030
0.027
75-76
-0.247
0.164
0.346 *
0.272
0.339 *
77-80
-0.181
**
0.247 * *
0.173 * *
81-84
-0.172
**
0.078
0.130 *
0.139 *
0.186
85-89
- 0.294 * *
0.061
0.195
0.074
0.248 * *
89-92
-0.283
**
0.127 * *
0.061
0.110
0.128 *
28.09
75-92
-0.231
**
0.132 *
0.162 * *
0.098 * *
0.196 * *
86.60 * '
0.086
0.177
13.78 *~
0.045
25.24 * *
- 0.081
-0.067
16.79 * "
81-84
**
0.041
-0.049
0.009
0.001
4.64
0.108
21.94 9.06 44.40 * *
UK Index Return -0.012
7.50
0.119 **
25.98
**
20.05
*~
35.13 * * *
Seasonal component 75-76
-0.428
**
77-80
-0.248
**
-0.018
0.160
0.166 * *
-0.084
0.054
-0.059
81-84
-0.247
**
85-89
-0.358
**
89-92
-0.311
**
0.083
0.026
75-92
- 0.305 * *
0.052
0.086 * *
*
H o rejected
0.001
0.102
-0.001
0.131
0.112 *
33.74 *
0.192 * *
52.44 * *
0.073
(I.102 * *
46.06 * *
0.021
0.124 * *
141.26 * '
0.009
at the 5 % l e v e l ( S t u d e n t t-test).
* * H 0 r e j e c t e d at the 1% level ( S t u d e n t t-test).
wrong For return
specification each of
frequencies Ho: where
fi
H,"
day, the are
we
of the
econometric
compute
the
week.
Under
equal
to 0.2.
model,
number
the
null
of
a parametric-free times
that
hypothesis
(no
return
test is performed. is the
lowest
day-of-the-week
daily effect),
f, =f2 = L =f4 =f5 is the
frequency
3(i,j)
~{1,2
of lowest .....
5},
return
of the
week
i4=jandJl. 4~fj.
occurring
on
day
i.
1476
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
ez
2
o
z ~3
M. Dubois, P. Lout~et / Journal of Banking & Finance 20 (1996) 1463-1484
g. =eq [-..
g m
g~
r13
<<.
<
.
1477
1478
M. Dubois, P. Louvet/ Journal of Banking & Finance 20 (1996) 1463-1484
e.
~
3:
3 ~
3:
o?
3~
3:
~:
3::.
3 ~
3
3 ~
[..., e,i
~eq
3
Z~ \
3:
3
3 ,.-i o ~,
I
[..
3 ,.d
3~ tt~
3
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
~5
o
e. o
©
z~
¢.~A
~e~
o~.
~-eq v
1479
1480
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
The test statistic is computed as follows:x42 = E~ l ( n i - T ) 2 / T where n i is the number of weeks in which the lowest return takes place on day i. If H 0 is rejected, we determine if specific days for which f, is significantly higher than 0.2 15 exist. However, the stationarity of daily returns is assumed. Seven indexes out of nine exhibit a day-of-the-week for the full period (see Table 6). As found previously, a Monday effect is observed except for Japan and Australia where the lowest returns occur on Tuesday. When sub-periods are considered, the sample size is reduced and results are not always significant. However, Monday and Tuesday are observed frequently while Wednesday just appears once. The recent modification in the Japan market behaviour is confirmed and M o n d a y becomes the day with the lowest returns over the last sub-period. Non-parametric tests are less biased by outliers but they lack power, however our conclusions remain unchanged. The same analysis was conducted with seasonal components. While Monday was found to be the day with the lowest returns of the week in most countries, this result is no longer true with seasonal components. W e find a negative component on Monday in France, the U S A and the United Kingdom and on Tuesday (or M o n d a y and Tuesday) for the rest of the world (see Table 7). Relating these results with instantaneous and one-day lag correlations is striking. Dominant markets (i.e. U S A and the United Kingdom) exhibit a Monday effect. We also observe this effect on Monday (on European or less integrated markets) or Tuesday when trading is non synchronous. Parametric and non-parametric methods lead to very similar results except for the G E R index and the H K index (see Tables 3 and 7). In this case, the highest frequency of bad components 16 occurs on Tuesday while the worst mean daily component is observed on Monday. This is possibly due to a few number of very low returns and justifies the non-parametric approach. To make our results comparable with those of Chang et al. (1993), we run the tests for the 8 5 - 9 2 sub-period. The main difference between both studies is that we find other days of the week to have the lowest returns. As in Chang et al. (1993), the significant lowest returns are obtained for Canada, Hong-Kong, France, Switzerland and the United Kingdom. No significant effect is found for Australia, Germany, and the USA. 17 However, our results are somewhat conflicting when the seasonal compo-
15 Under the null hypothesis f,. < 0.2. As it was suggested by an anonymous referee, an easy way of showing the presence of outliers is to rank daily returns and examine the top and the bottom deciles. If seasonality is persistent, Monday (or Tuesday) returns are expected to figure heavily in the bottom decile while Wednesday (or Friday) are expected to be in the top decile. Computations made for four indexes FRA, JAP, US(SP) and UK confirm this conjecture. To save place, these results are not presented here. They are available upon request. 16 Extreme returns are more frequent on Mondays (see Jansen and De Vries, 1991; Longin, 1993). 17 Japan is not examined for this period because the number of trading days per week changed at the end of 1988.
M. Dubois, P. Lout,et / Journal of Banking & Finance 20 (1996) 1463-1484
1481
nent approach is used. We show that Monday is not the unique day of the week to exhibit a high frequency of bad components. Tuesday is also significant for four countries: Canada, Hong-Kong, France and Switzerland. We agree with their suggestion that the day-of-the-week effect is not due to European institutions because market organisations across countries have nothing in common. Moreover, two other countries out of Europe are concerned.
4. Conclusion This paper examined the international day-of-the-week effect for nine markets. Standard statistical procedures (parametric and non-parametric) were used in conjunction with a moving average approach. We find negative returns on Monday, which are compensated by abnormal positive returns on Wednesday, with the exception of Japan and Australia. These markets exhibit a significant negative effect on Tuesday over the whole sample period, but Monday returns are negative for the last sub-period since Tokyo has been closed on Saturday and Sunday. Non-parametric tests do not lead to the same conclusions. The Monday component is more likely to be negative for the US and UK markets. However, it turns to be the Tuesday component for the rest of the world. The FRA index is specific in the sense that Monday returns are computed as the difference in Log between Tuesday and Monday opening prices. Information arriving after Monday closing and before Tuesday opening are incorporated into Monday returns in place of Tuesday returns for other countries. Correlations between indexes tend to confirm the conjecture that the observed lag is possibly due to non-synchronous trading. Settlement procedures distort returns so that international comparisons are quite difficult to undertake. The London Stock Exchange and the Paris Bourse are forward markets. After correcting for these effects, Monday coefficients are negative for the whole period and our conclusions remain unchanged. The shape of contemporaneous and one-day lag correlations due to non-synchronous trading may be explained, at least partly, by the dominant-satellite market relationship. However, the day-of-the-week effect remains unexplained for at least the US and UK markets. Low trading volumes on Monday (see Theobald and Price (1984) for the United Kingdom, Louvet and Taramasco (1991) and Hamon and Jacquillat (1992) for France) suggest that institutional investors are less active on this day. In this case, the day-of-the-week effect is related to the inelasticity of the demand. Recently, Abraham and Ikenberry (1994) explored this hypothesis for the US market and found that individual investors exert a selling pressure on Monday and to some extent on Tuesday. Given our results (see Table 7), this explanation is attractive and has to be tested at an international level. This is left for further research.
1482
M. Dubois, P. Lou~et / Journal of Banking & Finance 20 (1996) 1463-1484
,o
¢q
t"q
t"N
¢'q
r,~, t"q ' ~
"4"
~-J
t"q t"q t'q
¢'q
"~
~c5 t'~lt~t'xl
(",1 t"q
t",l
"T'T~ .....,
'-.D r',-. r',-- ~
',D ~t3 ~,O ~t~
+
+
d~d~
z
+
+
+~ -
-
g, ° ,1
<
e-;
.<
~
=+
N~0 2 "o
~
~
~.~ -
~_~.~
r¢3
- -
~,
~.~
0
M. Dubois, P. LouL,et/ Journal of Banking & Finance 20 (1996) 1463-1484
1483
Acknowledgements W e t h a n k O. T a r a m a s c o f o r c o m p u t e r a s s i s t a n c e . F i n a n c i a l a s s i s t a n c e f r o m t h e F o n d s N a t i o n a l d e la R e c h e r c h e gratefully acknowledged.
Scientifique Suisse (grant n°12-30998.91)
is
References Abraham, A. and D. Ikenberry, 1994, The individual investor and the weekend effect. Journal of Financial and Quantitative Analysis 29, 263-277. Admati+ A. and P. Pfleiderer, 1989, Divide and conquer: A theory ot intraday and day-of-the-week mean effects, Review of Financial Studies 2, 189-223. Anderson, T.W., 1984, An introduction to multivariate statistical analysis, Publications in Probability and Mathematical Statistics, 2 ed. (Wiley, New York) Barone, E., 1990, The Italian stock market efficiency and calendar anomalies, Journal of Banking and Finance 14, 483-510. Baillie, R. and R. DeGennaro, 1989, The impact of delivery terms on stock return volatility, Journal of Financial Services Research 3, 55-76. Board, J.L. and C.M. Sutcliffe, 1988, The weekend effect in the UK stock market returns, Journal of Business Finance and Accounting 15, 199-213. Bollerslev, T., R. Chou and K. Kroner, 1992, ARCH modelling in finance: A review of the theory and empirical evidence, Journal of Econometrics 52, 5-59. Cadsby, C., 1989, Canadian calendar anomalies and the capital asset pricing model, In: R. Guimaraes, B. Kingsman and S. Taylor, eds., Reappraisal of the efficiency of financial markets, NATO ASI Series, Vol. F54 (Springer Verlag, Berlin) 199-226. Chang, E., M. Pinegar and R. Ravichandran, 1993, International evidence on the robustness of the day-of-the-week effect, Journal of Financial and Quantitative Analysis 28, 497-514. Condoyanni, L., S. McLeay and J. O'Hanlon, 1989, An investigation of daily seasonality in the Greek equity market, In: R. Guimaraes, B. Kingsman and S. Taylor, eds., Reappraisal of the efficiency of financial markets, NATO ASI Series, Vol. F54 (Springer Verlag, Berlin) 229-257. Connolly, R., 1989, An examination of the robustness of the week-end effect, Journal of Financial and Quantitative Analysis 24, 133-156. Connolly, R., 1991, A posterior odds analysis of the week-end effect, Journal of Econometrics 49. 51-104. Cross, F., 1973, Bebaviour of stock prices on Fridays and Mondays, Financial Analysts Journal 29, 67-69. Fama, E., 1965, The behavior of stock market prices, Journal of Business 38, 34-105. Fama, E. and K. French, 1988, Permanent and temporary components of stock prices, Journal of Political Economy 96, 246-273. French, K., 1980, Stock returns and the week-end effect, Journal of Financial Economics 8, 55 7l). French, K. and R. Roll, 1986, Stock return variance: The arrival of information and the reaction of traders, Journal of Financial Economics 17, 5-26. Gibbons, M. and P. Hess, 1981, Day-of-the-week effects and asset returns, Journal of Business 54, 579-596. Hamon, J. and B. Jacquillat, 1990, Saisonnalitfis dans la semaine et la s~ance ~ la bourse de Paris, CEREG working paper 9007 (Universit6 Paris-Dauphine, Paris). Hamon, J. and B. Jacquillat, 1992, Le march~ fran~ais des actions, Etudes empiriques 1977-1991 (Presses Universitaire de France, Paris).
1484
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
Harris, L., 1986, A transaction data study of weekly and intradaily patterns in stock returns, Journal of Financial Economics 16, 99-117. Jaffe, J. and R. Westerfield, 1985, Patterns in Japanese common stock returns: Day-of-the-week and turn-of-year effects, Journal of Financial and Quantitative Analysis 20, 261-272. Jaffe, J., R. Westerfield and C. Ma, 1989, A twist of the Monday effect in stock prices: Evidence from the US and the foreign stock market, Journal of Banking and Finance 13, 641-650. Jansen, D. and C. De Vries, 1991, On the frequency of large stock returns: Putting booms and busts into perspectives, Review of Economics and Statistics 73, 18-24. Jennergren, P. and B. Sorensen, 1989, Random walks and anomalies on the Copenhagen Stock Exchange in the 1890's, In: R. Guimaraes, B. Kingsman and S. Taylor, eds., Reappraisal of the efficiency of financial markets, NATO ASI Series, Vol. F54 (Springer Verlag, Berlin) 261-282. Keim, D., 1987, Daily returns and size-related premiums: One more time, Journal of Portfolio Management, Winter, 41-47. Keim, D. and R. Stambaugh, 1984, A further investigation of the week-end effect in stock returns, Journal of Finance 39, 819-840. Lakonishok, J. and M. Levi, 1982, Week-end effects on stock returns: A note, Journal of Finance 37, 883-889. Lakonishok, J. and E. Maberly, 1990, The week-end effect: trading patterns of individual and institutional investors, Journal of Finance 45, 231-243. Lakonishok, J. and S. Smidt, 1988, Are seasonal anomalies real? A ninety year perspective, Review of Financial Studies 1,403-425. Lee, I., R. Pettit and M. Swankoski, 1990, Daily return relationships among Asian stock markets, Journal of Business Finance and Accounting 17, 265-284. Levi, M., 1988, Week-end effects in the stock market returns: An overview, In: E. Dimson, ed., Stock market anomalies (Cambridge University Press, Cambridge) 43-51. Longin, F., 1993, Booms and crashes application of the extreme value theory to the US stock market, IFA working paper 179 (London Business School, London). Louvet, P. and O. Taramasco, 1990, L'effect 'jour de la semaine ~ la Bourse de Paris': Une approche par les moyennes mobiles, Finance 11, 83-109. Louver, P. and O. Taramasco, 1991, L'effet 'jour de la semaine 5 la Bourse de Paris': Un effet transactionnel, Journal de la Soci&6 Statistique de Paris 133, no. 2, 50-76. Merton, R., 1990, Continuous-time finance (Basil Blackwell, Oxford). Penman, S., 1987, The distribution of earnings news over time and seasonalities in aggregate stock returns, Journal of Financial Economics 18, 199-228. Peterson, D., 1990, Stock return seasonalities and earnings information, Journal of Financial and Quantitative Analysis 25, 187-201. Porter, D., 1990, The probability of a trade at the ask: An examination of interday and intraday behavior, Journal of Financial and Quantitative Analysis 27, 209-228. Poterba, J. and L. Summers, 1988, Mean reversion in stock prices: Evidence and implicatons, Journal of Financial Economics 22, 27-44. Rogalski, R., 1984, New findings regarding day-of-the-week returns over trading and non-trading periods, Journal of Finance 39, 1603-1614. Santesmeses, M., 1986, An investigation of the Spanish stock market seasonalities, Journal of Business Finance and Accounting 13, 267-276. Smirlock, M. and L. Starks, 1986, Day-of-the-week and intraday effects in stock returns, Journal of Financial Economics 17, 197-210. Solnik, B. and L. Bousquet, 1990, Day-of-the-week effect on the Paris Bourse, Journal of Banking and Finance 14, 461-468. Theobald, M. and V. Price, 1984, Seasonality estimation in thin markets, Journal of Finance 39, 377-392. Yadav, P. and Pope, P., 1992, Intraweek and intraday seasonalities in market risk premia: Cash and futures, Journal of Banking and Finance 16, 233-270.
Journal of Banking& Finance 20 (1996) 1463-1484
FINANCE
The day-of-the-week effect: The international evidence M. Dubois a,*, p. Louvet b a The Universi~ ofNeuchgttel, Groupe de Gestion d'Entreprise, Pierre-h-Mazel 7, Neuchhtel, CH 2000 Switzerland Pzerre Mendbs-France University Grenoble, France b
.
•
Received 12 April 1994; accepted 5 July 1995
Abstract We re-examine the day-of-the-week effect for eleven indexes from nine countries during the 1969-1992 period. The standard methodology as well as the moving average methodology are used and we find returns to be lower at the beginning of the week (but not necessarily on Monday) for the full period. As in Chang et al. (International evidence on the robustness of the day-of-the-week effect, Journal of Financial and Quantitative Analysis 28 (1993), 497-514), the anomaly disappears for the most recent period in the USA. However, the effect is still strong for European countries, Hong-Kong and Toronto. JEL classification: G 12 Keywords." Day-of-the-weekeffect; Seasonal component;Internationalstock indexes
1. Introduction Since the results provided by Cross (1973) attesting that returns on the Standard and Poors index are significantly negative on Mondays, many researchers have detected a day effect on stock returns. French (1980), Keim and Stambaugh (1984), examining longer periods, or Rogalski (1984) choosing the DJIA index, confirmed the phenomenon which changes over time (see Smirlock and Starks,
* Correspondingauthor. Tel.: 41 38 21 28 71; fax: 41 38 21 29 40. This paper was presented at the EFA meeting(1994). 0378-4266/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. SSDI 0378-4266(95)00054-2
1464
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
1986). Harris (1986), Lakonishok and Smidt (1988) and Keim (1987) studied interactions with both size and month effects. Gibbons and Hess (1981), Lakonishok and Levi (1982) noted abnormal high returns at the end of the week, and Cadsby (1989) identified a Monday effect for the Canadian stock market. On Asian markets, Japanese indexes show negative returns on Tuesday. This was proved by Jaffe and Westerfield (1985) and Lee et al. (1990) respectively. However, no significant day anomalies affect the Stock Exchanges in Hong-Kong, Korea, Taiwan or Singapore. In Europe, seasonal patterns vary across countries and time periods. Spanish (Santesmeses, 1986) and Danish markets (Jennergren and Sorensen, 1989) do not experience a day effect; a negative return is observed on Monday on the London Stock Exchange (Theobald and Price, 1984) and the Paris Bourse (Hamon and Jacquillat, 1990; Louvet and Taramasco, 1990; Solnik and Bousquet, 1990). Returns are found to be negative on Tuesday and Wednesday on the Greek Stock Exchange (see Condoyanni et al., 1989), and on Monday and Tuesday on the Milan Stock Exchange (Barone, 1990). Merton (1990) and Levi (1988), among others, wondered about statistical methods used to detect such anomalies and they cast some doubt on approaches relying exclusively on empirical evidence. Using more sophisticated methodologies, Connolly (1989) showed that the magnitude of Monday returns is weak in the USA. Moreover, after correcting the critical t-value for sample size with a Bayesian approach, Monday returns are no longer negative at conventional levels (see Connolly, 1991). For the most recent period, the day-of-the-week effect has disappeared in most countries (see Chang et al., 1993). However, five European markets are still negative on Monday. 1 On the other hand, Jaffe et al. (1989) found that the negative effect occurred when the market return was negative the previous week, 2 the effect being insignificant when the market return was positive. Different economic rationales were hypothesized. Settlement delays vary among countries and could explain part of the previous findings (see Gibbons and Hess, 1981; Baillie and DeGennaro, 1989). Admati and Pfleiderer (1989) and Porter (1990) demonstrated that the market-making process could induce intraweek patterns. But this explanation does not fully account for day-of-the-week effects because market-makers do not exist in continental Europe. Penman (1987) suggested that bad earnings announcements may be responsible for the seasonality but this was not confirmed by Peterson (1990) and Connolly (1991). Chang et al. (1993) examined the pattern of macroeconomics new releases but the evidence is weak. Lakonishok and Maberly (1990), Theobald and Price (1984) and Louvet and
i These results contradict those of Sentesmeses' study, who does not find a day-of-the-week for Spain before 1984. 2 This effect is possibly due to positive first-order autocorrelation.
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
1465
Taramasco (1991) hypothesized: (a) a cyclical behaviour of shareholders and (b) seasonal fluctuations in transaction volumes. In this paper we address the issue in a different way by focusing on the mean value of the seasonal component of each day-of-the-week return. We test the equality of these components with a parametric as well as a non-parametric approach. The rationale for the last type of test is the presence of 'outliers' in our sample. 3 The paper is organised as follows. Section 2 outlines the methodology. Seasonal components are computed for each day of the week and in this way, we test the stability of the day-of-the-week effect. Section 3 presents evidence based on the most important capital markets of America, the Pacific Basin and Europe. Commonly used indexes are employed for each country. Section 4 concludes.
2. The moving average approach Previous researches generally detected daily abnormal returns by using an analysis of variance. This method is not fully satisfactory because returns are required to be (a) normal, (b) independent and (c) stationary. To avoid hypothesis (a), Gibbons and Hess (1981) used the standard procedure and a non-parametric test (Kruskal-Wallis' analysis of variance) but conclusions remain unchanged. Employing robust to non-normality and heteroskedasticity techniques, Connolly (1989), 4 Connolly (1991) and Chang et al. (1993) showed that the day-of-the-week effect is weak. In this paper, daily returns are analysed as time series and not as independent observations of a given sample. The existence of systematic daily fluctuations (seasonal components) is tested as it is usually done in time series analyses. The trend and seasonal effects are computed. 2.1. T h e d a i l y return p r o c e s s
Let Rj,~ be the logarithmic return of an index the day j of the week s. We assume that Rj., is generated by the following process: Rj.. = Sj + F,. j + o'jEj..~
(1)
where t = 5s + j , j = Monday, Tuesday . . . . . Friday, and s ~ {1 . . . . . p}, . . . Ft = F.i , random trend with o-~ << cri? ' ~rj' variance of daily returns, e, = ei..~ are independent variables N(0, 1), (rj = the standard deviation of day j, S/ = additive daily seasonal component.
In our opinion, outliers cannot be removed from the sample. However, the influence of extreme values must be reduced to put forth the regularities of the seasonal components. 4 Different estimators of returns dispersion giving less weight to outliers are used. A GARCH ( 1,1 ) model is presented too, but Bollerslev et al. (1992 p. 22) pointed out that "a failure to take proper account of such deterministic influences might lead to a spurious seasonal ARCH effect".
M. Dubois, P. Louvet/ Journal of Banking & Finance 20 (1996) 1463-1484
1466
Seasonal components are normalised so that the sum of the components for a given week is zero. This model extends the random walk model where F t is assumed to be constant over time. First, the model allows expected returns to change over time with both information flow and modifications in the investors' preferences, the presupposed sources o f randomness. Changes in the shape of the returns density function are weak at the day level. This hypothesis is compatible with previous researches by F a m a and French (1988) and Poterba and Summers (1988) who found that the permanent component of returns decreases slowly over time. However, these results were obtained with monthly or annual returns. Second, a seasonal component can affect the risk. There is no rationale to assume that the trend alone is affected by seasonal fluctuations: F a m a (1965) was the first to show that the variance is abnormally low on Monday. 5 The tests presented here only concern mean returns and mean seasonal components.
2.2. The moving average approach The moving average operator is calculated using five days windows and is centred on the current day. 6 The moving average characterizes the trend of current daily returns which are no more supposed to be constant over time. Removing the trend from the current return, we find the seasonal component plus a white noise. Let M t, be the moving average for day t:
lk=+2 M j ' s = M t = 5 k Y "R 2t+k==-
lk=+2 5k y'=.z[Ft+k+Sj(t+k)
+~(t+k)et+k]"
(2) It was assumed above that ~rF2, << cry,
-
lk=+2 ~ F ( t + k ) = F t, 5k= 2 -
e t are independent and N ( 0 , 1),
lk=+2 5k=_2 1-1 k=+2 and el, t N ( 0 , 1 ) w i t h
]1/2
o-,,j = /-~k=~ 2tTj2[ .
(3)
Because ~1E kk= = -+2 2 S = 0, we find M t-=- F t + (rl,jel, j
5 Fama (1965) finds a 20% decrease in variance. French and Roll (1986) show that the variance of common equities exhibits a seasonality. 6 Until 1989, Tokyo was open on Saturday mornings. Thus, from 1969 to 1989, the moving average is computed with six days; since 1989, a standard five days moving average operator has been used.
M. Dubois, P. LouL, et / Journal o[Banking & Finance 20 (1996) 1463-1484
1467
Let A i., = A r be the difference between Rj. ~ and Mj.~, A i,., = Rj..~ - Mj,.~ = Fj, s + Sj.., + o)ej,~ - (Fj..~ + o ' l . j e , . j . s )
= Si.., + °2.Je2.J.,
and A the covariance matrix of hi. Note that cov(et, e , j ) = 0 for t i s~ tj does not imply that c o y ( e 2 . , / e 2 , , j ) = 0, because E2, t is a linear function of e,_ 2, et 1, e,, e, + 1, ~, + 2- Because the variance is possibly seasonal, we used a Hotelling-T 2 test, the distribution of which does not depend on the correlation matrix. 2.3. T h e d a t a
A daily record of values for eleven stock market indexes was collected from 7 The period under study is from January 2, 1969 to December 30, 1992 except for the Sydney and Hong-Kong Stock Exchange and the Nikkei Indexes (see Appendix A). The indexes used in this study are representative of each market and account for approximately 85% of the world market value of listed securities at the end of 1992. 8 Employing different sub-periods, we also test seasonal stability. Weeks with incomplete data, less than five returns per week or six for Japan when the market was open on Saturday, are eliminated to concentrate the study on the Monday effect. By eliminating incomplete weeks, we avoid the interaction between day-of-the-week and Holiday effects. Daily returns are computed as tollows: DataStream.
It
R,= 100×InIt-
j
I t is the value of the index at time t. Indexes are computed with closing prices except for the SBF 240 Index (France)9 where opening prices are used. A question arises in deciding to which day the return is affected. Solnik and Bousquet (1990) chose to compute Monday returns as the difference in Log prices between Monday opening and Friday opening arguing that 90% of the transactions take place at this time. Hamon and Jacquillat (1990) compute Monday returns as the difference in Log prices between Tuesday opening and Monday opening. But negative returns on Mondays are related to the low volume that day. The last
7 As it was underlined by Board and Sutcliffe (1988), the omission of dividends induces a downward bias in computing returns. When dividends are taken into account, the pattern of returns does not change significantly(see also Theobald and Price (1984)). This is the reason why dividends are neglected in this research. Topix and Nikkei indexeswere provided to us by Yamaichi Securitiesin Geneva because Saturday figures are omitted in DataStream. We are grateful to CED1F-Universit6de Lausanne and Yamaichi Securities in Geneva for providingus the data. 8 Source: Frdrration Internationaledes Bourses de Valeurs (FIBV), Geneva, Annual Report 1993. 9 The SBF 240 Index is computed with opening prices, see Solnik and Bousquet (1990, p. 463).
M. Dubois, P. Loucet / Journal of Banking & Finance 20 (1996) 1463-1484
1468
convention was retained in this paper because the correspondence between return and trading volume seasonalities (see Louvet and Taramasco, 1991) suggests the last convention to be more accurate. As far as we are concerned, one of the most important differences across markets is the settlement procedure. Two main systems exist in the world (see Appendix A). The first one is characterized by fixed delays and the second by fixed settlement dates. In both situations, observed prices include the cost of carry which is computed using calendar days:
V=
1 + rt × ~-,/360
where: IIP~, It rt
rt
= = = =
price at time t of a stock (or an index) settled at time t + "rt, spot price at time t considering an instantaneous cash settlement, spot interest rate on day t ending at t + r t, length of the interval of time between transaction and payment.
Cash returns are not exactly equal to returns computed from observed prices except in special cases: It c
1 + r t × ~t/360
Ie
RC = ln-7~-- = l n - ~ lt l It-l,'rt_l
(4)
Ln l + rt_l X rt_J360
1 + r t X ~-t/360 R c = R, - In 1 + r t _ J × ~',_ 1 / 3 6 0 '
'
(5)
Assuming r t ..~ r t_ 1 = r for consecutive days, 1 + r × 7"t/360 e c = e t - In
1 + r × ~'t- 1/360
-- e t -
r(o't-
"/'t- 1) '
(6)
the difference between R c and R t results from r t :g -r,_ j for certain days of the week. 2.3.1. Fixed
settlement
d e l a y io
Delivery of securities and receipt of payment occur a fixed number of business days (one in Hong-Kong to five in Canada and USA) after the transaction. The cost of carry does not bias the return measure when the delay and the number of business days in the week are equal (i.e. r t = "rt 1 Vt). Otherwise, the cost of carry has a negative effect on Mondays (equal to - h r / 3 6 0 where h is the number of closing days during a week 11), recovered another day of the week. It is
10 The bank float problems in U.S. stock transactionsmentionedby Lakonishok and Levi (1982) are ignored. 11 h = 1 for Japan and h = 2 for other countries in the sample.
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
1469
Friday, Thursday or Wednesday when the settlement is at T + l, T + 2 or T + 3. Because delays of payment do not affect weekly returns, seasonal components reflect the same pattern as crude returns. 2.3.2. F i x e d s e t t l e m e n t d a t e 12
This situation corresponds to the settlement procedure for stocks registered on the Official List of the London Stock Exchange (LSE) and the March6 ~ R~glement Mensuel in the Paris Bourse where the most important firms are listed. These procedures are discussed in Yadav and Pope (1992, p. 235) for the LSE and by Solnik and Bousquet (1990) for the Paris Bourse. The main difference between them is that the settlement period begins the same day of the week (Friday 3.30 p.m.) and lasts for two weeks (sometimes three weeks) for the LSE, while the day varies and the period is approximately one month in the French system. Supposing t - 1 and t belong to two different account periods, let t - 1 ~ [ Pt ] and t ¢ [ P2] we have % = % I + 8 (where 8 is the number of days in the current account period). Other things being equal, the price increases the first day of a new settlement period by an amount of 8 r / 3 6 0 . During the period, one day of credit is lost every day ( r / 3 6 0 ) , except around the weekend where three days are lost (3 r/360).
3. Empirical results First, the day-of-the-week effect is tested using an analysis of variance and it is shown that standard hypotheses do not hold any longer. Second, seasonal components are computed and the stability of these estimates is examined. Third, a non-parametric test is performed. 3.1. S t a n d a r d m e t h o d o l o g y
Assuming that daily returns are normal, independent and identically distributed, the day-of-the-week effect is tested via an analysis of variance. In this case, the estimated covariance matrix of daily returns must be o~21, where ~r 2 is the constant variance of the series, equal for each day of the week, and I is a 5 × 5 identity matrix. Using the sphericity-test (see Anderson, 1984, p. 427), we strongly reject independence and homoskedasticity for almost all indexes and sub-periods at 1%. ~3
12 We have no information on how this problem is solved by Chang et al. (1993). 13 At 5%, homoskedasticitywas not rejected for the FAZ index during the 85-88 subperiod.
1470
M . D u b o i s , P. L o u v e t / J o u r n a l o f B a n k i n g & F i n a n c e 2 0 ( 1 9 9 6 ) 1 4 6 3 - 1 4 8 4
Table 1 Daily return over the period a Index
Monday
CAN US-SP US-DJ
0.123
-
- 0.105 - 0.087
JAP-TSE(69-88) JAP-TSE (89-92) JAP-NIK (71-88) JAP-NIK(89-92) HK (73-89) AUS (80-92) GER FRA
-0.006 -0.128 -0.20
-0.021 0.034 0.033 0.071
0.082 0.1}93 0.076 0.154
0.042 -0.161 0.052 0.083
- 0.099
- 0.081
-0.021 0.064 0.080 -0.065
0.064 0.120 0.093 0.074
- 0.107 -
0.123
0.079 0.125 56.19"* 998 0.051 3.40 197 0.080 0.132 67.02 * * 900 0.075 3.64 197 0.189 24.01 * * 1003 0.107 12.42 * 666
- 0.098
0.025 0.118
0.039 - 0.139
- 0.227
No. of obs.
0.082 0.063 0.052
-0.044
0.2110 -0.029 0.186 0.053
Satur- T 2 day
0.061 0.028 0.023
-0.066 -0.035 -0.033
- 0.172
-
UK SWI
Tuesday Wednes- Thursday Friday day
0.047 0.101 0.024 0.063
0.073 -0.022 0.069 0.105
49.79 * * 1224 19.41 * * 1229 11.83 * 1226
18.30 55.06 26.95 53.93
** ** ** **
1202 1206 1239 1154
a Bold (italic) characters indicate the highest (lowest) return of the week. * H 0 (daily returns are equal) rejected at the 5% level. * * H 0 rejected at the 1% level.
T h e equality o f daily m e a n returns is tested with the H o t e l l i n g T2-statistic w h e r e [ix] is the multivariate normal v e c t o r o f daily returns. The main difference with the standard m e t h o d o l o g y is that heteroskedasticity and linear d e p e n d e n c i e s a m o n g c o m p o n e n t s are allowed. H0 :
/xl = ~2 =/-~3 = ~lz4 =/-L5 w h e r e / z i is the e x p e c t e d return on day i.
Hi:
3(i,j)el,2
.....
5, i : ~ j a n d / x i v ~ / x ;.
The d a y - o f - t h e - w e e k effect is always significant at the 5% level and in almost all cases at the 1% level (see T a b l e 1). A m e r i c a n , E u r o p e a n and H o n g - K o n g markets exhibit daily returns w h i c h h a v e a close profile: n e g a t i v e returns on M o n d a y and positive returns on W e d n e s d a y and Friday. W e obtain negative returns on T u e s d a y for Australian ( 1 9 8 0 - 1 9 9 2 ) and Japanese Markets ( 1 9 6 9 1988). N o n - s y n c h r o n o u s trading m a y be an explanation for the one-day lag as was h y p o t h e s i z e d by Jaffe and W e s t e r f i e l d (1985). As elsewhere, returns are higher on W e d n e s d a y and Friday. T h e s e findings support the hypothesis o f a universal effect spreading all around the w o r l d and leave u n a n s w e r e d the M o n d a y effect on the H o n g - K o n g market. If the T u e s d a y effect on Australian and Japanese markets results f r o m the M o n d a y effect o b s e r v e d on other markets, correlations a m o n g daily returns with a o n e - d a y lag b e t w e e n W e s t e r n and Eastern countries m u s t be h i g h e r than instantaneous correlations. S y n c h r o n o u s and one-day lag pairwise correlations b e t w e e n
1471
M. Dubois, P. Louvet / Journal o f Banking & Finance 20 (1996) 1 4 6 3 - 1 4 8 4
Table 2 Daily return 85-92 a Index
Monday
Tuesday
CAN US-SP US-DJ
- 0.072 - 0.022 - 0.003
- 0.007 0.096 0.111
0.079 0.110 0.117
0.025 0.013 0.013
0.054 0.1145 0.015
JAP-TSE (89-92) JAP-NIK (89-92) HK AUS
- 0.128 - 0.172 - 0.277
- 0.066 -0.035 0.137
-0.010
- 0.053
- 0.044 0.029 0.199 0.075
- 0.139 -0.161 0.096 0.074
0.051 0.075 0.193 0.1199
3.40 3.64 10.40 * 4.73
197 197 4(/3 41 I
GER FRA UK SWI
-
- 0.012 0.005 0.066 -0.045
0.072 0.169 0.1 0.105
0.092 0.142 0.061 0.114
0.065 0.022 0.106 0.116
4.95 16.12 * * 16.66 ' * 21.28 ' *
404 402 411 393
O.103 0.089 0.138 0.167
Wednesday
Thursday
Friday
T2 6.01 2.61 3.48
No. of obs. 41 I 408 410
a Bold (italic) characters indicate the highest (lowest) return of the week. * H 0 (daily returns are equal) rejected at the 5% level. * * H 0 rejected at the 1% level.
i n d e x e s w e r e first c o m p u t e d . 14 C o n t e m p o r a n e o u s c o r r e l a t i o n s across i n d e x r e t u r n s w i t h i n a g e o g r a p h i c a l z o n e are b i g g e r t h a n c o r r e l a t i o n s w i t h a o n e - d a y lag. A s e x p e c t e d , this r e l a t i o n is r e v e r s e d w h e n w e c o n s i d e r c o r r e l a t i o n s w i t h U S i n d e x e s : p(US-SP,;
JAP-TSEt)=O.095
and p(US-SP,;
AUS t) = 0.019
while Q(US-SPt;
1) = 0 . 2 8 9 a n d Q ( U ~ S - S P t ; A U S t _ 1) = 0.511. M o r e o v e r , t h e c o r r e l a t i o n b e t w e e n M o n d a y r e t u r n s o f the U S - S P a n d T u e s d a y r e t u r n s o f the J A P - T S E is 0 . 4 0 8 ( 0 . 7 3 7 for J A P - N I K ) , w h i l e it is 0 . 2 9 0 ( 0 . 2 8 9 for J A P - N I K ) for t h e o t h e r d a y s o f the week. C o r r e l a t i o n s b e t w e e n E u r o p e a n c o u n tries a n d J a p a n are s i g n i f i c a n t l y p o s i t i v e o n M o n d a y a n d nil the rest o f the week. No significant differences appear between US-DJ and AUS. S y n c h r o n o u s a n d o n e - d a y lag c o r r e l a t i o n s b e t w e e n the H K a n d the U S i n d e x e s or J a p a n e s e i n d e x e s are l o w ( m a x i m u m e q u a l to 0 . 1 6 ) a n d the H o n g - K o n g S t o c k E x c h a n g e s e e m s to b e w e a k l y i n t e g r a t e d . T h e s e f i n d i n g s m a y e x p l a i n the fact that H K d o e s n o t e x h i b i t n e g a t i v e r e t u r n s o n T u e s d a y . I n f o r m a t i o n d o e s n o t s e e m to b e solely the o r i g i n o f the d a y - o f - t h e - w e e k effect. T h e last s u b - p e r i o d ( 1 9 8 5 - 1 9 9 2 ) is q u i t e p u z z l i n g (see T a b l e 2). R e s u l t s are d i f f e r e n t a n d the d a y - o f - t h e - w e e k e f f e c t is n o l o n g e r s i g n i f i c a n t in A m e r i c a n o r in the Pacific B a s i n c o u n t r i e s w i t h t h e e x c e p t i o n o f H o n g - K o n g . T h e s e results are s i m i l a r to t h o s e o f C h a n g et al. ( 1 9 9 3 ) w i t h o u t c o r r e c t i o n for s a m p l e size.
JAP-TSEt
14 Correlations are calculated using weeks with five returns only. Contemporaneous pairwise correlations, correlations with one-day lag and correlations between Monday and Tuesday are available upon request from the authors.
1472
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
However, Monday returns have the lowest return of the week and are negative in each country under consideration.
3.2. Seasonal components, stability and settlement effects The aim of the method is to remove market trends because they prevent us from measuring the permanency and the stability of seasonal components. If negative returns on Mondays are due to negative trends as noticed by Jaffe et al. (1989), we avoid this problem by eliminating the trend. Monday seasonal components indicate how much lower the return is on that day compared to the rest of the week. Table 3 presents empirical values of seasonal components for each index and the whole period. The main conclusions of Section 3.1 are still valid. Eight countries out of nine have a significant negative Monday component (see Table 3). Magnitudes are close for American and European markets ( - 0.10% and - 0 . 1 6 % ) and twice as much for Hong-Kong ( - 0 . 2 5 2 % ) . The negative Monday component is a well established fact in most countries including Japan (at the 5% level). As it was found by other researchers, seasonality is strong for each country in the sample from 1969 to 1989. The Wednesday component is also significantly positive in eight countries out of nine, Australia being an exception.
3.2.1. Seasonal component stability The sample is divided into six four-year sub-periods. Daily components are found to be different from zero in most countries: Monday or Tuesday is negative and Wednesday is positive (see Table 4). Thursday and Friday are not presented here because we do not find any significant pattern for these days. Monday seasonal components are almost always negative for American, European and Hong-Kong markets, and as a consequence the day-of-the-week may not be the result of a statistic pitfall. As daily returns are strongly volatile over short periods of time (four years), estimated components are not significant for each sub-period. However, only five coefficients out of 60 are positive, confirming the persistence of low returns on Monday. However, the Monday component is no longer significant for the most recent period in America; Japan and Australia exhibit a negative (not significant at the usual levels) component on Monday, and Tuesday is now positive. When computed over four-years sub-periods, seasonal components are unstable. 3.2.2. Correcting settlement effects As shown above (see Section 2.3.2), the London Stock Market as well as the Paris Bourse are affected by intricate settlement procedures. Correct seasonal components are obtained by eliminating the cost of carry. Returns spanning two settlement periods are adjusted by deducting the interest component from the first return of a settlement period. The one month London Euro-currency rate was used as proxy for the risk free rate for both GBP and FFR. The tests were conducted for the 1975-1992 period. Data were collected from Datastream.
M. Dubois, P. Lout~et/ Journal of Banking & Finance 20 (1996) 1463-1484
©
~
~ ~
~
~
~ i ~
o ~ = ~
I
~-~
I
I
~N
o .
©
III
I l l l l l
.fi o I
~
I
I
I
<<<<~<
I,II
~£
1473
M. Dubois, P. Louver/Journal of Banking & Finance 20 (1996) 1463-1484
1474
Table 4 Seasonal components analysis a
Monday
Index
69-72
73-76
CAN
- 0 . 1 2 8 **
-0.152
US-SP
-0.243 * *
-0.135 *
US-DJ HK
-0.240 * * n.a.
-0.118 - 0.309
GER FRA
-0.123 * -0.203 * *
UK SWI JAP-NIK JAP-TSE AUS Tuesday SWI JAP-NIK JAP-TSE
77-80
81-84
85-89
89-92
- 0 . 2 0 3 **
- 0 . 2 4 4 **
- 0 . 1 7 3 **
-0.004
-0.124
-0.189
0.074
-0.122 * 0.080
-0.073 - 0.383 *
-0.153 - 0.289
0.079 - 0.368 *
-0.087 -0.160 * *
-0.040 -0.217 * *
-0.078 -0.051
-0.159 -0.242 * *
-0.106 -0.089
-0.091 -0.076
-0.178 -0.154 * *
-0.082 -0.094 * *
-0.114" -0.113 *
-0.214"* -0.193 *
- 0 . 1 5 7 ** -0.227 * *
n.a. -0.007 n.a.
n.a. -0.035 n.a.
-0.042 -0.025 n.a.
-0.007 0.087 * - 0.031
0.141 * * -0.274 * * - 0.066
-0.096 -0.051 - 0.038
-0.129 *
-0.007
-0.147 * *
-0.075
-0.104
-0.050
n.a. -0.096
-0.133 * -0.110 *
-0.195 * * -0.155 * *
-0.202 * * -0.201 * *
-0.211 -0.195 *
0.034 0.010
-0.283 *
0.076 0.020 0.021 0.026 0.154 0.014 0.089 0.026 0.067
AUS Wednes- C A N US-SP day US-DJ HK GER FRA UK SWI JAP-NIK JAP-TSE
**
-0.120 *
n.a.
n.a.
n.a.
-0.175 * *
0.063 0.186 * * 0.144 * * n.a. 0.064 0.219 * * 0.031 0.125
0.109 * 0.030 0.043 0.320 0.025 0.061 0.123 0.025
0.091 * 0.097 * 0.080 0.008 0.049 0.122 * 0.098 0.061
0.090 * 0.026 0.007 0.302 * 0.087 0.071 0.052 0.079 *
0.137 0.125 0.128 0.161 0.147 0.133 * 0.143 * 0.156 *
0.109 0.076
0.070 * 0.049
0.074 0.069
0.075 0.048
0.013 - 0.004
n.a.
0.034
0.092
0.003
n.a. - 0.017
AUS
n.a.
n.a.
a H0: Sj = 0 the corresponding seasonal component is nil. n.a. not available. * H 0 rejected at the 5% level (Student t-test). * * H 0 rejected at the 1% level (Student t-test).
After correction in London, seasonal
for settlement
nor in Paris
component
difference
is l a r g e r
is o b t a i n e d
c i e n t is n o l o n g e r
procedures,
for the full period after
correction
for the last period
significant
fundamental (see Table for
1989-1992,
the
patterns
do not change
5). The
magnitude
cost
carry.
of
where
of the
The
the Monday
main coeffi-
in Paris.
3.3. N o n - p a r a m e t r i c tests The but
this
Hotelling-T hypothesis
2 statistic
assumes
is q u e s t i o n a b l e .
that daily To
avoid
returns
are multivariate
misleading
conclusions
normal due
to
a
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (19961 1463-1484
1475
Table 5 Daily returns and seasonal components after settlement-effect correction Period
Monday
Tuesday
Wednesday
Thursday
Friday
T2
FRA index Return 75-76
0.055
0.135
0.088
-0.059
77-80
-0.191 0.132
*
0.077
0. 132 *
0.087
0.094
81-84
- 0.008
0.092
0.087
0.007
0.023
85-89
-0.152
0.115
0.159 *
0.106
(I. 187 ~
89-92
- 0.084
0.062
I/. 103
0.022
75-92
-0.108
0.110 * *
0.079 *
0.056
- 0.075 **
0.056
9.51 12.02 * 4.23 14.54 * 5.96 30.78 * *
Seasonal component 75-76
-0.208
**
0.038
0.115
0.105
77-80
-0.202
**
0.009
0.078
0.038
0.061
0.017
0.088
14.35
0.061
-0.040
85-89
-0.227
89-92
- 0.086
0.075
0.103
0.022
75 92
- 0.150 * *
0.004
0.078 * *
(I.030
0.027
75-76
-0.247
0.164
0.346 *
0.272
0.339 *
77-80
-0.181
**
0.247 * *
0.173 * *
81-84
-0.172
**
0.078
0.130 *
0.139 *
0.186
85-89
- 0.294 * *
0.061
0.195
0.074
0.248 * *
89-92
-0.283
**
0.127 * *
0.061
0.110
0.128 *
28.09
75-92
-0.231
**
0.132 *
0.162 * *
0.098 * *
0.196 * *
86.60 * '
0.086
0.177
13.78 *~
0.045
25.24 * *
- 0.081
-0.067
16.79 * "
81-84
**
0.041
-0.049
0.009
0.001
4.64
0.108
21.94 9.06 44.40 * *
UK Index Return -0.012
7.50
0.119 **
25.98
**
20.05
*~
35.13 * * *
Seasonal component 75-76
-0.428
**
77-80
-0.248
**
-0.018
0.160
0.166 * *
-0.084
0.054
-0.059
81-84
-0.247
**
85-89
-0.358
**
89-92
-0.311
**
0.083
0.026
75-92
- 0.305 * *
0.052
0.086 * *
*
H o rejected
0.001
0.102
-0.001
0.131
0.112 *
33.74 *
0.192 * *
52.44 * *
0.073
(I.102 * *
46.06 * *
0.021
0.124 * *
141.26 * '
0.009
at the 5 % l e v e l ( S t u d e n t t-test).
* * H 0 r e j e c t e d at the 1% level ( S t u d e n t t-test).
wrong For return
specification each of
frequencies Ho: where
fi
H,"
day, the are
we
of the
econometric
compute
the
week.
Under
equal
to 0.2.
model,
number
the
null
of
a parametric-free times
that
hypothesis
(no
return
test is performed. is the
lowest
day-of-the-week
daily effect),
f, =f2 = L =f4 =f5 is the
frequency
3(i,j)
~{1,2
of lowest .....
5},
return
of the
week
i4=jandJl. 4~fj.
occurring
on
day
i.
1476
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
ez
2
o
z ~3
M. Dubois, P. Lout~et / Journal of Banking & Finance 20 (1996) 1463-1484
g. =eq [-..
g m
g~
r13
<<.
<
.
1477
1478
M. Dubois, P. Louvet/ Journal of Banking & Finance 20 (1996) 1463-1484
e.
~
3:
3 ~
3:
o?
3~
3:
~:
3::.
3 ~
3
3 ~
[..., e,i
~eq
3
Z~ \
3:
3
3 ,.-i o ~,
I
[..
3 ,.d
3~ tt~
3
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
~5
o
e. o
©
z~
¢.~A
~e~
o~.
~-eq v
1479
1480
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
The test statistic is computed as follows:x42 = E~ l ( n i - T ) 2 / T where n i is the number of weeks in which the lowest return takes place on day i. If H 0 is rejected, we determine if specific days for which f, is significantly higher than 0.2 15 exist. However, the stationarity of daily returns is assumed. Seven indexes out of nine exhibit a day-of-the-week for the full period (see Table 6). As found previously, a Monday effect is observed except for Japan and Australia where the lowest returns occur on Tuesday. When sub-periods are considered, the sample size is reduced and results are not always significant. However, Monday and Tuesday are observed frequently while Wednesday just appears once. The recent modification in the Japan market behaviour is confirmed and M o n d a y becomes the day with the lowest returns over the last sub-period. Non-parametric tests are less biased by outliers but they lack power, however our conclusions remain unchanged. The same analysis was conducted with seasonal components. While Monday was found to be the day with the lowest returns of the week in most countries, this result is no longer true with seasonal components. W e find a negative component on Monday in France, the U S A and the United Kingdom and on Tuesday (or M o n d a y and Tuesday) for the rest of the world (see Table 7). Relating these results with instantaneous and one-day lag correlations is striking. Dominant markets (i.e. U S A and the United Kingdom) exhibit a Monday effect. We also observe this effect on Monday (on European or less integrated markets) or Tuesday when trading is non synchronous. Parametric and non-parametric methods lead to very similar results except for the G E R index and the H K index (see Tables 3 and 7). In this case, the highest frequency of bad components 16 occurs on Tuesday while the worst mean daily component is observed on Monday. This is possibly due to a few number of very low returns and justifies the non-parametric approach. To make our results comparable with those of Chang et al. (1993), we run the tests for the 8 5 - 9 2 sub-period. The main difference between both studies is that we find other days of the week to have the lowest returns. As in Chang et al. (1993), the significant lowest returns are obtained for Canada, Hong-Kong, France, Switzerland and the United Kingdom. No significant effect is found for Australia, Germany, and the USA. 17 However, our results are somewhat conflicting when the seasonal compo-
15 Under the null hypothesis f,. < 0.2. As it was suggested by an anonymous referee, an easy way of showing the presence of outliers is to rank daily returns and examine the top and the bottom deciles. If seasonality is persistent, Monday (or Tuesday) returns are expected to figure heavily in the bottom decile while Wednesday (or Friday) are expected to be in the top decile. Computations made for four indexes FRA, JAP, US(SP) and UK confirm this conjecture. To save place, these results are not presented here. They are available upon request. 16 Extreme returns are more frequent on Mondays (see Jansen and De Vries, 1991; Longin, 1993). 17 Japan is not examined for this period because the number of trading days per week changed at the end of 1988.
M. Dubois, P. Lout,et / Journal of Banking & Finance 20 (1996) 1463-1484
1481
nent approach is used. We show that Monday is not the unique day of the week to exhibit a high frequency of bad components. Tuesday is also significant for four countries: Canada, Hong-Kong, France and Switzerland. We agree with their suggestion that the day-of-the-week effect is not due to European institutions because market organisations across countries have nothing in common. Moreover, two other countries out of Europe are concerned.
4. Conclusion This paper examined the international day-of-the-week effect for nine markets. Standard statistical procedures (parametric and non-parametric) were used in conjunction with a moving average approach. We find negative returns on Monday, which are compensated by abnormal positive returns on Wednesday, with the exception of Japan and Australia. These markets exhibit a significant negative effect on Tuesday over the whole sample period, but Monday returns are negative for the last sub-period since Tokyo has been closed on Saturday and Sunday. Non-parametric tests do not lead to the same conclusions. The Monday component is more likely to be negative for the US and UK markets. However, it turns to be the Tuesday component for the rest of the world. The FRA index is specific in the sense that Monday returns are computed as the difference in Log between Tuesday and Monday opening prices. Information arriving after Monday closing and before Tuesday opening are incorporated into Monday returns in place of Tuesday returns for other countries. Correlations between indexes tend to confirm the conjecture that the observed lag is possibly due to non-synchronous trading. Settlement procedures distort returns so that international comparisons are quite difficult to undertake. The London Stock Exchange and the Paris Bourse are forward markets. After correcting for these effects, Monday coefficients are negative for the whole period and our conclusions remain unchanged. The shape of contemporaneous and one-day lag correlations due to non-synchronous trading may be explained, at least partly, by the dominant-satellite market relationship. However, the day-of-the-week effect remains unexplained for at least the US and UK markets. Low trading volumes on Monday (see Theobald and Price (1984) for the United Kingdom, Louvet and Taramasco (1991) and Hamon and Jacquillat (1992) for France) suggest that institutional investors are less active on this day. In this case, the day-of-the-week effect is related to the inelasticity of the demand. Recently, Abraham and Ikenberry (1994) explored this hypothesis for the US market and found that individual investors exert a selling pressure on Monday and to some extent on Tuesday. Given our results (see Table 7), this explanation is attractive and has to be tested at an international level. This is left for further research.
1482
M. Dubois, P. Lou~et / Journal of Banking & Finance 20 (1996) 1463-1484
,o
¢q
t"q
t"N
¢'q
r,~, t"q ' ~
"4"
~-J
t"q t"q t'q
¢'q
"~
~c5 t'~lt~t'xl
(",1 t"q
t",l
"T'T~ .....,
'-.D r',-. r',-- ~
',D ~t3 ~,O ~t~
+
+
d~d~
z
+
+
+~ -
-
g, ° ,1
<
e-;
.<
~
=+
N~0 2 "o
~
~
~.~ -
~_~.~
r¢3
- -
~,
~.~
0
M. Dubois, P. LouL,et/ Journal of Banking & Finance 20 (1996) 1463-1484
1483
Acknowledgements W e t h a n k O. T a r a m a s c o f o r c o m p u t e r a s s i s t a n c e . F i n a n c i a l a s s i s t a n c e f r o m t h e F o n d s N a t i o n a l d e la R e c h e r c h e gratefully acknowledged.
Scientifique Suisse (grant n°12-30998.91)
is
References Abraham, A. and D. Ikenberry, 1994, The individual investor and the weekend effect. Journal of Financial and Quantitative Analysis 29, 263-277. Admati+ A. and P. Pfleiderer, 1989, Divide and conquer: A theory ot intraday and day-of-the-week mean effects, Review of Financial Studies 2, 189-223. Anderson, T.W., 1984, An introduction to multivariate statistical analysis, Publications in Probability and Mathematical Statistics, 2 ed. (Wiley, New York) Barone, E., 1990, The Italian stock market efficiency and calendar anomalies, Journal of Banking and Finance 14, 483-510. Baillie, R. and R. DeGennaro, 1989, The impact of delivery terms on stock return volatility, Journal of Financial Services Research 3, 55-76. Board, J.L. and C.M. Sutcliffe, 1988, The weekend effect in the UK stock market returns, Journal of Business Finance and Accounting 15, 199-213. Bollerslev, T., R. Chou and K. Kroner, 1992, ARCH modelling in finance: A review of the theory and empirical evidence, Journal of Econometrics 52, 5-59. Cadsby, C., 1989, Canadian calendar anomalies and the capital asset pricing model, In: R. Guimaraes, B. Kingsman and S. Taylor, eds., Reappraisal of the efficiency of financial markets, NATO ASI Series, Vol. F54 (Springer Verlag, Berlin) 199-226. Chang, E., M. Pinegar and R. Ravichandran, 1993, International evidence on the robustness of the day-of-the-week effect, Journal of Financial and Quantitative Analysis 28, 497-514. Condoyanni, L., S. McLeay and J. O'Hanlon, 1989, An investigation of daily seasonality in the Greek equity market, In: R. Guimaraes, B. Kingsman and S. Taylor, eds., Reappraisal of the efficiency of financial markets, NATO ASI Series, Vol. F54 (Springer Verlag, Berlin) 229-257. Connolly, R., 1989, An examination of the robustness of the week-end effect, Journal of Financial and Quantitative Analysis 24, 133-156. Connolly, R., 1991, A posterior odds analysis of the week-end effect, Journal of Econometrics 49. 51-104. Cross, F., 1973, Bebaviour of stock prices on Fridays and Mondays, Financial Analysts Journal 29, 67-69. Fama, E., 1965, The behavior of stock market prices, Journal of Business 38, 34-105. Fama, E. and K. French, 1988, Permanent and temporary components of stock prices, Journal of Political Economy 96, 246-273. French, K., 1980, Stock returns and the week-end effect, Journal of Financial Economics 8, 55 7l). French, K. and R. Roll, 1986, Stock return variance: The arrival of information and the reaction of traders, Journal of Financial Economics 17, 5-26. Gibbons, M. and P. Hess, 1981, Day-of-the-week effects and asset returns, Journal of Business 54, 579-596. Hamon, J. and B. Jacquillat, 1990, Saisonnalitfis dans la semaine et la s~ance ~ la bourse de Paris, CEREG working paper 9007 (Universit6 Paris-Dauphine, Paris). Hamon, J. and B. Jacquillat, 1992, Le march~ fran~ais des actions, Etudes empiriques 1977-1991 (Presses Universitaire de France, Paris).
1484
M. Dubois, P. Louvet / Journal of Banking & Finance 20 (1996) 1463-1484
Harris, L., 1986, A transaction data study of weekly and intradaily patterns in stock returns, Journal of Financial Economics 16, 99-117. Jaffe, J. and R. Westerfield, 1985, Patterns in Japanese common stock returns: Day-of-the-week and turn-of-year effects, Journal of Financial and Quantitative Analysis 20, 261-272. Jaffe, J., R. Westerfield and C. Ma, 1989, A twist of the Monday effect in stock prices: Evidence from the US and the foreign stock market, Journal of Banking and Finance 13, 641-650. Jansen, D. and C. De Vries, 1991, On the frequency of large stock returns: Putting booms and busts into perspectives, Review of Economics and Statistics 73, 18-24. Jennergren, P. and B. Sorensen, 1989, Random walks and anomalies on the Copenhagen Stock Exchange in the 1890's, In: R. Guimaraes, B. Kingsman and S. Taylor, eds., Reappraisal of the efficiency of financial markets, NATO ASI Series, Vol. F54 (Springer Verlag, Berlin) 261-282. Keim, D., 1987, Daily returns and size-related premiums: One more time, Journal of Portfolio Management, Winter, 41-47. Keim, D. and R. Stambaugh, 1984, A further investigation of the week-end effect in stock returns, Journal of Finance 39, 819-840. Lakonishok, J. and M. Levi, 1982, Week-end effects on stock returns: A note, Journal of Finance 37, 883-889. Lakonishok, J. and E. Maberly, 1990, The week-end effect: trading patterns of individual and institutional investors, Journal of Finance 45, 231-243. Lakonishok, J. and S. Smidt, 1988, Are seasonal anomalies real? A ninety year perspective, Review of Financial Studies 1,403-425. Lee, I., R. Pettit and M. Swankoski, 1990, Daily return relationships among Asian stock markets, Journal of Business Finance and Accounting 17, 265-284. Levi, M., 1988, Week-end effects in the stock market returns: An overview, In: E. Dimson, ed., Stock market anomalies (Cambridge University Press, Cambridge) 43-51. Longin, F., 1993, Booms and crashes application of the extreme value theory to the US stock market, IFA working paper 179 (London Business School, London). Louvet, P. and O. Taramasco, 1990, L'effect 'jour de la semaine ~ la Bourse de Paris': Une approche par les moyennes mobiles, Finance 11, 83-109. Louver, P. and O. Taramasco, 1991, L'effet 'jour de la semaine 5 la Bourse de Paris': Un effet transactionnel, Journal de la Soci&6 Statistique de Paris 133, no. 2, 50-76. Merton, R., 1990, Continuous-time finance (Basil Blackwell, Oxford). Penman, S., 1987, The distribution of earnings news over time and seasonalities in aggregate stock returns, Journal of Financial Economics 18, 199-228. Peterson, D., 1990, Stock return seasonalities and earnings information, Journal of Financial and Quantitative Analysis 25, 187-201. Porter, D., 1990, The probability of a trade at the ask: An examination of interday and intraday behavior, Journal of Financial and Quantitative Analysis 27, 209-228. Poterba, J. and L. Summers, 1988, Mean reversion in stock prices: Evidence and implicatons, Journal of Financial Economics 22, 27-44. Rogalski, R., 1984, New findings regarding day-of-the-week returns over trading and non-trading periods, Journal of Finance 39, 1603-1614. Santesmeses, M., 1986, An investigation of the Spanish stock market seasonalities, Journal of Business Finance and Accounting 13, 267-276. Smirlock, M. and L. Starks, 1986, Day-of-the-week and intraday effects in stock returns, Journal of Financial Economics 17, 197-210. Solnik, B. and L. Bousquet, 1990, Day-of-the-week effect on the Paris Bourse, Journal of Banking and Finance 14, 461-468. Theobald, M. and V. Price, 1984, Seasonality estimation in thin markets, Journal of Finance 39, 377-392. Yadav, P. and Pope, P., 1992, Intraweek and intraday seasonalities in market risk premia: Cash and futures, Journal of Banking and Finance 16, 233-270.