ACADEMY OF ECONOMIC STUDIES DOCTORAL SCHOOL OF FINANCE AND BANKING DISSERTATION PAPER The day of the week effect on stock market return and volatility: International evidence Student: Sorin Stoica Supervisor: Professor Moisa Altar BUCHAREST, JULY 2008

Contents 1.Introduction 2. Literature review 3.Data and Model description 4.Empirical results 5.Conclusions 6.Bibliography

1. Introduction A market is efficient if prices fully and instantaneously reflect all available information and no profit opportunities are left unexploited. In an efficient situation, new information is unpredictable, so stock market returns cannot be predicted and there is therefore no trading pattern, which an investor can follow in order to make unexpected profits. *(The efficient-market hypothesis was developed by Professor Eugene Fama at the University of Chicago Graduate School of Business as an academic concept of study through his published Ph.D. thesis in the early 1960s at the same school) The day of the week effect refers to the existence of a pattern of stock returns during the week, a seasonal «anomaly», which contradicts the «Efficient Market Hypothesis» *

2. Literature review Cross (1973) and French (1980) were the first to observe a specific seasonality in stock returns during the week, that was named «Day of the Week Effect». According to this phenomenon, the average stock market return on the last trading day of the week (Friday) is positive and is the highest across all days of the week and the return on the first trading day of the week (Monday) is negative and is the lowest across the same period. French (1987) examine the relationship between stock prices and volatility and report that unexpected stock market returns are negatively related to the unexpected changes in volatility. Campbell and Hentschel (1992) report similar results and argue that an increase in stock market volatility raises the required rate of return on common stocks and hence lowers stock prices. Glosten (1993) and Nelson (1991), on the other hand, report that positive unanticipated returns reduce conditional volatility whereas negative unanticipated returns increase conditional volatility. Chen (2001) examine the day of the week effect in the stock markets of China for the recent years. The conclusion is consistent with the efficient market;

Kiymaz and Berument (2003) investigate the day of the week effect on the volatility and return of major stock markets (German, Japan, US, Canada and United Kingdom) for the time period from 1998 to Their findings are consistent with the day of the week effect both for returns and volatility. Patev (2003) examine the presence of the day-of-the-week effect anomaly in the Central European stock markets during the period 1997 to Their results indicated that the Czech and Romanian markets have significant negative Monday returns while the Slovenian market has significant positive Wednesday returns and has non-significant negative returns on Fridays. The Polish and Slovak markets have no day-of-the week effect anomaly. Cabello and Ortiz (2004) investigate the day of the week and month of the year effect for Latin America stock markets. The paper supports the existence of calendar anomalies. They find the lowest and negative returns on Mondays and high returns on Fridays. Hui (2005) examines the day of the week effect at Asian-Pacific markets during the period of Asian financial crisis and also tests the presence of weekend effect in developed stock markets of US and Japan. The paper supports no evidence of the day of the week effect in capital markets for the recent years, in both Asian Pacific and US capital markets.

3. Data and Model description 3.1 Data Period ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Downtrend1/10/ /3/2003 1/10/ /3/2003 1/10/ /3/2003 1/10/ /3/2003 1/10/ /3/2003 1/10/ /3/2003 (390) Uptrend31/3/ /6/ /3/ /6/ /3/ /6/ /3/ /6/ /3/ /6/ /3/ /6/2008 (1365) The data set used in this study consists of six European Index values obtained from Bloomberg. For econometric reasons, for working days that the stock markets did not open and of course the indices did not change, the value of the previous day has been used. The returns used in each of the time series are computed as follows: Notes: Numbers in parentheses depict observations used in each period

3.3 Model description represents returns on a selected index are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t is a measure of the risk premium are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t the GARCH term the ARCH term The first GARCH-M (1, 1) model investigate the day of the week effect in stock return and it consists of the following two equations: represents returns on a selected index are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t is a measure of the risk premium are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t the GARCH term the ARCH term In both models the Wednesday dummy variable is excluded to avoid the dummy variable trap The mean equation allows for an autoregression of order 1 in the mean of returns since most of the returns data exhibit a small but significant first order autocorrelation the mean

represents returns on a selected index are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t is a measure of the risk premium are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t the GARCH term the ARCH term The second GARCH-M (1, 1) model investigate the day of the week effect in both stock return and volatility and it consists of the following two equations: represents returns on a selected index are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t are the dummy variables for Monday, Tuesday, Thursday, and Friday at time t the GARCH term the ARCH term The quasi-maximum likelihood estimation (QMLE) method introduced by Bollerslev and Wooldridge (1992) is used to estimate parameters The mean equation allows for an autoregression of order 1 in the mean of returns since most of the returns data exhibit a small but significant first order autocorrelation the mean

Notes: p values are reported in brackets; ** denotes significance at the 1% level of significance The return series are nonsymmetric and leptokurtic compared to the normal distribution According to Augmented Dickey - Fuller test all return series are stationary Whole period (Returns) ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Mean E E E-05 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Observations 1754 ADF (returns) ** [0] ** [0] ** [0] ** [0] ** [0] ** [0] 4. Empirical results 4.1 Testing the series

Down trend (Returns) ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Observations 389 ADF Test ** [0] ** [0] ** [0] ** [0] ** [0] ** [0] Notes: p values are reported in brackets; ** denotes significance at the 1% level of significance The return series are nonsymmetric and leptokurtic compared to the normal distribution According to Augmented Dickey - Fuller test all return series are stationary

Notes: p values are reported in brackets; ** denotes significance at the 1% level of significance The return series are nonsymmetric and leptokurtic compared to the normal distribution According to Augmented Dickey - Fuller test all return series are stationary Up trend (Returns) ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Observations 1365 ADF (returns) ** [0] ** [0] ** [0] ** [0] ** [0] ** [0]

Whole period MeanMOTUWETHFRF-statProb BET CAC DAX FTSE MADRID MIBTEL E E Whole period Std. Dev.MOTUWETHFRLeveneProb BET CAC DAX FTSE MADRID MIBTEL The descriptive statistics for each day of the week The F-Stat refers to the F-Statistic of the Equality of means test. If p-value < 0.050, then the hypothesis of equal means is rejected The L-Value refers to the Levene Value of the Equality of variance test. If p-value < 0.050, then the hypothesis of equal variances is rejected

Down Trend MeanMOTUWETHFRF-statProb BET CAC DAX FTSE MADRID MIBTEL Down trend Std. Dev.MOTUWETHFRLeveneProb BET CAC DAX FTSE MADRID MIBTEL The F-Stat refers to the F-Statistic of the Equality of means test. If p-value < 0.050, then the hypothesis of equal means is rejected The L-Value refers to the Levene Value of the Equality of variance test. If p-value < 0.050, then the hypothesis of equal variances is rejected

Up trend MeanMOTUWETHFRF-statProb BET CAC DAX FTSE MADRID MIBTEL Up trend MeanMOTUWETHFRLeveneProb BET CAC DAX FTSE MADRID MIBTEL The F-Stat refers to the F-Statistic of the Equality of means test. If p-value < 0.050, then the hypothesis of equal means is rejected The L-Value refers to the Levene Value of the Equality of variance test. If p-value < 0.050, then the hypothesis of equal variances is rejected

Whole Period Return ecuation ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Constant-0,00030, , , , ,001476* ( )( )( )( )( )( ) Monday-0, , , , , ,001503* ( )( )( )( )( )( ) Tuesday0, , , , , ,001336* ( )( )( )( )( )( ) Thursday3,06E-051,58E-04-3,39E-057,46E-04-1,83E-04-8,49E-04 ( )( )( )( )( )( ) Friday6,61E-051,05E-04-2,41E-049,46E-04-2,99E-04-6,52E-04 ( )( )( )( )( )( ) Return(t-1)5,53E-02-6,60E-02**-4,93E-02*-8,99E-02**-3,58E-02-5,85E-02** ( )( )( )( )( )( ) Risk0, , , , , , ( )( )( )( )( )( ) 4.2 The Results of the regressions Notes: Standard errors are reported in parentheses ; ** denotes significance at the 1% level of significance The day of the week effects in returns for whole period

Volatility ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Mean3,01E-05**1,93E-06**2,07E-06*1,46E-06**2,14E-06**1,15E-06* ( )( )( )( )( )( ) ARCH0,177732**0,090911**0,089462**0,089707**0,097743**0,073798** ( )( )( )( )( )( ) GARCH0,721278**0,897015**0,899845**0,899368**0,887776**0,916383** ( )( )( )( )( )( ) Whole Period Ljung– Box Q statistics ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL 52,54678,39858,23896,10783,75315,7284 [0.769][0.136][0.144][0.296][0.585][0.334] 107,255712,55911,5046,97646,62379,4085 [0.509][0.128][0.175][0.539][0.578][0.309] 1524,40917,95417,33612,6319,49812,492 [0.058][0.265][0.299][0.631][0.192][0.642] 2031,86524,68122,08820,8623,09617,725 [0.045][0.214][0.336][0.405][0.284][0.606] 2537,9925,99524,72728,88125,63218,442 [0.046][0.408][0.478][0.269][0.427][0.823]

Whole Period ARCH- LM test ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL 50, , , ,699284, , [ ][ ][ ][ ][ ][ ] 100, , , , , , [ ][0.5062][ ][ ][ ][ ] 150, , , , , , [ ][ ][ ][ ][ ][ ] 200, , , , , , [ ][ ][ ][ ][ ][ ] 250, , , , , , [ ][ ][ ][ ][ ][ ] The conditional variances are always positive and are not explosive in our samples. According to the Ljung–Box Q statistics we can not reject the null hypothesis that the residuals are not autocorrelated. The ARCH-LM test does not indicate the presence of a significant ARCH effect in any of the sampled markets except MADRID.

Whole period Return ecuation ROMANIA BET 10 FRANCE CAC 40 GERMAN Y DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Constant-0,000780, , , , , ( )( )( )( )( )( ) Monday-0, , ,000250, , ,00151* ( )( )( )( )( )( ) Tuesday0, , ,00090, , ,00131* ( )( )( )( )( )( ) Thursday2,38E-052,15E-04-3,07E-057,93E-04-2,94E-04-8,24E-04 ( )( )( )( )( )( ) Friday2,48E-041,85E-04-1,75E-049,84E-04-2,73E-04-6,65E-04 ( )( )( )( )( )( ) Return(t-1)6,06E-02-6,63E-02**-5,00E-02*-8,89E-02**-3,62E-02-6,06E-02** ( )( )( )( )( )( ) Risk0, , , , , ,00411 ( )( )( )( )( )( ) The day of the week effects in returns and volatilities for whole period * Statistically significant at the 5% level. ** Statistically significant at the 1% level.

Whole Period Volatility ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL Mean-9,87E-064,92E-061,32E-05-2,95E-071,13E-051,42E-06 ( )( )( )( )( )( ) ARCH0,210745**0,093075**0,087229**0,089355**0,094191**0,072936** ( )( )( )( )( )( ) GARCH0,662341**0,896094**0,901471**0,900508**0,892052**0,915054** ( )( )( )( )( )( ) Monday7,72E-05-1,42E-05-1,48E-05-4,13E-06-1,35E-051,25E-05 ( )( )( )( )( )( ) Tuesday1,00E-04-9,59E-08-1,69E-058,89E-06-1,42E-05-1,51E-05 ( )( )( )( )( )( ) Thursday3,89E-059,30E-07-1,73E-053,18E-06-2,06E-055,68E-06 ( )( )( )( )( )( ) Friday2,48E-05-2,07E-06-6,38E-065,01E-072,03E-06-3,61E-06 ( )( )( )( )( )( ) The conditional variances are always positive and are not explosive in our samples.

Whole Period Q stat ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL 53,02368,50648,79646,06074,04585,5976 [0.696][0.13][0.117][0.3][0.543][0.347] 108,279312,75912,0847,0246,81989,1098 [0.407][0.12][0.148][0.534][0.556][0.333] 1525,04318,23818,17812,55120,13512,019 [0.049][0.25][0.253][0.637][0.167][0.678] 2031,95225,25522,88120,82123,84617,078 [0.044][0.192][0.295][0.408][0.249][0.648] 2538,2126,57825,59428,61926,71417,848 [0.044][0.377][0.429][0.28][0.37][0.849] The Ljung–Box Q statistics for the normalized residuals at 5-, 10-, 15-, 20-, and 25-day lags None of these coefficients are statistically significant. Therefore, we cannot reject the null hypothesis that the residuals are not autocorrelated.

Whole Period ARCH- LM test ROMANIA BET 10 FRANCE CAC 40 GERMANY DAX 30 UK FTSE 100 SPAIN MADRID ITALY MIBTEL 50, , , , , , [ ][ ][ ][ ][ ][ ] 100, ,882570, , , , [ ][ ][ ][ ][ ][ ] 150, , , , , , [ ][ ][ ][ ][ ][ ] 200, , , , , , [ ][ ][ ][ ][ ][ ] 250, , , , , , [ ][ ][ ][ ][ ][ ] Engle’s ARCH-LM for whole period Engle’s ARCH-LM test does not indicate the presence of a significant ARCH effect in any of the sampled markets except MADRID. This finding indicates that the standardized residual terms have constant variances and do not exhibit autocorrelation except MADRID.

The results for downtrend period The day of the week effects in returns for downtrend period There is no coefficient of dummy’s variables statistically significant. Thus, we don’t find the evidence for the existence of the classical day of the week effect. The estimated coefficients for BET 10, MADRID and MIBTEL are lowest on Mondays but they are statistically insignificant. The coefficient of the conditional standard deviation of the return equation (risk) is positive for BET10 (0,347303), CAC 40 (0,115031), DAX 30 (0,058048), FTSE 100 (0,178102), MADRID (0,224529) and MIBTEL (0,218751). However, the estimated coefficients are not statistically significant. The conditional variances are always positive and are not explosive in our samples. According to the Ljung–Box Q statistics we cannot reject the null hypothesis that the residuals are not autocorrelated. The ARCH-LM test does not indicate the presence of a significant ARCH effect in any of the sampled markets. This finding indicates that the standardized residual terms have constant variances and do not exhibit autocorrelation.

The day of the week effects in returns and volatilities for downtrend period The estimated coefficients for dummy’s variables in volatility equation are not statistically significant except the ones from Monday and Tuesday for BET10, the one from Tuesday for DAX 40 and the one from Friday for FTSE 100 who are statistically significant. Not only we don’t find strong evidence for the existence of the classical day of the week effect, but there is no any obvious pattern in coefficient’s significances. The coefficients of the conditional standard deviation of the return equation (risk) are positive for all markets. However, the estimated coefficients are not statistically significant except BET10. The conditional variances are always positive and are not explosive in our samples According to the Ljung–Box Q statistics we cannot reject the null hypothesis that the residuals are not autocorrelated. The ARCH-LM test does not indicate the presence of a significant ARCH effect in any of the sampled markets

The results for uptrend period The day of the week effects in returns for uptrend period The estimated coefficient of the Mondays’ dummy variable for MIBTEL (-0,001503) is negative and statistically significant at the 1% level, suggesting that Mondays’ returns are smaller than those of Wednesdays. Also the estimated coefficient of the Tuesdays’ dummy variables for MIBTEL (-0,001316) is negative and statistically significant at the 1% level, suggesting that Tuesdays’ returns are smaller than those of Wednesdays. All the rest of dummy’s coefficients are not statistically significant. The coefficient of the conditional standard deviation of the return equation (risk) is positive for CAC 40 (0,09187), DAX 30 (0,158252), MADRID (0,108172), MIBTEL (0,012795) and it is negative for BET10 (-0,08354), FTSE 100 (-0,005897), However, the estimated coefficients are not statistically significant. There is no classical version of the day of the week effect and no substantial day effect for the developed stock markets. The conditional variances are always positive and are not explosive in our samples. According to the Ljung–Box Q statistics we cannot reject the null hypothesis that the residuals are not autocorrelated. ARCH-LM test does not indicate the presence of a significant ARCH effect in any of the sampled markets except MADRID.

The estimated coefficients for dummy’s variables in volatility equation are not statistically significant. Thus, there is no evidence of a day of the week in volatility. The coefficients of the conditional standard deviation of the return equation (risk) are positive for all markets except BET10 (-0,071027) and FTSE100 (-0,008442) who are negative. However, the estimated coefficients are not statistically significant. The estimated coefficient of the Mondays’ dummy variable in the return equation for MIBTEL (-0,00143) is negative and statistically significant at the 1% level, suggesting that Mondays’ returns are smaller than those of Wednesdays. Also the estimated coefficient of the Tuesdays’ dummy variables in the return equation for MIBTEL (-0,00129) is negative and statistically significant at the 1% level, suggesting that Tuesdays’ returns are smaller than those of Wednesdays. The conditional variances are always positive and are not explosive in our samples. According to the Ljung–Box Q statistics we cannot reject the null hypothesis that the residuals are not autocorrelated. ARCH-LM test does not indicate the presence of a significant ARCH effect in any of the sampled markets except MADRID. The day of the week effects in returns and volatilities for uptrend period

5. The Conclusions Finally, the conclusion of this study is that the phenomenon of the «Day of the Week Effect» seems to be weaker than it was in previous decades as a result of investor’s behavior. Investors are more mature, well educated, with more professional attitude, characteristics that help stock markets to become more efficient. The phenomenon of the «Day of the Week Effect» seems to disappears from the developed stock markets and not to have a specific pattern in general. Nowadays, the stock markets are more liquid than ever and seem to be more efficient that the previous decades because of the easiest capital transmission, the technological changes and the changes in the stock market microstructure. So, it is logical for investors to react more mature, something that induces less inefficient results.

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