On the robustness of week-day effect to error distributional assumption: International evidence

Accepted Manuscript On the Robustness of Week-day Effect to Error Distributional Assumption: International Evidence Sabri Boubaker, Naceur Essaddam, Duc Khuong Nguyen, Samir Saadi PII: DOI: Reference:

S1042-4431(16)30155-X http://dx.doi.org/10.1016/j.intfin.2016.11.003 INTFIN 902

To appear in:

Journal of International Financial Markets, Institutions & Money

Received Date: Revised Date: Accepted Date:

8 January 2015 30 August 2016 3 November 2016

Please cite this article as: S. Boubaker, N. Essaddam, D.K. Nguyen, S. Saadi, On the Robustness of Week-day Effect to Error Distributional Assumption: International Evidence, Journal of International Financial Markets, Institutions & Money (2016), doi: http://dx.doi.org/10.1016/j.intfin.2016.11.003

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On the Robustness of Week-day Effect to Error Distributional Assumption: International Evidence

Sabri Boubakera,b, Naceur Essaddamc, Duc Khuong Nguyend,*, Samir Saadie a

Champagne School of Management, Groupe ESC Troyes, Troyes, France b IRG, Université Paris Est, Paris, France c Royal Military College of Canada, Kingston, Ontario, Canada d IPAG Business School, Paris, France e University of Ottawa, Ottawa, Ontario, Canada

Abstract We examine the robustness of the week-day effect both in the mean and conditional volatility using 51 stock market indices while controlling for volatility clustering and allowing three specifications of the error distributions. We show that the evidence of week-day effect in mean and conditional volatility is sensitive to the choice of the underlying distribution. Our results are not limited to the classic setting of examining week-day effect but also extend to settings that account for conditional and unconditional market risk. The evidence of “wandering weekday” effect is found to vary with the error distributional assumptions. Moreover, we document that the 2008 financial crisis lessened the week-day effect in the mean but at the same time magnified such effect in the conditional volatility. Our findings, which are robust to the presence of outliers and to different model specifications and to the presence of structural breaks, suggest that empirical regularity in financial series may be econometrically fragile in the sense of Leamer (1985). It also corroborates the calls that followed the recent financial crisis about the hazard of using models that are based on unrealistic assumptions. JEL classifications: G10, G12, C10, C22 Keywords: Error Distributional Assumptions; Week-day effect; Wandering week-day effect; Volatility; GARCH.

_________________________ *

Corresponding author: 184 Boulevard Saint-Germain, 75006 Paris, France. Phone: +33 (0)1 53 63 36 00 - Fax: +33 (0)1 45 44 40 46 Email addresses: S. Boubaker ([email protected]), N. Essaddam ([email protected]), D.K. Nguyen ([email protected]), S. Saadi ([email protected])

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On the Robustness of Week-day Effect to Error Distributional Assumption: International Evidence

Abstract We examine the robustness of the week-day effect both in the mean and conditional volatility using 51 stock market indices while controlling for volatility clustering and using three specifications of the error distributions. We show that the evidence of week-day effect in mean and conditional volatility is sensitive to the choice of the underlying distribution. Our results are not limited to the classic setting of examining week-day effect but also extend to settings that account for conditional and unconditional market risk. We extend our analysis to “wandering week-day” effect, and find that it also varies with the error distributional assumptions. Moreover, we document that the 2008 financial crisis lessened the week-day effect in the mean but at the same time magnified such effect in the conditional volatility. Our findings are robust to the presence of outliers, to different model specifications, and to the presence of structural breaks. Our study suggests that empirical regularity in financial series may be econometrically fragile in the sense of Leamer (1985). It also corroborates the calls that followed the recent financial crisis about the hazard of using models that are based on unrealistic assumptions.

JEL classifications: G10, G12, C10, C22 Keywords: Week-day effect, Error Distributional Assumptions;; Wandering week-day effect; Volatility; GARCH.

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“Dogmas and doctrines holding that markets worked well and that they were self-correcting once again came to predominate. This time, the theories were more sophisticated, but the underlying assumptions were equally irrelevant. These ideas helped shaped the intellectual milieu which gave rise to the flawed policies that, in turn, gave rise to the crisis.” Joseph E. Stiglitz (2009)

I. Introduction In his opening plenary keynote address at the American Economic Association 2010 Meeting, Nobel Prize Laureate Joseph Stiglitz asserts that the recent financial crisis serves as a call for better allocation of financial economics research efforts in which models are built on more realistic assumptions.1 In the same vein, Colander et al. (2010) and Eichengreen (2008), among others, are critical of market participants for applying the results of academic research without appropriate reservation.2 Academics are also blamed for not warning users of the limitations associated with its preferred models. In particular, academics are criticized for excessive reliance on models, which, besides being too complex, ignore the key elements driving outcomes in realworld markets (e.g., Roldán, 2009; Willett, 2009). Although traditional econometric methods (e.g., bootstrap and asymptotic distribution theory) deal with estimator uncertainty relative to the population parameter via the sampling error, rigorous model evaluation remains the key issue (e.g., Hendry and Mizon, 1978, 1990, 2000). Failure to deal adequately with the latter issue may result in optimistic but spurious goodness-of-fit statistics as the sampling error is reduced by data perturbations or re-weightings, but the statistical inferences may be fragile. In this paper, we consider the possibility that the reason numerous studies detect empirical regularity in financial time series may be explained as 1

Stiglitz, J.E. (2010). Homoeconomicus: The Impact of the Economic Crisis on Economic Theory. American Economic Association Annual Meeting, Atlanta, Georgia. 2 Among the assumptions that lead to devastating outcomes are (1) the belief that home prices will never fall, (2) investors have homogenous beliefs (i.e. representative agent) and rational expectations, (3) banks and other financial institutions do not play a critical role and hence are excluded from models, and (4) financial markets tend towards equilibrium.

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an artifact of econometric fragility in the sense of Leamer (1983, 1985). Leamer (1985) asserts: “Because no prior distribution can be taken to be an exact representation of opinion, a global sensitivity analysis is carried out to determine which inferences are fragile and which are sturdy”. By implication, the objective of a global sensitivity analysis is to quantify the estimator uncertainty that is associated with model specification. To establish whether changes in model specification (e.g., error distribution) influence the robustness of estimator inferences, Leamer (1985) recommends that the researcher selects alternative assumptions and identifies the corresponding interval of inferences: “Conclusions (would be) judged sturdy only if the neighborhood of assumptions is wide enough to be credible and the corresponding interval of inferences is narrow enough to be useful” (Leamer, 1985). Leamer’s recommendation that the researcher should exhaust all attempts “to combat the arbitrariness associated with the choice of prior distribution” (Leamer, 1986) takes on additional significance when conducting data-driven empirical research. This is an important point in light of the assertion by Colander et al. (2010) that “the current approach of using pre-selected models is problematic and we recommend a more data-driven methodology.” To assess whether empirical regularities observed in financial time series are a consequence of econometric fragility, we confine our research to the so-called ‘week-day’ effect in stock markets. The week-day effect, also known as day-of-the-week effect, is one of the most investigated calendar regularity in financial time series. Another reason for our choice of the week-day phenomena is that we choose to focus on the potential ‘fragility of inferences’ (in over 50 stock markets) and not on examining all empirical regularities. Future research can extend our analyses to other market anomalies and examine whether our main findings can be generalized to

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other settings. Another reason for our choice is that early literature reports numerous attempts to proffer explanations for the week-day effect in stock markets,3 however, none of the suggested explanations can consistently and fully explain the empirical results. Moreover, as noted by Hansen et al. (2005) these theoretical explanations have only been developed after the empirical “discovery” of the anomalies. Accordingly, the main objective of this paper is to examine the robustness of the weekday effect to error distributional assumptions in both return and conditional variance for 51 stock market indices. We examine our main testable hypothesis within the classic week-day approach as well as within the context of risk-adjusted returns (Brooks and Persand, 2001), time-varying risk-adjusted returns (Brooks and Persand, 2001), and the recent “wandering week-day” effect (Doyle and Chen, 2009). We further augment our analysis by examining whether the sensitivity of week-day effect to error distributional assumptions depends on the period of the study and on financial market turmoil. To account for autocorrelation, non-normality and volatility clustering in our data, we use an AR(k)-GARCH(p,q) type model under normal as well as two other error distributions known to suitably fit financial time series: Student-t distribution, and Generalized error distribution (GED).4 Thus, our main testable hypothesis is that evidence of week-day effect is robust to error distributional assumption in both return and conditional variance. Moreover, we explicitly test whether the GARCH error terms are independent and identically distributed (i.i.d hereafter) using the BDS test, a powerful test originally designed by Brock et al. (1996). This 3

These explanations include the release of adverse information over the weekend, thin trading, settlement procedures, specialists’ strategies in response to informed traders, speculative short sales, and measurement errors in stock prices (e.g., Wang et al. 1997; Michayluk and Sanger, 2006). 4 The Student’s t and GED are heavy-tailed distributions with positive excess kurtosis relative to a normal distribution, which has excess kurtosis of 0. Excess kurtosis is 6/(df - 4), where df = degrees of freedom, for the Student’s t-distribution. For the GED, the value of the shape parameter determines the thickness of the tail. When this parameter has a value less than 2, the distribution is thick-tailed. The extant literature guides the appropriate choice of these distributions as error terms. For example, Nelson (1991) popularized GARCH models with GED errors. Brenner et al. (1996) show that Student-t distribution better characterizes short-term interest rates.

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assumption is of great importance for an appropriate examination of the week-day effects that is, to the best of our knowledge, ignored in extant studies. Indeed, a rejection of i.i.d assumption indicates the existence of a hidden unexplained structure in the residual terms and if not accounted for, may spuriously increase the statistical significance of dummy variables ‘days’ leading to an erroneous conclusion. The present study makes several important contributions. First, it adds to the recent and growing literature questioning the economic significance, the persistence and even the existence, of the week-day effect. In fact, in a recent review of week-day effect literature, Philpot and Peterson (2011, p. 814) conclude that although early work was consistent in documenting such calendar anomaly in the U.S. as well as in other foreign markets, “over the years, as researchers developed new datasets and statistical methods, the reported effects began to reverse, migrate to other days, and even vanish.” For instance, Hansen, Lunde, and Nason, (2005) examine several calendar effect using a powerful test-statistic that limits data-mining bias, and find that evidence of calendar effect in equity returns has diminished overtime except in small-cap stock indices. Galai et al. (2008) add that most of the traditional week-day effect in the U.S. equity market is the result of presence of outliers in the data. Markedly, the documented fragility of week-day effect evidence is not limited to equity markets. For example, Aggrawal, Mehdian and Perry (2003) look at the week-day effect in daily returns of six futures contracts, and find no consistent evidence of such regularity. Yamori and Kurihara (2004) examine the daily returns of 29 foreign exchange rates and report evidence of the week-day effect in the 1980s for some currencies, which however disappears for almost all currencies in the 1990s. Bouges et al. (2009) show that there is no evidence of week-day effect in returns on American depository receipts over the period 1998-2004.

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Second, the current work answers the aforementioned calls for a better allocation of financial economics research efforts where analyses are built on more realistic assumptions (e.g., Colander et al. 2009; Eichengreen, 2008; Stiglitz, 2009). In fact, we show that the cautions raised by, among others, Roldán, (2009), Willett (2009), Stiglitz (2009), and Colander et al. (2010) are also applicable to week-day effect. It should be noted however that our main finding does not necessarily imply that week-day effect is spurious or it is the result of data mining, but it calls for a more in-depth and careful examination of calendar effects in the sense of Leamer (1985). Third, the present study examines whether the approaches, proposed by Brooks and Persand (2001) as well as Doyle and Chen (2009), in examining week-day effect are sensitive to the choice of the underlying distribution. Brooks and Persand (2001) put forward an approach that augments the classic examination of week-day effect by introducing market risk factor that can also vary across the days of the week. More recently, Doyle and Chen (2009) propose the “wandering week-day” effect where systematically high or low returns depend on the choice of subsample considered. Doyle and Chen (2009, p. 1389) note that “all stock markets may be in a permanent state of flux so that different researchers looking at the same series may variously report the standard effect, an absence of the effect, a reversal, or a totally new configuration, depending upon the haphazard sampling of the time period they analyze.” The present study is the first to show that week-day effect accounting for unconditional risk (Brooks and Persand, 2001), week-day effect accounting for conditional risk (Basher and Sadorsky, 2006), and wandering week-day effect (Doyle and Chen, 2009) are also sensitive to the choice of the underlying distribution. Fourth, our findings have implications not only for the empirical literature on market anomalies but also for investment strategies designed around them. For instance, showing that

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evidence of week-day effect is sensitive to underlying distribution may explain why the bulk of the post-2003 studies reject the utility of designing trading rules based on the week-day effect (Philpot and Peterson, 2011). The rest of this paper proceeds as follows. Section II describes the data and presents some initial tests for the week-day effect. Section III considers a GARCH specification with three distributions (i.e. normal, Student-t, and Generalized error) and tests for the week-day effect for the mean and variance under each of the three distributions. Section IV presents and discusses the empirical results. Section V concludes the paper. II. Data and Some Preliminary Statistical Tests Our data consist of the daily returns for the main stock market indices of 51 countries. Data are gathered from DataStream. The daily rate of change is computed as the natural logarithmic first difference of the daily closing index price: r t = ln S t − ln S t − 1

where St denotes the daily index price, at time t. Panel A of Table 1 provides descriptive statistics for aggregate daily changes. The columns on the far right of Panel A give the starting date and number of observations of each return series. All of the 51 series end on December 31, 2012. The Bulgarian series has the fewest data point (i.e. 3195) as it starts on October 3, 2000. The longest time series is shared by 17 out of 51 indices and includes 10,435 observations starting on January 03, 1973. Panel B of Table 1 gives descriptive statistics for daily changes of each day of the week. Over the 51 return series, the lowest returns occur generally on Monday or Tuesday, while the highest returns occur largely on Friday. The overall results from Table 1 suggest that the daily return differs within week days. This said, however, more rigorous analysis should be undertaken before making any assertion.

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We now employ some common tests to further validate the initial observations from Table 1. We start by testing for the homogeneity or constancy of variances across the days of a week using Levine test, which is robust to departure from normality. Table 2 presents the results from applying the Levine test. The test statistic is significantly different from zero for 38 out of the 51 series, hence rejecting the null hypothesis that the variance is the same across different days for those series. The results suggest employing Games & Howell’s test for those 38 series and Bonferroni test to the remaining 13 returns series. To save space, we do not report the results of Games & Howell’s test and Bonferroni test. The test statistics reject the null hypothesis that the mean is constant over the week for 29 out of the 51 returns series, suggesting the existence of the week-day effect in those series. The results for the remaining indices provide weak, if any, support for the week-day anomaly. Both sub-sets include series from developed and developing countries. It is noteworthy, however, that Games & Howell’s and Bonferroni tests assume that the series are normally distributed and do not control for autocorrelation neither for heteroscedasticity. - Tables 1 and 2 about here – III. Testing for Week-day Effect in Mean and Variance under Different Error Distributional Regimes Results from previous section could be spurious because of the possibility of the series being auto-correlated and the fact that they are heteroskedastic. The test for constancy of mean across time is best examined in a regression context. First, we follow the standard model used in previous studies and then we correct for non-normality and volatility clustering. Using the standard OLS methodology, we run a regression of the daily rates of change on a constant term

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and 5 dummy variables, one for each week-day. To deal with linear dependency, we include one lag value of the daily rates of change to the regression equation: 5

rt = α + ν rt −1 + ∑ β j Day j + ε 1t

(1)

j=2

where r is the daily rate of change at time t, α is a constant term, and Friday is the base condition t

for the Day dummies. Recall that Levine test rejects the assumption of homogeneity of variance for most of the series. Accordingly, we estimate Equation (1) with GARCH (p,q) type model including models such as PGARCH, GARCH-M and FIEGARCH. We choose the best GARCH (p,q) that fits the data series on the basis of the AIC criterion. To examine whether volatility changes across day of the week, we introduce the week-day dummies into the conditional variance equation of the selected GARCH type model: 5

σ t2 = η + λ (L ) ω t2 + θ (L ) σ t2 + ∑ β j Day

j

(2)

j=2

where σ is the conditionally variance, η is a constant term, and Friday is the base condition for 2 t

the Day dummies. Equations 1 and 2 are estimated jointly. If all the coefficients for dummy variables in Equation 1 are insignificantly different from zero, then we reject the week-day effect assumption in mean. Similarly, if all the coefficients for dummy variables in Equation 2 are insignificantly different from zero, then we reject the week-day effect assumption in volatility. To capture the fat tails in our data, we use two distributions that are known to better fit financial time series: Student-t error distribution and the Generalized error distribution (GED) proposed by Nelson (1991).5 Nelson (1991) recommends GED to capture the fat tails usually

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If a random variable Xt has a GED with mean zero and unit variance, the probability density function of Xt is given by: f (X t ) =

υ

− (1 2 ) X t λ

υ

λ ⋅ 2 (υ +1) / υ Γ (1 υ )

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observed in the distribution of financial time series. Estimations of GARCH (p, q) with normal, Student-t, and GED will be reported to assess the impact of the choice of the error distribution on evidence of week-day effect in stock market returns and volatility, and then find which distribution should be considered when analysing such market anomaly. As stated above, the present paper also examines the sensitivity of the approaches proposed by Brooks and Persand (2001) and Doyle and Chen (2009) to the choice of error distribution assumptions: (a) Introducing mark-risk factor Brooks and Persand (2001) suggest taking into account the effect of equity market risk on seasonality. To do so, we add to Equation (1) a market risk factor proxied by the excess returns on the MSCI World stock market index (i.e. MRt): 5

rt = α + ν rt −1 + ∑ β j Day j + δ MR MR t + ε 2 t

(3)

j=2

where Friday is the base condition for the Day dummies. (b) Introducing market-risk factor that varies across week-days In an alternative approach, we follow Brooks and Persand (2001) and allow for risk to vary across the days of the week:6 5

5

j =2

j =2

rt = α +νrt −1 + ∑ β j Day j + ∑δ MR (Day j MRt ) + ε 3t

(4)

where Γ( ) is the gamma function, υ is a positive parameter governing the thickness of the tails of the distribution λ is a constant given by  2 −2

λ= 

Γ (1 υ )   Γ (3 υ )  υ

1 2

Note that for υ =2 and constant λ =1, the GED is the standard normal distribution. For more details about the generalized error distribution, see Hamilton (1994). 6 It is noteworthy that Module (3) and Module (4) are unconditional models where market-risk factor is assumed to have a symmetric impact on the return of each of the market indices considered in our study. In unreported analyses, and to consider the possible asymmetric effect of market-risk factor, we have repeated our analysis using two conditional models following Module (4) an Module (5) of Basher and Sadorksy (2006), and find that our conclusion still hold.

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where Friday is the base condition for the Day dummies. (c) Wandering week-day effect

Finally, we examine whether evidence of wandering week-day effect, if any, is sensitive to the choice of error distribution. To do so, we follow Dayle and Chen (2009) and estimate the following model: 5

n

j=2

i =1

5

n

rt = α + νrt −1 + ∑ β j Day j + ∑θ i Yeari + ∑∑ λij Yeari × Day j + ε 4t

(5)

j = 2 i =1

where n is the number of year in each return series, Friday is the base condition for the Day dummies, and the starting year (of each series in our sample) is the base condition for the Year dummies. IV. Empirical Results

A variety of volatility models has been proposed in the literature. Particular classes of models that demonstrate great flexibility in capturing multiplicative dependence in a series are called ARCH type models, originally introduced by Engle (1982). Based on the AIC criterion, GARCH (1,1) outperforms, in numerous attempts (not reported), other ARCH type models such as PGARCH, GARCH-M, FIEGARCH as well as bilinear models. This is consistent with the results of Hansen and Lunde (2005) who compare 330 ARCH-type models in terms of their ability to describe the conditional variance and find that a GARCH (1,1) outperforms all tested models. Hence, we run four specifications: (1) OLS model, (2) AR(1)-GARCH (1,1) with error terms being normally distributed, (3) AR(1)-GARCH (1,1) with error terms following Student-t distribution, (4) AR(1)-GARCH (1,1) with error terms distributed following GED. For each model specification, we use a battery of diagnostic tests aimed to examine normality assumption (Jarque-Bera test), homogeneity of variance assumption (Engle’s (1982)

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Lagrange Multiplier), and whether the model has captured nonlinear dependencies (BDS test of Brock et al., 1996).7 It is not surprising that the standard OLS model fails to capture non-linearity in about 95% of the 51 returns series as the BDS test strongly rejects the i.i.d assumption at 1% significance level for those series. The AR(1)-GARCH(1,1) with error terms distributed as Student-t or GED, however, seems to be well suited to model the stock returns series. In fact, BDS test fails to reject the null hypothesis that the standardized residuals are i.i.d random variables at 1 percent degree of significance. Thus, each model captures all the non-linearity in the data used, and the conditional heteroscedasticity is the cause of the non-linearity structure. To conserve space, we only report the analyses for ten illustrative countries from different regions in the world, namely Canada, Germany, Malaysia, Mexico, Philippines, Romania, Singapore, the U.K., the U.S., and Venezuela. As stated above, we consider the normal distribution as well as the student-t, and GED to capture fat tails in the data and see whether week-day effect in both mean and conditional volatility, if any, are sensitive to the particular specification of the underlying distribution. Our core results, presented in Table 3, can be summarized as follows: First, the results from GARCH models are different from those of standard OLS estimation. This suggests that it is important to control for volatility clustering when testing for week-day effect. More importantly, only 3 series (i.e. Denmark, Finland and Korea) out of the 51 stock market indices did not exhibit any sensitivity in the week-day effect to the error distribution assumption, either in mean or in conditional volatility. About 61% (31 out of 51) of the series exhibit sensitivity to error distribution in mean returns, and nearly 81% (41 out of 51) display sensitivity in conditional volatility. We also find that 49% (25 out of 51) of the series show sensitivity in both mean and conditional volatility, including country index series of

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The diagnostic test results are not reported to conserve space, but are available from the authors upon request.

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Australia, Brazil, Bulgaria, China, Colombia, Germany, Indonesia, and Sweden. Of the 51 countries return indices, return series from Russia, South Africa and the United Kingdom do not exhibit any sensitivity to error distribution in conditional volatility. In the case of South Africa, for instance, there is strong evidence of week-day effect in both mean and conditional volatility, but only the dummy variables in the mean equation seem to be affected by choice of the error distribution assumption. It is noteworthy that evidence for sensitivity of week-day effect to the distribution of error terms is not related to whether a stock market is in a developed or developing country. Similarly, we did not find any week-day effect pattern that is associated with a country’s degree of economic development. If we consider for instance the two countries with the world’s most developed stock markets (the United States and the United Kingdom), we report strong evidence for week-day effect in mean for the United Kingdom but weak, if any, evidence for the United States. The U.S. return series exhibits, however, strong evidence of week-day effect in the conditional volatility, which is not the case for the U.K. series. Given that evidence of week-day effect depends on the distributional assumptions, the question one should ask is which of the three distributions should be considered. To answer this question, we examine which of the three GARCH models best fit our data. The decision is made based on the AIC criterion, and this for all the 51 market indices. We can see from Table 3 that, taken together, the GARCH (1,1) with a GED is the best specification. The second best model seems to be the one with Student-t, and not surprisingly, in the last position is the GARCH (1,1) with normal distribution. The least we can derive from this result is that examining week-day effect assuming a normal distribution is not appropriate. -Table 3 about here –

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Brooks and Persand (2001) suggest controlling for the effect of equity market risk when examining seasonality. To do so, we estimate Equation (3) which contains a market risk factor proxied by the excess returns on the MSCI World stock market index. We also estimate Equation (4) where this market risk is allowed to vary across the weekdays. The results from estimating Equations (3) and (4) jointly with Equation (2), reported in Table 4 and Table 5 respectively, show that when accounting for time-invariant market risk, evidence of week-day effect continues to be sensitive to the choice of distribution of error terms in both mean and conditional volatility for about 88% (45 out of 51) of the series considered in this study.8 When we allow for risk to vary across the days of the week, the percentage increases to 96% (49 out of 51). Our results remain qualitatively similar when we use excess returns on S&P500 index instead of excess return on MSCI World stock market index as a proxy for equity market risk.9 More importantly, Our main conclusion continues to hold when we consider week-day effect that accounts for the conditional risk as in Basher and Sadorsky (2006).10 In an interesting development in the week-day effect literature, Doyle and Chen (2009) propose the “wandering week-day” effect where systematically high or low returns depend on the choice of subsample considered. To examine the sensitivity of “wandering week-day” effect to the error distributions we estimate Equation (5) jointly with Equation (2), where we consider normal distribution as well as the Student-t, and GED. Table 6 presents our empirical results where, to conserve space, we again report only the estimate of the coefficients associated with the day dummies for ten illustrative countries from different regions in the world. In support to

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To conserve space, we only present the estimate of the coefficients associated with the day dummies for ten illustrative countries from different regions in the world. 9 As in Chan and Woo (2012), our choice of S&P500 index is based on evidence that US equity market is highly correlated with those of many other countries around the world (e.g. Agrawal and Tandon, 1994; Clare et al., 1998). The results with S&P500 index can be made entirely available upon request. 10 We are referring in particular to Model (4) and Model (5) in Basher and Sadorsky (2006), page 622.

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our main hypothesis, we find that evidence of “wandering week-day” effect tends to be sensitive to the choice of error distribution assumption, and that this sensitivity is found in about 82% (42 out of 51) of the series. -Tables 4, 5 and 6 about here – Besides the sensitivity to error distribution, we also examine how major financial turmoil can affect the week-day effect. To do so, we consider the recent international financial crisis of 2008 by repeating the same analysis over 5 years before (from 01/01/2003 to 31/12/2007) and 5 years after this crisis (from 01/01/2008 to 31/12/2012). This setting will also allow us to see whether evidence of week-day effect is sensitive to the sub-period of analysis. The results for the 2008 crisis, reported in Table 7, show several interesting observations. First, evidence of weekday effect tends to diminish substantially and even disappear during the period following the recent financial crisis. More precisely, the week-day effect observed in the pre-crisis period for Romania, Thailand, the United Kingdom and the United States disappear in the post-period crisis period. Second, contrary to the week-day effect for the mean, the evidence of week-day effect in the conditional variance accentuates after the 2008 crisis, this being reported for virtually all the series in our study. The results from Table 7 suggest that major financial crisis tend to reduce the week-day effect in the mean but at the same time magnify such effect in conditional volatility. These interesting findings are new to the literature and require further analyses to understand why financial turmoil has such an effect on daily returns. Though we leave this to future work, we argue that the increased market efficiency following stock market crashes may explain the weaker week-day effect, and the excess volatility of stock prices following a crisis is likely to be behind the stronger week-day effect in conditional volatility.

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Finally, to see whether our results are due to the presence of extreme values in our return data, we repeat the above analysis while excluding the returns with higher absolute values and thus cutting down the sample by 1% and 3%. The results, not reported here, are qualitatively similar to those obtained with the full sample. Consequently, we may conclude that our findings are not influenced by outliers. Moreover, due to space limitation, we have only discussed results relative to estimating Equation (1) jointly with Equation (2), however same conclusion holds when we account for market risk (Equations 3 and 4) and when we examine “wandering weekday” effect (Equation 5). - Table 7 about here As an additional analysis, we have repeated our analyses based on sub-periods that are constructed around structural break dates. Accordingly, we first identify structural breaks in the return series of our dataset and the dates of their occurrence by using the sequential testing approach proposed by Bai (1997) and Bai and Perron (1998). In particular, we consider an AR(1) model with a constant term for each return series, which also allows for serial correlation in the errors. The investigation of the structural instability then consists of testing the alternative that the AR(1) coefficient varies through time against the null hypothesis of stability (or no structural break). This test is carried out by applying the sequential testing procedure of l+1 versus l breakpoints over the sample period while allowing for heterogeneous error distributions across breaks. Following Bai and Perron (1998), we initially allow up to 5 breakpoints in the model and impose a trimming percentage of 15% to restrict the minimum number of observations per regimes.11 Table 8 presents the test results for return series that exhibit structural break(s), where we report the number of breaks and the exact date of each identified break. Out of 51 index 11

Our results remain intact when we restrict the trimming percentage to 10% and 5%. In addition, they are consistent with the global Bai-Perron test for m unknown breaks based on the information criteria (AIC and BIC).

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series in our sample, 16 show evidence of one or more structural breaks. In particular, we find breaks in the series that belongs to the following countries: Austria, Bulgaria, Chile, Colombia, Finland, Greece, Indonesia, Ireland, Japan, Luxemburg, Philippine, Portugal, Slovenia, Sri Lanka, Sweden, and Venezuela. It is clear that most of series with breaks are emerging markets series, which can be explained by their market openings policy or specific events. As far as our study is concerned, we repeat all our analyses by estimating Equations (1), (3), (4) and (5) jointly with Equation (2) for each of the 16 series for sub-periods defined by the structural break dates reported in Table 8. The results, not reported here but available upon request, show that evidence of week-day effect continues to be sensitive to the choice of error distribution assumptions, in the classic week-day effect setting, as well as when we account for risk-adjusted returns (Brooks and Persand, 2001) and unconditional risk (Basher and Sadorsky, 2006). Our conclusion also holds when “wandering week-day” effect of Doyle and Chen (2009) is examined over sub-periods based on identified structural breaks. - Table 8 about here Taken together, our core results suggest that evidence week-day effect in mean and conditional distribution are (1) sensitive to the choice of error distribution, (2) are influenced by financial turmoil, and (3) tend to change over time (i.e. sensitive to the period of study). Our findings cast doubt on the various arguments which have been put forwards to date in the literature to explain the week-day effect, and open a new window of research to dig into the real cause of this market anomaly and other calendar anomalies such as holiday effect (Chong et al., 2005), turn-of-the-month effect (Agrawal and Tandon, 1994), turn-of-the-year effect (Agrawal and Tandon, 1994), and January effect (Keims, 1983).

18

V. Conclusion

This paper provides a thorough and comprehensive analysis of the week-day effect in returns and conditional volatility for an international sample of 51 stock market indices. Our main objective is to scrutinize the overwhelming support for what is considered a calendar anomaly since most of the previous studies stand on assumptions which are strongly rejected for financial time series. Our preliminary analyses, based on the standard method used in earlier studies, assuming both homoscedasticity and normality, provide evidence of the week-day effect. However, when volatility clustering is taken into account and allowing for normal as well as two other types of error distribution that are known to suitably portray financial time series (Student-t and GED), we find that the week-day effect in both mean and conditional volatility is not robust to the choice of error distribution, and that it varies with the period of study. Our findings are not limited to the classic week-day effect but also extend to the week-day effect that controls for conditional and unconditional market risk as well as for the presence of outliers and the presence of structural breaks. It is also worth noting that the evidence of “wandering week-day” effect varies with the error distributional assumptions and that the 2008 crisis is found to lessen the week-day effect in the mean but amplify it in the conditional volatility. Overall, our results suggest that the various theoretical explanations put forward in the literature to explain the week-day effect may not be valid and therefore call for new economic explanations of this market anomaly. As noted by Hansen, Lunde, and Nason (2005) the actual theoretical explanations have been suggested only subsequent to the empirical “discovery” of the anomalies. Moreover, our results serve as a warning that the error distributional assumptions are critical to the correct identification of the empirical regularities in financial data, because the latter may be an artifact of model inadequacy and statistical inferences which could lead to

19

econometrically fragile findings in the sense of Leamer (1985). It is important to note that the current work does not aim to provide recommendations on the most appropriate model or/and error distribution to use when examining week-day effect in each stock market. Rather, it shows that the cautions raised by, among others, Roldán, (2009), Willett (2009), Stiglitz (2009), and Colander et al. (2010) are also applicable to week-day effect. Finally, our results do not necessarily imply that the week-day effect is a spurious or the result of data mining, but call for a more in-depth and careful examination of this calendar effect.

20

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25

Table 1. Descriptive Statistics This table provides the descriptive statistics of daily returns for the main stock market indices of 51 countries. The sample is gathered from DataStream and ends on December 31, 2012. The starting dates are specified in columns 2 and 9. The Daily return is computed as the natural logarithmic first difference of the daily closing price of each stock index.

Panel A: Aggregate Returns N

Mean

Std.Dev

Skewness

ARGENTINA AUSTRALIA AUSTRIA BELGIUM BRAZIL BULGARIA CANADA CHILE

Starting Date 05/01/1988 02/01/1973 02/01/1973 02/01/1973 05/07/1994 03/10/2000 03/01/1973 04/07/1989

6520 10435 10435 10435 4825 3195 10434 6130

0.0022 0.0003 0.0003 0.0003 0.0006 0.0007 0.0003 0.0006

0.0289 0.0107 0.0096 0.0095 0.0164 0.0187 0.0092 0.0093

2.01 -1.46 -0.20 -0.17 0.42 0.25 -0.56 0.21

35.37 36.70 13.44 10.55 12.19 58.69 13.09 6.00

CHINAA COLOMBIA CYPRUS CZECH REP.

27/08/1991 03/01/1992 24/12/1992 10/11/1993

5570 5477 5223 4994

0.0008 0.0006 -0.0001 0.0003

0.0231 0.0103 0.0182 0.0142

2.09 0.08 2.33 1.32

DENMARK FINLAND FRANCE GERMANY

03/01/1973 28/03/1988 03/01/1973 03/01/1973

10435 6461 10435 10435

0.0004 0.0004 0.0003 0.0003

0.0108 0.0176 0.0119 0.0106

GREECE HONGKONG HUNGARY INDIA

05/01/1988 03/01/1973 24/06/1991 02/01/1990

6520 10435 5616 6000

0.0004 0.0005 0.0005 0.0007

INDONESIA IRELAND ITALY JAPAN

03/04/1990 03/01/1973 03/01/1973 03/01/1973

5935 10435 10435 10435

KOREA LUXEMBURG

10/09/1987 03/01/1992

6603 5477

Country

N

Mean

Std.Dev

Skewness

Kurtosis

MALAYSIA MEXICO NETHERLAND NEWZEALAND NORWAY PAKISTAN PERU PHILIPPINE

Starting Date 03/01/1986 05/01/1988 02/01/1973 05/01/1988 03/01/1980 17/07/1992 04/01/1994 10/09/1987

7042 6520 10435 6520 8608 5337 4955 6603

0.0004 0.0010 0.0003 0.0002 0.0004 0.0004 0.0005 0.0006

0.0136 0.0145 0.0110 0.0093 0.0146 0.0172 0.0112 0.0136

0.63 0.41 -0.17 -0.05 -0.39 0.11 0.10 0.63

41.75 8.81 7.62 15.22 9.47 16.77 10.89 11.91

29.20 15.14 45.78 31.26

POLAND PORTUGAL ROMANIA RUSSIA

02/03/1994 03/01/1990 06/12/1996 28/01/1998

4914 5999 4192 3894

0.0002 0.0001 0.0009 0.0013

0.0174 0.0101 0.0232 0.0279

0.00 -0.12 3.06 0.79

6.56 10.25 85.83 14.16

0.64 -0.08 -0.12 0.02

36.26 7.32 5.45 13.80

SINGAPORE SLOVENIA SOUTH AFRI. SPAIN

03/01/1973 01/01/1999 03/01/1973 03/03/1987

10435 3652 10435 6740

0.0002 0.0001 0.0006 0.0003

0.0133 0.0095 0.0128 0.0125

-0.28 -0.27 -0.44 -0.02

20.63 9.85 8.30 6.15

0.0176 0.0174 0.0164 0.0169

0.26 -0.80 -0.15 0.62

6.61 24.08 10.38 24.32

SRILANKA SWEDEN SWITZ TAIWAN

02/06/1987 05/01/1982 03/01/1973 10/09/1987

6675 8085 10435 6603

0.0006 0.0005 0.0002 0.0003

0.0131 0.0141 0.0093 0.0186

0.76 0.13 -0.51 0.14

72.34 5.00 12.63 3.11

0.0005 0.0003 0.0003 0.0002

0.0208 0.0119 0.0136 0.0111

5.95 -0.26 -0.09 -0.19

273.67 12.46 4.92 11.39

THAILAND TURKEY UK US

05/01/1987 05/01/1988 03/01/1973 03/01/1973

6781 6520 10436 10434

0.0005 0.0018 0.0003 0.0003

0.0177 0.0255 0.0109 0.0107

0.29 0.25 -0.06 -0.54

7.40 4.50 7.92 16.69

0.0004 0.0004

0.0183 0.0101

0.20 0.14

4.58 7.52

VENEZUELA

03/01/1990

5999

0.0013

0.0199

2.09

37.06

Kurtosis

Country

26

Panel B: Mean Returns by Week-days Country

Monday

Tuesday

Wednesday

Thursday

Friday

Country

Monday

Tuesday

Wednesday

Thursday

Friday

ARGENTINA

-0.0005

0.0020

0.0048

0.0024

0.0021

MALAYSIA

-0.0010

0.0003

0.0011

0.0007

0.0011

AUSTRALIA

-0.0001

-0.0004

0.0006

0.0009

0.0005

MEXICO

-0.0004

0.0008

0.0013

0.0018

0.0015

AUSTRIA

0.0003

0.0001

0.0002

0.0002

0.0005

NETHERLAND

-0.0001

0.0004

0.0003

0.0004

0.0004

BELGIUM

0.0000

-0.0001

0.0003

0.0006

0.0005

NEWZEALAND

-0.0007

0.0001

0.0005

0.0006

0.0003

BRAZIL

-0.0008

0.0006

0.0014

0.0001

0.0019

NORWAY

0.0000

-0.0002

0.0002

0.0011

0.0010

BULGARIA

-0.0002

0.0004

0.0012

0.0011

0.0011

PAKISTAN

-0.0006

0.0000

0.0018

0.0005

0.0004

CANADA

-0.0005

0.0003

0.0005

0.0004

0.0008

PHILIPPINE

0.0003

-0.0006

0.0009

0.0012

0.0011

CHILE

-0.0008

0.0004

0.0009

0.0008

0.0018

PERU

0.0003

0.0003

0.0000

0.0002

0.0016

CHINAA

0.0005

-0.0003

0.0021

-0.0002

0.0019

POLAND

0.0009

-0.0005

-0.0003

0.0008

0.0004

COLOMBIA

0.0002

0.0001

0.0009

0.0004

0.0015

PORTUGAL

0.0000

-0.0001

0.0000

0.0001

0.0005

CYPRUS

-0.0002

-0.0012

0.0004

0.0000

0.0004

ROMANIA

-0.0002

0.0003

0.0015

0.0017

0.0011

CZECH REP.

0.0005

0.0001

0.0001

0.0010

0.0000

RUSSIA

0.0015

0.0009

-0.0004

0.0013

0.0029

DENMARK

0.0005

0.0003

0.0004

0.0004

0.0004

SINGAPORE

-0.0010

-0.0003

0.0010

0.0007

0.0009

FINLAND

0.0000

-0.0004

-0.0001

0.0010

0.0013

SLOVENIA

-0.0013

-0.0007

0.0002

0.0009

0.0015

FRANCE

-0.0006

0.0002

0.0005

0.0008

0.0009

SOUTH AFRI.

-0.0001

0.0003

0.0015

0.0010

0.0003

GERMANY

0.0000

0.0002

0.0004

0.0002

0.0004

SPAIN

0.0001

0.0004

-0.0002

0.0002

0.0008

GREECE

-0.0007

-0.0004

0.0004

0.0007

0.0019

SRILANKA

-0.0005

-0.0007

0.0008

0.0009

0.0023

HUNGARY

0.0012

0.0003

0.0003

0.0001

0.0006

SWEDEN

0.0005

0.0001

0.0004

0.0007

0.0009

HONGKONG

-0.0004

-0.0001

0.0013

0.0002

0.0014

SWITZ

-0.0004

0.0001

0.0005

0.0004

0.0007

INDIA

0.0010

0.0005

0.0011

0.0000

0.0006

TAIWAN

0.0001

-0.0004

0.0008

0.0001

0.0010

INDONESIA

-0.0003

-0.0001

0.0006

0.0006

0.0015

THAILAND

-0.0014

-0.0002

0.0014

0.0003

0.0026

IRELAND

0.0001

0.0002

0.0005

0.0003

0.0006

TURKEY

-0.0001

0.0008

0.0020

0.0027

0.0034

ITALY

-0.0007

0.0000

0.0006

0.0008

0.0010

UK

-0.0006

0.0007

0.0004

0.0003

0.0009

JAPAN

-0.0003

-0.0003

0.0007

0.0005

0.0003

US

-0.0002

0.0005

0.0006

0.0003

0.0003

VENEZUELA

-0.0007

0.0003

0.0020

0.0010

0.0037

KOREA

0.0000

0.0003

0.0009

0.0003

0.0005

LUXEMBURG

0.0002

0.0000

0.0007

0.0000

0.0010

27

Table 2. Test of Equality of Variance: Levine test This table presents the results from applying the Levine test to the daily returns of 51 stock market indices. Country ARGENTINA AUSTRALIA AUSTRIA BELGIUM BRAZIL BULGARIA CANADA CHILE CHINAA COLOMBIA CYPRUS CZECHREP DENMARK FINLAND FRANCE GERMANY GREECE HUNGARY HONGKONG INDIA INDONESIA IRELAND ITALY JAPAN KOREA LUXEMBURG

Levene Statistic 4.209 2.135 5.216 .678 2.003 1.649 5.032 2.357 11.487 7.624 1.271 1.664 .938 2.970 2.251 4.671 12.424 .392 11.919 4.731 .632 4.767 14.473 5.118 18.873 3.933

df1

df2

p-value

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

6515 10430 10430 10430 4820 3190 10429 6125 5565 5472 5218 4989 10430 6456 10430 10430 6515 5611 10430 5995 5930 10430 10430 10430 6598 5472

.002 .074 .000 .607 .091 .159 .000 .051 .000 .000 .279 .155 .440 .018 .061 .001 .000 .814 .000 .001 .640 .001 .000 .000 .000 .003

Country MALAYSIA MEXICO NETHERLAND NEWZEALAN NORWAY PAKISTAN PHILIPPINE PERU POLAND PORTUGAL ROMANIA RUSSIA SINGAPORE SLOVENIA SOUTHAFRI SPAIN SRILANKA SWEDEN SWITZ TAIWAN THAILAND TURKEY UK US VENEZUELA

Levene Statistic 3.842 4.377 5.592 1.917 2.825 10.584 3.189 1.007 5.098 1.954 3.331 1.487 14.852 2.336 6.971 3.041 .222 4.934 10.157 18.536 5.269 10.320 1.207 2.553 .592

df1

df2

p-value

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

7037 6515 10430 6515 8603 5332 6598 4950 4909 5994 4187 3889 10430 3647 10430 6735 6670 8080 10430 6598 6776 6515 10431 10429 5994

.004 .002 .000 .105 .023 .000 .013 .402 .000 .099 .010 .203 .000 .053 .000 .016 .926 .001 .000 .000 .000 .000 .306 .037 .669

28

Table 3. Introducing Dummy Variables into the Mean Equation as well as Conditional Variance Equation 2 This table presents the results of estimating AR(1)- GARCH (1,1), where rt and σ t are returns and conditional variance, respectively

σ t2

rt Model Ols Normal CANADA Student t GED Ols

MALAYSIA

Normal Student t GED Ols Normal

PHILIPPINE

Student t GED Ols Normal

SINGAPORE Student t GED

Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value Coef. P-value

Mon. -.001 0.000 -.001 0.000 -.001 0.000 -0.001 0.000 -.002 0.000 -.001 0.000 -.001 0.000 -.001 0.001 -.001 0.140 -.001 0.021 -.001 0.006 -.001 0.072 -.002 0.000 -.002 0.000 -.001 0.000 -.001 0.000

Tues. -.001 0.071 0.000 0.056 0.000 0.158 0.000 0.092 -.001 0.182 0.000 0.098 0.000 0.078 0.000 0.027 -.002 0.003 -.001 0.000 -.001 0.000 -0.001 0.032 -0.001 0.015 -0.001 0.000 -0.001 0.001 -0.001 0.002

Wed. 0.000 0.243 0.000 0.661 0.000 0.423 0.000 0.545 0.000 0.908 0.000 0.667 0.000 0.112 0.000 0.089 0.000 0.803 0.000 0.472 0.000 0.813 0.000 0.164 0.000 0.583 0.000 0.715 0.000 0.903 0.000 0.802

Thur. 0.000 0.077 0.000 0.215 0.000 0.167 0.000 0.137 0.000 0.350 0.000 0.875 0.000 0.657 0.000 0.556 0.000 0.728 0.000 0.647 0.000 0.708 0.000 0.563 0.000 0.584 0.000 0.101 0.000 0.217 0.000 0.377

Mon.

Tues.

Wed.

Thur.

AIC -6.56

0.000 0.000 0.000 0.006 0.000 0.013

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.040 0.000 0.634 0.000 0.842

0.000 0.277 0.000 0.226 0.000 0.286

-6.98 -7.04

GERMANY

-7.04 -5.77

0.000 0.000 0.000 0.001 0.000 0.000

0.000 0.000 0.000 0.044 0.000 0.008

σ t2

rt

0.000 0.000 0.000 0.002 0.000 0.002

0.000 0.010 0.000 0.609 0.000 0.441

-6.44 MEXICO -6.60 -6.59 -5.79

0.000 0.000 0.000 0.001 0.000 0.000

0.000 0.000 0.000 0.009 0.000 0.393

0.000 0.322 0.000 0.114 0.000 0.169

0.000 0.050 0.000 0.006 0.000 0.036

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.064 0.000 0.508 0.000 0.495

0.000 0.018 0.000 0.922 0.000 0.776

-6.03

ROMANIA

-6.16 -6.15 -5.82 -6.28 UK -6.37 -6.36

Mon. 0.000 0.154 0.000 0.089 0.000 0.322 0.000 0.296 -.002 0.002 -.001 0.160 -.001 0.015 -.001 0.112 -.001 0.280 -.001 0.150 -.001 0.012 0.000 0.354 -.002 0.000 -.001 0.000 -.001 0.000 -.001 0.000

Tues. 0.000 0.614 0.000 0.234 0.000 0.918 0.000 0.948 0.000 0.539 0.000 0.778 0.000 0.405 0.000 0.392 -.001 0.593 0.000 0.839 0.000 0.406 0.000 0.574 0.000 0.723 0.000 0.216 0.000 0.267 0.000 0.191

Wed. 0.000 0.906 0.000 0.430 0.000 0.586 0.000 0.402 0.000 0.940 0.001 0.118 0.000 0.327 0.001 0.031 0.001 0.649 0.000 0.429 0.000 0.800 0.000 0.517 -.001 0.080 0.000 0.111 0.000 0.098 0.000 0.089

Thur. 0.000 0.564 0.000 0.371 0.000 0.397 0.000 0.302 0.000 0.446 0.000 0.418 0.000 0.632 0.000 0.416 0.001 0.580 0.000 0.671 0.000 0.670 0.000 0.492 -.001 0.076 -.001 0.008 -.001 0.012 -.001 0.008

Mon.

Tues.

Wed.

Thur.

AIC -6.25

0.000 0.000 0.000 0.930 0.000 0.406

0.000 0.000 0.000 0.238 0.000 0.027

0.000 0.000 0.000 0.120 0.000 0.026

0.000 0.000 0.000 0.004 0.000 0.005

-6.64 -6.70 -6.69 -5.65

0.000 0.000 0.000 0.058 0.000 0.040

0.000 0.000 0.000 0.239 0.000 0.157

0.000 0.000 0.000 0.918 0.000 0.505

0.000 0.768 0.000 0.319 0.000 0.483

-5.99 -6.08 -6.08 -4.70

0.000 0.000 0.000 0.001 0.000 0.000

0.000 0.762 0.000 0.483 0.000 0.496

0.000 0.003 0.000 0.912 0.000 0.666

0.000 0.486 0.000 0.500 0.000 0.584

-5.23 -5.40 -5.41 -6.21

0.000 0.322 0.000 0.997 0.000 0.838

0.000 0.403 0.000 0.525 0.000 0.786

0.000 0.608 0.000 0.775 0.000 0.955

29

0.000 0.366 0.000 0.389 0.000 0.431

-6.55 -6.58 -6.57

σ t2

rt Model Ols Normal USA Student t GED

Coef. P-value Coef. P-value Coef. P-value Coef. P-value

Mon. 0.000 0.139 0.000 0.244 0.000 0.344 0.000 0.189

Tues. 0.000 0.482 0.000 0.970 0.000 0.883 0.000 0.586

Wed. 0.000 0.408 0.000 0.251 0.000 0.290 0.000 0.092

Thur. 0.000 0.958 0.000 0.980 0.000 0.677 0.000 0.719

σ t2

rt

Mon.

Tues.

Wed.

Thur.

AIC -6.23

0.000 0.000 0.000 0.522 0.000 0.160

0.000 0.026 0.000 0.012 0.000 0.028

0.000 0.000 0.000 0.013 0.000 0.004

0.000 0.165 0.000 0.955 0.000 0.706

-6.60 -6.64 -6.65

VENEZUALA

Mon. -.005 0.000 -.002 0.000 -.001 0.015 -.001 0.017

Tues. -.003 0.000 -.001 0.019 0.000 0.039 0.000 0.046

Wed. -.002 0.051 0.000 0.511 0.000 0.145 0.000 0.039

Thur. -.003 0.000 -.002 0.000 0.000 0.114 0.000 0.021

Mon.

Tues.

Wed.

Thur.

AIC -5.02

0.000 0.000 0.000 0.014 0.000 0.003

0.000 0.000 0.000 0.226 0.000 0.007

0.000 0.000 0.000 0.011 0.000 0.016

0.000 0.000 0.000 0.082 0.000 0.000

-5.54

30

-6.10 -6.06

Table 4. Introducing Market-Risk Factor (Brooks and Persand, 2001) This table presents the results of estimating AR(1)-GARCH (1,1) with a market-risk factor. α and η are constant terms; λ and θ are the ARCH and GARCH parameters, respectively.

σ t2

rt Model Normal Coef. P-value Student t Coef. P-value GED Coef. P-value MALAYSIA Normal Coef. P-value Student t Coef. P-value GED Coef. P-value Normal Coef. PHILIPPINE P-value Student t Coef. P-value GED Coef. P-value Normal Coef. P-value Student t Coef. P-value SINGAPORE GED Coef. P-value Normal Coef. P-value Student t Coef. USA P-value GED Coef. P-value CANADA

Mon. -.001 0.203 -.001 0.000 -.001 0.000 -.001 0.000 -.002 0.000 -.001 0.000 -.001 0.120 -.001 0.002 -.001 0.000 -.001 0.000 -.002 0.000 -.001 0.000 0.000 0.904 0.000 0.552 0.000 0.041

Tues. -.001 0.371 0.000 0.024 0.000 0.003 0.000 0.082 -.001 0.000 0.000 0.068 -.001 0.583 -.001 0.000 -.001 0.000 -0.001 0.018 -0.001 0.001 -0.001 0.000 0.000 0.346 0.000 0.934 0.000 0.405

Wed. 0.000 0.473 0.000 0.026 0.000 0.005 0.000 0.764 0.000 0.266 0.000 0.245 -.008 0.006 0.000 0.915 0.000 0.960 0.000 0.939 0.000 0.194 0.000 0.544 0.000 0.159 0.000 0.189 0.000 0.936

Thur. -.001 0.378 0.000 0.024 0.000 0.019 0.000 0.508 -.001 0.005 0.000 0.897 0.000 0.615 0.000 0.956 0.000 0.862 0.000 0.208 -.001 0.006 0.000 0.096 0.000 0.137 0.002 0.020 0.000 0.708

Mon. 0.000 0.000 0.000 0.999 0.000 0.170 0.000 0.000 0.000 0.000 0.000 0.003 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.631

Tues. 0.000 0.000 0.000 0.039 0.000 0.602 0.000 0.000 0.000 0.000 0.000 0.027 0.000 0.000 0.000 0.010 0.000 0.868 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.577 0.000 0.000

σ t2

rt Wed. 0.000 0.050 0.000 0.535 0.000 0.006 0.000 0.000 0.000 0.043 0.000 0.008 0.000 0.446 0.000 0.201 0.000 0.035 0.000 0.000 0.000 0.000 0.000 0.515 0.000 0.000 0.000 0.043 0.000 0.001

Thur. 0.000 0.300 0.000 0.035 0.000 0.337 0.000 0.002 0.000 0.000 0.000 0.448 0.000 0.023 0.000 0.014 0.000 0.038 0.000 0.000 0.000 0.000 0.000 0.440 0.000 0.131 0.000 0.816 0.000 0.000

AIC -7.29

Mon. 0.000 0.852 -7.50 GERMANY 0.000 0.739 -7.49 0.000 0.646 -6.47 -.001 0.001 -6.55 -.001 0.048 MEXICO -6.63 -.001 0.034 -6.03 -.001 0.122 -6.16 ROMANIA -.002 0.012 -6.14 -.001 0.094 -6.46 -.001 0.000 -6.49 -.001 0.000 UK -6.55 -.001 0.000 -7.72 -.004 0.000 -7.78 VENEZUALA -.002 0.000 -7.77 -.002 0.000

Tues. 0.000 0.562 0.000 0.827 -.001 0.006 0.000 0.471 -.001 0.264 0.000 0.259 0.000 0.776 -.001 0.183 0.000 0.479 0.000 0.048 0.000 0.075 0.000 0.139 -.002 0.000 -.001 0.003 -.001 0.000

Wed. 0.000 0.453 0.000 0.893 0.000 0.927 0.001 0.125 0.000 0.575 0.011 0.008 0.000 0.546 0.000 0.670 0.000 0.524 -.001 0.002 -.001 0.007 -.001 0.005 -.001 0.011 -.001 0.322 -.001 0.001

Thur. 0.000 0.392 0.000 0.224 0.002 0.079 0.000 0.255 0.000 0.387 0.000 0.670 0.000 0.915 -.001 0.389 0.000 0.011 -.001 0.003 -.001 0.006 -.001 0.003 -.004 0.000 -.001 0.000 -.001 0.000

Mon. 0.000 0.000 0.000 0.139 0.000 0.062 0.000 0.000 0.000 0.000 0.000 0.581 0.000 0.000 0.000 0.025 0.000 0.001 0.000 0.044 0.000 0.013 0.000 0.966 0.000 0.000 0.000 0.000 0.000 0.000

Tues. 0.000 0.001 0.000 0.699 0.000 0.360 0.000 0.000 0.000 0.000 0.000 0.732 0.000 0.691 0.000 0.002 0.000 0.612 0.000 0.019 0.000 0.038 0.000 0.479 0.000 0.000 0.000 0.000 0.000 0.000

Wed. Thur. 0.000 0.000 0.000 0.065 0.000 0.000 0.022 0.081 0.000 0.000 0.001 0.026 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.967 0.064 0.000 0.000 0.084 0.821 0.000 0.000 0.001 0.001 0.000 0.000 0.911 0.778 0.000 0.000 0.065 0.464 0.000 0.000 0.056 0.510 0.000 0.000 0.498 0.052 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

AIC -6.93 -6.97 -6.97 -6.23 -6.31 -6.36 -5.25 -5.41 -5.43 -7.01 -7.03 -7.03 -5.41 -5.98 -5.89

31

Table 5. Time-varying Market-Risk Factor across Week-days (Brooks and Persand, 2001) 2 This table presents the results of estimating AR(1)-GARCH (1,1) with a market-risk factor where rt and σ t are returns and conditional variance respectively.

σ t2

rt Model Normal Coef. P-value Student t Coef. P-value GED Coef. P-value MALAYSIA Normal Coef. P-value Student t Coef. P-value GED Coef. P-value Normal Coef. PHILIPPINE P-value Student t Coef. P-value GED Coef. P-value Normal Coef. P-value Student t Coef. P-value SINGAPORE GED Coef. P-value Normal Coef. P-value Student t Coef. USA P-value GED Coef. P-value CANADA

Mon. -.001 0.000 -.001 0.000 -.001 0.000 -.001 0.000 -.002 0.000 -.001 0.000 -.001 0.015 -.001 0.001 -.001 0.191 -.002 0.000 -.002 0.000 -.002 0.000 -.001 0.003 -.001 0.118 -.001 0.001

Tues. -.001 0.001 -.001 0.223 -.001 0.000 0.000 0.060 -.001 0.000 0.000 0.060 -.002 0.000 -.002 0.000 -.001 0.014 -.001 0.000 -.001 0.000 -.001 0.000 -.001 0.002 -.001 0.005 -.001 0.000

Wed. -.001 0.001 -.001 0.002 -.001 0.000 0.000 0.951 -.001 0.046 0.000 0.211 0.000 0.350 0.000 0.422 0.000 0.031 0.000 0.172 0.000 0.356 0.000 0.372 -.001 0.000 -.001 0.001 -.001 0.000

Thur. -.001 0.000 -.001 0.001 -.001 0.000 0.000 0.436 -.001 0.000 0.000 0.877 0.000 0.517 0.000 0.555 0.000 0.457 -.001 0.015 -.001 0.036 0.000 0.055 -.001 0.000 -.001 0.000 -.001 0.000

Mon. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.782 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Tues. 0.000 0.000 0.000 0.000 0.000 0.003 0.000 0.000 0.000 0.000 0.000 0.252 0.000 0.000 0.000 0.042 0.000 0.420 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

σ t2

rt Wed. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.010 0.000 0.007 0.000 0.492 0.000 0.137 0.000 0.223 0.000 0.930 0.000 0.608 0.000 0.543 0.000 0.000 0.000 0.000 0.000 0.000

Thur. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.356 0.000 0.037 0.000 0.218 0.000 0.029 0.000 0.277 0.000 0.334 0.000 0.017 0.000 0.000 0.000 0.000 0.000 0.000

AIC -7.36

Mon. 0.000 0.098 -7.39 0.000 GERMANY 0.227 -7.40 -0.001 0.000 -6.47 -0.001 0.041 -6.54 -0.001 0.002 MEXICO -6.62 -0.001 0.021 -6.03 -0.001 0.092 -6.11 ROMANIA -0.002 0.005 -6.15 -0.001 0.183 -6.46 -0.001 0.000 -6.53 -0.001 0.000 UK -6.53 -0.001 0.000 -7.47 -0.002 0.000 -7.50 VENEZUALA -0.001 0.027 -7.51 0.000 0.392

Tues. -.001 0.024 0.000 0.140 -.001 0.000 0.000 0.374 -.001 0.010 -.001 0.086 0.000 0.657 -.001 0.209 0.000 0.824 -.001 0.001 -.001 0.001 0.000 0.123 -.001 0.018 0.000 0.094 0.000 0.569

Wed. 0.000 0.318 0.000 0.235 -.001 0.000 0.000 0.352 0.000 0.990 0.000 0.485 0.000 0.543 0.000 0.604 0.000 0.828 -.001 0.000 -.001 0.000 -.001 0.000 0.000 0.516 0.000 0.587 0.000 0.499

Thur. -.001 0.008 -.001 0.017 -.001 0.000 0.000 0.311 -.001 0.035 0.000 0.695 0.000 0.971 0.000 0.387 0.000 0.513 -.001 0.000 -.001 0.000 -.001 0.000 -.002 0.000 0.000 0.046 0.000 0.482

Mon. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.016 0.000 0.129

Tues. 0.000 0.000 0.000 0.000 0.000 0.003 0.000 0.057 0.000 0.000 0.000 0.455 0.000 0.430 0.000 0.597 0.000 0.659 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.000 0.015

Wed. Thur. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.001 0.000 0.000 0.078 0.906 0.000 0.000 0.726 0.718 0.000 0.000 0.878 0.779 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.038 0.029 0.000 0.000 0.061 0.021

AIC -6.85 -6.89 -6.89 -6.25 -6.30 -6.33 -5.24 -5.42 -5.42 -6.91 -6.93 -6.93 -5.54 -6.09 -6.12

32

Table 6. Wandering Week-day effect This table presents the results of estimating AR(1)-GARCH (1,1) with a market-risk factor where rt and

σ t2

rt Model Normal Coef. P-value Student t Coef. P-value GED Coef. P-value MALAYSIA Normal Coef. P-value Student t Coef. P-value GED Coef. P-value Normal Coef. PHILIPPINE P-value Student t Coef. P-value GED Coef. P-value Normal Coef. P-value Student t Coef. P-value SINGAPORE GED Coef. P-value Normal Coef. P-value Student t Coef. USA P-value GED Coef. P-value CANADA

Mon. 0.000 0.011 0.000 0.171 -.001 0.001 -.001 0.001 -.001 0.000 -.001 0.000 -.001 0.023 -.001 0.006 -.001 0.039 -.001 0.000 -.001 0.000 -.001 0.000 0.000 0.097 0.000 0.463 0.000 0.029

Tues. 0.000 0.247 0.000 0.752 0.000 0.153 0.000 0.140 -.001 0.001 0.000 0.023 -.002 0.000 -.002 0.556 -.001 0.005 -.001 0.002 -.001 0.003 -.001 0.000 0.000 0.308 0.000 0.794 0.000 0.020

Wed. 0.000 0.343 0.000 0.941 0.000 0.226 0.000 0.675 0.000 0.536 0.000 0.132 0.000 0.389 0.000 0.696 0.000 0.305 0.000 0.806 0.000 0.980 0.000 0.937 0.000 0.637 0.000 0.895 0.000 0.021

Thur. 0.000 0.070 0.000 0.383 0.000 0.112 0.000 0.939 -.001 0.034 -.002 0.035 0.000 0.574 0.000 0.925 0.004 0.021 0.000 0.096 0.000 0.121 0.000 0.143 0.000 0.892 0.000 0.265 0.000 0.872

Mon. 0.000 0.000 0.000 0.000 0.000 0.115 0.000 0.000 0.000 0.002 0.000 0.003 0.000 0.000 0.000 0.128 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.174 0.000 0.611 0.001 0.028

Tues. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.012 0.000 0.000 0.000 0.006 0.000 0.421 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.031 0.000 0.210 0.000 0.547

σ t2 are returns and conditional variance, respectively. rt

Wed. 0.000 0.602 0.000 0.000 0.003 0.081 0.000 0.000 0.000 0.565 0.000 0.004 0.000 0.297 0.000 0.023 0.000 0.210 0.000 0.167 0.000 0.887 0.000 0.633 0.000 0.000 0.000 0.006 0.000 0.008

Thur. 0.000 0.080 0.000 0.000 0.000 0.064 0.000 0.004 0.000 0.000 0.000 0.625 0.000 0.024 0.000 0.052 0.000 0.030 0.000 0.005 0.000 0.323 0.000 0.038 0.000 0.000 0.000 0.008 0.000 0.033

AIC -7.31 -7.29 -7.36 -6.47 -6.54 -6.62 -6.04 -6.11 -6.16 -6.45 -6.51 -6.52 -7.16 -7.21 -7.24

σ t2

Mon. Tues. Wed. Thur. Mon. Tues. Wed. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.385 0.881 0.114 0.591 0.000 0.000 0.006 0.000 0.000 0.000 0.000 0.000 0.000 0.000 GERMANY 0.328 0.725 0.286 0.545 0.804 0.162 0.005 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.001 0.002 0.042 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.449 0.834 0.053 0.793 0.003 0.018 0.005 -.001 -.003 0.000 0.000 0.000 0.000 0.000 0.149 0.005 0.299 0.623 0.000 0.009 0.004 MEXICO -0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.025 0.200 0.134 0.692 0.001 0.190 0.039 -.001 0.000 0.001 0.000 0.000 0.000 0.000 0.142 0.940 0.327 0.676 0.000 0.812 0.003 -.002 0.000 0.000 0.000 0.000 0.000 0.000 ROMANIA 0.007 0.431 0.984 0.652 0.003 0.461 0.901 -.001 0.000 0.000 -.001 0.000 0.000 0.000 0.013 0.406 0.822 0.038 0.001 0.563 0.631 -.001 0.000 -.001 -.001 0.000 0.000 0.000 0.000 0.119 0.014 0.002 0.116 0.072 0.500 -.001 0.000 0.000 -.001 0.000 0.000 0.000 0.000 0.231 0.037 0.003 0.742 0.071 0.674 UK -0.001 0.000 -.001 -.001 0.000 0.000 0.000 0.000 0.067 0.311 0.001 0.014 0.032 0.171 -.002 -.001 0.000 -.002 0.000 0.000 0.000 0.000 0.021 0.339 0.000 0.000 0.000 0.000 VENEZUALA -.001 -.001 0.000 -.001 0.000 0.000 0.000 0.001 0.003 0.065 0.006 0.008 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.062 0.174 0.053 0.041 0.000 0.179 0.016

Thur. AIC 0.000 -6.80 0.005 0.000 -6.86 0.000 0.000 -6.82 0.000 0.000 -6.21 0.368 0.000 -6.26 0.000 0.000 -6.29 0.775 0.000 -5.23 0.456 0.000 -5.43 0.562 0.000 -5.43 0.008 0.000 -6.87 0.218 0.000 -6.87 0.107 0.000 -6.88 0.610 0.000 -5.51 0.000 0.000 -6.09 0.000 0.000 -6.11 0.024

33

Table 7. Examining the Sensitivity to Error Distribution Assumptions before and after the 2008 Crisis. 2 This table presents the results of estimating AR(1)- GARCH (1,1) before and after January 01, 2008, where rt and σ t are returns and conditional variance, respectively.

σ t2

rt CANADA

Model ols Normal

Before Student t GED ols Normal After Student t GED GERMANY

Model ols Normal

Before Student t GED ols Normal After Student t GED

Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue

Mon. -0.001 0.000 -0.001 0.000 -0.001 0.000 -0.001 0.000 -0.002 0.096 0.000 0.693 0.000 0.738 0.000 0.473 Mon. 0.001 0.611 0.001 0.403 0.001 0.204 0.001 0.382 -0.001 0.531 0.000 0.609 0.000 0.638 0.000 0.945

Tues. -0.001 0.012 0.000 0.048 0.000 0.151 0.000 0.082 0.001 0.611 0.000 0.719 0.000 0.793 0.000 0.848 Tues. 0.002 0.065 0.001 0.244 0.002 0.084 0.001 0.152 -0.002 0.061 -0.001 0.218 -0.001 0.278 -0.001 0.327

Wed. 0.000 0.265 0.000 0.667 0.000 0.327 0.000 0.416 0.000 0.778 0.000 0.922 0.000 0.830 0.000 0.641 Wed. 0.001 0.380 0.002 0.093 0.001 0.182 0.001 0.202 -0.001 0.487 0.000 0.584 0.000 0.833 0.000 0.384

Thur. -0.001 0.037 0.000 0.182 0.000 0.123 0.000 0.097 0.000 0.879 0.000 0.854 0.000 0.689 0.000 0.740 Thur. 0.001 0.608 0.001 0.442 0.001 0.466 0.001 0.498 -0.001 0.153 -0.001 0.458 0.000 0.436 0.000 0.436

Mon.

Tues.

Wed.

Thur.

AIC -6.80

0.000 0.000 0.000 0.010 0.000 0.022

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.039 0.000 0.548 0.000 0.883

0.000 0.466 0.000 0.346 0.000 0.416

-7.10 -7.16 -7.15 -5.65

0.000 0.069 0.000 0.172 0.000 0.125 Mon.

0.000 0.000 0.000 0.000 0.000 0.000 Tues.

0.000 0.781 0.000 0.997 0.000 0.833 Wed.

0.000 0.085 0.000 0.149 0.000 0.166 Thur.

0.000 0.197 0.000 0.379 0.000 0.398

0.000 0.674 0.000 0.508 0.000 0.483

0.000 0.122 0.000 0.443 0.000 0.315

0.000 0.749 0.000 0.814 0.000 0.846

-6.21 -6.23 -6.24 AIC -5.50 -5.88 -5.92 -5.93 -6.53

0.000 0.799 0.000 0.852 0.000 0.968

0.000 0.006 0.000 0.347 0.000 0.184

0.000 0.220 0.000 0.450 0.000 0.964

0.000 0.729 0.000 0.799 0.000 0.864

-6.76 -6.82 -6.82

34

MALAYSIA

Model ols Normal

Before Student t GED ols Normal After Student t GED MEXICO

Model ols Normal

Before Student t GED ols Normal After Student t GED

Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue

Mon. -0.001 0.070 -0.001 0.029 -0.001 0.127 -0.001 0.120 -0.001 0.131 0.000 0.308 0.000 0.294 0.000 0.527 Mon. -0.002 0.000 -0.001 0.005 -0.002 0.000 -0.001 0.002 0.001 0.482 0.001 0.299 0.001 0.351 0.001 0.377

Tues. 0.000 0.480 -0.001 0.101 -0.001 0.216 -0.001 0.143 -0.001 0.467 0.000 0.738 0.000 0.851 0.000 0.779 Tues. -0.001 0.438 0.000 0.786 0.000 0.335 0.000 0.320 0.000 0.662 0.000 0.923 0.000 0.960 0.000 0.912

Wed. 0.000 0.711 0.000 0.441 0.000 0.896 0.000 0.554 0.000 0.685 0.001 0.197 0.001 0.118 0.001 0.020 Wed. 0.000 0.983 0.001 0.127 0.000 0.404 0.001 0.068 0.000 0.820 0.000 0.716 0.000 0.650 0.000 0.436

Thur. 0.000 0.610 0.000 0.341 0.000 0.365 0.000 0.313 0.000 0.975 0.000 0.365 0.000 0.719 0.000 0.324 Thur. 0.000 0.461 0.000 0.449 0.000 0.740 0.000 0.439 0.000 0.807 0.000 0.659 0.000 0.755 0.000 0.766

Mon.

Tues.

Wed.

Thur.

AIC -7.14

0.000 0.339 0.000 0.162 0.000 0.221

0.000 0.662 0.000 0.527 0.000 0.779

0.000 0.000 0.000 0.003 0.000 0.008

0.000 0.652 0.000 0.656 0.000 0.925

-7.33 -7.38 -7.39 -6.83

0.000 0.917 0.000 0.354 0.000 0.425 Mon.

0.000 0.001 0.000 0.020 0.000 0.042 Tues.

0.000 0.702 0.000 0.554 0.000 0.455 Wed.

0.000 0.017 0.000 0.249 0.000 0.292 Thur.

0.000 0.000 0.000 0.126 0.000 0.063

0.000 0.000 0.000 0.460 0.000 0.321

0.000 0.000 0.000 0.798 0.000 0.225

0.000 0.862 0.000 0.413 0.000 0.544

-7.23 -7.29 -7.30 AIC -5.59 -5.88 -5.98 -5.98 -5.96

0.000 0.555 0.000 0.489 0.000 0.615

0.000 0.084 0.000 0.223 0.000 0.244

0.000 0.090 0.000 0.473 0.000 0.422

0.000 0.226 0.000 0.374 0.000 0.388

-6.45 -6.48 -6.49

35

PHILIPPINE

Model ols Normal

Before Student t GED ols Normal After Student t GED ROMANIA

Model ols Normal

Before Student t GED ols Normal After Student t GED

Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue

Mon. -0.002 0.110 -0.001 0.106 -0.001 0.056 -0.001 0.169 0.000 0.836 -0.001 0.476 0.000 0.882 0.000 0.695 Mon. -0.001 0.685 -0.003 0.004 -0.003 0.003 -0.003 0.009 -0.001 0.668 0.000 0.858 -0.001 0.437 0.000 0.905

Tues. 0.000 0.936 0.000 0.879 -0.001 0.534 0.000 0.996 -0.001 0.455 -0.001 0.481 -0.001 0.367 0.000 0.804 Tues. -0.001 0.415 -0.002 0.127 -0.002 0.073 -0.001 0.198 0.000 0.944 0.001 0.294 0.001 0.494 0.000 0.550

Wed. -0.001 0.565 0.000 0.770 0.000 0.619 0.000 0.870 0.002 0.080 0.000 0.571 0.001 0.411 0.001 0.124 Wed. 0.000 0.855 -0.001 0.378 -0.001 0.440 -0.001 0.594 0.001 0.629 0.001 0.374 0.000 0.949 0.000 0.922

Thur. 0.002 0.112 0.002 0.055 0.001 0.070 0.002 0.031 0.000 0.804 0.000 0.893 0.000 0.895 0.000 0.737 Thur. 0.002 0.238 0.000 0.881 -0.001 0.531 0.000 0.994 0.001 0.539 0.001 0.140 0.000 0.943 0.001 0.272

Mon.

Tues.

Wed.

Thur.

AIC -6.17

0.000 0.759 0.000 0.910 0.000 0.891

0.000 0.329 0.000 0.133 0.000 0.119

0.000 0.721 0.000 0.963 0.000 0.866

0.000 0.637 0.000 0.793 0.000 0.954

-6.28 -6.34 -6.34 -6.06

0.000 0.506 0.000 0.626 0.000 0.645 Mon.

0.000 0.869 0.000 0.576 0.000 0.799 Tues.

0.000 0.838 0.000 0.845 0.000 0.900 Wed.

0.000 0.441 0.000 0.054 0.000 0.536 Thur.

-6.35

0.000 0.002 0.000 0.039 0.000 0.051

0.000 0.496 0.000 0.541 0.000 0.586

0.000 0.043 0.000 0.358 0.000 0.305

0.000 0.053 0.000 0.127 0.000 0.174

-5.37

-6.40 -6.40 AIC -4.91

-5.42 -5.43 -5.52

0.000 0.029 0.000 0.678 0.000 0.150

0.000 0.642 0.000 0.137 0.000 0.388

0.000 0.874 0.000 0.209 0.000 0.625

0.000 0.000 0.000 0.002 0.000 0.001

-5.71 -5.82 -5.83

36

SINGAPORE

Model ols Normal

Before Student t GED ols Normal After Student t GED UK

Model ols Normal

Before Student t GED Ols Normal After Student t GED

Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue

Mon. -0.001 0.159 -0.001 0.267 -0.001 0.372 -0.001 0.211 -0.001 0.175 -0.001 0.178 -0.001 0.060 -0.001 0.166 Mon. -0.001 0.091 -0.001 0.112 -0.001 0.116 -0.001 0.097 0.000 0.796 0.000 0.993 0.000 0.795 0.000 0.999

Tues. -0.001 0.160 -0.001 0.051 -0.001 0.096 -0.001 0.091 -0.001 0.431 -0.001 0.151 -0.001 0.246 -0.001 0.210 Tues. -0.002 0.041 -0.001 0.011 -0.002 0.006 -0.001 0.008 0.001 0.394 0.001 0.495 0.001 0.368 0.001 0.418

Wed. -0.001 0.376 -0.001 0.364 0.000 0.490 0.000 0.621 0.000 0.653 0.000 0.957 0.000 0.965 0.000 0.951 Wed. -0.001 0.062 -0.001 0.044 -0.001 0.044 -0.001 0.101 -0.001 0.689 0.000 0.872 0.000 0.830 0.000 0.814

Thur. -0.001 0.278 -0.001 0.314 0.000 0.457 0.000 0.592 -0.001 0.398 -0.001 0.107 -0.001 0.197 -0.001 0.100 Thur. -0.001 0.208 -0.001 0.230 -0.001 0.226 -0.001 0.337 0.000 0.881 0.000 0.887 0.000 0.695 0.000 0.606

Mon.

Tues.

Wed.

Thur.

AIC -6.57

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.536 0.000 0.891 0.000 0.724

0.000 0.009 0.000 0.105 0.000 0.183

0.000 0.219 0.000 0.252 0.000 0.312

-6.78 -6.81 -6.81 -5.95

0.000 0.009 0.000 0.014 0.000 0.033 Mon.

0.000 0.021 0.000 0.048 0.000 0.061 Tues.

0.000 0.200 0.000 0.077 0.000 0.050 Wed.

0.000 0.374 0.000 0.505 0.000 0.467 Thur.

-6.43

0.000 0.936 0.000 0.836 0.000 0.926

0.000 0.024 0.000 0.143 0.000 0.088

0.000 0.068 0.000 0.113 0.000 0.123

0.000 0.789 0.000 0.833 0.000 0.981

-7.00

-6.45 -6.45 AIC -6.70

-7.02 -7.02 -5.59

0.000 0.111 0.000 0.203 0.000 0.252

0.000 0.002 0.000 0.006 0.000 0.010

0.000 0.715 0.000 0.541 0.000 0.644

0.000 0.000 0.000 0.421 0.000 0.000

-5.94 -5.95 -5.96

37

USA

Model Ols Normal

Before Student t GED Ols Normal After Student t GED VENEZUELA

Model Ols Normal

Before Student t GED Ols Normal After Student t GED

Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue Coef Pvalue

Mon. 0.000 0.872 0.001 0.353 0.000 0.561 0.000 0.962 0.000 0.826 0.001 0.383 0.000 0.877 -0.001 0.219 Mon. -0.003 0.002 -0.003 0.026 -0.003 0.001 -0.002 0.000 0.000 0.860 0.000 0.577 0.000 0.964 0.000 0.267

Tues. 0.000 0.615 0.001 0.372 0.001 0.263 0.001 0.348 0.001 0.333 0.000 0.656 0.000 0.746 -0.001 0.510 Tues. -0.003 0.006 -0.003 0.064 -0.002 0.015 -0.002 0.000 0.001 0.546 0.000 0.349 0.000 0.753 0.000 0.223

Wed. 0.001 0.387 0.001 0.074 0.001 0.035 0.001 0.068 0.000 0.737 0.000 0.720 0.000 0.938 0.000 0.741 Wed. -0.001 0.207 -0.002 0.141 -0.001 0.076 -0.002 0.003 0.001 0.418 0.000 0.537 0.000 0.530 0.000 0.183

Thur. 0.000 0.897 0.000 0.686 0.000 0.663 0.000 0.718 0.000 0.779 0.001 0.222 0.001 0.183 0.001 0.148 Thur. -0.002 0.139 -0.002 0.177 -0.002 0.014 -0.002 0.000 0.003 0.012 -0.004 0.000 0.000 0.892 0.000 0.167

Mon.

Tues.

Wed.

Thur.

AIC -6.82

0.000 0.951 0.000 0.668 0.000 0.698

0.000 0.000 0.000 0.006 0.000 0.004

0.000 0.257 0.000 0.664 0.000 0.516

0.000 0.749 0.000 0.994 0.000 0.990

-6.96 -6.98 -6.99 -5.41

0.000 0.913 0.000 0.953 0.000 0.929 Mon.

0.000 0.005 0.000 0.035 0.000 0.042 Tues.

0.000 0.865 0.000 0.917 0.000 0.954 Wed.

0.000 0.000 0.000 0.000 0.000 0.429 Thur.

-5.94

0.000 0.119 0.000 0.470 0.000 0.771

0.000 0.002 0.000 0.102 0.000 0.796

0.000 0.000 0.000 0.111 0.000 0.280

0.000 0.000 0.000 0.005 0.000 0.270

-6.28

-5.97 -6.00 AIC -5.98

-6.47 -6.60 -5.65

0.000 0.000 0.000 0.493 0.000 0.000

0.000 0.000 0.000 0.430 0.000 0.323

0.000 0.000 0.000 0.459 0.000 0.111

0.001 0.000 0.000 0.767 0.000 0.075

-6.53 -7.81 -7.54

38

Table 8. Results of the Sequential Testing Procedure for Multiple Breaks This table presents the results of identifying the structural breaks in each return series. We use the sequential testing approach proposed by Bai (1997) and Bai and Perron (1998) to examine the potential structural changes in the return series of our dataset. * indicates that the null hypothesis of l break(s) is rejected at the 5% level. Critical values are obtained from Bai and Perron (2003). Break Test

F-statistic

Critical Value

Number of breaks

BULGARIA

0 vs. 1 * 1 vs. 2 *

21.98193 25.78278

8.58 10.13

2

Break dates 09/16/2002 10/08/2007

COLOMBIA

0 vs. 1 * 1 vs. 2 * 2 vs. 3 *

8.891078 13.04028 22.75551

8.58 10.13 11.14

3

10/17/1997 11/09/2001 01/31/2006

CHILE

0 vs. 1 * 0 vs. 1 *

18.73982 26.56574

8.58 8.58

1 1

02/08/1994 12/01/1999

SRI LANKA

0 vs. 1 *

10.00722

8.58

1

03/19/2009

FINLAND

0 vs. 1 * 1 vs. 2 *

14.29602 25.1542

8.58 10.13

2

09/09/1992 03/08/2000

GREECE

0 vs. 1 *

13.93909

8.58

1

09/22/1999

INDONESIA

0 vs. 1 *

9.098568

8.58

1

10/16/2002

IRELAND

0 vs. 1 *

10.33597

8.58

1

02/22/2007

JAPAN

0 vs. 1 *

18.23996

8.58

1

06/15/1987

LUXEMBURG

0 vs. 1 *

19.3447

8.58

1

03/14/2000

AUSTRIA

0 vs. 1 * 1 vs. 2 *

12.34776 25.17922

8.58 10.13

2

08/26/1982 10/12/1989

PHILIPPINE

0 vs. 1 *

11.54389

8.58

1

03/19/2009

PORTUGAL

0 vs. 1 * 1 vs. 2 *

8.90815 23.14444

8.58 10.13

2

06/29/1993 04/24/1998

SWEDEN

0 vs. 1 *

10.06211

8.58

1

03/08/2000

SLOVENIA

0 vs. 1 * 1 vs. 2 *

37.41455 16.64783

8.58 10.13

2

07/23/2003 08/13/2007

VENEZUELA

0 vs. 1 * 1 vs. 2 *

8.743773 10.88049

8.58 10.13

2

09/25/1997 05/09/2002

39

Research highlights • We examine the robustness of the day-of-the-week (DW) effects for 51 stock markets. • Evidence of DW effects is sensitive to the underlying distributions and the study period. • Findings also hold when models with unconditional/conditional risk-adjusted returns, “wandering week-day” effect and structural breaks are used. • Financial crises lessen the DW effect in the mean, but magnify it in the volatility. • The DW anomaly is better investigated using models with fat-tailed distributions.

40