The Turn-of-the-Month puzzle: An empirical examination of iShares

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UNIVERSITY OF GRONINGEN • JUNE 2009

The Turn-of-the-Month puzzle: An

empirical examination of iShares

In the period between 1993 and 2009

BOUKE HULZENGA*

ABSTRACT

This paper studies the Turn-of-the-Month (TOM) effect in the period between 1993 and 2009, using nine iShares indices. The structure of iShares makes them particularly suitable for attempting to exploit any seasonal patterns in security returns. We find highly significant positive returns around the TOM for all examined countries, except for Malaysia. On average 85% of the total increase of the indices is earned in the TOM period, supporting the view that the TOM effect is still strongly present. In addition, several hypotheses are tested that try to explain the anomalous pattern, however, none of these is proven to be conclusive. A trading strategy is developed to exploit the seasonal effect. This strategy beats a simple buy and hold strategy in both return and riskiness.

* Bouke Hulzenga (1383582) is master student at the Department of Finance, University of Groningen. I am very grateful to my supervisor, Prof. dr. R.A.H. van der Meer for guidance and very helpful comments.

Keywords: Turn-of-the-Month effect; Explaining Hypotheses; Trading strategies JEL code: G14 - Information and Market Efficiency

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I. Introduction

Seasonal anomalies in stock returns have generated considerable public attention in recent years Researchers have devoted a considerable amount of research toward it, trying to document the existence and its potential for generating abnormal returns. An economic anomaly is a result inconsistent with the economics paradigm. Almost all theories in finance are based on the belief that behavior can be explained by assuming that agents have stable, well defined preferences and make rational choices consistent with those preferences in markets that clear (Thaler, 1987). An empirical result is called anomalous when it is difficult to “rationalize”. These anomalies cannot be explained by the usual models, and thus potentially challenge the efficient market hypothesis. According to this hypothesis, investors are unable to earn above average returns, because all information is reflected in stock prices. Well known calendar anomalies are the January effect, where firms generate higher returns in January, the Monday effect, where stock returns are low on Mondays compared to other week days, and the Turn-of-the-Month (hereafter, TOM) effect, where stock returns are high around the turn of the month. These anomalies often have significant economic impact. According to modern theory, however, they should not be persistent after being discovered. This issue remains an open question.

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5 This paper will evaluate if the TOM effect is still present, controlling for problems encountered by previous studies. In addition, several explaining hypothesis are tested using a unique dataset. Furthermore, we will try to examine the possibility of constructing a trading strategy to beat the market over time, depending on the results of our empirical analysis. This paper contributes to the already large body of research on calendar anomalies because it makes use of tradable iShares indices instead of non-tradable indices. iShares are exchange traded funds (ETFs), investment vehicles that track any one of a wide range of indices and sectors. (Barclays Global Investors, 2009). According to Chu et al. (2007), the structure of iShares makes them particularly suitable for attempting to exploit any seasonal patterns in security returns. iShares have become popular with investors because they are designed to replicate the holdings, performance, and yield of their underlying indices.

The paper is organized as follows. In Section II, we discuss the literature to date concerning the TOM effect. We examine the existence of the effect, factors that can explain its occurrence, and possible problems with anomaly studies. Moreover, an overview of studies covering investment strategies using calendar anomalies is presented. In Section III, first the data on iShares is provided, this along with its descriptive statistics. In addition, the TOM methodology is provided, divided in four parts. First, methods to discover the anomaly are discussed. Second, we discuss the methodology of the explaining hypotheses. Third, we present the methodology of our robustness checks. Finally, the formulation of trading rules is explained. In Section IV, the results of the empirical analysis are presented. Section V concludes.

II. Literature Review

A. Turn-of-the-month Effect

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6 the month, identified as the first nine trading days of the month plus the last trading day of the previous month. The second half of the trading months contributed nothing. The magnitude of this effect was by no means small; it was of similar magnitude as the well-known weekend effect reported by French (1980) and Gibbons and Hess (1981). This pattern exists in both large and small capitalization stocks and is independent of other known calendar anomalies, such as the January effect. Ariel (1987) further notes that the phenomenon is especially strong in the five day period between the last trading day of one month and the fourth trading day of the next month (trading days -1 through +4). Lakonishok and Smidt (1988) added 65 years of new data, compared to Ariel (1987), they found that the four days at the turn of the month accounted for all positive returns to the Dow Jones Industrial Average (DJIA) in the 90 year period of 1897-1986. This implicated a notable fact, namely that the DJIA goes down during the Rest-of-the-Month (hereafter, ROM). The authors suggest that the monthly leap in returns may be liquidity driven and is a result of the buying and selling activity of pension fund managers around the TOM.

Jacobs and Levy (1988) find that returns are high for each day from the last trading day in the previous month to the third trading day in the current month. The average return of the four trading days in the month is 0,118 percent, versus 0,015 percent for all trading days. However, they also find that this anomaly, which existed for almost a century, had weakened somewhat in de most recent decade. Pettengill & Jordan (1988) analyzed two US indices in the period between 1962 and 1985, including both large and small firms, while simultaneously controlling for the January and turn-of-the-year (TOY) effects. They found a highly significant regularity associated with the TOM. Returns in de four day period around the TOM accounted for more than 50 percent of total monthly return. Moreover, the TOM effect was found to be equally strong for large and small firms. A similar pattern was found in trading volume, but insufficient to account for all of the returns seasonality.

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7 market microstructure. Since market microstructure itself is dynamic, TOM effects documented are also subject to change without notice. Marquering, Nisser and Valla (2006) examine several well-known market anomalies, including the TOM effect, using daily DJIA returns over the period 1960-2003. They report that most of the anomalies under consideration weakened substantially, and some of them even disappeared completely. They state that right after the year of initial publication the strength of an anomaly is dramatically decreased. However, the TOM effect still seems present, whereas others disappeared. Marquering, Nisser and Valla (2006) argue that transaction costs may be too high for arbitrage opportunities.

B. International Evidence

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8 87% of the monthly return, in the stock markets of fifteen countries where the TOM pattern exists.

C. Explaining Hypotheses

C.1. Liquidity Hypothesis

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9

C.2. Information Release Hypothesis

Penman (1987) provides an analysis of a relationship between earnings news and seasonalities in stock returns. He find that the arrival of (on average) favorable earnings news at the beginning of calendar quarters 2 through 4 coincides with a seasonality in aggregate returns, giving an implication for the information release hypothesis. Nikkinen, Sahlström, and Äijö (2007) provide a new and economically plausible explanation for TOM and intra-month anomalies in their paper. They suggest that these anomalies arise from clustered information, namely from important macroeconomic news announcements, which are released systematically at a certain point each month. They examined the Standard & Poor 100 index, which contains the largest firms in the US, and discovered the existence of TOM effects and intermonth effects. However, once the effect of macroeconomic news announcements had been taken into account, these anomalies disappeared. The findings of Nikkinen, Sahlström, and Äijö (2007) imply for the US stock market that the TOM effect is explained by the systematic clustering of important macroeconomic news announcements. Nikkinen, Sahlström, and Äijö (2009) repeat their analysis on the three major European stock indices, which are France, Germany and the United Kingdom, and find similar results. This indicates that the TOM and intermonth effect are caused by US macroeconomic news. Gerlach (2007) examined several major US indices and his results also support the information release hypothesis. Almost all calendar anomalies disappeared, including the TOM effect, after adjusting for macroeconomic news events. He concludes that institutions and market psychology are unlikely to be the main sources of these anomalies.

C.3. Risk Hypothesis

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10 there are indeed higher risks on different weekdays. Studies on any seasonality in variance have been limited, especially for the TOM anomaly.

C.4. Window Dressing Hypothesis

Ziemba (1991) states that portfolio balancing effects are partially explaining the TOM effect. Portfolio balancing is often referred to as window dressing and is a strategy used by mutual funds and portfolio managers to improve the appearance of their portfolio performance before presenting it to clients and shareholders. Portfolio managers are reluctant to report portfolios containing shares that performed poorly. The practice of deleting such shares from portfolios at quarter or year end increases returns at TOM days. However, the international markets examined by Cadsby and Ratner (1992) provide no support for this hypothesis. They state that the TOM effect is not generally attributable to quarterly window dressing.

D. Problems Anomaly Studies

As Lakonishok and Smidt (1988) argue in their paper, the widespread findings of the TOM effect could be just the product of sampling error and data mining. Even if there exist no calendar anomalies, an extensive search or data mining exercise across a large number of possible calendar effects can yield significant results of an “anomaly” by pure chance (Hansen, Lunde and Nason, 2005). Moreover, theoretical explanations have been suggested only after the empirical discovery of the anomalies, these have never been given ex ante from economic theory.

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11 important to test for the existence of these regularities in data samples that are different from those in which they were originally discovered.

Another angle of incidence is the efficient market hypothesis. Fama (1970) noted this fact early on, pointing out that tests of market efficiency also jointly test a maintained hypothesis about equilibrium expected asset returns. Thus, whenever someone concludes that a finding seems to indicate market inefficiency, it may also be evidence that the underlying asset-pricing model is inadequate. It is also important to consider the economic relevance of a presumed anomaly. Jensen (1978) stressed the importance of trading profitability in assessing market efficiency. In particular, if anomalous return behavior is not definitive enough for an efficient trader to make money when trading on it, then it is not economically significant.

Kunkel, Compton, and Beyer (2003) argued that a response to these criticisms is to appeal to unique data sources and robust methodologies. If an anomaly can be shown to exist in many markets and under test conditions that are robust to violations of the Ordinary Least Squares (OLS) assumptions, it provides greater support for the existence of the anomaly.

E. Investment Strategies using the Turn-of-the-Month

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12 achieved by simply buying and holding the stock account, and a 5.8 percent rate on the money market account.

Jacobs and Levy (1988) argue that calendar anomalies are difficult to exploit as a stand-alone strategy because of transaction cost considerations. However, calendar return patterns can be beneficial in timing a preconceived trade. Pettengill & Jordan (1988) used an investment strategy where they ignored transaction costs. They held the S&P index long for the first half of the month and went short during the last half of the month. This strategy earned them more than double compared to a simple buy and hold strategy. Nevertheless, the inclusion of transactions costs would probably have made such a strategy unprofitable. Pettengill & Jordan (1988) argued that not all market participants pay transaction costs because certain kind of mutual funds allow cost-free switching from equity to money market funds.

III. Data & Methodology

A. Data

In order to address the above mentioned problems of data snooping and data mining, this study will use a dataset that has never been used until now to detect the TOM anomaly, namely, eight international iShares indices and the Standard and Poor’s Depository Receipts (SPDR) fund. These international iShares are country-specific series of securities that track the price and yield of specific Morgan Stanley Capital International (MSCI) country indices. In 1993, the American Stock Exchange launched the SPDR fund, whose shares were traded in real time and tracked the S&P 500 stock market index. This was the first exchange-traded fund (ETF), and it is still trading in the United States. Later, Barclays Global Investors launched other ETFs, labeling them iShares. iShares are index funds, priced and traded intraday, purchased on margin, sold short (even on a downtick), traded using stop and/or limit orders, and allow investors to buy or sell shares based on the collective performance of an entire portfolio (Barclays Global Investors, 2009). Advantages of iShares over normal shares are tax efficiency, lower costs, transparency, buying and selling flexibility, all day tracking and trading and simple diversification.

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13 gains. This occurs because turnover is virtually non-existent, since the underlying investments are rarely sold. This virtually eliminates annual capital gain distributions and the taxes that go with them. Because an ETF is not actively managed, generally ETFs only sell securities to reflect changes in its underlying index. Exchange trading of ETFs further enhances their tax efficiency, because investors who want to liquidate shares in an ETF simply sell them to other investors in the secondary market. Because of this structure, ETFs, other than open-end investment companies (mutual funds), are not required to sell securities to meet redemptions. Consequently, this structure removes the generation of trading-related capital gains that would be taxable for remaining investors. ETFs also have significantly lower annual expense ratios than mutual funds. This is due again, in part, to passive management and the lack of a need to incur management expenses or trading costs to issue or redeem shares. iShares expense ratios are between 0.09% and 0.75%. Compared to mutual fund ratios which can run twice as high, ETFs are demonstrable bargains. (Barclays Global Investors, 2009)

Table I

List of Countries and period of investigation

The table provides the nine countries under analysis. In addition, the starting and ending dates are presented for all nine iShare indices, as well as the number of observations, i.e., the number of trading days during the time period.

Name Period Observations

North America Start End

iShares MSCI Canada 1-4-1996 1-5-2009 3293

iShares MSCI Mexico 1-4-1996 1-5-2009 3293

iShares MSCI United States (SPDR) 1-2-1993 1-5-2009 4094

Europe

iShares MSCI France 1-4-1996 1-5-2009 3293

iShares MSCI Germany 1-4-1996 1-5-2009 3293

iShares MSCI United Kingdom 1-4-1996 1-5-2009 3293

Asia

iShares MSCI Hong Kong 1-4-1996 1-5-2009 3293

iShares MSCI Japan 1-4-1996 1-5-2009 3293

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14 iShares are listed on the major stock exchanges in the world, accounting for more than €107 billion in assets under management. The structure of iShares makes them particularly suitable for exploiting seasonal patterns. Due to their low costs and high flexibility, iShares arbitrage barriers are low. Olienyk et al. (1999) argue that, unlike market proxies used in previous studies, iShares represent directly tradable assets and overcome problems of non-synchronous trading and illiquidity.

This paper will analyze the TOM effect in the North American region, Europe and Asia. The countries under analysis are the largest in their region, and available as iShares: The United States, Canada, Mexico, Germany, France, United Kingdom, Hong Kong, Japan and Malaysia. Daily closing prices for iShares from nine countries were extracted from Yahoo Finance for the period between March 18, 1996 and May 1, 2009. The SPDR ETF whose shares are traded in real time and tracking the Standard & Poor 500 index, started at the 29th of January, 1993, is also extracted from the database. This index is later renamed as the US iShare index. The period under investigation is selected because iShare indices commenced trading in the beginning of 1993 for the US, but not until 1996 for all other countries. Table I presents the iShare indices and their corresponding country and sample period.

B. Methodology

Returns are calculated for each iShare index i using the iShare daily closing prices Pit for all

indices. Continuously compounded returns are then computed from these daily closing prices for each individual index. The continuously compounded return is the value of Ritthat satisfies













=

−1

ln

it it it

P

R

(1) B.1. Turn-of-the-Month Effect

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15 Lakonishok and Smidt (1988) use, and contains most of the trading days in any month. While individual months vary in the number of trading days, the actual number ranges between 18 and 23. Daily returns of our iShare indices are examined using the same procedure of Kunkel, Compton and Beyer (2003) with the following standard OLS regression:

t t t t t t

D

R

=

β

₋₉ ₋₉_,

+

β

₋₈ ₋₈_,

+

...

+

β

₈ ₈_,

+

β

₉ ₉_,

+

ε

(2)

where Rit is the return on day t for index i; Di,tare dummy variables for the first and last nine

trading days of each month, where D-9,t corresponds to Trading Day -9, D-8,t corresponds to

Trading Day -8, continuing through to D9,t, which corresponds to Trading Day + 9. The

coefficients on the dummy variables, β-9to β9, are the mean returns for the 18 trading days and εt

is the error term.

Summary statistics of the distribution of the error terms are presented in Table II, including the mean return, median return, maximum, minimum, standard deviation, skewness, kurtosis, and the Jarque-Bera statistic. Daily returns will be tested on normality using the Jarque-Bera test, which uses the kurtosis and skewness. The high Jarque-Bera statistic in all countries indicates significant non-normality in the distribution and the high kurtosis points toward leptokurtic data. Ignoring this phenomenon will still result in unbiased coefficients, but these will be no longer the best linear unbiased estimators. Moreover, the standard errors of the coefficients could be inappropriate, and hence any inferences made could be misleading (Brooks, 2008).

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16 is that the variance is constant over time, however, for asset return series in finance this often is not the case.

Table II

Distribution of the error terms from the OLS model

The table presents the summary statistics of the error terms using the OLS model from equation (2) for each country individually. The Mean, Median, Maximum, Minimum, Standard Deviation, Skewness, Kurtosis, and Jarque-Bera statistic are presented. The statistics are taken over 3293 (4094 for the US) observations for each country. a indicates that the Jarque-Bera statistic is larger than 5,99 and thus the null hypothesis of a normal distribution is rejected.

Canada Mexico United

States France Germany

United Kingdom

Hong

Kong Japan Malaysia

Mean 0,0001 0,0003 0,0001 0,0001 0,0001 0,0001 0,00001 0,0001 -0,0001 Median 0,0007 0,0010 0,0005 0,0006 0,0007 0,0004 0 0,0001 0 Maximum 0,12 0,19 0,13 0,12 0,18 0,15 0,18 0,15 0,17 Minimum -0,26 -0,19 -0,10 -0,12 -0,12 -0,13 -0,13 -0,11 -0,14 Standard Deviation 0,016 0,022 0,013 0,017 0,018 0,016 0,022 0,017 0,023 Skewness -1,65 -0,02 -0,06 -0,14 0,02 -0,16 0,30 0,37 0,42 Kurtosis 26,50 10,97 13,61 9,01 10,81 12,21 9,80 8,68 10,59 Jarque-Bera 7724 a ₈₇₂₁a ₁₉₁₉₁a ₄₉₇₀a ₈₃₇₀a ₁₁₆₅₀a ₆₄₀₁a ₄₅₀₆a ₈₀₀₅a

In order to mitigate the abovementioned violations of the OLS model, we perform our analysis using a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. GARCH (p,q) models are capable of capturing the three most observed empirical features in stock return data, namely leptokurtosis, skewness, and volatility clustering. This model was first proposed by Bollerslev (1986). We will use a Student-t distribution instead of the normal distribution for our model because it is able to provide a more robust interpretation of the t-statistics in the presence of leptokurtic data (de Jong et al., 1992). According to Connolly (1989), this is useful because the unconditional leptokurtosis may be traced to non-normality in the conditional error distribution and/or to time varying heteroskedasticity. If the estimate of the degree of freedom (v) is greater than thirty but α1 and β1 are positive, time varying

heteroskedasticity accounts for the non-normal error distribution. If the v estimate is less than ten and α1andβ1are positive, both non-normality and time-varying heteroskedasticity produce the

fat tailed error distribution. In this case, the latter will cause the distribution to be fat tailed since

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17 We employ the GARCH (1,1) model that is specified in (3) and (4), with a normal regression and a conditional variance regression accounting for volatility, respectively.

t t t t t it

D

R

=

δ

₋₉ ₋₉_,

+

δ

₋₈ ₋₈_,

+

...

+

δ

₈ ₈_,

+

δ

₉ ₉_,

+

ε

(3)

∑

= − = −

+

=

p j j t j q i i t i t

u

h

1 2 1 2

σ

β

α

ω

(4)

Here, Rit is the index return that is considered to be linearly related to the explanatory dummy

variables (Dt), for index i at day t, and an error term εt. The dummy variables Dt represent the

days around the TOM. Intercept terms are omitted to avoid dummy variable traps in the regressions. The coefficients δ in equation (3) represent the size and the direction of the return on each TOM day for the index i. ht is the conditional variance. It is a one-period ahead estimate

for the variance, and it is calculated based on any past information thought relevant. ω is the constant, αi is the ARCH term and βjis the GARCH term. Significance of αiimplies the existence

of the ARCH-process in the error term, which could indicate volatility clustering. Inspection of Table AI reveals that both heteroskedasticity and autocorrelation are highly present when using the OLS method, but both completely disappear with the implementation of the GARCH (1,1) model. Hence, the GARCH(1,1) is robust to violations in normality, heteroskedasticity and autocorrelation. Fama (1998) argued in his paper that long-term return anomalies are sensitive to methodology. They tend to become marginal or even disappear when exposed to different models for expected returns or when different statistical approaches are used to measure them. We can conclude that most long-term anomalies can reasonably be attributed to chance. Most research to date uses the standard OLS model. Therefore, by using this GARCH (1,1), we will control for this critique.

After testing for possible TOM effects, we will test the TOM effect directly by comparing TOM returns to the ROM returns. We follow the same procedures used by Lakonishok and Smidt (1988) and Pettengill and Jordan (1988). The following GARCH (1,1) regression is used for each country separately:

t TOM

it

D

(18)

18

∑

= − = −

+

=

u

h

1 2 1 2

σ

β

α

ω

(6)

where Rit is the return on day t for index i; α is the intercept representing the mean return for the

ROM period; DTOM is the dummy variable for the TOM period (retrieved from the first

regression analysis outcome); the coefficient β represents the difference between the mean TOM return and the mean ROM return; and εt is the error term. ht is the conditional variance.

B.2. Explaining Hypotheses

In addition to the regular tests to reveal the presence of the TOM effect we will employ several additional tests to unravel the existence of the TOM effect. Three hypotheses which try to explain the TOM effect are closely examined. These are the liquidity hypothesis, the information release hypothesis and the risk hypothesis.

B.2.1. Liquidity Hypothesis

In this section we will investigate whether the TOM liquidity hypothesis can be accepted in our dataset of iShare indices. Ogden (1990) and others suggests that the TOM regularity exists because of increased liquidity at month ends. We will examine this phenomena following the same methodology of Booth et al. (2000). First, day t returns for each index are standardized by subtracting the mean return of all other days of the current month using the following equation:





























+

−

=

∑

− − = = +

17 /

1 9 9 1 t k k t ik ik it it

R

AR

(7)

where ARit is the mean adjusted return for index i on day t and Ritis its daily return on the same

day when t ≠ 0. As a liquidity proxy we use the daily share volume of each iShare index i at day

t, i.e., VOLit.

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19

1

17

1 9 9 1

−









































+

=

∑

− − = = + t k k t ik ik it

it

VOL

SVOL

(8)

where SVOLit is the standardized share volume for index i on day t. We will initially test whether

there are TOM effects for our mean adjusted return and standardized volume measures. Summary statistics of our measures of mean adjusted return standardized volume are presented in Table BI in the Appendix. The distribution of the mean adjusted return is non-normal, so a GARCH(1,1) model will be used. First, the mean adjusted return ARit is regressed with

regression (3), using ARit instead of Rit. Second, the standardized share volume is estimated with

regression (2), now using SVOLit instead of Rit. Since the creation of the iShare indices, a total of

213 TOMs for the US and 156 TOMs for the other countries took place. However, in the startup period of the index, the volumes were highly volatile because the iShare indices were not traded on a regular basis. In order to mitigate this problem, we will use only the last 150 TOMs for the US and for the other countries the last 100 TOMs.

After establishing if there exists a TOM effect in the mean adjusted return and standardized volume, we will test this empirically using a regression between a constant and the dependent variable ARit and SVOLit on day t. A standard OLS regression is used and it is specified as

follows

it it

it

c

SVOL

AR

=

+

ν

(9)

where ARit is the mean adjusted return for index i on day t, c the intercept, νit the coefficient

explaining the size and direction of the relationship between return and liquidity, and SVOLit is

the standardized share volume for index i on day t. Significance of νit would imply a relationship

between liquidity and returns around the TOM.

B.2.2. Information Release Hypothesis

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20 listed in Table III. Following, for example, Ederington and Lee (1996) and Heuson and Su (2001), the dates for the release of macroeconomic news are used as information events.

In order to examine to what extend macroeconomic news announcements affect the iShare indices we use the following regression model:

it m mt m it

c

MACRO

R

=

+

∑

θ

+

ε

= 10 1 (10)

where Rit is the return on the selected index i on day t, c is the constant, θm is the coefficient for

each macroeconomic event m. MACROmt is the dummy variable for each of the macroeconomic

news announcements m, that takes the value of 1 if news m occurs on day t, and zero otherwise.

Table III

US Macroeconomic news announcements

The table shows the ten most important United States macroeconomic news events. The release date shows the average release day of the month as measured in trading days. Also included are the symbols and issue frequency.

Reports (m) Symbol Issued Release date

Institute for Supply Management: Manufacturing ISM Monthly 1.0

Institute for Supply Management: Nonmanufacturing ISMS Monthly 3.0

Employment EMP Monthly 4.0

Retail Sales RS Monthly 9.3

Producer Price Index PPI Monthly 9.9

Industrial Production IP Monthly 11.2

Consumer Price Index CPI Monthly 11.8

Consumer Confidence CONSCON Monthly 18.8

Gross Domestic Product GDP Quarterly 19.4

Employment Cost Index EMPCOST Quarterly 19.7

Source: Nikkinen, Sahlstrom and Aijo (2008)

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21 observed in the residuals estimated from Model (10) (Nikkinen, Sahlström, and Äijö, 2007). The following regressions, using a GARCH (1,1) model as used previously, takes almost the same specification as model (3) and (5), except now it uses the residual of model (10) as the dependent variable. t t t t t it

δ

D

δ

D

δ

D

δ

D

ε

=

₋₉ ₋₉_,

+

₋₈ ₋₈_,

+

...

+

₈ ₈_,

+

₉ ₉_,

+

(11) t TOM it

α

β

D

ε

=

+

(12)

With conditional variance equation:

∑

= − = −

+

=

u

h

1 2 1 2

σ

β

α

ω

(13)

Insignificance of the results from regression (11) and (12) would imply that US macroeconomic news announcements cause the TOM effect to exist.

B.2.3. Risk Hypothesis

Most research up to now fails to take into account the effects of risk into their analysis, so we will examine whether there is a relation between the TOM effect and higher risk. It could be that the higher return around the TOM is just a reward for bearing higher risk during that period. Using the GARCH (1,1) model as expressed in equation (3) and (4), we will account for the possibilities that the market can be more or less volatile around the TOM. Consequently, abnormal significant returns could then be explained by abnormal risk. This proposition can be tested by including dummy variables to capture any systematic increase in variance around the TOM. Specifically, the variance equation is given by

t t t t p j j t j q i i t i t

u

y

D

y

D

y

D

y

D

h

₉ ₉_, ₈ ₈_, ₈ ₈_, ₉ ₉_, 1 2 1 2

_...

+

=

₋ ₋ ₋ ₋ = − = −

∑

α

β

σ

ω

(14)

where ht is the conditional variance, Dd,t the dummy variable representing the days around the

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22 Combining equation (3) and (14) will reveal whether volatility is related to abnormal positive returns around the TOM.

B.3. Robustness of the Results

In addition to the TOM test and explaining hypotheses, we consider three robustness checks which are used to test the strength of our results. First, we will control for the January effect/turn-of-the-year effect. Second, we control for sentiment in the market, comparing a rising market with a declining market, known as bull and bear market, respectively. Finally, we measure to what extent the anomalous pattern deviates after controlling for the 2007-2009 financial crisis.

B.3.1. January Effect

Some authors, for instance Pearce (1996), argue that the TOM effect is essentially caused by the January effect. Studies by among others Keim (1983) and Roll (1983) showed that small capitalization stocks tend to heavily outperform large capitalization stocks on the last trading day of December and the first five trading days in January, also called the January/turn of the year (TOY) effect. To control for this theory, we run the regression specified in (3) and (4) once again, excluding the TOM from December to January, to establish a regression free of the January effect.

B.3.2. Controlling for Sentiment

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23 dummy variables, one for a bull market and one for a bear market, which is then multiplied with the original regression from equation (3). This regression takes the following form:

t d period t t it

D

R

=

∑

δ

+

ε

− = 9 9 (15)

∑

= − = −

+

=

u

h

1 2 1 2

_β

_σ

α

ω

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Here, Rit is the index return that is considered to be linearly related to the explanatory dummy

variables Dt, Dperiod and an error term εt. The dummy variables Dt represent the days around the

TOM, ranging from -9 to 9. The coefficients δ in equation (15) represent the size and the direction of the return on each TOM day for the index i. The dummy variable Dperiod represents

the sub period under analysis, where period can be either a bull market or a bear market. When in a

bull market the dummy gets a value of 1, and zero otherwise. For the bear market dummy the opposite holds. ht is the conditional variance equation from the GARCH (1,1) model to control

for heteroskedasticity and autocorrelation. Mexico is excluded because we could not make a sound distinction between a bull and a bear market, what resulted in too few observations.

B.3.2. Controlling for the Influence of the 2007-2009 Financial Crisis

In addition to the test where we differentiated between bearish and bullish market sentiment, we will also investigate whether the latest subprime mortgage crisis, which ultimately resulted in a global financial crisis, has any impact in the TOM pattern. In order to do so, we follow the same methodology presented in equation (15) and (16). We will first test whether our results change if the period of the crisis is left out of our initial sample period, and thereafter test our regression directly onto the period of the crisis. The dummy variable Dperiod will first represent the period

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C. Trading Rules

After establishing a possible pattern of abnormal returns around the TOM, we will analyze the possibility of exploiting this pattern using iShares. Will an investment strategy focused on the return pattern around the TOM generate higher returns? We follow the procedure of Kunkel & Compton (1998), investing in iShares at the TOM and in a money market account for the other days in the period. Results will explain whether it will be beneficial for investors to switch between iShares and a money market account. Following Henzel and Ziemba (1996), no transaction costs are included, since institutional investors could use futures to implement such strategies which dramatically reduce the impact of transaction costs.

IV. Results

A. Turn-of-the-Month Effect

The mean returns calculated using regressions (3) and (4) are summarized in Table IV. Examining the table reveals a systematic pattern of significant higher returns on trading day 1, which is visualized in Figure 1. All countries, except for Malaysia, experience a highly significant positive return at the 1% level on this day. For day -1, five countries experience a positive return, significant at the 5% and 10%. Day 2 experiences two highly significant positive returns, and another two significant positive returns. Judging by these figures, a TOM effect is likely to exist in all countries, except for Malaysia. The effect is most intense in Canada and Mexico, with 3 days of significant positive returns around the TOM. Another important observation is that almost all mean returns around the days -4 to 4 are positive, and that the other days in the month are predominantly negative, providing evidence in support of the notion of a TOM pattern for most of the countries. Japan experiences a highly significant positive return on day 1, and significant negative returns on days 5 and 6. These results are contradicting the findings of Ziemba (1991), who found a TOM pattern around days -5 to 2, resulting from a different loan payment system. The significance of the term βj in the conditional variance

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Figure 1. Mean percentage daily returns by trading day of the month

The figure presents the average daily returns (%) between the nine countries for each trading day of the month calculated using the data presented in table IV.

ten and α1andβ1are positive, implying that the GARCH process alone it not sufficient to fully

account for the excess kurtosis in the returns.

Now that we have established that there are symptoms of a TOM effect in the selected countries, we will empirically test this assumption using equations (5) and (6). DTOM is a dummy

variable for the TOM period. We will test three possible TOM periods, in order to examine the robustness of the results. The first TOM period uses the period between day -1 and 2, which is selected after the analysis of Table IV, and contains the most significant positive returns around the TOM. The second period under analysis uses the window running from day 1 to 3, without the inclusion of the last trading day of the previous month. The third period is defined as day -1 to 4, following the standard period used by Lakonishok and Smidt (1988) and Ariel (1987). Regression results are presented in Table V. The coefficient βTOM represents the difference

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Table IV

Mean rates of return by trading day of the month

The table presents regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in equations (3) and (4) with a student-t distribution. The dependent variable is the return on the iShares index for each country. The independent variables are the dummy variables D-9,9 which correspond to the days around the TOM, δ-9,9 represent the coefficients of the dummy variables, which are the mean percentage rates of return for each day. ω, α1and β1 are the

conditional variance parameters. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and ***denotes 1% significance level. The table also presents the regression statistics R-Squared, Adjusted R-Squared, Durbin-Watson and the degrees of freedom of the Student-t distribution. Both R-squared and Adjusted R-squared are not deemed relevant in our research since they do not contribute to explaining the power of our model, so they will be left out in further models using dummy variables.

Coefficient Canada Mexico United States France Germany United

Kingdom Hong Kong Japan Malaysia

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27

Table IV—Continued

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28

Table V

Test for TOM periods

The table contains regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in equations (5) and (6) with a student-t distribution. The dependent variable is the return on the iShares indices for each country. α is the intercept. The independent variables are the dummy variables representing the TOM period 1, 2 and 3, with coefficients βTOM. ω, α1 and β1 are the conditional variance

parameters. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and *** denotes 1% significance level.

Canada Mexico United

United

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existence of a TOM effect. The first period, with the interval [-1,1], shows the most convincing support for this notion. The interval which was first discovered by Ariel (1989), which period is between day -1 and 4, also show highly significant results. The second TOM interval shows the least high significant returns for the difference between the TOM and ROM, but still has four highly significant results and three significant results, which are at the 5% and 10% significance level, respectively. The TOM effect is strongest in North America and Europe, and weakest in the Asian countries. The second TOM period is negative, albeit not significant, in Malaysia. The intercept α, which represents the mean return for the ROM period, has a highly significant positive return for Canada and the US in all three periods. Moreover, this figure is positive in all three periods for all countries, except for Japan. This finding does not support the results of Lakonishok and Smidt (1988), who found that during the ROM the DJIA declined on average. Using the results reported in Table V, mean percentage returns for TOM and ROM are calculated. These are provided in Table VI.

Table VI

Percentage contribution TOM periods

The table reports the percentage contribution of returns during each TOM period for all the countries taken over the whole sample period. Numbers are extracted from the results in Table V. For example, in the case of Canada, 71,57% of the whole increase was earned in the TOM1 period, ranging between day -1 and day 1.

TOM1 [-1,1] TOM2 [1,3] TOM3 [-1,4]

Canada 71,57% 68,08% 69,73% Mexico 86,50% 77,72% 81,84% United States 62,82% 70,48% 53,14% France 81,13% 67,51% 82,62% Germany 85,42% 72,54% 85,08% United Kingdom 91,93% 87,01% 92,28% Hong Kong 92,54% 84,36% 96,31% Japan 116,36% 116,76% 131,12% Malaysia 85,14% -32,57% 82,92% Mean 85,94% 67,99% 86,12%

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31 (1987), who did not find evidence of foreign TOM effects and even found a reverse effect for

Japan.

TOM periods one and three, with an average return contribution of 85,94% in period one, and 86,12% for period three, are the two strongest TOM periods. When we compare these outcomes to the work of Lakonishok and Smidt (1988), who reported that the TOM period accounted for a 100% increase in the DJIA, one can see that the TOM effect has weakened for the US. There, the TOM period accounted for only 53,14% for the increase. Nevertheless, the TOM effect remains very strong for the other countries in the sample. This confirms the results of Marquering, Nisser and Valla (2006) in case of the US and those of Kunkel, Compton and Beyer (2003) and Cadsby and Ratner (1992) for the other countries.

B. Explaining Hypothesis

B.1. Liquidity Hypothesis

Table VII presents the regression results of equation (3), using ARit instead of Rit. A similar

pattern as in the previous section can be observed around day 1, where eight out of nine mean returns are highly significantly positive at the 1% level. Moreover, day 5 experiences five significant negative returns, albeit at the 5 and 10% level. However, this day is outside the traditional TOM period of [-1,4]. Nonetheless, these results are less striking when compared to the results of our previous analysis. Table VIII shows the regression results from equation (3) using SVOLitinstead of Rit. All countries, except for the US and Japan, experience a significant

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Table VII

Standardized mean rates of return by trading day of the month

The table presents regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (3) and (4) with a student-t distribution. The mean adjusted return ARit is regressed with regression (3), using ARit instead of Rit, as calculated in (7). The dependent variable

is the return on the iShares index for each country. The independent variables are the dummy variables D-5,5 whichcorrespond to the days around the TOM, δ-5,5 represent the coefficients of the dummy variables, which are the mean percentage rates of return for each day. ω, α1 and β1 are the conditional variance parameters. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and *** denotes 1% significance level.

Canada Mexico United States France Germany United

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Table VIII

Standardized mean volume by trading day of the month

The table reports regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using a standard OLS model specified in (2). The standardized volume measure is regressed with regression (2), using SVOLit instead of Rit , as calculated in (8). The dependent variable is the return on the

iShares index for each country. The independent variables are the dummy variables D-5,5 whichcorrespond to the days around the TOM, δ-5,5 represent the coefficients of the dummy variables, which are the mean percentage rates of return for each day. ω, α1 and β1 are the conditional variance parameters. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and *** denotes 1% significance level.

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Table IX

TOM Liquidity test

The table presents regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using a standard OLS model specified in (9). The dependent variable is the mean adjusted return, specified in (7). The independent variable is the standardized volume measure as presented in (8). Standard errors are reported in brackets below the coefficients. The table also presents the regression statistics R-Squared and the F-statistic. *denotes 10% significance level, **denotes 5% significance level, and *** denotes 1% significance level.

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The regression results, which are provided in Table IX, document a significant positive relationship between returns and trading activity at the TOM for France and the United Kingdom at the 10% level. These results are similar to those of Booth et al. (2000), who found a positive significant relation in Finland. A highly significant negative relationship is found for Canada. The US does not experience a significant increase of volume around day 1, however it is larger than the average ROM days. These mixed results are difficult to explain, but part of the story is the difference in micro structure of the markets (Booth et al. (2000)). In research of Pettengill and Jordan (1988) a relation was found between relative volume and returns, however, they also concluded that the results were insufficient to account for all the return variation. Overall, our results are inconclusive, so we are inclined not to accept the assumption that higher trading volume accounts for the TOM effect. Therefore, we do not support the view of Ogden (1990) and Siegel (1991), who stated that higher liquidity around the TOM results from higher buying pressure.

B.2. Information Release Hypothesis

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36 that once the effect of macroeconomic news announcements has been taken into account, the

TOM effect no longer exists. Examining Table XI does not support this view, since day -1 and 2 still experience significant positive returns. Subsequently, even after the inclusion of macroeconomic news events, we still find evidence in favor of a TOM effect, albeit less striking after the correction. Consequently, we cannot accept the hypothesis that macroeconomic news announcements are the main drivers of the TOM effect.

B.3. Risk Hypothesis

The empirical results from the conditional variance equation (14) are presented in Table XII. For all days around the TOM the average volatility is measured. Day 1, which had the most striking evidence of high positive volatility in the aforementioned results, has three countries with significant positive volatility. Moreover, all other countries also experience more risk, albeit not significant. Day -1 has overall negative returns, except for the UK and Japan. On day 2 and 3 we report both positive and negative volatility, a structural pattern throughout the countries is not observed. Consequently, these mixed results are not consistent with our conjecture that returns around the TOM are a compensation for bearing higher risk. Therefore, we cannot accept the risk hypothesis.

C. Robustness of the Results

C.1. Turn-of-the-Year/January Effect

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Table X

Mean rate of return during United States macroeconomic news events

The table presents regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (11) with a student-t distribution. The dependent variable is the return on the iShares index for each country. The independent variables are the dummy variables ISM, ISMS, EMP, RS, PPI, IP, CPI, CONSCON, GDP and EMPCOST, which are abbreviations of the important US macroeconomic news announcements provided in Table IV. Dummy variables receiving a 1 corresponding the day (rounded down) and zero otherwise θmare the coefficients for each

announcement m. ω, α1 and β1 are the conditional variance parameters. Standard errors are reported in brackets below the coefficients. *denotes 10% significance

level, **denotes 5% significance level, and ***denotes 1% significance level.

United

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Table XI

Residual regressions correcting for US macroeconomic news

The table presents regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (11) and (12) with a student-t distribution. The dependent variable is the residual (εt) for each country from regression (10). The independent variables

are the dummy variables D-9,9 whichcorrespond to the days around the TOM, δ-9,9 represent the coefficients of the dummy variables, which are the mean

percentage rates of return for each day. ω, α1 and β1 are the conditional variance parameters. Standard errors are reported in brackets below the coefficients.

*denotes 10% significance level, **denotes 5% significance level, and ***denotes 1% significance level.

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Table XI—Continued

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Table XII

Mean volatility by trading day of the month

The table contains regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, of the conditional variance equation specified in (10), using the GARCH(1,1) model. The independent variables are dummy variables of the days around the TOM, with coefficients γ-9,9. ω, α1 and β1

are the conditional variance parameters. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and *** denotes 1% significance level.

Canada Mexico United States France Germany United

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Table XII—Continued

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Table XIII

Mean rates of return by trading day of the month excluding the January effect

The table presents regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (3) and (4) with a student-t distribution. The dependent variable is the return on the iShares index for each country. The independent variables are the dummy variables D-9,9 whichcorresponds to the days around the TOM, δ-9,9 represents the coefficients of the dummy variables, which are the mean percentage

rates of return for each day. ω, α1and β1 are the conditional variance parameters. Standard errors are reported in brackets below the coefficients. *denotes 10%

significance level, **denotes 5% significance level, and *** denotes 1% significance level.

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44

Table XIII—Continued

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C.2. Sentiment

Table XIV presents, for each country, the periods where the market was bullish or bearish, following a graphical analysis of the stock price indices. Most countries experienced in the middle of the nineties a period of increasing share prices, until the period of the internet crash in 2000. After 2002, another period of surging prices occurred, until the credit crisis struck the financial world. The North American and European stock markets are most similar in their pattern, often closely following the movements of the US market. After the establishment of the bull and bear market periods, the results of the regression analysis are provided in Tables XV and XVI. The number of TOMs are also included in the table. We start with Table XV for the bull period, where the average number of observations is around 100, which is enough to base inferences on. Again, day 1 experiences highly significant positive returns, similar to the results of the first regressions. Moreover, day 2 also shows for all countries except France significant positive returns.

Table XIV

Bull and Bear periods

The table provides the time periods for a bull and bear market for each country, except Mexico.

bull bear bull bear bull bear

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Table XV

Mean rates of return by trading day of the month during bullish markets

The table presents regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (15) and (16) with a student-t distribution. The dependent variable is the return on the iShares index for each country. The independent variables are the product of the dummy variables D-9,9 whichcorresponds to the days around the TOM and Dperiod which corresponds to the period, now a bull market, δ-9,9 represents the coefficients of the dummy variables, which are the mean percentage rates of return for each day. ω, α1 and β1 are the conditional variance

parameters. In addition, the number of TOMs are included. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and ***denotes 1% significance level.

Canada United States France Germany United

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Table XVI

Mean rates of return by trading day of the month during bearish markets

The table reports regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (15) and (16) with a student-t distribution. The dependent variable is the return on the iShares index for each country. The independent variables are the product of the dummy variables D-9,9 whichcorresponds to the days around the TOM and Dperiodwhich corresponds to the period, which is now the bear market, δ-9,9 represents the coefficients of the dummy variables, which are the mean percentage rates of return for each day. ω, α1 and β1 are the conditional variance

parameters. In addition, the number of TOMs is included. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and ***denotes 1% significance level.

Canada United States France Germany United

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Table XVI—Continued

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When comparing this to the same regression that took in account the whole period between 1993 and 2009, some differences are spotted. At day -1 there are less significant positive returns for the Bullish period, however, day 2 experiences more significant positive returns. All-in-all, this provides a strong proof in favor of a monthly effect in the bullish market. The regression results, with the inclusion of a dummy variable in the period where the market is bearish, are summarized in Table XVI. Again, the number of TOMs is presented. This number is on average lower for the bear market, which gives our results less precision. However, table XVI provides some interesting results. Our strong significant positive return on day 1 almost completely disappears, with only the US and UK still experiencing significant positive returns. Day 2 shows negative returns for all countries, with UK and Malaysia being significantly negative. These outcomes are different when compared to the results of the bull market, supporting the conjuncture that sentiment is important to the existence of a return pattern around the TOM. These results are, however, conflicting with earlier findings of Kunkel, Compton and Beyer (2003), who found a TOM pattern for Japan during a bear market. Hence, we conclude that the persistence of the TOM is dependent on the sentiment in the market. A link between the information release hypothesis can be drawn; when the market is bullish, US macroeconomic news is usually bad, diminishing a probable TOM effect, and vice versa.

C.3. Controlling for the Influence of the 2007-2009 Financial Crisis

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Table XVII

Mean rates of return by trading day of the month in the period before the 2007-2009 financial crisis

The table reports regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (15) and (16) with a student-t distribution. The dependent variable is the return on the iShares index for each country. The independent variables are the product of the dummy variables D-9,9 whichcorresponds to the days around the TOM and Dperiodwhich corresponds to the selected period, which the period before the

credit crisis, δ-9,9 represents the coefficients of the dummy variables, which are the mean percentage rates of return for each day. ω, α1 and β1 are the conditional

variance parameters. In addition, the number of TOMs is included. Standard errors are reported in brackets below the coefficients. *denotes 10% significance level, **denotes 5% significance level, and ***denotes 1% significance level.

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Table XVII—Continued

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Table XVIII

Mean rates of return by trading day of the month during the 2007-2009 financial crisis

The table reports regression results for nine countries, over 4094 observations for the US and 3293 for all other countries, using the GARCH(1,1) model specified in (15) and (16) with a student-t distribution. The dependent variable is the return on the iShares index for each country. The independent variables are the product of the dummy variables D-9,9 whichcorresponds to the days around the TOM and Dperiodwhich corresponds to the selected period, which is the period during the

credit crisis, δ-9,9 represents the coefficients of the dummy variables, which are the mean percentage rates of return for each day. ω, α1 and β1 are the conditional

variance parameters. In addition, the number of TOMs is included. Standard errors are reported in brackets below the coefficients. Also reported is the date where the markets declined following reports of the crisis. *denotes 10% significance level, **denotes 5% significance level, and ***denotes 1% significance level.

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Table XVIII—Continued

The Turn-of-the-Month puzzle: An empirical examination of iShares