January Effect in the French Market: The case of CAC40 Index

Transcription

1 International Academic Institute for Science and Technology International Academic Journal of Accounting and Financial Management Vol. 5, No. 3, 2018, pp ISSN International Academic Journal of Accounting and Financial Management January Effect in the French Market: The case of CAC40 Index El Khoury, Rim a, Jad Nahas b a Faculty of Business Administration and Economics, Notre Dame University, Lebanon (Corresponding Author). b Faculty of Business Administration and Economics, Notre Dame University, Lebanon. Abstract Efficient Market Hypothesis (EMH) implies that the future price of a stock is unpredictable with respect to currently available information. This study has examined the weak form of the Efficient Market Hypothesis of the French market, by specifically examining the existence of January effect in the CAC 40 index in France. Daily observations for a period of ten years from March 1, 2005 until September 30, 2015 have been used. Different statistically tests were applied including symmetric GARCH and asymmetric GARCH models (mainly T-GARCH). January month did not exhibit higher return, suggesting that there is no opportunity for investors to take advantage of any month. Furthermore, no significant return was found in any other month, suggesting that the CAC 40 index follows a random walk and hence the French market is weak form efficient. Keywords: Efficient Market Hypothesis, CAC40, French market, January effect, GARCH 96

2 1. Introduction Capital market, which is broadly divided into stock market and bond market, is essential for the economic growth of a country. An important attribute of capital market is the efficient market hypothesis (EMH) introduced by Fama (1965), according to which stock prices fully reflect all available information and new information should rapidly adjust into prices, so that no investor can generate excess returns by the use of such information. This implied that, in an efficient market, security prices fluctuations are considered to be completely random and prices should follow a random walk. Due to its huge implications in the financial markets, the EMH becomes one of the well-researched areas in finance by generating debate among financial researchers. Over the years, plenty of researches have been conducted to find evidence against the efficient market hypothesis. Anomalies related to the EMH started to appear in both developed and emerging markets. Researchers have found evidence for the presence of calendar anomalies in the stock markets, including January effect. Essentially, January effect refers to the occurrence of higher returns in January as compared to the average returns of other months of the year. This said, many argued that over the last twenty years, financial markets became more efficient mainly due to improvements in trading system s technology, reductions in the cost of information and relaxation of legal restrictions on international capital flows. Currently, with the presence of advanced and technological financial systems, it is important to test if such profit opportunities still exist. Thus, this paper will test the presence of January effect in the French market taking into consideration the CAC40 index. The rest of this paper is organized as follows. Section 2 describes the Efficient Market Hypothesis and the calendar/january anomalies. A review of previous empirical findings related to January anomaly in the U.S and around the globe is presented in Section 3. A brief description of the Paris Bourse and CAC40 index is presented in Section 4, while Sections 5 and 6 deal with data and methodology used in this study, respectively. Findings and analysis is presented in Section 7, followed by a conclusion in Section Literature Review 2.1. Market Efficiency The theory of random walk was first introduced by Louis Bachelier in 1900, who found no apparent pattern in stock prices. Another formulation of this theory came later with the paper of Kendall (1953). He concluded that "in series of prices which are observed at fairly close intervals the random changes from one term to the next are so large as to swamp any systematic effect which may be present. The data behave almost like wandering series" (Kendall, 1953, p.11). Such conclusion by Kendall can be considered as a direct definition of the random walk hypothesis which has been popularized later on by different researchers. In 1959, Harry Roberts compared Kendall s findings to a roulette wheel whereas each outcome is statistically independent of past history as if no attention is paid for recent spins. He also mentioned: In gambling expression, this roulette wheel has no memory (Roberts, 1959, p.1). Although his paper was similar to Kendall s work, Roberts emphasis was on American indices and individual companies. His conclusion was totally consistent with Kendall s findings, stating that changes in price series always behave as if they had been generated by a simple chance model (Roberts, 1959). The mid 1960s was a turning point in research concerning the random walk theory. In 1965, Fama had defined the random walk market as a market where a series of successive price movements are completely independent. The efficient market hypothesis (EMH) is defined as a market where 97

3 information is equally and freely available to all participants, with large numbers of rational investors competing actively; and where prices quickly adjust to fully reflect all available information (Fama, 1965). Fama (1970) made three different distinctions of EMH based on the relevant information set. The different versions of market efficiency are the weak form, the semi-strong form and the strong form of market efficiency. First, the Weak form efficiency emphasizes that prices of stocks fully reflect all historical information of past prices, so that no investor can generate excess return on the basis of past information, indicating the invalidity of technical or chartists analysts. Second, the semi-strong form efficiency asserts that stock prices reflect all publicly available information and this information should be known to all investors. Thus, any public announcements such as earnings, stock splits, takeovers, etc are reflected in the stock prices. From that perspective, fundamental analysis is wasteful. Third, the strong form efficiency is where prices must, in addition to the past prices information and public information, reflect all private (insider) information so that no one can have an advantage while trading (Hameed, Ashraf, and Siddiqui, 2006). Many financial analysts view the strong form of market efficiency as extreme and only exist in theory (Brealey, Allen, & Myers, 2006). Fama s paper (1970) became a core document in the new quantitative finance and a cornerstone for all future market efficiency studies Calendar or Seasonal Anomalies The Efficient Market Hypothesis suggests that markets are rational and prices always fully reflect available information so that no investor can beat the market and realize abnormal profits. Nevertheless, it is found that some markets are deviating from the rules of the EMH. Those deviations which cannot be explained through the Efficient Market Hypothesis are called financial market anomalies. Those anomalies can be divided into three basic types: Calendar or seasonal anomalies, Fundamental anomalies, and Technical anomalies. Fundamental anomalies include book to market effect, dividend yield, neglected stocks (small firm effect), and price-earnings ratio, while technical anomalies include momentum effect, moving average, and trading range break. This part will only describe calendar or seasonal anomalies. Calendar anomalies are associated with particular time periods and include the weekend effect, turn of the month effect, holiday effect, turn of the year effect, and January effect. The weekend effect is associated with stock returns on Mondays, which are found to be lower than the returns on the immediately preceding Friday. Like other anomalies, empirical evidences are conflicting. Rogalski (1984) decomposed the period from Friday close to Monday close into two parts; non-trading day (from Friday close until Monday open) and trading day (from Monday open until Monday close). By studying the S&P500 index for the period from 1979 until 1984 and the DJIA from 1974 until 1984, he concluded that the negative return on Monday accrued primarily from Friday close to Monday open and that the mean return from Monday trading day is undistinguishable from the mean return of any other trading day. Smirlock and Starks (1986) studied the hourly returns of the DJIA for the period of 20 years from 1963 until The period of their study was decomposed into three parts and their results had changed overtime. First, from 1963 until 1968, the calculated returns from Friday close to Monday open were positive, but, in fact the negative return after the Monday open made the average return of the day negative. Second, from 1968 until 1974, returns were negative on the opening hours of Monday. Finally, in the last period, their results showed that although the opening hours of Monday showed negative returns, the trading returns of the 98

4 entire day were positive. Harris (1986) collected and analyzed 14 months of complete transaction records for the NYSE in order to better understand the weekly and intraday price patterns. Two major conclusions were found in his paper. The first is that, for large firms, the negative Monday close to close return appears between Friday close and Monday open, whereas for small firms, it appears during the Monday trading day. Secondly, he found out that the returns were always positive in the first 45 minutes of trading except for Monday where the trading returns were negative. As for the explanation for the weekend effect, Lakonishok and Maberly (1990) claimed that part of the weekend effect is attributed to the increase in trading activity on Monday, while Damodaran (1989) attributed it to the delayed announcements of the bad news often reported on Friday. The holiday effect suggests a significant difference between stock returns of the days preceding or immediately after a holiday and the rest of the working days of the week. This anomaly comes in two forms: pre-holiday effect and post-holiday effect. Lakonishok and Smidt (1988) found a substantial positive pre-holiday return for a considerable period of time, which can be attributed to investors optimism in the days before the public holiday. This investors psychology contributes to the higher average return on pre-holiday days, which is reverted after the shocks to a low post holiday returns. As for turn of the month effect, according to Lakonishok and Smidt (1984), stock prices are likely to increase in the last day of the month and the three upcoming days of the following month. They added that the return of these consecutive four days exceeds the return of the entire month. This issue had been also discussed by Agrawal and Tandon (1994). They enlarged their study to cover eighteen countries all over the world. In ten out of eighteen countries, the average return from the last trading day of the month until the fourth day of the upcoming month was higher relative to an average day, confirming Lakonishok and Smidt s findings. January effect states that the returns in January are higher than the returns in all other months. Wachtel (1942) studied the different fluctuations of stock prices in 1942 and discovered the presence of the January effect. January effect can be explained by three hypotheses. First, according to the tax-lossselling hypothesis, at the end of the year investors engage in selling stocks which did not perform well during the year to mitigate negative tax consequences at the end of each year. At the beginning of the year, investors re-enter the market by buying back these stocks or attractive stocks. Such scenario will put a downward pressure on prices in December and positive pressure in January (Klock & Bacon, 2014). Second, according to Window dressing hypothesis developed by Haugen and Lakonishok (1987), portfolio managers normally take steps to make their portfolios look better to boost their performance. They tend to sell their risky securities by the end of each year to make their portfolios seem less risky, and buy them back at the beginning of the year in order to earn higher returns. Studies showed that at the beginning of each year, these stocks will outperform the market leading to a high return (Klock & Bacon, 2014). Third, the information hypothesis attributed the excess January return to significant information releases in the first days of January (Rozeff & Kinney, 1976). 3. Empirical Evidence of January Effect Under the weak market efficiency form, different tests were used to either accept or reject the EMH validity. Practically, serial correlation tests, unit root test, and variance ratio test have been commonly used for testing the weak form efficiency. First, the serial correlation tests measure the relationship between a stock return in one period and its return in the previous period. If the coefficient of correlation 99

5 obtained is significantly different from zero, then the hypothesis of weak form efficiency is rejected. Unit root series are characterised as non-stationary with a tendency to return to a long run path. Therefore, for the market to be weak form efficient, non-stationary is a needed condition. Variance ratio tests can be used in order to test whether asset prices and returns are predictable. The test of Lo and MacKinlay (1988) compares the variance of difference in prices or returns of time series data over different interval. It is based on the assumption that if a series follows a random walk, the variance of q period difference should be q times the variance of its one period difference. This test can be used to test the random walk under two different assumptions: homoscedastic and heteroskedastic (Lo & MacKinlay, 1988). Chow and Denning (1993) suggested the multiple variance test, which provides the joint probability instead of individual results for each time interval. For the market to be efficient, the variance ratio should be equal to one. January effect has been investigated in many studies, with mixed evidence. The presence of a positive January effect was found by Rozeff and Kinney (1976), when an equally weighted index of New York Stock Exchange was examined between 1904 and January returns appeared to be more than eight times higher than returns during a typical month. Furthermore, the positive and significant return in January in the U.S stock markets was found by Branch (1977), Dyl (1977), Keim (1983), Roll (1983), Reinganum (1983), Haugen and Jorion (1996), Mehdian and Perry (2002). For example, Reinganum (1983) supported higher profits in January for small firms. He also found that companies with largest price declines exhibited highest returns during first days in January, which could be attributed to tax-loss selling hypothesis. Similarly, Arsad and Coutts (1997) found a significant positive returns in January after the introduction of capital gains tax in Furthermore, other studies report positive and high return in January (Mills, Siriopoulos, Markellos, & Harizanis, 2000; Aggarwal & Rivoli, 1989). Choudhry (2001) tested January effect from 1871 to 1913 for American, British and German Markets. Using GARCH model, he concluded that January effect was present and significant. Asteriou and Kavetsos (2006) tested the existence of January effect in eight transition economies, namely the Czech Republic, Slovakia, Hungary, Poland, Lithuania, Russia, Slovenia and Romania, from 1991 until 2003 using monthly time series data for the stock markets for each country. They concluded their paper stating that in most of the countries of the chosen sample, the January effect exists with strong evidence for Poland, Romania and Hungary. Using monthly data for the period of 1970 to 2005, Moosa (2007) showed a significant January effect in the US stocks except for the period of where a negative July effect dominated. Sudarvel and Velmurugan (2015) investigated the existence of January effect in the Indian Banking sector for the period of thirteen years from January 2002 until June Using the regression model methodology, they were able to demonstrate the existence of January effect in the banking sector in India. Moller and Zilca (2008) found evidence to suggest that returns in January are significantly higher than returns recorded for the remaining months of the year in United States. Similar findings were detected in Canada (Berges, McConnel, & Schlarbaum, 1984), Japan (Kato & Schallheim, 1985), Malaysia (Nassir & Mohammad, 1987), U.K (Mills & Coutts, 1995), Turkey (Balaban, 1995), Emerging Asian Pacific Stock Market (Ho, 1990), Greece (Fountas & Segredakis, 2002; Mills, Siriopoulos, Markellos & Harizanis, 2000), Chile, Greece, Korea, Taiwan and Turkey (Fountas & Segredakis, 2002), India (Pandey, 2002), Sweden (Hellstrom, 2002), Nepal (Bahadur & Joshi, 2005), Poland, Romania, Hungary and Slovakia (Asteriou & Kovetsos, 2006), Argentina (Rossi, 2007). 100

6 However, conflicting results are also available. Gu (2002) that that January effect is declining in the US market and Schwert (2003) reached the same conclusion especially in the period from 1980 to Lindley, Liano, and Slater (2004) found that January effect was not significant in many years during Floros (2008) rejected January effect for three stock indices in Athens stock exchange market and found a positive higher return in months other than January, although insignificant. Giovanis (2009) found the presence of January effect in only seven stock markets out of fifty five stock markets. Furthermore, higher monthly returns are reported in December for twelve stock markets. Li (2013) studied the January effect in the financial services industry in Canada. The results of the paper showed a weak January effect in small-cap firms only before With recent years, this effect had diminished with the appearance of more efficient capital markets. Maghayereh (2003) found a strong evidence that January effect does not exist in Amman Stock Exchange from by applying GARCH and GJR models. Ahsan and Sarkar (2013) examined the existence of the January effect in Bangladesh taking into consideration the Dhaka Stock Exchange (DSE). Using a period of 25 years from 1987 until 2012, they found that although the January effect does not exist in the DSE, there is a significant positive abnormal return in the month of June, raising question about the Efficient Market Hypothesis. In summary, evidence related to January effect is mixed. 4. Paris Bourse and CAC 40 Paris Bourse has been classified as one of the most important stock exchanges in Europe (Business World Magazine, 2014). In terms of domestic market capitalization, it was ranked in the fifth place after New York, NASDAQ, Tokyo and stock exchanges. The CAC 40 (CAC stands for Compagnie Nationale des Agents de Change) is a French stock market index that measures the performance of the 40 largest, publicly traded companies on the Euronext market. In fact, CAC 40 was introduced for the first time in December 31, 1987 with a base value of 1,000. It is a capitalization-weighted index that is considered as one of the main indices in the Euronext alongside with Brussels BEL 20, Amsterdam AEX and Lisbon PSI 20. Actually, the CAC 40 is considered to be a strong indicator of the economic performance of not only France, but of Europe as a whole. Table 1 shows the 40 companies included in the CAC 40 index with the weighting of each company as of 31st of December As shown in the table, many companies listed on the CAC40 stock index are highly globalized such as L Oreal, AXA, and Michelin, having large operations in foreign markets. Actually, these companies conduct about two third of their business outside France, even outside Europe. The accurate evidence for this point is that 45% of the listed companies are held by foreign shareholders such as Germans, Americans, British and Japanese (Overview of the CAC40 stock index, n.d). Currently, the most heavily weighted company on the CAC40 index is the pharmaceutical company- Sanofi with 12.14%. 101

7 Table 1: CAC40 Index constituents Company Ticker Industrial classification Weight (%) ACCOR AC Travel and Leisure 0.65 AIR LIQUIDE AI Chemicals 4.08 AIRBUS GROUP AIR Industrial goods and services 2.84 ARCELORMITTAL MT Basic resources 1.69 AXA CS Insurance 3.40 BNP PARIBAS BNP Banks 6.24 BOUYGUES EN Construction and materials 0.60 CAP GEMINI CAP Technology 0.70 CARREFOUR CA Retail 1.54 CREDIT AGRICOLE ACA Banks 1.02 DANONE BN Food and beverage 4.07 ENGIE ENGI Utilities 1.89 ESSILOR INTL. EI Health care 2.05 KERING KER Retail 1.64 KLEPIERRE LI Real estate 0.96 LAFARGEHOLCIM LTD LHN Construction and materials 1.25 LEGRAND LR Industrial goods and services 1.14 L OREAL OR Personal and household goods 3.65 LVMH MC Personal and household goods 5.02 MICHELIN ML Automobiles and parts 1.85 NOKIA NOKIA Technology 0.76 ORANGE ORA Telecommunication 2.27 PERNOD RICARD RI Food and beverage 2.52 PEUGEOT UG Automobiles and parts 0.58 PUBLICIS GROUPE SA PUB Media 1.19 RENAULT RNO Automobiles and parts 1.10 SAFRAN SAF Industrial goods and services 1.08 SAINT GOBAIN SGO Construction and materials 1.78 SANOFI SAN Health care SCHNEIDER ELECTRIC SU Industrial goods and services 4.04 SOCIETE GENERAL GLE Banks 3.04 SODEXO SW Travel and leisure 0.57 SOLVAY SOLB Chemicals 0.94 TECHNIP TEC Oil and gas 1.18 TOTAL FP Oil and gas UNIBAIL-RODAMCO UL Real estate 2.31 VALEO FR Automobiles and parts 0.54 VEOLIA ENVIRON. VIE Utilities 0.44 VINCI DG Construction and materials 2.42 VIVENDI VIV Media

8 Source: Overview of the CAC40 stock market index 5. Data and Descriptive Statistics The time series data used in this study to test the January effect consists of daily closing prices of the main market index of France, mainly the CAC 40 stock index. Historical daily prices are collected from Yahoo Finance from March 1, 2005 until September 30, 2015 resulting in 2,751 observations and all tests were run using Eviews 7 and Stata Softwares. The choice of a French stock market index rather than individual stocks to test the January effect is based on Officer s finding (1975) that calendar effects can be more easily detected in the market indexes than in individual stock prices. Thus, the dependent variable used will be the return of the CAC 40 index, proxied by the log difference change in the price index. The continuously compounded rate of return is calculated using the closing price as follows: (1) where is return, is natural log, and are the index price at time t and t-1, respectively. The basic descriptive statistics for the return of the index for ten years, for each of the twelve months from January until December, are presented in Table 2. Surprisingly, Table 2 shows that January has a negative mean return, same as the months for May, June, August, September, October and November, the lowest of which is June with a value of %. The highest mean return of the CAC 40 index was in the month of December showing a positive return of 0.080%, just a little higher than the second high April and third high July. As to the mean return of January, it is negative, but just in the middle place (in the 7 th place) neither significantly higher nor lower than the most of the other months. The mean daily returns range from % in June and 0.080% in December. As for the degree to which the distribution is symmetrical measured by the skewness, January, February, April, June, July, August and October months are negatively skewed, thus having more negative returns than positive. The other months are positively skewed which means that they have more positive returns than negative. As for the kurtosis, it ranges from 3.02 in July to in December, higher than 3, suggesting that daily returns are leptokurtic with higher peaks and fatter tails than a normal distribution. Table 2: descriptive statistics for the CAC 40 index Month Nb of obs. Mean return St deviation Skewness Kurtosis January % February % March % April % May % June % July % August % September %

9 October % November % December % Return 2, Another surprising result is the link between return and standard deviation. For most of months, the higher volatility does not lead to a higher return. Some months have abnormally higher volatility with a lower return such as October, September, November and December. The last row shows that the mean return over the entire period is slightly positive ( ), positively skewed with a value of 0.023, with positive excess kurtosis, indicating more positive returns than negative, and higher peak and heavily tailed distribution. 6. Methodology 6.1. Regression Model To test the January effect, this study will use a Dummy variable model. This methodology was firstly created by Keim in 1983 and has been widely used in the US market to test the January effect by Jones, Pearce and Wilson in Furthermore, this methodology had spread out to other countries and it was used by Kato and Schallheim in 1985 to test the existence of the January effect in Japan and by Ahmad and Hussain in 2001 to test the same anomaly in Malaysia. Consequently, this methodology will be used by regressing twelve dummy variables on the CAC 40 index daily return using the regression equation: Where is defined as the daily return, K=12 and (i=1 to 12) are the twelve dummy variables for twelve months, where takes the value of 1 if the corresponding return falls on January, and 0 otherwise, continuing until the last dummy variable which takes a value of 1 if stock return belongs in days of December, and 0 otherwise. is the residual and obeys the normal distribution (Borges, 2009). The estimated coefficient of each variable is the stock index average return for each month in these years. Thus, a positive and significant coefficient of supports the existence of January effect. The first studies of calendar effects such as French (1980) and Jaffe and Westerfield (1985) had employed the ordinary least square regression model (OLS). However, OLS can be used if the residuals are normally distributed, serially uncorrelated, and with constant variance (Wooldridge, 2003). This said, the use of OLS regression can lead to several problems since the stock market index returns are likely to be auto-correlated, the residuals are likely not normal, and the variance of residuals may not be constant as pointed out by Connolly (1991). Thus, the OLS method has been applied in all estimations, but the results are not reported as heterosckedasticity and autocrrelation were present. (2) 104

10 6.2. GARCH Methodology International Academic Journal of Accounting and Financial Management, The OLS regression will be replaced by an ARCH model as proposed by Engle (1982). ARCH models consider that the variance of the predicted error term is directly related to the size of the previous period s error terms, which gave rise to volatility clustering (Liu & Hung, 2010). In 1986, Bollerslev introduced Generalized autoregressive conditional heteroskedasticity (GARCH) whereas he modified the ARCH model adding one condition to the previous one, so that the conditional variance at a given time t is not only affected by the lag of the squared residual from the previous period, but also affected by the last period s forecast variance. Hence, he formed the GARCH model explained in the following formula: (3) The variance of the residuals is expressed as the sum of a moving average polynomial of order q on past residuals (ARCH term) plus an autoregressive polynomial of order p on past variances (GARCH term). Typically, the most used GARCH model is the GARCH (1,1), which includes one lag, both in the ARCH term (last period volatility) and in the GARCH term (last period variance), stated in the following formula: (4) Where: is the conditional variance of the residual in time t, w stands for the mean, stands for the news about volatility from the previous period, measured by the lagged squared residual (ARCH term), stands for last period forecast variance (GARCH term). Nevertheless, GARCH model is a symmetric model in the volatility s response to positive and negative shocks. When it comes to stock indices, it is often observed that negative shocks in the market are followed by higher volatilities in prices and returns than positive shocks for the same magnitude (Giovanis, 2009). Thus, an asymmetric model will be used in order to enable conditional variance to respond asymmetrically to rises and falls in innovations. Glosten, Jagannathan, and Runkle (1993) proposed an asymmetric GARCH model that is the TARCH model known as the Threshold ARCH model or the GJR-GARCH model. Typically, a specification of with p=q=1 is sufficient, so that the TARCH(1,1) is as follows: (5) (6) is a dummy variable that takes a value of 1 when <0, d=1, and 0 when 0. So, in this model, good news ( >0), and bad news ( <0 ) have differential effects on the conditional variance. Good news has an impact of α, while bad news has an impact of α + γ. If γ >0, we say that the leverage effect exists; if γ 0, then, the news impact are asymmetric. When the γ value is equal to zero, TARCH model will be the same as the symmetric GARCH model (Glosten et al, 1993). Furthermore, the asymmetric of the data will be tested using the significance level of the coefficient related to TARCH. It should be mentioned that the Hannan Quinn information criterion (HQC), the Akaike Information criterion (AIC), the Bayesian Information Criterion (BIC), in addition to the Bollerslev-Wooldridge quasi-maximum likelihood estimation will be used in order to choose the most suitable model. The 105

11 Akaike information criterion (AIC) estimates the quality of each model relative to each of the other models. Thus, AIC is considered as a mean for model selection (Arnold, 2010). The Bayesian Information Criterion (BIC), developed by Schwarz in 1978 also known for Schwarz criterion, is partially based on the likelihood function and at the same time closely related to the Akaike information criterion (Lee, Noh, and Park, 2014). On the other hand, Hannan and Quinn (1979) introduced the HQ as a criterion that would serve as a compromise between a consistent criterion (namely the BIC) and an asymptotically efficient criterion (namely AIC). The likelihood estimation is an estimate of a well-defined parameter in a statistical model, which is formed after maximizing a function that is related to the logarithm of the likelihood function. Thus, the model with the smallest criterion value for AIC, BIC, and HQ and the maximum likelihood will be used and only the optimum model will be presented. 7. Empirical Analysis January effect will be tested through a regression analysis where the dependent variable is defined as the daily return of the CAC 40 index and the independent variables are twelve dummy variables representing twelve months, as follows: There are some stochastic assumptions (normality, autocorrelation, stationarity, and homosckedastciity) that should be tested and satisfied to ensure that the results of the OLS regression are efficient Normality Jarque-Bera test (Jarque and Bera, 1987) will be used to test whether the residuals are normally distributed. The results in Table 3 suggests that the null hypothesis of normality is rejected as the p-value for the Jarque Bera test is zero, suggesting that the residuals are not normally distributed. Table 3: Jarque Bera test for OLS regression residuals Mean Std. dev. Skewness Kurtosis Jarque bera probability 5.45e Autocorrelation Randomness in return series or no-autocorrelation can be inferred only if the correlation between current and previous returns is zero. In order to test the autocorrelation in the residuals, the Ljung box (Ljung & Box, 1978) test will be used. This test investigates whether a group of autocorrelations of a time series are different from zero, providing a superior fit for the chi-square distribution for little samples. As shown in Table 4, the test has been conducted by including twelve lags of the dependent variable in the test regression. AC (Autocorrelation) shows the correlation between the current return of the index and its lagged value. For example, using Lag of 3, AC reports that the correlation between the current value and its value three days ago is On the other hand, PAC (Partial Autocorrelation) shows that the 106

12 correlation between the current return of the index and its value three days ago is without taking into consideration the effect of the two previous days. Results in Table 4 show a highly significant negative autocorrelations at the first three lags with high Q- statistics at all lags. For higher order autocorrelations, up to lag 9 and 10, all return series show a consistent pattern of negative autocorrelation. Negative autocorrelation indicates mean reversion in return suggesting that prices and return eventually move back towards the mean or average. Additionally, the p-value for all lags is 0.000, suggesting the presence of autocorrelation till order 12. Therefore, autocorrelation needs to be corrected to keep the standard errors efficient if OLS regression is to be used. Table 4: Correlogram of Residuals Lag AC PAC Q-Stat Prob * * * * * * * * * * * Note: * denote statistically significant at 99% confidence level Unit Root The presence of unit root or non-stationarity (random walk) is a common observation in the case of time series data. Data should be stationary, otherwise, using OLS regression will lead to spurious results. This study employs the Augmented Dickey Fuller (ADF) to test the presence of unit root in the time series. As suggested by Dickey and Fuller (1979), we augment the standard Dickey-Fuller test by lags of the dependent variable but taken in first difference in order to eliminate autocorrelation from the residuals. The ADF statistic is negative, and the more negative it is, the stronger the rejection of the hypothesis that there is unit root at a given level of confidence (Cheung & Lai, 1995). Generally, the Augmented Dickey Fuller test derived from an autoregressive (AR) model involves one of the following three regressions. The first regression model considers a constant and a trend, while the second regression model considers only a constant with no trend and the third regression model does not consider neither a constant nor a trend. The choice of the model will depend on the presence or absence of a deterministic trend (Sephton, 2008). 107

13 return International Academic Journal of Accounting and Financial Management, Figure 1: CAC40 index returns from January 2005 until September jan jan jan2015 daily Figure 1 shows the returns of the CAC40 index for the entire period. According to the graph, returns are fluctuating around a mean of zero without any deterministic trend, so the Augmented Dickey Fuller test is tested using the regression model without a constant neither a trend as follows: (7) Results in Table 5 show a high t-statistic value of , and the MacKinnon approximate p-value is which is absolutely less than the critical values at the 1% and 5% significance levels. Specifically, the CAC 40 index return series implies that the data is stationary, thus rejecting the random walk hypothesis. Table 5: Augmented Dickey Fuller test Augmented Dickey Fuller test for unit root Number of observations: 2176 Interpolated Dickey Fuller Test Statistics 1% Critical 5% Critical 10% Critical Value Value Value Z(t) MacKinnon approximate p-value for Z(t) = Heteroscedasticity test Homoskedasticity assumption was questioned by many researchers and scholars especially the ones concerned with financial market studies and these researchers were able to demonstrate that the variance of the error terms is a time varying variance and that volatility shocks today will influence the expectation of volatility many periods in the future. Both findings show that the variance of the residuals tends to be 108

14 time varying and clustered, which is the so called heteroskedasticity. Heteroscedasticity is tested on the residuals of the OLS regression of equation 2 using the ARCH-LM test, by regressing the squared residuals on the lagged squared residuals and a constant using five, twelve and twenty lags. If the null hypothesis, that the residuals are homoskedastic, is rejected, then OLS model will be substituted by the autoregressive conditional heteroscedasticity (ARCH) model which corrects the variability in the variance of the residuals. Results in Table 6 indicates that residuals are not homoscedastic and that the variance of the residuals is time varying. Table 6: ARCH LM test on the OLS regression residuals using 5, 12 and 20 lags Heteroskedasticity test: ARCH Number of Lags Prob. F * * * Prob. Chi-Square * * * Note: * denote statistically significant at 99% confidence level. Given that the data is stationary and residuals are not normally distributed, are autocorrelated and heteroscedastic, OLS regression will be replaced by an ARCH model as proposed by Engle (1982) Model Selection: ARCH, GARCH and TARCH models First, it is important to test the presence of ARCH effects. First, the results shown in Table 6 ensures the presence of ARCH effect in the residuals of the OLS regression model. Second, data are stationary as shown in Table 5. Third, the presence of heteroskedasticity in the residuals of the OLS regression model and the absence of unit root in the data supports the use of the ARCH model in order to test the presence of the January effect. An extension of ARCH model is the generalized ARCH (GARCH), which adds lags of the variance to the standard ARCH, such as GARCH(1,1) suggesting one lag to the regression residual (1 ARCH term) and one lag of the variance itself (1 GARCH). According to Brooks and Persand (2003), GARCH (1,1) is enough to deal with financial time series and it is often rare to need a higher order of GARCH in the finance literature. However, the conditional variance might show asymmetric behavior. Black (1976) found that positive and negative shocks have different effects on volatility, whereby volatility is more sensitive to negative shocks. Thus, another extension of GARCH is the threshold GARCH model or T-GARCH, where positive and negative news are treated asymmetrically. In order to choose among GARCH (1, 1) and TARCH (1, 1, 1), the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIS), the Hannan Quinn (HQ), and the Maximum likelihood criterion will be taken into consideration and the most suitable model is the one minimizing the AIC, the BIC and the HQ, and maximizing the likelihood estimation. Table 7 summarizes the different values of each criterion for both tests: GARCH (1, 1) and TARCH (1, 1, 1). TARCH (1, 1, 1) model has a lower AIC, BIC, HQ and a higher Likelihood than the GARCH (1, 1) model. Thus, it is safe to use the TARCH (1, 1, 1) model instead of the GARCH (1, 1) model. 109

15 Table 7: values of different criterions for GARCH and TARCH Criterion GARCH (1, 1) TARCH (1, 1, 1) AIC BIC HQ Likelihood If the coefficient of the TARCH model appears to be statistically significant, it would be an additional reason to choose TARCH model instead of GARCH. TARCH model would enable conditional variance to respond asymmetrically to rises and falls in innovations (Giovanis, 2009). Table 8: TARCH model results Variance Equation C 2.86E E * RESID(-1)^ * RESID(-1)^2 *(RESID(-1)<0) * GARCH(-1) * Note: * denote statistically significant at 99% confidence level. Table 8 shows that the p value of the TARCH (1, 1, 1) model is lower than 0.05, statistically significant. This significance ensures the presence of asymmetric information and demonstrates that the GARCH model cannot be used to estimate the model s variance Determining the TARCH order According to Bollerslev, Chou, and Kroner (1992), the first order to TARCH provides a good representation of a wide variety of volatility processes. To ensure that the first order of the TARCH model appropriate, the autocorrelation test should be performed again on the standardized residuals and on the square of the standardized residuals to prove that the first order of the TARCH model is correct. While p should eliminate autocorrelation in the standardized residuals, q should eliminate autocorrelation in the square of the standardized residuals. If autocorrelation is present in the standardized residuals, then p should be increased consistently until autocorrelation is eliminated. If autocorrelation is present in the square of the standardized residuals, then q should be increased consistently until autocorrelation is eliminated too. Autocorrelation tests will start with the first order. Firstly, the Ljung Box test is performed on the standardized residuals to ensure that the first order of p is accurate. Table 9 shows that the standardized residuals of the first order TARCH model are not autocorrelated having a p value equals to until twelve lags, higher than the confidence interval, thus accepting the null hypothesis and rejecting the alternative one. This first test shows that the first order of the p value of the TARCH model is correctly used and there is no need to increase it. 110

16 Table 9: autocorrelation test on standardized residuals of the first TARCH model order AC PAC Q-Stat Prob Secondly, the Ljung Box test is performed on the square of the standardized residuals to ensure that the first order of q is accurate and it should not be increased. Table 10 shows that the squared residuals of the first order TARCH model are not auto-correlated having a p value equals to 0.62 until twelve lags, higher than the confidence interval, accepting the null hypothesis, and rejecting the alternative one. This second test shows that the first order of q in the TARCH model is correctly used and there is no need to increase it too. Table 10: autocorrelation test on the square of the standardized residuals of the first TARCH model order AC PAC Q-Stat Prob

17 7.7. TARCH Model findings International Academic Journal of Accounting and Financial Management, Finally after concluding that TARCH (1,1) is the most suitable model to test the January effect in the CAC 40 index, the model s results are reported in Table 11. In order to have a January effect, or any other month effect, the probability of the dummy variable related to this month (D1 in case of January) should be statistically significant i.e. less than 5%. Table 11: First order of TARCH model findings Variable Coefficient Std. Error z-statistic Prob. D D D3 5.23E D D D D D8 6.93E D D E D D Table 11 shows that none of the probabilities related to the twelve dummy variables are significant. Thus, the seasonality effect related to the January effect does not exist in the CAC40 index, concluding that the index is weak form efficient. In addition, in all other months, the index does not exhibit significant return, which means that investors cannot rely on historical data to formulate profitable strategies and achieve abnormal returns. Taking into consideration that the CAC40 is a very important indicator of the economic and financial performance in France and Europe (Ryland, 2003), this finding can be generalized in order to consider the French market to be weak form efficient when it comes to the January effect. 8. Conclusion An efficient market is where all investors are well informed about all relevant information, and stock prices quickly adjust to new information. Accordingly, no investor can beat the market by generating abnormal returns. In the weak form efficient, stock prices reflect all historical information, so technical analysis is useless. Although the Efficient Market Hypothesis is a simple theory in principle, it is yet debatable whether the market follows the rules of EMH. Thus, the purpose of this thesis was to investigate the Efficient Market Hypothesis (EMH) in the French market, by testing its weak form. The weak form market efficiency for the CAC 40 index was specifically tested by examining the presence of January effect using a daily return data from January 2005 until September To achieve this purpose, a regression model with twelve dummy variables related to each month was run. In an attempt to select the best model to account for return and volatility in the French stock market, three models (ARCH, 112

18 GARCH, and TARCH) were examined. The result from most of the statistical properties favored TARCH(1,1,1) as the best model to account for return and volatility in the market. The TARCH model suggests the existence of a leverage effect on the CAC40 index as there is dissimilar reaction of investors toward good and bad news in the market. Analysis of the dummies which represent each month from TARCH modeled reveals no January effect. The month of January did not exhibit a significant positive return, supporting the efficiency of the CAC40 index in its weak form. In addition, all other months were tested for the same purpose, and results showed that none of the twelve months confirm the presence of significant positive or negative return. The policy implication of this finding is that investors should not rely on monthly effects to identify the presence of abnormal returns and formulate profitable strategies. In summary, findings support the idea behind the weak form of the EMH related to the randomness of the returns, whereby prices of the CAC40 index were completely random and there were no seasonality in its prices. In testing this form of the EMH, this paper takes into consideration only one anomaly in the weak form. Therefore, though the results lead us into believing that the CAC 40 index is weak form efficient, yet we choose to remain cautious in letting our belief transcend into a generalization. Thus, it is recommended to extend this study by testing the presence of other seasonal anomalies such as Monday effect and turn of the month effect, and to test other market efficiency anomalies in the weak form of the EMH in order to assert the acceptance of the weak form of the EMH in the French market. Reference Aggarwal, R., and Rivoli, P. (1989) Seasonal and Day-of-the-Week Effects in Four Emerging Stock Markets. The Financial Review, 24 (7), Agrawal, A., and Tandon, K. (1994). Anomalies or illusions? Evidence from stock markets in eighteen countries. Journal of International Money and Finance, 13(1), Ahsan, M., and Sarkar, A.H. (2013). Does January effect exist in Bangladesh?. International Journal of Business and Management, 8(7), Arnold, T. (2010). Uninformative Parameters and Model Selection Using Akaike's Information Criterion. Journal of Wildlife Management, 74(6): Arsad, Z., and Coutts, G.A. (1997). Security price anomalies in the London International Stock Exchange: a 60 year perspective. Applied Financial Economics, 7, Asteriou, D., and Kavetsos, G. (2006). Testing for the existence of January effect in transition economies. Applied Financial Economics Letters, 2, Bachelier, L. (1900). Theorie de la speculation. Annales Scientifiques de l École Normale Supérieure, 3 (17), Bahadur, K. C. F., and Joshi, N. K. (2005). The Nepalese stock market: efficiency and calendar anomalies. Economic Review, 17, Balaban, E. (1995). January effect, yes! what about mark twain effect? (Research Department Paper No. 9509). Retrieved from the Central Bank of the republic of Turkey: 637fd6ae51cd/9509eng.pdf?MOD=AJPERES&CACHEID=45844d87-a a2d- 637fd6ae51cd. 113