The January Effect re-evaluated
Abstract: This thesis investigates the January effect in recent data and empirically tests an extension of the efficient market hypothesis which suggests that in the case of the January effect, investors learn gradually over time (Easterday, 2009). To this end regressions are carried out using monthly holding period returns of NYSE firms over the 1992-2012 period. The sample firms are divided in ten equally weighted portfolios to resemble ten deciles based on market capitalization. The results show that the January effect is present, although only in the lower decile portfolios containing the small stocks. The effect is still present when risk is taken into account by incorporating the CAPM model in the regressions. A statistically significant downwards trend is found concerning the January effect, but this trend is of such low magnitude that it is concluded that the downwards trend holds no economical significance.
Author: Franciscus Hoedemaker
Student number: 5984262
Supervisor: Shivesh Changoer MSc.
Date: 31 Jan. 14
1. Introduction
The January effect is one of the most intriguing and investigated seasonal anomalies in the financial market (Haugen and Jorion, 1996). It was first brought to attention by Wachtel (1942), who in his paper concluded that small capitalization stocks outperformed the market as a whole in the month of January. At the time the discovery of the phenomenon did not make much of an impact. It made a much larger impact when it was reintroduced by Rozeff and Kinney (1976) because at that time it challenged the accepted paradigm of efficient markets. This is the main idea of the efficient market hypothesis (EMH) which was developed by Fama (1970) and asserts amongst other things that prices reflect all available information and that a January return premium would be arbitraged away immediately. Easterday (2009) offers an interesting extension of this theory when he poses the possibility that investors, as a group, can learn gradually from new information as opposed to the common idea that the reaction of investors is reflected in an almost instant price adjustment in stocks. By theory of this idea, the January effect should have a declining nature as this would indicate that the markets are efficient the way Easterday describes. In such a market, the higher returns in January would be noticed by investors and arbitraged away gradually due to more investors learning about it and being able to arbitrage it. These investors would buy small capitalization stocks in December and sell at the end of January to profit from the anomaly. Most papers concerning the January effect have presented considerable evidence that this arbitraging is not taking place. Mehdian and Perry (2002) offer increased trading by institutional investors, faster information processing and lower transaction costs as possible causes for a decline in the January effect. This thesis re-evaluates the January effect in recent data and empirically tests Easterdays theory of gradual learning from investors. The research question of this thesis is then to what extent and in what form the January effect is still present and if it is gradually diminishing over time. The results show that the effect is present in the sample period, although it is predominately present in the portfolios with the lower capitalization firms. The effect is still present after taking market exposure risk into account by incorporating the CAPM model. The results also provide evidence for a statistically significant downwards trend but this trend is of such a small magnitude that it is of no economical relevance. This thesis investigates the existence of the January effect in new data, whether it diminishes over time and if the higher excess returns during the month of January are due to the presence of higher risk. Haugen and Jorion (1996) covered the first two parts of this thesis in their research and found positive evidence for existence, as well as no diminishing, of the January
effect. Rozeff and Kinney (1976) investigated the January effect in relation to the difference in volatility between months and came to the conclusion that the January effect may be a phenomenon of risk compensation in the month. This thesis aims to re-evaluate these conclusions in newer data to see if time has changed anything. In the next paragraph the relevant literature will be discussed after which the possible explanations given thus far for the existence of the January effect will be discussed. Paragraph four then entails a description of the data and the model that is used for the quantitative part of the research. Then follow the results and accompanying analysis in paragraph five. Paragraph six entails a discussion and conclusion to the research. Lastly, there is a reference list.
2. Literature review
This paragraph describes the important literature concerning the January effect, what the most common possible explanations are for the January effect and what this thesis aims to contribute. The January effect was originally discovered by Wachtel (1942). However, the anomaly only became popular when it was reintroduced by Rozeff and Kinney (1976). This was after the efficient market hypothesis had become the accepted paradigm. Keim (1983) investigated the January effect further, especially in relation to the small firm effect. The small firm effect is a theory that firms with a small market capitalization outperform larger companies, it is one of the factors in the Fama French three factor model which also contains market return and book-to-market values as factors that describe a portfolio’s rate of return (Fama and French, 1993). Keim (1983) found that a large part of the small firm effect is due to anomalous January returns. However, he states that hypotheses of others to explain the size effect appear unable to explain the January effect. Keim gives the example of an omitted risk factor as a possible explanation of the size effect. This omitted risk factor could then also explain part of the January effect. However, Keim concludes that the behaviour observed in January cannot be only because of the omitted risk factor because risk alone cannot explain higher than normal returns in the same month each year. For his study he uses data from the CRSP daily stock files for the seventeen-year period from 1963 to 1979. The sample contains firms which had returns on the CRSP files during the entire calendar year and which were listed on the NYSE or AMEX. He ranked the sample firms each year based on market capitalization and divided the yearly distributions of market values equally into ten portfolios based on size. With the first portfolio holding the smallest firms and the tenth one containing the largest firms. He then first checks the size anomaly and finds evidence that excess returns
are a monotone decreasing function of firm size as measured by total market value of equity1. He finds that the average daily excess return of the portfolio of smallest firms is approximately 0.082 percent and for the portfolio with the largest firms the average daily excess return is -0.038 percent. Keim then proceeds to investigate the month to month stability of this size effect. He tests the null hypothesis for equal expected returns in every month of the year. He therefore regresses daily excess return on a constant and eleven dummy variables for each month of the year except January and he does this for every market capitalization decile. The constant then measures the excess return for January and the coefficients of the dummy variables represent the differences between the excess return for January and the excess returns for the remaining months. The null hypothesis entails that the estimates of the coefficients are all close to zero. An F-statistic for the joint significance of the dummy variables should be insignificant. Keim reveals that the F-statistic belonging to the portfolio with the smallest capitalization firms is significant at any level and allows rejection of the null hypothesis. The coefficients of the dummy variables for the non-January months are approximately the same. Results from this regression then indicate that average January excess returns for smaller market capitalization firms are disproportionately large in comparison to the other months.
Keim then further investigates the excess returns within January and he finds that a large portion of the size effect takes place during the first five trading days of the year. To test this, he computes the difference between the smallest and largest market value portfolios for these first five days. Keim concludes that the effect is predominately present in the first trading day of the year and that the effect diminishes greatly directly hereafter, although not enough to disappear. He concludes also that approximately 10.5 percent of the annual size effect for an average year in the sample is due to the first trading day of the year. For the first five trading days this portion is 26.3 percent.
Haugen and Jorion (1996) replicate the research of Keim with newer data. They examine the monthly returns to NYSE firms from 1926 through 1993. They also divide their sample into 10 portfolio’s on the basis of market capitalization and find evidence that the January effect is persistent over time. They regress the excess returns on a dummy variable for January Jt and
1
Due to the fact that every year, firms enter or leave the sample because of bankruptcies, mergers, listings and delistings, the total amount of sample firms is not stable over time. It ranges from approximately 1500 in the beginning of the sample period to 2400 during the end.
find significant evidence of a January premium for excess returns. They also find that the null hypothesis of a zero January premium is more difficult to reject as the market capitalization of the stocks in the portfolio grows. In the tenth portfolio, with the largest mean market capitalization, the null hypothesis cannot be rejected. This is further evidence for the strong relation between the January effect and the small firm effect. To test for a trend in the January effect, whether increasing or decreasing, they repeat the aforementioned regression and add a long-term time trend variable LTt equal to year t minus 1977. The product of Jt and LTt then measures any long-term trend in the January premium over the whole sample period. The results of this second regression give no substantial evidence for a significant time trend in the difference between the return in January in comparison with the other months of the year over the entire sample period. Next, Haugen and Jorion investigate the presence of a trend after the January effect was reintroduced with substantial impact in 1976. To test for this, they again repeat the first described regression and this time, add a short-term time trend variable STt which takes a value of year t minus 1977 after 1976 and 0 otherwise. The product of Jt and STt then measures any trend in the January effect since its more impactful reintroduction in 1976. The results of this third regression do not provide any statistically significant coefficients belonging to the time trend variable in any market capitalization decile. This leads the authors to conclude that the January effect is consistent and that it is not declining.
After Keims paper was published, there was no research critiquing the existence of the January effect for a long time. Some twenty years later, research emerged concerning the January effect which did not agree with Keims conclusions. For instance, Gu (2003) and Schwert (2003) claim that the effect is disappearing over time after 1988, suggesting a trend towards market efficiency. Gu states that there is evidence for a decline when the results of Keim (1983) are taken as a benchmark. Schwert (2003) states in his paper that many of the well known financial anomalies do not hold up in different sample periods. He argues that a reason for this is that most anomalies seemingly disappear right after the papers that pointed them out were published. He further states that the January effect became weaker in the years after it was first documented in academic literature. Schwert concludes from this that research findings were effectively causing the financial market to become more efficient. He admits that there is some evidence that the January effect still exists, but he finds it interesting that the January effect seemingly does not exist in the portfolio returns of investors who focus on small capitalization firms.
Mehdian and Perry (2002) examine three large US stock market indices over a 1964-1998 time period: the Dow Jones Composite, the New York Stock Exchange Composite and the Standard & Poors 500. They provide evidence that the January effect is disappearing completely, although slowly, from 1987 onward. In their paper they regress the daily percentage return of the different stock indices on dummy variables from all the months of the year except one. They find evidence supporting the January effect in every stock market index. They then perform a series of Chow breakpoint tests to test the null hypothesis that the estimated coefficients from their regression are stable over the entire sample period. They use 1 October 1987 as the breakpoint due to the fact that this was right before the stock market crash of 1987, also known as Black Monday. They however give no further explanation as to why they believe the January effect should decline after 1987, one reason at least is because Keims sample period ends before this year. These Chow tests produce significant F-statistics which lead to a rejection of the null hypothesis of stable coefficients. Mehdian and Perry then conclude that there is evidence for a January effect before the 1987 market crash, but that there is no evidence of the effect in the era after the market crash. They conclude this for each of the investigated stock market indices.
So it seems that the January effect is not unanimously agreed upon. Easterday (2009) challenges Gu, Schwert and Mehdian and Perry, as he proposes the possibility that the apparent decline found by their papers is due to the use of years of unusually high January returns as a benchmark. He agrees with the premise of the papers as he argues that because investors cannot unlearn information, the January effect should decline monotonically over time, if it declines at all. Easterday states that this idea that stock markets learn slowly and become more efficient over longer periods of time is troublesome. He bases this notion on the strong evidence of quick price adjustments to event announcements. However, he offers the theory that because the combined January small firm effect is evidently not adjusting quickly, the slow learning by investors is a possible explanation for a gradual decrease over time.
The notion that stock markets react rapidly to new information is based on the weak-form efficient market hypothesis. Bodie et al (2011) state that this hypothesis asserts that stock prices reflect all information that can be gathered by examining market trading data such as the history of past prices. They further state that the weak-form hypothesis implies that it is futile to analyze trends. Past stock price data are publically available and if such data would convey information about future performance, investors would already have learnt about it and arbitraged away the anomaly. Easterday (2009) believes that in the case of the January
small firm effect, investors do not behave typically and are in fact slow learners. He gives no apparent reason for the fact that their behaviour is not in line with the efficient market hypothesis. He starts his paper by re-evaluating the hypothesis that the January effect is diminishing or disappearing completely over time. For this part of his research, he focuses on data concerning NYSE and AMEX firms during the time period 1946-2007. He divides the firms in deciles based on market capitalization and breaks the sample in three sub-periods. The first period is 1946-1962, the second is 1963-1979 which is the period observed by Keim (1983) and the third period is 1980-2007. Easterday argues that to accurately measure whether there is a decline apparent concerning the January effect, a sufficiently long sample period is necessary. This is a critique aimed at the papers of Gu (2003), Schwert (2003) and Mehdian and Perry (2002) which do not take into account the period before Keims sample period. Easterday checks if the excess returns in January during the periods before and after Keims sample period are approximately the same and lower than the excess returns in Keims sample period. He does this for every market capitalization decile. Easterday uses t-tests to test the significance of the difference in excess returns between Keims period and both the first and the third sub-period. The difference in excess returns between Keims period and the others is significant and the difference between the first and the third sub-period is not significantly different from zero. He also finds that the January premium in the sub-period that coincides with Keims sample period is larger than in the other two sub-periods. Easterday concludes that the January effect has not declined since Keims paper, but has simply reverted to levels that existed before that time period.
Easterday then plots the time series of January return premiums for firms in the smallest market capitalization decile for the whole sample period 1946-2007. This plot shows increased magnitude and variance for the January returns of Keim’s (1983) sample period. Easterday confirms this using an F-test to reject the null hypothesis that the variance of January return premiums from firms with small market capitalization during the second sub-period is equal to the variance in sub-sub-period 1 or sub-sub-period 3. In conclusion, when a longer sample period is used and an unstable volatility over time is taken into account, Easterday does not find convincing evidence that the January effect is steadily diminishing or disappearing over time. However, he does find evidence for a decline of the effect when only sample-period 2 and 3 are considered.
The aim of this thesis is to empirically research the January effect in more recent data. CRSP returns for the NYSE will be used for better comparison, as well as the technique of dividing
the sample stocks into ten portfolio’s based on market capitalization. The next paragraph discusses a possible explanation for the January effect. In the paragraph thereafter, the presence of the January effect in newer data is investigated. After this, the same effect will be checked in relation to the small firm effect. Next, this paper looks at the possible existence of a decline in the effect in recent years, which would indicate the markets becoming more efficient. Lastly, the risk in January will taken into account by using the Capital Asset Pricing Model (CAPM) to calculate the beta and adjust the holding period returns on the basis of systemic risk.
3. The tax loss selling hypothesis
One of the most common explanations given for the January effect is the tax loss selling hypothesis. This hypothesis entails that investors tend to sell their bad performing stocks in December because of tax reasons and then wait until January to buy new stocks again to complete their portfolios. This theory is not without critique as empirical research has proven for example that the January effect is very much present in countries where the tax cycle does not end in December. Another example is the fact that Keim (1982) shows that the January effect is on average, larger in the period from 1930 through 1940 than in any subsequent period. The January effect should be less significant before World War II because in that period, personal tax rates were relatively low compared to post-World War II. If it really is tax loss selling at the end of the year that is causing the January effect, then the magnitude of the measured January effect should vary with the level of personal income tax rates. Given these results, Keim (1983) concludes that the January effect is not clearly supported empirically. Nevertheless, Easterday (2009) investigates the year-end tax loss selling by looking at trading volumes in January compared to other months of the year. He does this also to look for evidence that investors are arbitraging away the January effect. For this he investigates the smallest capitalization decile only, as the effect is mostly present in this category of firms. Because Easterday predicts that both these phenomena entail higher stock trading activity in December as well as in January, he excludes January observations from the regression equation testing the December dummy variable and vice versa, in order to avoid the January data interfering with the test. Easterday uses the following regression model:
Where the fraction of outstanding shares traded per month is regressed on holding period return and a dummy variable for January with December observations excluded from the sample. The intercept α then means the average trading volume for the eleven month period. The coefficient for holding period return β1 measures the average correlation between trading volume and return for the eleven month period. The coefficient belonging to the dummy variable β2 measures the incremental trading volume in January relative to the intercept. The same regression is made for December with the January data excluded. The mean of β1 is significantly positive for both regressions which indicates that the amount of shares traded is positively associated with the holding period return. The coefficient β2 on the January month dummy however, is not significantly different from zero and this coefficient on the regression with the December month dummy is three times larger than its January counterpart and highly significant. This is evidence for the fact that December trading volume is significantly higher than the rest of the year, but trading volume in January is not different from the other months besides December. Based on these results, Easterday concludes that he does not find evidence that the large price changes of small capitalization firms in January are associated with increased trading volume during the month. Which challenges the tax loss selling hypothesis and at the same time provides evidence that the January effect is not arbitraged away by investors. Easterday offers some plausible explanations for why this is happening. First, he mentions the high transaction costs for small firms as a possible obstruction. Furthermore, he offers infrequent trading and low supply of small capitalization firms as a reason because these are problematic for quick portfolio construction. He concludes that while higher returns might be available, it may be impossible to build an arbitrage portfolio of sufficient dollar value to create a considerable economic profit.
4. Methodology
This section describes in detail the data used in this thesis and the sample selection. Next, the research design for the various topics is described and explained. The data used in this thesis is taken from the website of Wharton Research Data Services. The CRSP dataset is chosen as this dataset provides the necessary data and is used in most of the previous studies concerning this topic. Data of stocks traded at the New York Stock Exchange (NYSE) are investigated in the period starting in January 1992 and ending in December 2012. This time period is chosen because it nicely follows on the sample period investigated by Haugen and Jorion (1996). The
cut off point for the sample period is 1992. This point is chosen because approximately around this time, the U.S. stock markets were undergoing financial liberalization. With for example the Clinton administration, which started in 1993, signing over 270 trade liberalization pacts with other countries (Rabel, 2002, page 98). These pacts would entail new influences from abroad, which may have lead to a more efficient market. Monthly holding period return is examined and for the largest part of this paper the NYSE firms are ranked on the basis of market capitalization and put in 10 equally weighted portfolios. The CRSP database offers an option where this procedure is already applied to the NYSE dataset. CRSP ranks the NYSE firms at the end of each year and puts them in ten equal portfolios for the following year. The largest securities are put in portfolio 10 and the smallest in portfolio 1. The provided holding period returns are calculated with the inclusion of dividends. This thesis uses excess return as the explained variable and therefore the risk free rate is necessary. CRSP provides the risk free rate in the form of the monthly return on 30 day t-bills. Also provided are the equal-weighted and the value-weighted market portfolio of the NYSE.
The research design of this thesis is as follows. First, the data will be analysed and descriptive statistics will be presented. Next, certain univariate and multivariate regressions are carried out. This part is in itself divided in the following parts. First, this thesis investigates if the January effect is discernable in the returns of the equal-weighted and the value-weighted NYSE portfolios during the whole sample period. The excess return is used to take into account market movements. The following regressions will be carried out.
VW Excess Market Return = α + β1 JAN (1)
EW Excess Market Return = α + β1 JAN (2)
Where excess return is calculated by the holding period return of the particular market portfolio minus the risk free rate, which is the 30 day T-bill rate, and JAN is a dummy variable which takes on a value of 1 if the return is from January and 0 otherwise. Α indicates the mean monthly return of all the non-January months and β1 measures the return premium which takes place in January.
Next, the January effect will be investigated in relation to the small firm effect. To this end, the first regression (1) will be applied to the monthly holding period returns of the 10 portfolios, which are structured in such a way that they reflect the 10 deciles based on market
capitalization. The first portfolio has the firms with the smallest market capitalization. This gives the following regression.
Portfolioi Excess Return = α + β1 JAN for i = 1, ..., 10 (3) Where the portfolio i excess return is calculated by subtracting the risk free rate from the monthly holding period return of the ith portfolio. Because smaller capitalization stocks tend to be more volatile than stocks from large capitalization firms, the riskiness of one of the portfolios has to be dealt with. To take into account the effect of risk on return, the January dummy variable used in the above regressions will be used as an extension of the basic Capital Asset Pricing Model (CAPM). To this end, the following regression model is estimated for each of the 10 portfolios.
Portfolioi Excess Return = α + β1 Excess Market Return + β2 JAN (4) for i = 1, ..., 10
Here α can be interpreted as the mean monthly return of all the non-January months in case β1 is equal to 0. The coefficient β1 indicates how much exposure a particular portfolio has to general market movements as opposed to idiosyncratic factors and is estimated using the OLS regression analysis. The coefficient β2 again describes the estimated premium for a January return. The regression above is carried out two times, each time with a differently calculated excess market return. The excess market return is calculated by subtracting the risk free rate from the equal-weighted market portfolio as well as from the value weighted market portfolio. This is an important difference because of the relationship between the size effect and the January effect which was pointed out earlier. The choice of market return could be relevant because the equal-weighted portfolio gives much more weight to the smaller capitalization stocks than the value-weighted portfolio, in which stocks of the large firms have a greater weight.
Most of the earlier research has been conclusive concerning the fact that the January effect is predominately present in the smallest decile portfolio. Because of this, the following regressions will all use the excess return of this portfolio as the endogenous variable. To check if there are anomalies in other months, the third regression will be repeatedly estimated, eleven times for the eleven remaining months, using the first decile portfolio with a dummy variable for each of the non-January months.
Portfolio1 Excess Return = α + β1 M (5) for M = FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT, NOV and DEC
Here α is the mean excess return in the other months of the year and β1 measures the difference in return for each of the remaining months. This regression is essentially the same as regression (3), but then only for Portfolio1 and not using January but the other months of the year as a dummy variable.
Next, the data will be searched for a decline in the January effect, based on the expectation of the United States stock market becoming more efficient during the sample period. To this end, a time trend variable, taking the value of year – 1991, will be incorporated in the model. A trend variable is used because the expectation is that the stock markets are gradually becoming more efficient over time. Only the portfolio with the smallest capitalization stocks is used, as the January effect is most pronounced in this portfolio. The following regression model is estimated.
Portfolio1 Excess Return = α + β1 JAN + β2 JAN TREND (6) Where α stands for the mean monthly return of the non-January months. Coefficient β1 is again the return premium for the month of January and β2 measures any trend in this January return premium over the entire sample period. To take into account risk from market exposure, the above regression is estimated again but with inclusion of the CAPM. The following regression model is therefore estimated.
Portfolio1 Excess Return = α + β1 Excess Market Return + β2 JAN + β3 JAN TREND (7)
Of course, this regression will be carried out two times, for both the equal-weighted and value-weighted market portfolio return as the market return.
5. Results
This part of the thesis describes the results and proposes an analysis for them. First, some descriptive statistics will be provided and the second part will show the results of the regressions followed by an analysis.
Table 1 shows the descriptive statistics of the monthly excess returns of the relevant variables, with excess return calculated by subtracting the risk free rate from the monthly holding period return as provided by CRSP. The value and equal weighted market portfolio both consist of NYSE firms.
Variable Abbreviation Mean Std. Dev. Min Max Value Weighted market portfolio ERVW 0.0053 0.0413 -0.187 0.117
Equal Weighted market portfolio EREW 0.0077 0.0470 -0.215 0.226
Portfolio 1 ERP1 0.0118 0.0516 -0.164 0.263 Portfolio 2 ERP2 0.0071 0.0429 -0.165 0.221 Portfolio 3 ERP3 0.0077 0.0439 -0.190 0.206 Portfolio 4 ERP4 0.0075 0.0482 -0.222 0.233 Portfolio 5 ERP5 0.0085 0.0501 -0.227 0.251 Portfolio 6 ERP6 0.0081 0.0505 -0.238 0.228 Portfolio 7 ERP7 0.0070 0.0474 -0.208 0.199 Portfolio 8 ERP8 0.0074 0.0474 -0.236 0.146 Portfolio 9 ERP9 0.0074 0.0460 -0.213 0.168 Portfolio 10 ERP10 0.0047 0.0408 -0.175 0.109 Table 1: Descriptive statistic. The mean, standard deviation, minimum and maximum value are presented for the monthly excess returns of the market portfolio’s as well as the market capitalization decile portfolio’s.
The descriptive statistics show that the mean return of the equal weighted market portfolio is larger than the value weighted portfolio. This is logical as the equal weighted portfolio assigns more value to smaller capitalization stocks, which tend to have a higher return as discussed earlier. Portfolio 1 through 10 are equal to the ten deciles based on market capitalization and the statistics show that the lower deciles with the smaller capitalization stocks tend to produce a higher mean return than the higher deciles. This is again mostly due to the risk return relationship.
The following part of this thesis presents the results of the regressions discussed in chapter 3. All these regressions are carried out using the excess return which is calculated by subtracting the risk free rate from the monthly holding period return. The coefficients are provided with the standard errors beneath them in brackets and an asterisk (*) indicates that the coefficient is significant at the 5 percent level. First, this thesis investigates if the January effect is discernable in the returns of the equal-weighted and the value-weighted NYSE portfolios during the whole sample period. The results are presented in table 2.
Market Portfolio α β1 Value Weighted 0.00592* -0.00690
(0.00271) (0.00941)
Equal Weighted 0.00701* 0.00863 (0.00309) (0.01072)
Table 2: Result of regressions (1) and (2). Market portfolio excess return regressed on a January dummy: VW Excess Market Return = α + β1 JAN and EW Excess Market Return = α + β1 JAN
Two things are immediately apparent, the January dummy variable coefficient corresponding to the equal weighted portfolio is higher than that of the value weighted portfolio, which is negative. Second, neither coefficient of the January dummy variables is significant. Therefore it can be concluded that there is no significant January effect measurable for both market portfolios in the dataset used in this thesis.
Next are the results of regression (3), which is the above regressions estimated for each of the ten decile portfolios. Table 3 presents the results again with the standard errors beneath the coefficients.
Size Decile Portfolio α β1
1 0.00802* 0.04528* (0.00330) (0.01143) 2 0.00516 0.02354* (0.00279) (0.00968) 3 0.00623* 0.01750 (0.00287) (0.00997) 4 0.00683* 0.00843 (0.00317) (0.01098) 5 0.00838* 0.00099 (0.00330) (0.01144) 6 0.00838* -0.00367 (0.00333) (0.01153) 7 0.00750* -0.00560 (0.00312) (0.01081) 8 0.00828* -0.01043 (0.00311) (0.01080) 9 0.00788* -0.00583 (0.00302) (0.01049) 10 0.00531* -0.00782 (0.00268) (0.00929)
Table 3: Results of regression (3). Portfolio excess returns regressed on a January dummy: Portfolioi Excess Return = α + β1 JAN for i = 1, ..., 10
The results in table 3 show that there is only a significant January effect in the first and second size decile portfolio. The coefficient corresponding to the January dummy variable also tends to become higher when the size of the stocks in the portfolio goes down. Both these results indicates that the January effect is indeed strongly related to the small firm effect. This conclusion coincides with previous literature, for example by Haugen and Jorion.
The results of regression (4) are presented and discussed next. It is equal to regression (3) with the CAPM model incorporated in it. The regression is carried out using the excess return of the value weighted as well as the equal weighted NYSE portfolio for the excess market return. Table 4 presents the results.
Size Decile Portfolio α β1 β2
1 0.0032 0.7996* 0.0507* (0.0025) (0.0579) (0.0086) 2 0.0004 0.7958* 0.0290* (0.0017) (0.0413) (0.0061) 3 0.0011 0.8622* 0.0234* (0.0016) (0.0389) (0.0058) 4 0.0010 0.9722* 0.0151* (0.0017) (0.0409) (0.0060) 5 0.0021 1.0443* 0.0082 (0.0017) (0.0393) (0.0058) 6 0.0019 1.0798* 0.0037 (0.0015) (0.0367) (0.0054) 7 0.0013 1.0383* 0.0015 (0.0013) (0.0311) (0.0046) 8 0.0019 1.0717* -0.0030 (0.0011) (0.0260) (0.0038) 9 0.0015 1.0678* 0.0015 (0.0008) (0.0203) (0.0030) 10 -0.0004 0.9776* -0.0010 (0.0003) (0.0087) (0.0012)
Table 4: Results of regression (4)i. Portfolio excess returns regressed on a value weighted market beta and a January dummy: Portfolioi Excess Return = α + β1 Excess Market Return + β2 JAN for i = 1, ..., 10
The results show that the CAPM beta’s are all significant at the 5 percent level. The beta’s corresponding to the January dummy variable are significant for the first four decile portfolios. So when we take risk into account, it seems that the January effect is still present and again takes place predominately in the smaller size portfolios. The January effect also still
increases in magnitude in these portfolios. The model estimates a negative January effect for the eighth and ninth decile portfolio but this effect is too small to be relevant. This same regression is carried out using the excess return of the equal weighted NYSE portfolio. Those results are presented in table 5.
Size Decile Portfolio α β1 β2
1 0.0016 0.9097* 0.0374* (0.0017) (0.0351) (0.0059) 2 -0.0007 0.8469* 0.0162* (0.0009) (0.0198) (0.0033) 3 -0.0000 0.8913* 0.0098* (0.0008) (0.0166) (0.0028) 4 -0.0001 0.9931* -0.0001 (0.0007) (0.0158) (0.0026) 5 0.0011 1.0378* -0.0079* (0.0007) (0.0155) (0.0026) 6 0.0010 1.0518* -0.0127* (0.0006) (0.0140) (0.0023) 7 0.0006 0.9794* -0.0140* (0.0007) (0.0149) (0.0025) 8 0.0015 0.9632* -0.0187* (0.0009) (0.0185) (0.0031) 9 0.0013 0.9354* -0.0139* (0.0008) (0.0181) (0.0030) 10 0.0001 0.7317* -0.0141* (0.0014) (0.0293) (0.0049)
Table 5: Results of regression (4)ii. Portfolio excess returns regressed on a equal weighted market beta and a January dummy: Portfolioi Excess Return = α + β1 Excess Market Return + β2 JAN for i = 1, ..., 10
The first two things that stand out are the fact that all the beta’s corresponding to the January dummy variables are significant at the 5 percent level and that all of them are lower than their value weighted counterparts. Also, the negative January effect for the larger size portfolios, which was discussed earlier, is now substantially bigger. These results are shown in figure 1, which plots the beta corresponding to the January dummy variable for every decile portfolio.
Figure 1: January effect for every portfolio as estimated by regression (4)
It becomes clear from figure 1 that the January effect of each of the ten portfolio’s is the same when the value weighted or equal weighted portfolio is used for the estimation of the CAPM beta. Except for the fact that when the value weighted portfolio is used, the January effect seems to be larger in each of the ten decile portfolio’s and for each of these portfolio’s, this difference is roughly the same. This difference originates from the fact that the equal weighted market portfolio generates a higher return than the value weighted one, which is discussed earlier. Because the excess market return used for the estimation of the CAPM beta is higher, the January effect becomes lower. The difference between the two market portfolios is only a constant and the January effect is prominently present when using both. Therefore, it is not relevant for the conclusions of this thesis which of the two is used.
Next, the results of regression (5) are presented. This regression checks if there is a seasonal effect in any of the other months of the year. Because the January effect is shown to be predominately present in the first decile portfolio, the regression uses the excess return of this particular portfolio. The results are presented in table 6.
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 1 2 3 4 5 6 7 8 9 10 Value Weighted Equal Weighted
Month Dummy Variable α β1 FEB 0.0126* -0.0106 (0.0033) (0.0117) MAR 0.0123* -0.0070 (0.0034) (0.0117) APR 0.0108* 0.0109 (0.0033) (0.0117) MAY 0.0115* 0.0025 (0.0034) (0.0117) JUN 0.0126* -0.0099 (0.0033) (0.0117) JUL 0.0118* -0.0007 (0.0034) (0.0117) AUG 0.0127* -0.0119 (0.0033) (0.0117) SEP 0.0123* -0.0071 (0.0034) (0.0117) OCT 0.0137* -0.0240* (0.0033) (0.0116) NOV 0.0127* -0.0114 (0.0033) (0.0117) DEC 0.0097* 0.0242* (0.0033) (0.0116)
Table 6: Results of regression (5): Portfolio1 Excess Return = α + β1 M for M = FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT, NOV and DEC
The results show no significant seasonal effect for any of the other months of the year except for October and December. The peculiar thing about these months is that it seems that a negative effect is present. This means that during the 1992-2012 sample period, the excess returns during these months have been lower on average than in the rest of the year.
The results of regression (6) are presented and discussed next. The sample data will be tested for a decline in the apparent January effect in the first decile portfolio. To this end a time trend variable is used, taking the value of year – 1991. The results are presented in table 7.
Portfolio α β1 β2
1 0.0080* 0.0910* -0.0041*
(0.0032) (0.0227) (0.0017)
Table 7: Results of regression (6): Portfolio1 Excess Return = α + β1 JAN + β2 JAN TREND
All the coefficients are significant at the 5 percent level so it seems there is a statistically significant downwards trend in the first decile portfolio January effect for the researched data sample. Although the effect is statistically significant, it is very small. So it will probably not hold much economical meaning.
The regression is repeated with the incorporation of a CAPM beta, using the excess return of the value weighted NYSE portfolio as well as the equal weighted one. The results are presented in table 8. Market Portfolio α β1 β2 β3 Value Weighted 0.0033 0.7924* 0.0855* -0.0031* (0.0024) (0.0575) (0.0171) (0.0013) Equal Weighted 0.0016 0.9035* 0.0666* -0.0026* (0.0017) (0.0347) (0.0118) (0.0009)
Table 8: Results of regression (7): Portfolio1 Excess Return = α + β1 Excess Market Return + β2 JAN + β3 JAN TREND
The results again show that all the coefficients are statistically significant at the 5 percent level. Due to the incorporation of the CAPM beta, it seems that the trend coefficients have decreased in magnitude. The negative trend is also larger when the value weighted NYSE portfolio is used for the estimation of the CAPM beta. The same problem arises as with the previous regression because the negative trends are too small to be economically relevant, especially in proving that markets have gradually become more efficient during the last twenty years.
6. Discussion
This thesis investigated the January effect in recent data and empirically tested an extension of the efficient market hypothesis that in the case of the January effect, investors learn gradually over time. The effect entails the fact that small capitalization stocks seem to outperform the market as a whole in the month of January. The research question of this thesis is to what extent and in what form the January effect is still present in recent data and if it is gradually diminishing over time.
The paper of Keim (1983) reintroduced the idea of a January effect and provided evidence of its existence. Keim also proved the strong link between the January effect and the small firm effect by concluding that the effect predominately occurs for small capitalization stocks. In reaction to Keim, some papers came out stating that the effect was declining or even disappearing completely. Gu (2003) and Schwert (2003) claim that the January effect shows a downwards trend after the sample period of Keim. Mehdian and Perry (2002) conclude that there is no evidence for a January effect after 1987. However, they provide no theory as to why this should happen besides investors learning about it due to Keims paper. Haugen and Jorion (1996) investigated the January effect in the same manner Keim did in newer data and find significantly higher returns in January for small capitalization stocks. They do not however find any trend in the effect.
This thesis re-evaluated the January effect in recent data by looking at the monthly holding period returns of ten equally weighted portfolios, constructed to resemble the ten deciles based on market capitalization. The data concerns stocks traded at the NYSE, the sample period is 1992-2012 and the data is provided by CRSP. A series of regressions is estimated to test for the presence of a January effect, if there is an effect in other months of the year, if it is still present if risk is taken into account by implementing the CAPM model and if there is evidence for a decline in the effect.
The results show that there is a significantly higher return in January but only for the smaller capitalization stocks. This is an indication that the January effect is strongly related to the small firm effect, which coincides with previous literature. When the CAPM model is incorporated in the model, the results show that the January effect is still significantly present for the smaller size stocks. This is evidence that the January effect is not due to the higher market exposure of smaller capitalization stocks. The eleven other months of the year are also tested for higher returns and the results show that none of the other months have significantly
higher returns than the year average. It is worth noting that October and December seem to produce significantly lower returns than the other months in the year. The results of the regressions with a trend variable show that there is a significant downwards trend over the 1992-2012 sample period, even when the CAPM model is incorporated. This is in contrast to previous research where there was no statistically significant trend found. However, this negative trend is statistically significant but too small in absolute size to be of great economical relevance. The conclusion of this thesis is therefore that the January effect is still present and that there is no evidence suggesting a decline. This means that the theory of gradual learning by investors is not applicable to this anomaly. Haugen and Jorion offer a theory that perhaps the January effect is not a manifestation of investors behaving inefficient and that it is impossible to arbitrage the effect. They propose that maybe investors find it too risky to exploit the January effect and that this is a reason for its persistence.
Further research could investigate if the January is present in other markets. Perhaps the different circumstances of stock markets in upcoming economies are relevant to its presence. Investigating a different sample period could perhaps provide other insights in the anomaly. It is also worth researching why the January effect is persistent even after it has been public knowledge for such a long period.
7. References
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