University of Amsterdam
SCHOOL OF BUSINESS and ECONOMICS
MSc Economics & Business
The Impact of the Market Capitalization and Other Factors on
the January Effect in the FTSE Market Indices
Bachelor Thesis
Author: Jeffrey Vossen (10655182) Supervisor: Jan Lemmen
1 ABSTRACT
This thesis examines the existence of the January effect, the influence of the financial crisis and the influence of the economical state on the January effect. Furthermore, this thesis examines the seasonality of daily returns on the London stock market. This will be researched by testing five different models. This study investigates this on the FTSE 100, FTSE 250, FTSE SmallCap and the FTSE AIM market indices at the London stock market. The examined period is from January 1999 till May 2016, which contains the recent financial crisis. The sample period is divided in 3 sub-periods. The results show that the January effect exists only at the FTSE AIM index. This is consistent with prior research of Rozeff & Kinney (1976). The financial crisis has influence at the daily stock market returns in each market index, except for the FTSE 100. The financial crisis hasn’t influence on the January effect. This study provides also evidence for the size effect on the London stock market.
Keywords: January effect, size effect, the financial crisis, seasonality, economic sentiment, FTSE market indices,
JEL Classification: G12, G14
NON-PLAGIARISM STATEMENT
By submitting this thesis the author declares to have written this thesis completely by himself/herself, and not to have used sources or resources other than the ones mentioned. All sources used, quotes and citations that were literally taken from publications, or that were in close accordance with the meaning of those publications, are indicated as such.
COPYRIGHT STATEMENT
The author has copyright of this thesis, but also acknowledges the intellectual copyright of contributions made by the thesis supervisor, which may include important research ideas and data. Author and thesis supervisor will have made clear agreements about issues such as confidentiality.
Electronic versions of the thesis are in principle available for inclusion in any EUR thesis database and repository, such as the Bachelor Thesis Repository of the University of Amsterdam
2 TABLE OF CONTENTS
ABSTRACT ... 1
1. Introduction ... 3
2. Literature Review ... 5
2.1 Efficient market hypotheses ... 5
2.2 Existence of the abnormal returns in January ... 6
2.3 Previous research to the size effect of stock returns ... 10
3. Data and Methodology ... 14
3.1 Data ... 14
3.2 Methodology ... 15
4. Empirical Results ... 19
4.1 The existence of the January effect ... 19
4.2 The financial crisis and the January effect ... 20
4.3 The economic sentiment indicator ... 22
4.4 Seasonality in stock returns ... 22
4.5 Robustness check ... 25
5. Conclusion and Discussion ... 26
References ... 28
Appendix A: Results from regression 1 ... 31
Appendix B: Results from regression 2... 33
Appendix C: Results from regression 3... 36
Appendix D: Results from regression 4 ... 39
Appendix E: Results from regression 5 ... 41
Appendix F: Results from the robustness test ... 45
3
1. Introduction
In 1970 Eugene Fama introduced the market efficiency hypothesis (EMH). This hypothesis states that in an efficient capital market, security prices fully reflect available information in a rapid and equal fashion and thus provides unbiased estimates of the underlying values (Basu, 1977). According to the hypothesis it’s impossible for investors to beat the market in an efficient capital market, although financial investors are people with a very varied number of deviations from rational behavior, which is the reason why there is a variety of effects, which explain market anomalies. One of such financial market anomalies is the ‘January effect’.
Earlier empirical research in financial economics has proven that there is a potential January effect on different stock markets. Haugen & Jorion (1996) found evidence that the January effect still exists on the stock market of New York. Reinganum (1983) explores higher January returns for stocks that experience large declines in price in the preceding year. Starks et al. (2006) discover a significant January effect among a set of securities that are held only by individual investors, they also provide direct evidence that the January effect can be explained by the tax-loss-selling hypothesis. Though, instead of these findings, Marshall and Visaltanachoti (2010) conclude that the January effect cannot be implemented to earn statistically and economically significant risk-adjusted excess returns. Keim (1982) states that there is a January effect on both small and big caps stock markets, and that the abnormal excess return and firm size are
negatively correlated. According to Keim (1982) “the hypotheses advanced to explain the size effect appear unable to explain the January effect. Several alternative explanations with testable implications are discussed, but the tests are deferred for future research” (p.31).
The main research question in this thesis is to study the existence of abnormal returns in January on the FTSE 100, FTSE 250, FTSE SmallCap and FTSE AIM stock markets. This study examines also four sub questions.
Does the market capitalization of the stock markets have influence on the January effect?
Does the financial crisis have influence on the January effect?
Does the state of the economy have influence on the January effect?
Are there monthly seasonal patterns on the FTSE market indices?
I use the economic sentiment indicator (ESI) from the European Commission to test the influence of the state of the economy on the January effect. .
4 This study adds in the existing literature on some different ways. It contains different recent time periods in such way that we can see the effect of the financial crisis, in contrast most of the previous studies just take one time period. I investigate different market indices of the Financial Times Stock Exchange (FTSE) index at the London stock market from big to small caps. I
compare the coefficients of the different market indices, in order to test the size effect on the January effect. Previous studies didn’t take the state of the economy into-account in their
investigations. I will use the ESI to provide evidence if this has any influence on the stock market returns.
In this study, I sought to make a number of contributions. First, I provide evidence for the January effect at the FTSE AIM index and for the size effect in the London stock market. Second, this study finds a negative effect of the conversion period of the financial crisis on the average stock returns. Third, I provide evidence for the insignificant influence of the financial crisis and the state of the economy on the January effect. Furthermore, this study provides existence of seasonality in stock returns in all the market indices, except for the FTSE 100 index.
This thesis uses OLS regressions to estimate the coefficients of the monthly stock returns. The null-hypotheses from model 1 to 4 are tested with a T-test, the null-hypothesis of model 5 is tested with an F-test. The daily stock data used in this study contains serial correlation and heteroscedasticity, so I run the regressions with robust standard errors. The influence of the financial crisis and the monthly seasonal pattern in stock returns are tested with an F-test. Stock data, necessary for the regressions, are obtained from DataStream. In the conclusion I hope to get insight if an investor could gain from the January effect. After the review of previous studies in chapter 2, chapter 3 presents the data and the methodology used for the regressions in this thesis, chapter 4 provides the empirical results and chapter 5 gives a conclusion.
5
2. Literature Review
In the past decades, a lot of research has been done about the abnormality of stock returns in January. Some researchers saw the January effect as a point against the efficient market hypothesis. However, among the researchers, there is no consensus about the existence of the January effect on the stock market. There is consensus about the fact that small stocks
outperform big stocks, but this doesn’t automatically mean that the January effect is higher for small-capitalized stocks than for big capitalized stocks.
The first sub-section contains the efficient market hypothesis. After that, the second sub-section and most important section will discuss the existence of the January effect in chronological order. The third sub-section will provide an overview of the research done about the size effect on seasonal returns and the additional influence of this effect on the abnormal returns in January.
2.1 Efficient market hypotheses
In 1970 Eugene Fama introduces the market efficiency hypothesis (EMH), which states that in an efficient capital market, security prices fully reflect available information in a rapid and unbiased fashion and thus provide unbiased estimates of the underlying values (Basu, 1977). In addition to this explanation, Fama (1970) said “a market in which prices always “fully” reflect available information is called “efficient”. Investors can choose among the securities that represent ownership of firms’ activities under the assumptions that security prices, at any time “fully reflect” all available information” (p.387).
A direct implication is that it is impossible to “beat the market” consistently on a risk-adjusted basis, because market prices should only react to new information or changes in discount rates (Fama, 1970). If the phenomenon ’January effect’ really exists, this would be in odd with the market efficiency hypothesis, because the returns in January are higher than in other months, without any new information or changes in discount rates.
However, Fama (1970) makes a distinction in what is meant by 'all available information'. The efficient market hypothesis is divided in 3 forms; the weak form, the semi-strong form and the strong form. Poshakwale (2002) said the following about the weak-form EMH: “In other words, a market is considered weak form efficient if current prices fully reflect all information contained in historical prices, which implies that no investor can devise a trading rule based solely on past
6 price patterns to earn abnormal returns” (p.1276). Everyone is able to get information of
historical prices for low costs or no costs at all.
But, what about the abnormal returns in January on the stock market? The weak form of the EMH states that stock markets are efficient if prices are unpredictable. In the case when stock market returns have seasonal patterns, it seems that investors can predict the prices, so that the January effect is evidence against market efficiency. However, Rozeff & Kinney (1974) said: “The fact that expected returns vary by the month is not necessarily inconsistent with market
efficiency. This paper demonstrated that the simple random walk model does not hold, not that the market is inefficient with respect to information regarding seasonality” (p.396). Gultekin & Gultekin (1983) state that the random walk model implies that stock market returns are time invariant, so that stock price changes have the same distribution and are independent of each other.
Vasileiou (2012) examines whether the calendar anomalies are influenced by the financial crisis on the Greek stock market from 2002 till 2012. He provides evidence that the financial crisis has influence on the stock market returns, the volatility and the turn of the month effect. He suggests with these findings that the financial crisis not only influences the stock returns, but also it anomalies. However, one of these anomalies of the stock market is the January effect. Chaudhurg (2014) investigates how the financial crisis affects daily stock returns (including dividends) on the equally weighted S&P 500 index and 31 major U.S. stocks from January 2007 till December 2008. He provides evidence for large cumulative declines in stock prices during the financial crisis. Chaudhurg (2014) also gives evidence to the deterioration of the mean daily return, especially for the financial stocks starting in the early stage of the crisis.
2.2 Existence of the abnormal returns in January
Sidney B. Watchel (1942) was the first researcher who observed abnormal excess returns in January. He examines the seasonal returns from 1927 till 1942 in the Dow Jones Industrial Average. Previous studies before 1942 reject the existence of abnormal seasonality returns on the stock market. Beside the previous studies, the Harvard Committee strongly indicates the absence of any evidence for seasonality in security prices before 1917 (Watchel, 1942). Owens and Hardy (1925) confirmed this statement with the words: "Seasonal variations of security prices are impossible ... . If a seasonal variation in stock prices did exist, general knowledge of its
7 existence would put an end to it”1. Watchel (1942) examines the seasonality of abnormal returns on the Dow Jones Industrial Average stock market. He noticed that stocks with a small market capitalization have outperformed the market in January, with most of the disparity occurring before the middle of the month. Watchel (1942) also gives evidence to the presence of a January effect, but didn’t give an explanation for this phenomenon.
Rozeff & Kinney (1976) examined the monthly stock return on the New York Stock Exchange (NYSE) for 4 various periods from January 1904 till December 1974, from where they use the equally weighted NYSE prices. They take the dividends of the stock in account to calculate the monthly returns. They state that the mean return in January is higher than in the other eleven months. Other relative high returns are presented in the months July, November and December, and low mean returns are presented in February and June. Rozeff & Kinney (1974) state
that the surge in January returns is a possible result of investors selling loser stocks in December to lock in tax losses, causing returns to bounce back up in January, when investors have less incentive to sell. In the years from 1904 till 1974 the returns for small firms in January was 3.5%, whereas in others months the return was 0.5% (Rozeff & Kinney, 1976). This is called the tax-loss-selling hypotheses; it holds that prior to year-end, individual investors sell stocks that have declined in value to realize tax losses (Sikes, 2014).
Gultekin & Gultekin (1983) investigated the existence of seasonality from January 1959 till December 1979 on the international capital market. The stock-market returns in this study are computed from the indices reported in Capital International Perspective (CIP). Instead of Rozeff and Kinney, who used the equally weighted NYSE price, they used data from the CIP, which has value-weighted indices in local currencies. The use of equally weighed data gives more weight to small firms. Gultekin & Gultekin (1983) show test statistics that seasonality exists in most of the major industrial countries. The null-hypothesis that stock returns are time invariant is rejected for 12 countries from a total of 17 at the 10% significance level. They accept the null-hypothesis for the US market, which is at odds with previous results provided by Rozeff & Kinney and others.
Haugen & Jorion (1996) did research on the existence of the January effect on the NYSE all stock markets from 1926 till 1993. The existence of the January effect was already proven in previous studies at this market, but Haugen & Jorion (1996) examine if the abnormal returns in January still hold on in more recent years. The test results of the paper reveal no significance support for
8 a contention that the January effect is disappearing on the NYSE. They examine 5 different time periods from 1926 through 1993, and the January effect is clearly shown in all the sub-periods. Medhian and Perry (2002) investigated the NYSE composite, the Dow Jones composite and the S&P500 over the period from 4 June 1964 till 8 Augustus 1998. The monthly returns are calculated on the basis of the daily returns, in which they exclude the dividend pay-outs. They found evidence that after the stock market crash in 1987, the mean returns in January were no longer significantly positive.
Gu (2003) examines the dynamics and trend of the January effect of major U.S. stock indices, among others on the Dow Jones 30 Industrial Average from 1929 till 2000 and the S&P 500 from 1950 till 2000. The S&P500 stocks are value weighed, while the Dow Jones stocks are equally weighed. The daily returns in his examination are calculated as the natural logarithm
differentials of the index values. He maintains that both markets have experienced a decline in the January effect since 1988.
Starks et al. (2006) examine the January effect among the municipal bond closed end funds in the time period from 1990 to 2000. They exclude dividends in their calculation for the monthly return; they just use price level changes. They found significantly higher returns in January than in other months, with a significance level of 1%. The returns are about 2.17% higher than in the other eleven months. They also provide direct evidence supporting the tax-loss selling
hypothesis as an explanation of the January effect (Starks et al., 2006).
Haug & Hirschey (2006) did research to the January effect in 2 different stock markets whether the time periods overlap each other. They examine excess return in January on the CRSP value weighted portfolio returns from 1802 till 2004 and the U.S. equal weighed stock prices from 1927 till 2004. On the CRSP value weighted portfolio returns market, they didn’t find significant excess returns in January. The average return in January was just 1.10% and in many time periods negative. However, they found persistence of the excess returns in January on the U.S. equal weighted stock market, even during the Tax Performance Act of 1986. They conclude that the January effect is just a small cap phenomenon (Haug & Hirschey, 2006).
Sun & Tong (2010) investigate the January effect and the additional risk for investors. They examine to the monthly equally weighed return series of the CRSP database from 1926 to 2005. The results strongly indicate that it is the risk premium and not the risk itself that is higher in January. They take four samples with different firm sizes and provide direct evidence to the
9 January and size effect. Sun & Tong (2010) said “First, the January effect exists in all four
portfolios, but the magnitude and statistical significance tend to diminish as size increases”. Sanusi & Amhad (2016) did research to daily and monthly returns of the London-quoted oil and gas stocks and some other market indices of the London stock market from January 2004 till December 2012. They’ve calculated daily returns with price level changes (without dividends), monthly returns are based on the average daily returns. They couldn’t find significant evidence for abnormal returns in January on the London-quoted oil and gas. Instead of this finding, they provide significant evidence for abnormal returns on all the FTSE share indices on the London stock market in January, May and November. In their investigation, the statistical significant returns in January at the FTSE all share market index is higher than at the FTSE 100 index. This indicates that the January effect and market capitalization are negatively correlated at the London stock market.
Table 1 provides a list of previous findings on the abnormal returns on stock markets, as discussed on the previous pages.
Table 1: previous findings of the January effect Autor(s) (Publication year) Region Time Period Return calculation Equally/value weighted Results Watchel (1942) US; Dow Jones Industrial Average 1927-1942 - - Existence of seasonality returns Rozeff & Kinney
(1976)
US; NYSE
1904-1974
Ln((Pit+Dit)/Pit-1) Equally Evidence for seasonality in stock returns Gultekin & Gultekin (1983) Us NYSE 1926-1993
From CIP Value 12/17
countries seasonality returns Haugen & Jarion
(1996) US; NYSE all stock 1926-1993 - Equally + 4.2 %
10 Medhian & Perry
(2002) US; DJcomp NYSE S&P500 1964-1998
Ri= Log(Pit/Pit-1) Value + 5.97% + 5.244% + 4.657% Gu (2003) UK; S&P500 Dow Jones 1950-2000 1988-2000 Rjan=(1+JanRet)^12 Power Ratio; Rjan/Ryear Value Equally 1.22 to 1.18 1.32 to 1.20 Both decline in Jan effect Starks et al. (2006) Municipal bond closed end funds 1990-2000 R= (Pit-Pit-1)/Pit-1 - + 2.17%
Haug & Hirschey (2006) Us; NYSE 1802-2004 1927-2004 - Value Equally No evidence + 5.14%
Sun & Tong (2010)
CRSP
1926-2005
- Equally + 2.25%
Sanusi & Ahmad (2016) UK; FTSE O&G FTSE all share FTSE 100 2004-2012
Ri= Log(Pit/Pit-1) Equally No evidence + 3.392 % +2.932%
2.3 Previous research to the size effect of stock returns
Banz (1981) introduces the size effect on stock returns in 1981. He examines the relationship between the total market value of the common stock of a firm and its return on the NYSE from 1926 till 1973. The results in this study show that the common stock of a small firm, on average, had higher risk-adjusted returns. Banz (1981) named this relation between a firm’s
capitalization value and its stock return the ‘size effect’.
Reinganum (1982) examines the January effect to the CRSP daily files, which include all securities that have traded on the New York and American Stock Exchanges since July 1962. In his research he differentiates firms from the smallest capitalization portfolio to the largest. The smallest capitalization portfolio has an excess return in January of 3.73%. The largest
11 capitalization portfolio has an excess return in January of 0.19%. This provides evidence for the size effect. He also states that small firms experience large returns in January and exceptionally large returns during the first few trading days of January (p.103). Reinganum (1982) said “The empirical tests reported in this paper indicate that the abnormally high returns witnessed at the very beginning of January appear to be consistent with tax-loss selling”. Apart from the
seasonality issue, Reinganum (1982) still wonders why firms with a small capitalization still apparently earn higher significantly average returns than firms with a large capitalization over long periods of time.
Keim (1983) investigates the seasonal movement in stock prices at firms that where listed on the NSYE and AMEX, with the monthly returns from the CRSP files. He makes a distinguishing discovery in firm sizes to the seasonal movements, such as that he examines the size effect on this stock market. To calculate the firm sizes, he multiplied the common stock shares
outstanding at year-end by year-end prices of the common shares. Then he divides the yearly distribution of market values equity into ten portfolios, from small caps to big caps. The biggest capitalization firm, with a value of 1092.1 million, has an average excess stock return of -3.8%. However, the smallest capitalization firm, with a value of 4.4 million, has an average excess stock return of 8.2%. These findings differ 12% from each other. Keim (1983) states in his findings that the relation between abnormal returns and firm size always has to be negative and more pronounced in January than in any other month.
Gultekin & Gultekin (1983) investigate the existence of seasonality from January 1959 till December 1979 on the international capital market. They proved evidence for abnormal returns in January at 12 of the total from 17 countries. Beside de existence of the January effect, they examine the size effect of the seasonality in stock returns. Gultekin & Gultekin (1983) state that the seasonality in stock returns in these countries is not a size related anomaly.
Wong (1989) investigates the size effect on stock returns at the stock exchange of Singapore (SES) during the period from 1975 till 1985. This study used value-weighted portfolios. To calculate the market capitalization of the firms, he multiplied the shares outstanding times the market prices of the shares. The results show in January an abnormal return of 1.569% for the smallest capitalization portfolio and 1.149% for the biggest capitalization portfolio. According to Wong (1989) the returns on the common stock of SES firms are significantly related to the size of SES firms.
12 Fraser (1995) did research on the London stock exchange market, in particular to the
companies, which are included in the Hoare-Govett Smaller Companies Index over the period from May 1970 to October 1991. This index states that the companies can have a maximum market capitalization of £100m. Fraser (1995) gives evidence that smaller companies consistently outperform the market until 1989. Since 1989 the abnormal returns have
disappeared, probably because the deep recession period in which the UK ended up in the early 1990s.
Haug & Hirschey (2006) found evidence of abnormal returns in the month January on the NYSE stock market. The results in their paper state that equally weighted portfolios have an excess return of 5.14% in January instead of the other eleven months. However, they couldn’t find evidence for a January effect with value-weighted portfolios. Haug & Hirschey (2006) explain that small cap stocks play a larger role in equally weighted portfolios than in value-weighted portfolios. They used the famous Fama-French benchmark factors to summarize the
performance of small cap relative to large cap stocks. With the Fama-French portfolios from 1927 till 2004, they provide a return premium in January of 2.94% for small cap and 0.17% for big cap stocks.
Pandey & Seghal (2016) examine the size effect on the Indian stock market from October 2013 till January 2015. They investigate the NSE 500 companies and did find strong evidence for the size effect. With portfolios based on their market capitalization, the average return of the smallest portfolio has an average return of 8.51%, while the biggest portfolio has an average return of 0.96%. Pandal & Seghal (2016) also used 2 alternative measures of company size; total assets (a non-market based measure) and enterprise value, which also confirm the presence of a strong size effect.
Table 2 provides a list of previous findings on the abnormal returns on stock markets, as discussed above.
Table 2: previous findings about the size effect on stock returns Autor(s) (publication
year)
Region Time Period Results
Banz (1981) US;
NYSE
1926 - 1973 Existence size effect
13 New York and
American stock exchanges
Big cap +0.19%
Keim (1983) US;
NSYE & AMEX
1963-1979 Small cap + 8.2% Big cap -3.8% Gultekin & Gultekin
(1983)
US;
New York and American stock exchanges 1959 - 1979 12/17 countries January effect No size effect Wong (1989) Singapore; SES 1975-1985 Small cap + 1.569% Big cap + 1.149% Fraser (1995) UK; London stock exchange market May 1970 – October 1991 Small firms outperform the market
Haug & Hirschey (2006) US; NYSE; Fama-Bench portfolios 1927-2004 Small cap +2.94% Big cap +0.17%
Pandey & Seghal (2016) India; NSE 500 October 2003- January 2015 Small cap 8.51% (average) Big cap 0.96% (average)
14
3. Data and Methodology
This section describes the data and presents the research methodology of this study. In the first sub section the data sources will be provided. The second sub section provides the econometric models used to test for the existence of the January effect, the influence of the financial crisis, the influence of the state of the economy and the seasonality in stock returns. For testing the size effect, this study will evaluate the coefficients of the variable January of all the market indices with different market capitalizations.
3.1 Data
This study examines 4 samples of stock market indices at the London stock market during the non-financial crisis period, financial crisis conversion period and the advanced financial crisis period. DataStream is used to obtain the daily returns (including dividends) of the Financial Times Stock Exchange Index 100 (FTSE 100), FTSE 250, FTSE SmallCap and the FTSE AIM with equally weighted values. This thesis examines 4 different FTSE market indices, in order to provide evidence for the small size effect.
The daily returns of the stocks are computed with the following equation (included dividends);
The advantage of using daily prices over monthly closing prices per index is that more observations are used which increases the accuracy of the estimation.
This study examines the January effect in the following 3 sub-periods. Table 3: sample periods
Market Indices Sub-period 1 Period before the financial crisis
Sub-period 2 Conversion years of the financial crisis
Sub-period 3
Period during the advanced financial crisis FTSE 100 01/01/99 - 15/06/07 15/06/07 - 03/03/09 03/03/09 - 31/05/16 FTSE 250 01/01/99 - 23/05/07 23/05/07 - 21/11/08 21/11/08 - 31/05/16
15 FTSE Smallcap 01/01/99 - 04/06/07 04/06/07 - 09/03/09 09/03/09 - 31/05/16 FTSE AIM 01/01/99 - 16/07/07 16/07/07 - 09/03/09 09/03/09 - 31/05/16
The sub-periods are based on the highest and lowest adjusted closing price between 2006 and 2010. Appendix F shows figures of all the markets indices, which provides a clear overview of the conversion periods of the financial crisis.
For testing the influence of the state of the economy on the January effect, this study used the economic sentiment indicator. This sentiment indicator can be used by investors to see how optimistic or pessimistic people are to current market conditions. The ESI is calculated as an index with mean value of 100 and standard deviation of 10 over a fixed standardized sample period. ”In the last five decades, the European economic sentiment indicator (ESI) has
positioned itself as a high-quality leading indicator of overall economic activity” (Sorić, Lolić, & Čižmešija, 2015, p.1). The market is less efficient in periods with a low ESI (<100), such that the returns in times of a low ESI could possibly have a positive influence on the January effect. The data for the ESI is obtained from the European Commission.
3.2 Methodology
To empirically test the January effect in the London stock market, the same method will be used as in the researches of Jones et al. (1987) and Keim (1983). The returns will be submitted to linear regression using the Ordinary Least Squares (OLS) method. I run a regression on the daily stock returns, which is the dependent variable in all the regressions. This study runs the OLS regressions of equation (2) to (5) with robust standard errors, because these models contain serial correlation and heteroscedasticity.
The regression to estimate the existence of the January effect is as follow:
Where:
- Rt is the average return in month t
- 0 is the constant term, which is an indication for the average return in the other eleven months - January = 1 if month is January, 0 otherwise
16 Because the estimated coefficients reflect the difference between the average return in January and the other 11 months, the hypothesis to test the existence of the January effect is set up as follow:
H0: January = 0 H1: January > 0
The estimated coefficient of the month January reflects the difference between the average return in January and the other 11 months. When the null-hypothesis is rejected, the average monthly return in January is higher than in the other 11 months, which provide evidence for the existence of the January effect. This study expects to find a January effect on the FTSE SmallCap and FTSE AIM indices, because previous studies provide evidence for the small size effect on the January effect.
For testing the influence of the financial crisis at the January effect, I use the following regressions:
Where:
- Rt is the average return in month t
- 0 is the constant term, which is an indication for the average return in the other eleven months in times of non-financial crisis
- January = 1 if month is January, 0 otherwise
- Crisis = 1 if returns are estimate in the advanced period of the financial crisis, 0 otherwise - ConvCrisis= 1 if returns are estimate in the conversion period of the financial crisis, 0 other wise
- et is the error term
The period of non-financial crisis is omitted from the regressions, which prevent the equation to suffer from perfect multicollinearity. This indicates that the constant term of the regression presents the average return in times of non-financial crisis. Using a multiple regression model, it is tested whether the dummy’s Crisis and ConvCrisis have an explanatory function as it comes to the returns at the London stock market. When the null-hypothesis is accepted, the returns in January are equal in times of financial crisis and non-financial crisis. When the null-hypothesis is
17 rejected, the financial crisis has a significant influence on the returns at the London stock
market. In regression 3 two interaction terms between the month January dummy variable and the crisis sub-periods dummy variables are also added for both crisis sub-periods:
January*Crisis and January*Convcrisis. These variables are added such that this study can test whether the sub-periods of the financial crisis have significant influence on the January effect. This study expects to find a negative influence of the financial crisis on the stock returns and the January effect.
H0: crisis = ConvCrisis= 0 H0: January*Crisis = 0 H0: January*ConvCrisis = 0 H1: crisis= ConvCrisis ≠ 0 H1: January*Crisis ≠ 0 H1: January*ConvCrisis ≠ 0
This study also examines whether the January effect is stronger in times with a low economic sentiment (ESI) or not. To examine this, I use the following regression:
There is added 1 more dummy variable to regression 1: ESI (equal to 1 for the period of low economic sentiment (<100) and 0 otherwise). An interaction term between the month January dummy variable and the ESI dummy variable is also added: January*ESI. Using a multiple regression model it is tested whether the dummy ESI and the interaction term have an
explanatory function as it comes to the London stock market returns. When the coefficient of ESI significantly differs from zero, this implies that the return in times of low economic sentiment is different from the return in times of high economic sentiment. When the coefficient of the interaction term significantly differs from zero, this implies that the January effect is different in times of low economic sentiment. This study expects positive influence of the state of the economy on the average stock returns, but doesn’t expects any influence of the state of the economy on the January effect.
H0: 2ESI = 0 H0: 3January*ESI = 0 H1: 2ESI ≠ 0 H1: 3January*ESI ≠ 0
This study also runs a regression on the monthly seasonality of the returns; such that we can test which month estimate the highest average returns. The month January is omitted from the regression, which prevent the equation to suffer from perfect multicollinearity.
18 Where:
- Rt is the average return in month t
- 0 is the constant term, which is an indication for the return in January - M2t…12t = 1 if month is February … December, 0 otherwise
- et is the error term
H0: 1= 2= 3= 4= 5= 6= 7= 8= 9= 10= 11 = 0 H1: 1= 2= 3= 4= 5= 6= 7= 8= 9= 10= 11 ≠ 0
When the null-hypothesis is accepted, the market indices on the London stock market have the same returns in each month. However, when the null-hypothesis is rejected, there is existence of seasonality in the daily returns on the London stock market. This study expects seasonality in stock returns on the London stock market, because multiple studies prove seasonality in other stock markets.
19
4. Empirical Results
4.1 The existence of the January effect
Table 3 shows the results of the test for the existence of the January effect. This test is based on the regression in equation (1). For none of the market indices except the FTSE AIM index are returns in January significantly higher, which is at odds with the results of Sanusi & Ahmad (2016). The results in table 1 show evidence for the January effect at the 5% level at the FTSE AIM index, which would be consistent with the results of Starks et al. (2006) and Haug & Hirschey (2006).
Table 3; Test of the January effect:
Market Index Variable Coefficient Robust
standard errors
T-value P-value January effect FTSE 100 January -.0009819 . 0006352 -1.55 0.122 No Constant .0001713 . 0001877 0.91 0.362 FTSE 250 January -.0003602 . 0005664 -0.64 0.525 No
Constant .0003738 . 0001657 2.26** 0.024** FTSE SmallCap January .000235 .0003745 0.63 0.530 No
Constant .0001805 .0001107 1.63 0.103 FTSE AIM January .0008501 . 0004064 2.09** 0.037** Yes
Constant -.0000759 . 000136 -0.56 0.577 Note: * Significant at 10%, **Significant at 5%, *** Significant at 1%.
As we can see in table 1 above, if the market capitalization of a market index is smaller, the return in January became higher instead of the other eleven months. The correlation between the market capitalization of the market indices and the T-test coefficients of the variable January indicate a correlation of -0,970; a strong negative correlation. This provides evidence for the size effect, which would be consistent with the results of Keim (1983). The size effect on the returns in January states that stock markets with smaller market capitalizations have a higher
probability for significant abnormal returns in the month January than stock markets with higher market capitalizations.
20
4.2 The financial crisis and the January effect
Table 4 shows the results of the test for the influence of the financial crisis on the stock market returns. This test is based on the regression in equation (2). The results in Appendix 2 show that the F-statistic is significant in all the market indices except for the FTSE 100 index. This provides evidence for the influence of the entire financial crisis period on the stock returns, which would be in line with the results of Chaudhurg (2014). Table 4 provides evidence for the significant influence of the conversion period of the financial crisis to the stock returns at all the market indices, except for the FTSE 100 index. The advanced financial crisis period has at none of the market indices significant influence on the stock returns.
Table 4: Test of the influence of the financial crisis on the London stock market returns:
Market Index Variable Coefficient Robust
standard errors T-value P-value FTSE 100 January -.0122755 .0116078 -1.06 -.0350323 Crisis .0000435 .0003569 0.12 0.903 ConvCrisis .0897391 .0919344 0.98 0.329 Constant .0012247 .0010744 1.14 0.254 FTSE 250 January -.0004374 .0005326 -0.82 0.412 Crisis .0001892 .0003044 0.62 0.534 ConvCrisis .0024009 .000928 -2.59** 0.010** Constant .0005079 .0001861 2.73 0.006 FTSE SmallCap January .0002732 .00034 0.80 0.422
Crisis .0002367 .0002028 1.17 0.243 ConvCrisis .0023434 .0005509 -4.25*** 0.000*** Constant .0003167 .0001352 2.34 0.019 FTSE AIM January .000852 .0003713 2.29** 0.022**
Crisis .0002075 .0002577 0.80 0.421 ConvCrisis .0028975 .0005705 -5.08** 0.000** Constant .0001159 .0001918 0.60 0.546 Note: * Significant at 10%, **Significant at 5%, *** Significant at 1%, T-values and F-values are based on robust standard errors.
Table 5 on the next page shows the results of the test for the influence of the financial crisis on the January effect. This test is based on the regression in equation (3). The results in Appendix C
21 show that the F-statistic is insignificant in all the market indices. The sub-periods of the financial crisis also have insignificant T-values, which indicates that the financial crisis hasn’t significant influence on the January effect in all the market indices.
Table 5: Test of the influence of the financial crisis at the January effect:
Market Index Variable Coefficient Robust standard errors T-value P-value FTSE 100 January -.0010942 .000763 -1.43 0.152 Crisis 1.50e-06 .0003563 0.00 0.997 Convcrisis .09765 .0998408 0.98 0.328 Jan*Crisis .0009174 .0011306 0.81 0.417 Jan*Convcrisis -.1001374 .099884 -1.00 0.316 Constant .0002156 .0002489 0.87 0.386 FTSE 250 January -.0002643 .0005547 -0.48 0.634 Crisis .0002103 .0003209 0.66 0.512 Convcrisis -.0023306 .0009487 -2.46** 0.014** Jan*Crisis -.0002382 .0010071 -0.24 0.813 Jan*Convcrisis -.001128 .0044092 -0.26 0.789 Constant .0004925 .0001886 2.61** 0.009 FTSE SmallCaps January .0006653 .0003822 1.74* 0.082* Crisis .0002848 .0002145 1.33 0.184 Convcrisis -.0005466 .0005812 -3.77*** 0.000*** Jan*Crisis -.0005466 .0006362 -0.86 0.390 Jan*Convcrisis -.0016046 .0018169 -0.88 0.377 Constant .0002811 .0001381 2.0 0.042
FTSE AIM January .0008666 .0004841 1.79* 0.074
Crisis .0002331 .0002756 0.85 0.398
Convcrisis -.0029892 .0006115 -4.89*** 0.000*** Jan*Crisis -.0002908 .0007637 -0.38 0.597 Jan*Convcrisis .0008809 .0016659 0.703 0.53 Constant .0001139 .0001986 0.566 0.566 Note: * Significant at 10%, **Significant at 5%, *** Significant at 1%., T-values and F-values are based on robust standard errors.
22
4.3 The economic sentiment indicator
Table 6 shows the results of the test for the influence of the ESI on stock returns. This test is based on the regression in equation (4). The ESI coefficient is in none of the market indices significantly different from zero. This means that the return in times of low economic sentiment isn’t significantly different from the returns in times of high economic sentiment. Because of the non-significant coefficient of the variable Jan*ESIL in each market index, the January effect isn’t stronger in times with low economic sentiment.
Table 6: Test of the influence of the economic sentiment indicator on the January effect:
Market Index Variable Coefficient Robust
standard errors T-value P-value FTSE 100 January -.0012275 .0008551 -1.44 0.151 ESIL .0327424 .0332526 0.98 0.325 Jan*ESI -.0321613 .0332725 -0.97 0.334 Constant .0001255 .000208 0.60 0.546 FTSE 250 January -.0007019 .0007505 -0.94 0.350 ESI . 0001967 .0003693 0.53 0.594 Jan*ESI .0006307 .0010781 0.58 0.559 Constant . 0002974 .0001797 1.65* 0.098 FTSE SmallCap January .0001642 .0004873 0.34 0.736
ESI .0003071 .0002481 1.24 0.216 Jan*ESI .0000754 .0006968 0.11 0.914 Constant .0000615 .0001195 0.51 0.607 FTSE AIM January .0005003 .0005251 0.95 0.341 ESI -.0000904 .000283 -0.32 0.749 Jan*ESI .0008727 .0007163 1.22 0.223 Constant -.0000396 .0001754 -0.23 0.821 Note: * Significant at 10%, **Significant at 5%, *** Significant at 1%, T-values are based on robust standard errors.
23 Even though very little evidence is found for the existence of the January effect, the presence of other monthly seasonal effects can still be advantageous to investors. The results in Appendix E show that the F-statistic is significant in the FTSE SmallCap and the FTSE AIM indices at the 1% level, which would be consistent with the results of Rozeff & kinney (1983) and Watchel (1942). In the FTSE 250 index, the null-hypothesis of equal returns for each month of the year is rejected at the 10% level. In the FTSE 100, the null-hypothesis for equal returns for each month is
accepted. Table 7 contains monthly return differences for all the market indices, this test is based on the regression in equation (5). At the FTSE 100 index, the months April, December and October have significant higher returns than the other months. At the FTSE 250 index, the month December has significant higher returns and the month September has significant lower returns. At the FTSE SmallCap index, the month April has significant higher returns and the months June and September have significant lower returns. At the FTSE AIM index, the month January has significant higher returns, which is also shown in the results in table 3. However, the months March, May, June, July, September and October have significant lower returns than the other months. A remarkable observation in the monthly returns is that in all the market indices on the London stock market the month September estimates the lowest average returns.
Table 7: Test on the seasonal pattern in returns:
Market index Variable Coefficient Robust standard errors T-value P-value FTSE 100 February .0012371 .0008131 1.52 0.128 March .1330389 .1345904 0.99 0.323 April .0018377 .0007663 2.40** 0.017** May .0004807 .0007924 0.61 0.544 June -.0000384 .000766 -0.05 0.960 July .0011481 .0008619 1.33 0.183 Augustus .0007808 .0008582 0.91 0.363 September -.0000791 .0009596 -0.08 0.934 October .0017853 .0010109 1.77* 0.077* November .0010648 .0008692 1.23 0.221 December .0015594 .0007771 2.01** 0.045** Constant -.0008107 .0005765 -1.41 0.160 FTSE 250 February .0011271 .0007035 1.60 0.109 March .0005352 .0007093 0.75 0.451 April .0009426 .0007319 1.29 0.198
24 May .0000548 .0007788 0.07 0.944 June -.0005163 .0007181 -0.72 0.472 July .0001894 .0007239 0.26 0.794 Augustus .0006322 .000763 0.83 0.407 September -.001384 .0008107 -1.71* 0.088* October .0003088 .0008115 0.38 0.704 November .0006448 .0007616 0.85 0.397 December .0011684 .0006946 1.68* 0.093* Constant -.00004 .0005052 0.08 0.937 FTSE SmallCap February .0003005 .0004451 0.68 0.500
March -.0004247 .0004743 -0.90 0.371 April .0009261 .0004834 1.92* 0.055* May -.0004211 .0004947 -0.85 0.395 June -.000981 .00004613 -2.13** 0.033** July -.0003225 .0004717 -0.68 0.494 Augustus .0002916 .0004899 0.60 0.552 September -.0004924 .0005601 -3.13*** 0.002*** October -.0004924 .0005827 -0.84 0.398 November -.0003107 .0005027 -0.62 0.537 December .0005344 .0004295 1.24 0.213 Constant .0004155 .0003262 1.27 0.203 FTSE AIM February -.0001207 .0005592 -0.22 0. 829
March -.0020603 .0006299 -3.27*** 0. 001*** April -.0006611 .0006562 -1.01 0. 314 May -.0015128 .0006004 -2.52*** 0. 012*** June -.001827 .0005321 -3.43*** 0. 001*** July -.001644 .0005242 -3.14*** 0. 002*** Augustus -.0007218 .000574 -1.26 0. 209 September -.002153 .0006269 -3.43*** 0. 001*** October -.0017307 .0006599 -2.62*** 0. 009*** November -.0004973 .0005959 -0.83 0. 404 December -.000184 .0005316 -0.35 0. 729 Constant .0011147 .0003876 2.88*** 0. 004*** Note: * Significant at 10%, **Significant at 5%, *** Significant at 1%., T-values and F-values are based on robust standard errors
25
4.5 Robustness check
The regressions in this study can be run with homoscedastic or heteroskedastic standard errors. Heteroscedasticity occurs when different observations have different error variance. This sub-section provides evidence for the heteroscedasticity of the standard errors in equation (2) to (5). In the presence of heteroscedasticity, the OLS estimator is still unbiased but the estimators are inefficient because the true variance and covariance are underestimated (Goldenberg, 1964). This study examines the standard errors of the regressions with the White test. The White test is a statistical test that establishes whether the residual variance of a variable in a regression model is constant or not. When the null-hypothesis is accepted, the residual variance of the standard errors is homoscedastic (Daniel 2013). The White test uses the following linear regression:
Where the explanatory variables Z1, Z2,…., Zp are as follows:
If the number of explanatory variables (k) in the regression is 1 and we denote by X = X1, the above explanatory variables are Z1 = X1 and Z2 = X2, and p = 2.
If k = 2, the above explanatory variables are Z1 = X1, Z2 = X2, Z3 = X21 , Z4 = X2 2 and Z5= X1 ·X2, and p=5.
If k ≥ 3, we have the explanatory variables Z1 = X1, Z2 = X2,…, Zk = Xk, Zk+1 = X21 , Zk+2 = X22,…, Z2k = X2k , and p = 2·k
This study takes into account that n · R2 has the distribution χ2p, where R2 is the coefficient of determination for the regression. Homoscedasticity is accepted if n ·R2 < χ2p;ε (Daniel, 2013). Ho: homoscedasticity
H1: unrestricted heteroscedasticity
When the null-hypothesis is accepted, this study runs the regression with homoscedastic standard errors, otherwise with heteroskedastic standard errors. The results in Appendix F show that this study has to run the regressions from equation (1) with homoscedastic standard errors and the regressions from the equations (2) to (5) with heteroskedastic standard errors (robust option).
26
5. Conclusion and Discussion
This study examined the daily stock return in 4 market indices on the Financial Times Stock Exchange 100, FTSE 250, FTSE SmallCap and FTSE AIM. Although the analysis has mainly focused on the existence of the January effect, other potential influences on the January effect as well as other seasonal effects have also been examined. More specifically, this paper addressed the following questions: (1) Does the January effect exist on London stock market between January 1999 and May 2016?; (2) Does the financial crisis have influence on the January effect?; (3) does the state of the economy have influence on the January effect?; (4) is there existence of monthly seasonality in stock returns on the London stock market?
There is a lot of evidence proved in previous studies for the existence of the January effect, for example by Haugen & Jarion (1996) and Rozeff and Kinney (1976). However, the empirical results of the regression of equation (1) table 3 provide evidence for the absence of the January effect in 3 of the 4 market indices. This study didn’t find evidence for the existence of the January effect on the FTSE 100 index, which is at odds with the findings of Sanusi & Ahmed (2016). A possible reason for the different results is the different sample period. However, the results provide evidence for the January effect only on the FTSE AIM index from January 1999 till May 2016. So the January effect does only exists on the market index with the smallest market capitalization, which provides evidence for the size effect, which is in line with previous results of Keim (1983). The return in January exceeds the return in the other eleven months with 8.5 basis points at the FTSE AIM index. The transaction costs at the FTSE AIM index are 2 basis point, so that the January effect covers the transaction costs.
The empirical results of the regression of equation (2) show the significant influence of the financial crisis on all the market indices, except for the FTSE 100. This is consistent with the results of Chaudhurg (2014). In this thesis, the financial crisis is divided in 2 sub-periods; one period during the conversion of the financial crisis and one period during the advanced state of the financial crisis. The results show in all the market indices, except for the FTSE 100, that the conversion period of the financial crisis has significant influence on the stock returns. However, the advanced period of the financial crisis has insignificant influence on all the market indices. The empirical results of the regression of equation (3) show insignificant influence of both sub-periods of the financial crisis on the January effect.
The findings provided from the regression of equations (4) show a high insignificant influence of the state of the economy on the stock returns and the January effect. This indicates that the
27 economic sentiment indicator has no influence on the stock returns and the January effect. The results from the regression of equation (5) show evidence for the seasonality in stock returns in the FTSE250, FTSE SmallCap and the FTSE AIM market indices. This is consistent with the findings of Watchel (1942). A remarkable observation in the monthly returns is that in all the market indices on the London stock market the month September estimates the lowest average returns.
The main conclusion of this thesis is that the January effect only exists for market indices with a very low market capitalization and that the financial crisis and the state of the economy doesn’t have influence on this market anomaly. This indicates that it is very difficult for investors to gain from the January effect, because stock markets with small market capitalizations carry a higher risk and transactions costs than stock markets with high market capitalizations. Furthermore, the state of the economy doesn’t have influence on the January effect, so that investor couldn’t gain from this.
This study does not examine the reason for the insignificant January effect on higher capitalized market indices on the London stock market, this is left for future research. Future research also has to determine why the advanced period of the financial crisis hasn’t influenced the London stock market, is the London stock market recovering from the financial crisis? Furthermore, this study didn’t examine the reason for the low average returns in September, this is also left for future research.
28
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31
Appendix A: Results from regression 1
Regressions at each market indices from model 1: (1) FTSE 100: Number of obs = 4,523 F(1, 4521) = 2.63 Prob > F = 0.1052 R-squared = 0.0005 Root MSE = .01206
FTSE 100 Coefficient Robust standard errors T-value
P-value January -.0009819 . 0006352 -1.55 0.122 Constant .0001713 . 0001877 0.91 0.362 FTSE 250: Number of obs = 4,394 F(1, 4392) = 0.46 Prob > F = 0.4994 R-squared = 0.0001 Root MSE = .0105
FTSE 250 Coefficient Robust standard errors T-value P-value January -.0003602 . 0005664 -0.64 0.525 Constant .0003738 . 0001657 2.26 0.024 FTSE SmallCap: Number of obs = 4,543 F(1, 4541) = 0.47 Prob > F = 0.4950 R-squared = 0.0001 Root MSE = .00713
32 FTSE SmallCap Coefficient Robust standard
errors T-value P-value January .000235 .0003745 0.63 0.530 Constant .0001805 .0001107 1.63 0.103 FTSE AIM: Number of obs = 4,498 F(1, 4496) = 5.26 Prob > F = 0.0219 R-squared = 0.0010 Root MSE = .0086
FTSE AIM Coefficient Robust standard errors
T-value P-value
January .0008501 . 0004064 2.09 0.037
33
Appendix B: Results from regression 2
Regressions at each market indices from model 2:
0 FTSE 100: Number of obs = 4,523 F(3, 4519) = 1.06 Prob> F = 0.3657 R-squared = 0.0008 Root MSE = .01206
FTSE 100 Coefficient Robust standard errors T-value P-value January -.0009898 . 0006055 -1.63 0.102 Crisis . 0000816 . 0003384 0.24 0.810 ConvCrisis . 0005113 . 0008249 -0.62 0.535 Constant . 0002062 . 0002436 0.85 0.397
. test Crisis ConvCrisis ( 1) Crisis = 0 ( 2) ConvCrisis = 0 F( 2, 4519) = 0.26 Prob > F = 0.7701 FTSE 250: Number of obs = 4,394 F(3, 4390) = 2.67 Prob > F = 0.0460 R-squared = 0.0046 Root MSE = .01048
34 FTSE 250 Coefficient Robust standard
errors T-value P-value January -.0004374 .0005326 -0.82 0.412 Crisis .0001892 .0003044 0.62 0.534 ConvCrisis .0024009 .000928 -2.59 0.010 Constant .0005079 .0001861 2.73 0.006 . test Crisis ConvCrisis
( 1) Crisis = 0 ( 2) ConvCrisis = 0 F( 2, 4390) = 10.02 Prob > F = 0.0000 FTSE SmallCap: Number of obs = 4,543 F(3, 4539) = 7.35 Prob > F = 0.0001 R-squared = 0.0111 Root MSE = .00709
FTSE SmallCap Coefficient Robust standard errors T-value P-value January .0002732 .00034 0.80 0.422 Crisis .0002367 .0002028 1.17 0.243 ConvCrisis .0023434 .0005509 -4.25 0.000 Constant .0003167 .0001352 2.34 0.019 . test Crisis ConvCrisis
( 1) Crisis = 0 ( 2) ConvCrisis = 0 F( 2, 4539) = 10.72 Prob > F = 0.0000
35 FTSE AIM: Number of obs = 4,498 F(3, 4494) = 11.52 Prob > F = 0.0000 R-squared = 0.0116 Root MSE = .00855
FTSE AIM Coefficient Robust standard errors T-value P-value January .000852 .0003713 2.29 0.022 Crisis .0002075 .0002577 0.80 0.421 ConvCrisis .0028975 .0005705 -5.08 0.000 Constant .0001159 .0001918 0.60 0.546
. test Crisis ConvCrisis ( 1) Crisis = 0
( 2) ConvCrisis = 0 F( 2, 4494) = 14.91 Prob > F = 0.0000
36
Appendix C: Results from regression 3
Regressions at each market indices from model 3:
FTSE 100: Number of obs = 4,523 F(5, 4517) = 0.76 Prob > F = 0.5766 R-squared = 0.0012 Root MSE = .01206
FTSE 100 Coefficient Robust standard error T-value P>|t| value January -.0010942 .000763 -1.43 0.152 Crisis 1.50e-06 .0003563 0.00 0.997 Convcrisis . 0003465 . 0008594 -0.40 0.687 Jan*Crisis .0009174 .0011306 0.81 0.417 Jan*Convcrisis -.0021408 . 0030577 -0.70 0.484 Constant .0002156 .0002489 0.87 0.386
. test JanCrisis JanConvCrisis ( 1) JanCrisis = 0 ( 2) JanConvCrisis = 0 F( 2, 4517) = 0.69 Prob > F = 0.5019 FTSE 250: Number of obs = 4,394 F(5, 4388) = 1.61 Prob > F = 0.1533 R-squared = 0.0047 Root MSE = .01048
37 FTSE 250 Coefficient Robust standard
error T-value P>|t| value January -.0002643 .0005547 -0.48 0.634 Crisis .0002103 .0003209 0.66 0.512 Convcrisis -.0023306 .0009487 -2.46** 0.014** Jan*Crisis -.0002382 .0010071 -0.24 0.813 Jan*Convcrisis -.001128 .0044092 -0.26 0.789 Constant .0004925 .0001886 2.61** 0.009
. test JanCrisis JanConvCrisis ( 1) JanCrisis = 0 ( 2) JanConvCrisis = 0 F( 2, 4388) = 0.06 Prob > F = 0.9448 FTSE SmallCap: Number of obs = 4,543 F(5, 4537) = 4.96 Prob > F = 0.0002 R-squared = 0.0115 Root MSE = .00709
FTSE SmallCap Coefficient Robust standard error T-value P>|t| value January .0006653 .0003822 1.74* 0.082* Crisis .0002848 .0002145 1.33 0.184 Convcrisis -.0005466 .0005812 -3.77*** 0.000*** Jan*Crisis -.0005466 .0006362 -0.86 0.390 Jan*Convcrisis -.0016046 .0018169 -0.88 0.377 Constant .0002811 .0001381 2.0 0.042
. test JanCrisis JanConvCrisis ( 1) JanCrisis = 0
( 2) JanConvCrisis = 0 F( 2, 4537) = 0.67 Prob > F = 0.5097
38 FTSE AIM: Number of obs = 4,498 F(5, 4492) = 6.92 Prob > F = 0.0000 R-squared = 0.0117 Root MSE = .00856
FTSE AIM Coefficient Robust standard error T-value P>|t| value January .0008666 .0004841 1.79* 0.074 Crisis .0002331 .0002756 0.85 0.398 Convcrisis -.0029892 .0006115 -4.89*** 0.000*** Jan*Crisis -.0002908 .0007637 -0.38 0.597 Jan*Convcrisis .0008809 .0016659 0.703 0.53 Constant .0001139 .0001986 0.566 0.566
. test Jancrisis JanConvcrisis ( 1) Jancrisis = 0
( 2) JanConvcrisis = 0 F( 2, 4492) = 0.26 Prob > F = 0.7725
39
Appendix D: Results from regression 4
Regressions at each market indices from model 4:
(3) FTSE 100: Number of obs = 4,523 F(3, 4519) = 0.95 Prob > F = 0.4158 R-squared = 0.0006 Root MSE = .01206
FTSE 100 Coefficient Robust standard errors T-value P-value January -.0012275 . 0008551 -1.44 0.151 ESIL . 0001176 . 0004143 0.28 0.777 Jan*ESIL -.0004636 . 0012239 0.38 0.3705 Constant . 0001255 . 000208 0.60 0.546 FTSE 250: Number of obs = 4,394 F(3, 4390) = 0.44 Prob > F = 0.7253 R-squared = 0.0003 Root MSE = .01048
FTSE 250 Coefficient Robust standard errors T-value P-value January -.0007019 .0007505 -0.94 0.350 ESIL .0001967 .0003693 0.53 0.594 Jan*ESIL .0006307 .0010781 0.58 0.559 Constant .0002974 .0001797 1.65 0.098
40 FTSE SmallCap: Number of obs = 4,543 F(3, 4539) = 0.87 Prob > F = 0.4543 R-squared = 0.0006 Root MSE = .00713
FTSE SmallCap Coefficient Robust standard errors T-value P-value January .0001642 .0004873 0.34 0.736 ESIL .0003071 .0002481 1.24 0.216 Jan*ESIL .0000754 .0006968 0.11 0.914 Constant .0000615 .0001195 0.51 0.607 FTSE AIM: Number of obs = 4,498 F(3, 4494) = 3.05 Prob > F = 0.0276 R-squared = 0.0012 Root MSE = .0086
FTSE AIM Coefficient Robust standard errors T-value P-value January .0005003 .0005251 0.95 0.341 ESIL -.0000904 .000283 -0.32 0.749 Jan*ESIL .0008727 .0007163 1.22 0.223 Constant -.0000396 .0001754 -0.23 0.821
41
Appendix E: Results from regression 5
Regressions at each market indices from model 5: (4) FTSE 100: Number of obs = 4,523 F (11, 4511) = 1.36 prob > F = 0.1867 R-squared = 0.0029 Root MSE = .01206
FTSE 100 Coefficient Robust standard errors T-value P-value February .0012371 .0008131 1.52 0.128 March .000978 .0008494 1.15 0.250 April .0018377 .0007663 2.40 0.017 May .0004807 .0007924 0.61 0.544 June -.0000384 .000766 -0.05 0.960 July .0011481 .0008619 1.33 0.183 Augustus .0007808 .0008582 0.91 0.363 September -.0000791 .0009596 -0.08 0.934 October .0017853 .0010109 1.77 0.077 November .0010648 .0008692 1.23 0.221 December .0015594 .0007771 2.01 0.045 Constant -.0008107 .0005765 -1.41 0.160
. test February March April May June July Augustus September October November December = 0 H0: February = March = April = May = June = July = Augustus = September= October =
November= December = 0 F( 11, 4511) = 1.36 Prob > F = 0.1867
42 FTSE 250: Number of obs = 4,394 F(11, 4382) = 1.68 Prob > F = 0.0705 R-squared = 0.0043 Root MSE = .01049
FTSE 250 Coefficient Robust standard errors T-value P-value February .0011271 .0007035 1.60 0.109 March .0005352 .0007093 0.75 0.451 April .0009426 .0007319 1.29 0.198 May .0000548 .0007788 0.07 0.944 June -.0005163 .0007181 -0.72 0.472 July .0001894 .0007239 0.26 0.794 Augustus .0006322 .000763 0.83 0.407 September -.001384 .0008107 -1.71 0.088 October .0003088 .0008115 0.38 0.704 November .0006448 .0007616 0.85 0.397 December .0011684 .0006946 1.68 0.093 Constant -.00004 .0005052 0.08 0.937
. test February March April May June July Augustus September October November December = 0 H0: February = March = April = May = June = July = Augustus = September= October =
November= December = 0 F( 11, 4382) = 1.68 Prob > F = 0.0705
