BSc Banking and International Finance
“Is There Seasonality in the UK Stock Market?”
Student Name: Sharan Pawan Aggarwal
Student Number: 120000617
Supervisor’s name: Professor Alec Chrystal
Submission date: 2nd April 2015
"I certify that I have complied with the guidelines on plagiarism outlined in the Course Handbook in
the production of this dissertation and that it is my own, unaided work".
Signature:___________________________________
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“The seasonal effect is so pronounced that investing based solely on those calendar dates succeeds in the difficult task (even for professionals) of outperforming the market. And it does so while taking only 60% of market risk, a very important consideration.”
- Sy Harding
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ABSTRACT This study tests for the presence of monthly anomalies in UK stock markets. In
particular it reports tests for recurring seasonal patterns in the FTSE 100. It starts by
questioning whether or not there are any monthly seasonal patterns present in the
index, and if so then whether or not they are significant and have evolved over time.
To test this, the paper employs regression models of returns on the FTSE 100 on the
monthly dummy variables created; and breakpoint tests to come to an empirical
conclusion. The findings reveal that the most significant monthly seasonal patterns
exist in January, June and September, and this contradicts the efficient market
hypothesis (EMH). It is suggested that the existence of these seasonalities can be
explained by heterogeneous agent models (HAM). Evidence is found to support the
statement- “As January goes, so goes the year”, for the FTSE 100. Explanations are
also proposed for why each of the above three seasonalities exists. For example, the
negative returns in January might be linked to the size effect. Finally, the study
shows that if the rational investor switches his investment between the FTSE 100
and the S&P 500 at the right time, then he could gain from arbitrage. So knowledge
of seasonalities might help the investor make profits on average.
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Table of Contents
ACKNOWLEDGEMENTS 4
1) INTRODUCTION 5
2) LITERATURE REVIEW 7
2.1) AN OVERVIEW OF SEASONALITIES 7 2.2) A BRIEF CHRONOLOGICAL OVERVIEW OF PAST STUDIES AND TYPES OF
SEASONALITIES 7 2.3) SUGGESTED REASONS FOR THE EXISTENCE OF SEASONALITIES 9
3) DATA AND METHODOLOGY 15
3.1) DATA 15 CHART 3.1- ADJUSTED CLOSE (MONTHLY) FOR FTSE 100 15 3.2) METHODOLOGY 16 3.2.1) TESTING FOR STATIONARITY 16 3.2.2) CREATING DUMMY VARIABLES 18 3.2.3) RUNNING THE REGRESSION 19 3.2.4) TESTING FOR STRUCTURAL BREAKS IN THE DATA 20 3.2.5) RUNNING AN ALGORITHM 21 3.2.6) TESTING FOR RECURSIVE STABILITY 21
4. ANALYSIS AND FINDINGS 22
4.1) EMPIRICAL ANALYSIS 22 4.2) INVESTIGATION INTO THE JANUARY EFFECT, JUNE EFFECT AND SEPTEMBER
EFFECT 34 4.2.1) THE JANUARY EFFECT ON THE FTSE 100 34 4.2.2) THE JUNE EFFECT ON THE FTSE 100 37 4.2.3) THE SEPTEMBER EFFECT ON THE FTSE 100 39 4.3) TESTING CONSISTENCY OF THE NEGATIVE RETURNS 39 4.4) SWITCHING STRATEGIES FOR INVESTORS 40 4.5) IMPLICATIONS OF THE SEASONALITIES FOR THE EFFICIENT MARKET
HYPOTHESIS (EMH) 42
5) CONCLUSION 44
REFERENCES 47
APPENDICES 54
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ACKNOWLEDGEMENTS I am extremely thankful to Professor Alec Chrystal for the constant help, guidance,
patience and supervision given to me in the preparation of this paper. Professor Alec
Chrystal has taught me Foundations of Economics for Finance, Monetary Economics
and Economics of FOREX; which has laid a strong foundation for understanding
economic markets and how financial institutions exploit differences in market
mispricing. I am also grateful to Dr. Lorenzo Trapani from whom I have obtained a
thorough understanding of Financial Econometrics. The additional sophisticated
tests learnt by me have made this paper possible in its present perspective.
I would also like to thank my professors- Dr. Maria Carapeto, Dr. Paolo Volpin, Dr.
Aneel Keswani, Dr. Barbara Casu, Dr. Sonia Falconieri, Professor Carlos Ribeiro,
Mrs. Adarssh Wadhwa, Mr. Nikhil Pitale, and Mr. Satwant Singh Matta for all the
knowledge that they have imparted to me over the years.
I am also thankful to Mrs. Claudia Quinonez for her help with getting all the relevant
news from Bloomberg. I wish to thank Mr. Vinay Aggarwal and Dr. S.M. Katrak for all
their motivation and experienced insights as well as Mr. Suraj Kaeley for all his help
related to the Mutual Fund industry and for teaching me how, where, and when to
invest. The knowledge of market timing was a great driving force for my choice of
topic.
I would also like to extend my gratitude to my friends- Keith Boldeau, Manuel
Martinez, Ian Gaspar, Krista Stanley, Sach Bhansali, Meera Gulati, Muhammad
Yasin Soodeen, Saisha Moyce, Tomoghno Ghose, Eleana Toliou, Divij Dugar,
Ankrish Anand, Sparsh Kaeley, Arunav Vaish, and Araeyus Vakil for always being a
source of strength and inspiration, and for always encouraging me. I would like to
thank Mr. Dilip Parmar for all his help in accessing various resources.
Finally, I would like to dedicate this paper to my parents- Mr. Pawan Aggarwal and
Mrs. Anita Aggarwal; and to my sister- Nainika Aggarwal, who have been the
strongest influential source in my life, and helped me make all the hardest decisions.
I wish to thank them immensely for all their direction and support.
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1) INTRODUCTION The only thing that is constant in financial markets is change. However, there are
certain occurrences that show abnormal patterns (anomalies), which are termed as
seasonalities. These are predictable recurrences in time, based on historical data
and therefore are in line with the old adage- "history repeats itself".
The reason why seasonalities are of interest is because they contradict the famous
efficient markets hypothesis proposed by Fama (1970). By knowing what is going to
happen, the prices should ideally adjust to incorporate public information to be in line
with the hypothesis, however, these anomalies impact the price in the same
predictable way on average.
The main motivation for this paper is the January effect. The tax-loss selling
hypothesis which is explained in detail in Section 2.3 is very intriguing. It was
interesting to test whether this was the main factor that drove the January effect in
particular in the FTSE 100. However, the findings suggest that the theory of
heterogeneous agent models might fit better to the seasonal effects in the index,
along with the size effect, as suggested in previous studies by Fama and French
(1993) and various other academicians. It is also found that these might be reasons
for significantly negative returns on a recursive basis in January, June and
September in the FTSE 100.
The questions under study are whether or not there are any seasonalities in the
FTSE 100 by looking at a chronological order of academic studies on the various
types of seasonalities, and where and why they exist. The same can be found in
section 2.
Once the type of seasonalities to look for are identified in the data (which in this case
is monthly), dummy variables for each month are created to then form a regression.
The regressions are then tested for structural breaks, and then each sub-sample is
tested for significance to arrive at a final model to analyze which months are the
most significant (January, June and September). Finally the model’s recursive
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stability is tested for the entire time period. The procedure is explained in section 3,
and the outputs are analyzed in section 4.
Section 4 explains the possible reasons for the existence of each seasonality
identified, and tests whether or not the returns in January in the FTSE 100 can
predict the returns for the rest of the year, and the findings suggest that this might
actually be the case. This section also identifies possible strategies for an arbitrageur
to make money by switching his investments between the FTSE 100 and the S&P
500 or between the FTSE 100 and the FTSE 250, based on the months when one
outperforms the other. However, the cross-border switching strategies might entail
exchange rate risk due to the volatility of exchange rates. This might negate any
gains from such strategies.
Finally, section 5, provides a conclusion of the findings and highlights the areas
where there is scope for improvement or for further research.
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2) LITERATURE REVIEW
2.1) AN OVERVIEW OF SEASONALITIES There have been several studies on seasonal effects in the stock markets around
the world. The most documented seasonalities are the month-of-the-year, week-of-
the-month, day-of-the-week and hour-of-the-day effects. In addition to this there is
the half-month effect (wherein the returns are higher in the first half of the month)
and the turn-of-the-month effect (wherein the returns on the last day of the month are
statistically higher than those on other trading days), and the holiday effect.
Although they seem to exist, people cannot completely explain why they do, as they
successfully keep violating the Efficient Market Hypothesis (EMH), which in its semi-
strong form states that any historic or public information will immediately be
absorbed by the market and will be reflected in the current prices. However, if this is
the case, then the prices should be adjusting automatically to previous seasonalities,
and so nobody should be able to make any profits from trading on seasonalities. This
is a major criticism of seasonalities, as they are inconsistent with the EMH. In reality,
although people explain some of the factors that lead to their being, they still cannot
pin-point any one particular reason for them existing. It is a medley of probable
factors which contribute to their existence and as will be discussed in section 2.3, it
is actually the very rationality of the market makers themselves that somewhat
contributes to why they exist. However to understand seasonalities as they exist
today, one must understand how they have evolved over time. This is discussed in
section 2.2.
2.2) A BRIEF CHRONOLOGICAL OVERVIEW OF PAST STUDIES AND TYPES OF SEASONALITIES The first seasonal effects in US stock markets were pointed out by Watchel (1942)
and in Australia by Officer (1975). The ‘January effect’ was first documented by
Rozeff and Kinney (1976), when they documented that the average stock market
return was higher in January than in any other month. Shiller (1981) showed that
prices move away from fundamental values, since the variation in the stock prices is
too large to be explained by mere variation in dividend payments. Keim (1983)
showed that small firms’ returns were significantly higher than those of large firms in
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terms of seasonal and size effects during the month of January. This was confirmed
by Gultekin, M. and Gultekin, N. (1983) after studying the data of 17 industrial
countries with different tax laws.
A portion of the January effect might rest on the Tax-Loss Selling Hypothesis (This is
discussed in detail in Section 2.3). However, Reinganum (1983) found that the tax-
loss selling hypothesis could not explain the January Effect entirely.
Smirlock et al. (1986), found evidence of the day-of-the-week effect, which was later
built on by Agrawal and Tandon (1994) and Mills and Coutts (1995) who found that
mean stock returns were unusually high on Fridays and low on Mondays. Similarly,
Ross et al. (2002) had the same findings with the addition of high returns on
Wednesdays as well.
Chan (1986) found that the source of January seasonalities was actually in long-term
losses. In Malaysia, Nassir and Mohammad (1987) found that on an average returns
in other months were lower and negative when compared to January. Ritter (1988)
found that the percentage of individual’s stock purchases to sales was the highest in
beginning of January and vice versa at the end of December. In the UK, Lewis
(1989) reported the presence of seasonal effects. Jaffe et al. (1989) found a weak
monthly effect in stock returns in various countries.
Although there have been very few studies that have revealed the presence of
seasonal effects of stock returns for the emerging capital markets, such as those
conducted by Aggarwal and Rivoli (1989), Ho (1990), Lee et al. (1990), Lee (1992),
Ho and Cheung (1994), Kamath et al. (1998), and Islam et al. (2001); they appear to
bear significance with respect to the January effect, as will be seen in section 4.2.1,
as they in turn might cause currency seasonalities.
Raj and Thurston (1994) investigated the January and April effects in the New
Zealand stock market; however there was no evidence to suggest their existence.
The month-end effect in Denmark, Germany, and Norway was first reported by
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Bodreaux (1995). Pandey (2002) confirmed the presence of the January effect on
India’s benchmark index- the ‘Sensex’, of the Bombay Stock Exchange (BSE).
Brown et al. (2004) introduced a new type of January effect after studying data of the
NYSE, wherein the signs of the January returns have superior predictive value,
compared to the signs of any other calendar month’s returns for the purpose of
forecasting the returns for the next 1 year. This is suggestive of a lower mean
squared error in a forecasting model based on January returns, vis-à-vis other
months.
Lazar et al. (2005) confirm the existence of seasonality in the BSE that is consistent
with the tax-loss selling hypothesis. Contrarily, Alagidede et al. (2006) find an April
effect for Ghana’s stock market on examining the day-of-the-week and month-of-the-
year effects in stock returns. Doran et al. (2008) find that Chinese stock markets on
the whole, especially the very volatile Chinese stocks, outperform at the turn of the
Chinese New Year. However, this again, does not place any focus on January.
2.3) SUGGESTED REASONS FOR THE EXISTENCE OF SEASONALITIES
It must be evident by now that seasonalities could very well exist. The first studies
were conducted by Wachtel op. cit. (1942) and ever since, people have been
studying them. According to Ray (2012), “Such market anomalies are primarily due
to behavioral causes”. This was originally mentioned in a study by Schwert (2003).
Demand and Supply- Behavioral causes are not the only reason why seasonalities
might exist. It is definitely a possible contributor to their existence, but markets work
on demand and supply. Demand is arguably a greater driver of prices than supply in
most cases. When it comes down to just demand, the main determinants of quantity
demanded according to Lipsey and Chrystal (2011) are the price of the product, the
prices of other products, the consumer’s income and wealth, the consumer’s tastes,
and various individual-specific or environmental factors. The last two are related to
the behavior of the consumer. If demand for a product increases, it drives the price
up. The increase in revenue is reflected in the income statement of the company in
its quarterly filings and its annual report. If there are higher revenues, then the profits
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are higher, given constant costs, and therefore the rational investor would invest
more in that stock. However, the knowledge of the company’s earnings is not known
to one, till the announcement date, which is at the end of the quarter. As a result of
this, no matter how much the company sells during a particular month due to an end-
of-season-sale, ‘Black Friday’, ‘Boxing Day’, and so on, the stock prices won’t be
affected immediately, as the demand for the equity will only increase on and after the
announcement date.
Year-end Bonuses- Another potential contributor to the seasonal factor could be
year-end bonuses which are typically paid in January. This would increase the
marginal propensity to consume, and resultantly part of the bonus money may be
directed to buying stocks leading to a rally in share prices in January. Year-end
festivals may affect the expenditure behavior pattern of investors making them more
indulgent, though the enhanced purchasing power may be the main driver to buy
rather than the festive spirit.
Tax-Loss Selling Hypothesis- According to Marsh et al. (1982), the tax-loss selling
hypothesis states “Tax Laws influence Investors’ portfolio decisions by encouraging
the sale of securities that have experienced recent price declines so that the (short
term) capital loss can be offset against taxable income”. Resultantly, companies and
hedge funds may sell the shares that are making losses in the last month of the
accounting year (mainly December or March for companies and hedge funds or
March for individuals in most countries), leading to a fall in share prices, and then
use the net operating losses that they book in their year-end income statement, to
offset their profits within the same year, thus acting as a tax shield. The stocks sold
may be repurchased in bulk at the beginning of the next month (new accounting
year) at extremely low prices. The surge in demand may drive the prices of the
stocks back up. Sale of stocks in March may lead to an April effect, consistent with
the research conducted by Alagidede op. cit. (2006). The US ends its tax year in
December and even corporates follow the calendar year, which may lead to sale of
their loss-making investments in December to offset taxable income within the same
year. In UK, companies can choose any 12 month accounting period, but majority of
corporations select 31st December, or 31st March or 30th June year ends. As already
explained above, capital loss arising out of sale of shares in the last month of the
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relevant accounting year can be offset against the other profits available within the
same accounting year. Hence, excess selling of shares in December will drive down
the stock prices and renewed buying in the next month will drive the share prices up,
leading to the January effect. Likewise, March and June year ends might be
instrumental in the April and July effects. However, the whole hypothesis is purely
based on assumptions that these tax-loss sales will take place, and is based entirely
on the tax law that the country follows. Moreover, most investments are cross
border, which brings in other factors like exchange rate fluctuations and tax years in
multiple countries. Since the US share of cross-border holdings is the highest, the
tax-loss selling hypothesis and the January effect may mainly be associated to the
US since empirical studies have shown less evidence of the January effect in the
European countries. However, this hypothesis often fails to consider the size of the
company while explaining the January effect. The tax-loss selling
hypothesis could thus, better explain the positive January effect for small firms,
which have higher returns than the large firms. The size effect is consistent with the
studies conducted by Keim op. cit. (1983), Gultekin, M. and Gultekin, N. op. cit.
(1983) and Fama and French op. cit. (1993).
Research studies by Kang et al. (2011) reveal that the quantity of tax advantage the
seller may gain by selling the loss-making stock in the current year-end rather than
waiting to sell the stock till the beginning of the next year may impact the selling of
loss making shares. If the seller sells the stock in the following year, then he/she will
postpone the tax advantage arising out of the sale of the loss-making shares by one
year. Hence the tax advantage will be postponed to one year later and the seller will
incur a loss to the extent of the present value of the tax advantage (by discounting at
the one year interest rate), which may have been available to the seller that year
(opportunity cost). Therefore, the seller may be further tempted to sell the loss-
making shares in the last month of the current year itself, even at a price lower than
the intrinsic value, but the difference between the intrinsic value and the lower sale
price should not exceed the quantity of loss in the present value of the tax advantage
which may be incurred due to postponement of the tax advantage by one year (that
is it must have a positive NPV).
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Behavioral Patterns- The behavioral patterns would also explain to some extent
why there are turn-of-the-month, and day-of-the-week effects.
The turn-of-the-month effect was first established by Ariel (1987) who proved that
returns in the first half of the month were generally positive, whereas the returns in
the second half were either not existent or very less. Penman (1987) cites the
possible cause being better corporate news in the first half of the month compared to
the latter half. Lakonisok et al. (1988) study in US reveals that due to liquidity the
returns in ‘-4, +3’ trading days of the month exceed the gains of the entire month.
These results have been corroborated by Agrawal and Tandon op. cit. (1994) in 10
countries in their research covering 18 countries using a ‘-4, +4’ trading days model.
Studies by Gibbons and Hess (1981) and Keim and Stambaugh (1984) in the US
markets have found Friday returns to be much higher than other day returns
whereas Monday returns move in the opposite direction.
Research by Lakonishok et al. (1990) finds that trading by institutions is least on
Mondays and for individuals it is the opposite. Individuals buy less and sell more on
Mondays. Abraham et al. (1994) finds that unhealthy news on weekends and cash
flow requirements tend individuals to off-load more shares on Mondays. This is
consistent with the idea proposed by Lakonishok op. cit. (1990).
Heterogeneous Agent Models- People tend to follow a trend and keep doing
exactly what happened in the past, thus maintaining the seasonality, even if there
was absolutely no reason for it to exist, other than the fact that each investor thinks
that every investor would do what he/she does and would thus, end up maintaining
the seasonal effect. Therefore, very often seasonality is nothing more than the effect
of each investor free-riding on the rational expectation that all other investors will do
exactly what he does by mimicking the past. According to Hommes (2005), “Any
dynamic economic system is in fact an expectations feedback system. A theory of
expectation formation is therefore a crucial part of any economic model or theory”.
The January barometer states, “As goes January, so goes the year”. According to
this theory, January market movements can be used to envisage the returns for the
rest of the year. A possible explanation for this is that due to the old adage as
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mentioned above, speculators tend to influence the prices of the market based on
the opening price in January. Therefore, these models employ a lot of chart analysis
to predict price movements, and take positions based on historic trends. Thus, by
observing past seasonal effects, the speculators might maintain the trend.
The Turn of the Year- This may link back to the discussion on HAMs. Hedge fund
managers and other players may take positions based on their forecasts for the next
few months; which might be influenced by past trends. If the assessment is adverse,
short positions are placed and vice versa. This theory is based on the cash liquidity
in the market by the big fund houses which will impact the movement of stock prices.
Seasonalities driving other seasonalities- Another important contributor to
seasonalities in emerging markets is the demand for foreign exchange. This may be
linked to the tax-loss selling hypothesis and the January effect. However, the basic
concept is that currency seasonalities exist due to the demand for foreign equities.
The same is reflected in a paper by Li et al. (2011), where they examine 8 major
currencies from 1972-2010 and find that 6 currencies exhibit significantly higher
returns in the month of December and a reversal in January, leading to a significant
impact on currency hedgers, arbitrageurs and speculators.
Foreign investors in world markets may have a need to repatriate dividends earned /
proceeds from sale of shares to their home country towards the end of the year with
a view to have funds available in their home country for the purpose of paying
dividends to their investors. This sale of securities may be either due to the tax-loss
selling hypothesis, or simply due to the need for liquidity. As per the report of
Marples and Gravelle (2011), to encourage dividend repatriation earned abroad, the
US has given a tax concession which has resulted in an elevated volume of
repatriation back to the home country (US). The finding also includes, that to enable
repatriation, the proceeds overseas (in the foreign currency) would have to be
converted to the home currency (US dollars). Due to increased demand for dollars in
the foreign markets, which require conversion of the foreign currency to the home
currency at the given spot rate, the rate for dollars would appreciate and
correspondingly the value of the foreign currency would depreciate.
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Studies show that foreign investors return to emerging markets in January and with
them bring in foreign exchange capital inflows which may lead to an excess supply of
foreign currency in the emerging markets (say India). As per Agrawal, R. and
Agrawal, T. (2013) due to excess supply of foreign currency the same is likely to
depreciate in value when compared to the domestic currency of the emerging
market. Thus, seasonalities often drive one another.
Momentum- Jegadeesh and Titman (2001) explain that stocks that are winners
continue to be winners, whereas those that are losers in a particular year continue to
remain losers the next year. This is termed as the momentum effect. Therefore, the
winners of one year might continue to remain the winners the next year, thus
facilitating long positions in them on a seasonal basis and vice versa.
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3) DATA AND METHODOLOGY
3.1) DATA This paper aims at testing for the presence of seasonalities in the FTSE 100 and
seeing if there had been any form of evolution of the seasonalities (a structural break
in the data) over time.
The FTSE 100 is a subsidiary of the London Stock Exchange (LSE) group. The
acronym ‘FTSE’ stands for Financial Times Stock Exchange. It consists of the 100
companies on the LSE with the largest market capitalisation. It started on 3 January
1984 with a base level of 1000, and reached its peak on 30 December 1999.
CHART 3.1- ADJUSTED CLOSE (MONTHLY) FOR FTSE 100
Source: Yahoo Finance1
The observations are the adjusted monthly closing prices for the FTSE 100 from 3
January 1984 to 3 November 2014. The graph for the same is shown in Chart 3.12.
1 Yahoo Finance (2014) FTSE 100: Historical Prices [Online] Available at:
http://finance.yahoo.com/q/hp?s=%5EFTSE&d=9&e=15&f=2014&g=d&a=0&b=3&c=
1984&z=66&y=7986 [Accessed: 16 October 2014]
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The reason why the adjusted closing prices were chosen was because this would
negate the effect of any dividend announcements, stock splits and so on that could
take place in the companies listed on the FTSE 100. The data were based on the
closing prices because these were the prices at which the markets closed, and since
the seasonalities of interest were monthly rather than intra-day, the prices during the
day didn’t appear to make a difference to the study. The data might be prone to bias,
as they looked at the adjusted close instead of the unadjusted values, and so these
could have led to a different result as compared to previous studies.
3.2) METHODOLOGY
3.2.1) TESTING FOR STATIONARITY
The graph in Chart 3.1 showed an upward trend, and thus, it appeared to be non-
stationary. Creating a model based on non-stationary data would be spurious.
A weakly stationary series implies that at each point in time, the series has a
constant mean, variance and covariance. However, if even one of these conditions is
not satisfied, then the series is said to be non-stationary. Non-stationarity can be of 2
forms- Unit root/ Random walk and Trend Stationarity. If the series follows a random
walk, as it appears to be the general case with prices, then the variance of the series
tends to infinity, as it would be heteroskedastic, and would equal to 2 times t (where
2 is the variance of the series, and t is the time). As a result the variance would
increase linearly with time, and since time tends to infinity, so would the variance.
On the other hand, for a series that is stationary about a trend, the series will never
have a constant mean. Once again, this makes it impossible to predict. Thus, in
either case, the series must be 1st differenced to make it stationary. However, to
make sure whether the series is a random walk or trend stationary, it must be tested.
Therefore the first thing to do was to test for non-stationarity.
2 For the purpose of this paper, the range of months will be referred to as 1984M01 – 2014M11.
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There are a number of tests for stationarity; however the one used was introduced
by Phillips and Perron (1987). The PP test is better than that introduced by Dickey
and Fuller (1979), as it is non-parametric. This means that it solves the problem of
the ADF test, of choosing the correct number of lags, and employs the
Heteroskedasticity and Autocorrelation Corrections (HAC).
The ADF expression is as follows:
EQUATION 3.1
∆𝑦𝑡 = 𝜓𝑦𝑡−1 + ∑ 𝛽𝑗∆𝑦𝑡−𝑗 + 𝑢𝑡𝑝𝑗=1
Thus, this test is criticized on the grounds that it needs to find the accurate value of p
(the lags) so as to minimise loss of degrees of freedom. Hence, it is not a full-proof
method of testing for stationarity, as the only available selection methods are the
Schwert (1989) rule of thumb, of choosing the frequency of the data + 1 and the
information criteria. Therefore, this paper employed the PP test to look for non-
stationarity about an intercept and trend.
It uses the following equation:
EQUATION 3.2
∆𝑦𝑡 = 𝛽′𝐷𝑡 + 𝜋𝑦𝑡−1 + 𝑢𝑡
Where Dt is a vector of deterministic terms such as the constant, trend, etc.; and
H0 : 𝜋 = 0, as 𝜋 = 𝛽-1, and therefore, indicating that yt ~ I(1).
Thus, the test statistic was:
t = π̂
SE(π̂) ; and t* is derived using a Monte-Carlo simulation.
The test results would have-
H0 : The series of Adjusted Close of the FTSE 100 is non-stationary
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H1 : The series of Adjusted Close of the FTSE 100 is stationary about an intercept
and trend.
Since prices are generally non-stationary, the next step was to look at the returns
(the first difference):
Rt = ln(Pt/Pt-1)
Where Rt is a series of the returns on the FTSE 100 at time t,
And Pt is a series of the adjusted closing prices of the FTSE 100 at the end of the
month.
The PP test was then repeated, however this time on the returns, and now with the
following hypothesis-
H0 : The series of Returns has a unit root.
H1 : The series of Returns is stationary about an intercept.
3.2.2) CREATING DUMMY VARIABLES
The next step was to create dummy variables against which the returns on the FTSE
100 could be regressed so as to test for evolutions in the seasonalities. The following
12 monthly dummy variables were created.
DJAN = f(x) = {1, x = January0, x ≠ January
DFEB = f(y) = {1, y = February0, y ≠ February
DMAR = f(z) = {1, z = March0, z ≠ March
DAPR = f(a) = {1, a = April0, a ≠ April
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DMAY = f(b) = {1, b = May0, b ≠ May
DJUN = f(c) = {1, c = June0, c ≠ June
DJUL = f(d) = {1, d = July0, d ≠ July
DAUG = f(e) = {1, e = August0, e ≠ August
DSEP = f(g) = {1, g = September0, g ≠ September
DOCT = f(h) = {1, h = October0, h ≠ October
DNOV = f(i) = {1, i = November0, i ≠ November
DDEC = f(j) = {1, j = December0, j ≠ December
3.2.3) RUNNING THE REGRESSION
The 3rd step was to form an ordinary least squares (OLS) regression of the returns
on the dummy variables, ignoring DNOV, as if DNOV was included, then there would
be serial correlation between the dummy variables, leading to multicollinearity. Since
there was already a constant in the regression, there was no need to include DNOV,
as it was already represented in the constant. However, if the constant was
removed, then and only then DNOV could be included. However, in this case, the
regression was run without DNOV for the entire sample period of 1984M01 to
2014M11 and is as follows:
20
EQUATION 3.4
𝑅𝑡 = 𝛼 + 𝛽1𝐷𝐽𝐴𝑁𝑡 + 𝛽2𝐷𝐹𝐸𝐵𝑡 + 𝛽3𝐷𝑀𝐴𝑅𝑡 + 𝛽4𝐷𝐴𝑃𝑅𝑡 + 𝛽5𝐷𝑀𝐴𝑌𝑡 + 𝛽6𝐷𝐽𝑈𝑁𝑡 +
𝛽7𝐷𝐽𝑈𝐿𝑡 + 𝛽8𝐷𝐴𝑈𝐺𝑡 + 𝛽9𝐷𝑆𝐸𝑃𝑡 + 𝛽10𝐷𝑂𝐶𝑇𝑡 + 𝛽11𝐷𝐷𝐸𝐶𝑡 + 𝑢𝑡
The next step was to test for the above model’s parameters for significance. The p-
value of a variable tells one whether or not that variable is significant. The criteria are
based on the level of confidence. Given a standard normal distribution, and a 95%
confidence level, anything that falls outside the middle 95% of the normal
distribution, is insignificant. That leaves one with 5%, split equally on both tails.
Therefore, this is called a 5% significance level and is the p-value of the test.
Anything above a 5% level falls within the confidence interval and so the null is not
rejected, however, anything less than a p-value of 0.05 means that the null
hypothesis is rejected with a 95% confidence that the probability of wrongly rejecting
a correct null (Type 1 error) is less than 5%.
3.2.4) TESTING FOR STRUCTURAL BREAKS IN THE DATA
The next test was for parameter stability with an unknown break-point, as suggested
by Quandt (1960) and Andrews (1993), to determine exactly when the break was; so
that the dataset could be split into 2 periods, and subsequently tested individually for
the significance of the dummy variables. This test (Quandt-Andrews) is better than
that suggested by Chow (1960), as the Chow test requires one to know exactly when
the proposed break in the model is, and then based on that test to see if the break is
significant. The Quandt-Andrews test on the other hand is more sophisticated, and
tells one exactly when the most likely breaks in the data would be.
H0: There are no significant breaks in the data
H1: There is a significant break in the data
21
3.2.5) RUNNING AN ALGORITHM
The next step was to run an algorithm, wherein the same regression as was found in
equation 3.4, employed a general to specific approach to eliminate the insignificant
variables, and then tested for the presence of serial correlation in each limited
sample regression output, using the Breusche-Godfrey LM test for serial correlation
developed by Godfrey (1978) and Breusche (1979).
The following are the hypotheses of this test:
H0 : There is no serial correlation in the model.
H1 : There is serial correlation in the model.
If the p-value of F-stat > 0.05, then at a 5% significance level the null hypothesis
would not be rejected, and so the algorithm could be looped, till a final regression for
each sub-sample was reached, where all the lags were significant.
3.2.6) TESTING FOR RECURSIVE STABILITY
Finally, the regression was tested for stability by conducting a Cumulative Sum of
Squares (CUSUM) test, introduced by Brown op. cit. (1975) to test the constancy of
the regression coefficients in the linear relationship. This tests for the significance of
the departure of the series from its sample path, which has an expected mean of 0.
H0 : The series has no significant deviation from its mean (It is consistent).
H1 : The series deviates from its mean (It is inconsistent).
22
4. ANALYSIS AND FINDINGS
4.1) EMPIRICAL ANALYSIS
By conducting the PP test (Equation 3.2) for non-stationarity on the series of
adjusted closing prices, the following is observed:
The output is shown in Table 4.1.
TABLE 4.1- PP TEST FOR FTSE 100
H0 : The series of Adjusted Close of the FTSE 100 has a unit root.
H1 : The series of Adjusted Close of the FTSE 100 is stationary about an intercept
and trend.
The above are the hypotheses suggested by the test, and since, the p-value of this
test exceeds 0.05, it means that the test statistic for this test falls in the middle 95%
of the critical level’s positive and negative values. Thus, there is a 56.65% chance
that if this hypothesis is rejected, then it will be wrongly rejected.
Therefore, H0 is not rejected at the 5% significance level and so the logged
differences are taken, to work with the returns of the FTSE 100, in order to make the
series stationary.
23
𝑅𝑡 = 𝑙𝑛(𝑃𝑡/𝑃𝑡−1)
Where Rt is a series of the returns on the FTSE 100 at time t,
And Pt is a series of the adjusted closing prices of the FTSE 100 at the end of the
month.
CHART 4.1- RETURNS OF THE FTSE 100
TABLE 4.2- PP TEST FOR RETURNS ON THE FTSE 100
24
H0 : The series of Returns has a unit root.
H1 : The series of Returns is stationary about an intercept.
H0 is now rejected at the 5% significance level, and so the next step was to create
dummy variables against which the returns on the FTSE 100 could be regressed so
as to test for evolutions in the seasonalities.
On running the regression displayed in Equation 3.4, the output is as depicted in
Appendix 1.
All the months’ dummies have a p-value greater than 0.05, and so the model
appears to be very poor as none of them are significant. This is also indicated by the
extremely low R2 of 4.4% and an Adjusted R2 of 1.46%. The information criteria
range between -3.19 and -3.32 which are also pretty high, and to top it, the
probability of the F statistic, which shows the joint significance of the independent
variables is 0.13, and so it is well above 0.05. Here the hypotheses are as follows:
H0 : β1 = and β2 = and β3 = …. and β11 = 0
H1 : β1 ≠ 0 or β2 ≠ 0 or β3 ≠ 0 or …. β11 ≠ 0
Therefore, H0 is not rejected.
After this, the Quandt-Andrews breakpoint test is run, as explained in Section 3.2.4.
The results of the test are shown in Table 4.3.
25
TABLE 4.3- QUANDT ANDREW BREAKPOINT TEST
H0: There are no significant breaks in the data
H1: There is a significant break in the data
The null hypothesis is not rejected and so there appears to be no significant break
in the data. However, the test still shows that there is a break in the data in
November 1989. Therefore, this is used as the benchmark to create 2 samples- One
from 1984M01 to 1989M11, and the other from 1989M11 to 2014M11.
After this, the algorithm explained in section 3.2.5 for each sub-sample is employed.
SAMPLE 1- 1984M01 TO 1989M11:
On running the general model as shown in Appendix 2, the following regression is
arrived at.
26
TABLE 4.4- BREUSCHE-GODFREY LM TEST FOR SERIAL CORRELATION FOR MODEL 1
TABLE 4.5- SPECIFIC REGRESSION (MODEL 2) OF RETURNS ON ONLY JANUARY
TABLE 4.6- BREUSCHE-GODFREY LM TEST FOR SERIAL CORRELATION FOR MODEL 2
EQUATION 4.1
𝑅𝑡 = 0.007 + 0.0545𝐷𝐽𝐴𝑁𝑡 + 𝑢𝑡
27
For the time window of 1984M01-1989M11, when the algorithm is run on the data for
the regression from Equation 3.4, the findings suggest that all the dummy variables
are insignificant at a 5% significance level, however, DJAN is significant at a 10%
significance level. The model has an R2 of 15.21%, which is a huge improvement
from the model in Appendix 1, which has an R2 of 4.4%. On testing for serial
correlation, it is found that there is no autocorrelation (Table 4.4), as H0 of no
autocorrelation is not rejected. On removing all the dummies from the regression in
Model 1, except for DJAN, Model 2 is created, which is shown in Table 4.5. Now,
DJAN is arguably insignificant at the 5% level as it has a p-value of 0.0511, which is
on the borderline of non-rejection at the 5% significance level, however, it is highly
significant at the 10% level. Thus, this algorithm generates the regression for returns
on the FTSE 100 on the January dummy as is seen in Equation 4.1. Once again,
there is no serial correlation in the model. Therefore, this appears to be the first time
a seasonal effect in the FTSE 100 is observed, and this is the January effect.
Although it appears to be weak initially, probably due to the FTSE 100 just being
created, it still appears to exist in this period.
The same algorithm is then run on the sample from 1989M11 – 2014M11.
The results are depicted in Tables 4.7-4.9. The general regression is shown in
Appendix 3.
28
SAMPLE 2- 1989M11 TO 2014M11:
TABLE 4.7- BREUSCHE-GODFREY LM TEST FOR SERIAL CORRELATION FOR MODEL 3
TABLE 4.8- SPECIFIC REGRESSION (MODEL 4) OF RETURNS ON JANUARY, JUNE AND SEPTEMBER
TABLE 4.9- BREUSCHE-GODFREY LM TEST FOR SERIAL CORRELATION FOR MODEL 4
29
EQUATION 4.2
𝑅𝑡 = 0.0092 − 0.0188𝐷𝐽𝐴𝑁𝑡 − 0.0239𝐷𝐽𝑈𝑁𝑡 − 0.0227𝐷𝑆𝐸𝑃𝑡 + 𝑢𝑡
Model 3 is shown in Appendix 3. This time, although January is still only significant at
the 10% significance level, yet even June and September are significant. Moreover,
June and September are significant at a 5% level, thus indicating a very strong
influence on the FTSE returns. The LM test for serial correlation reveals that there is
no autocorrelation in the model. Therefore, the algorithm is looped to create Model 4,
shown in Table 4.8. All dummies except for DJAN, DJUN, and DSEP are eliminated.
The results are encouraging. There appears to be a very strong presence of a
January effect, a June effect and a September effect at the 5% significance level. In
fact, June and September are even significant at the 1% significance level. There is
no autocorrelation in the model, and therefore Model 4, should be the final
regression for the time period of 1989M11-2014M11. Equation 4.2 shows the same.
However, the strange and very interesting part about this model is that unlike most
previous studies, this model suggests negative returns in January as the coefficient
for the January dummy is negative. This is also the case for June and September. It
appears that Model 2 had a positive January effect, however, as time passed, and
the other seasonalities came into play, there was a strong reversal, and therefore,
the returns became negatively related to the above 3 seasonalities. So it now
becomes important to see whether or not this model stands true on a recursive basis
for the entire time period, and whether or not the individual seasonalities are
significant in this time frame.
Therefore, the CUSUM test is conducted on this model, to analyse if it is significant
at each point in time on a recursive basis for the entire sample period of 1984M01-
2014M11. The results are shown in Chart 4.2 below:
30
CHART 4.2- CUSUM TEST FOR RECURSIVE REGRESSIONS
H0 : The series has no significant deviation from its mean (It is consistent).
H1 : The series deviates from its mean (It is inconsistent).
Since the cumulative sum of squares is always within the confidence intervals, as
indicated by the red lines, there is no significant deviation from the mean and so the
regression holds true for the entire period of 1984M01 – 2014M11.
Then, the regression of FTSE 100 returns on DJAN, DJUN and DSEP is run
individually as shown in Tables 4.10, 4.11, and 4.12; followed by the respective
CUSUM tests depicted in Charts 4.3, 4.4, and 4.5.
31
TABLE 4.10- REGRESSION OF RETURNS ON DJAN (1989M11-2014M11)
TABLE 4.11- REGRESSION OF RETURNS ON DJUN (1989M11-2014M11)
32
TABLE 4.12- REGRESSION OF RETURNS ON DSEP (1989M11-2014M11)
CHART 4.3- CUSUM TEST FOR RECURSIVE REGRESSIONS (DJAN)
33
CHART 4.4- CUSUM TEST FOR RECURSIVE REGRESSIONS (DJUN)
CHART 4.5- CUSUM TEST FOR RECURSIVE REGRESSIONS (DSEP)
34
Although the R2 indicates otherwise, the p-values for the above 3 regressions as
shown in Tables 4.10, 4.11, and 4.12 tell a different story. The regressions are all
significant at a 10% significance level, and those of the returns on June and
September, are significant even at a 5% level. On a recursive basis, all 3 fluctuate
about the mean, and even though they depart from it closer to 2014 (Charts 4.3, 4.4,
and 4.5), yet they are all still significant as they are well inside the 5% confidence
intervals depicted by the dotted red lines.
Therefore, the seasonalities do appear to exist, both jointly and individually!
Moreover, they all confirm a negative relation between the respective seasonality
and the returns.
Thus, it is of interest to investigate further as to why these seasonalities exist, why
they are negatively related to returns on the FTSE 100 as opposed to what previous
studies suggest, and what their impact is on people’s lives. Also, it is interesting to
understand the evolution of these seasonalities over time, with a special emphasis
on the January effect.
4.2) INVESTIGATION INTO THE JANUARY EFFECT, JUNE EFFECT AND SEPTEMBER EFFECT
4.2.1) THE JANUARY EFFECT ON THE FTSE 100
All studies in the past have indicated a presence of a January effect, which leads to
strong positive returns in the month of January. It has been proposed that the most
popular factor responsible for this is the tax-loss selling hypothesis, explained in
section 2.3. However, another factor which might significantly contribute to the
January effect is the existence of heterogeneous agent models, wherein investors
free-ride on the rational expectation that every investor will do exactly what
happened in the past. As a result, they tend to drive prices up.
However, the sample under study reveals a negative January effect. It implies that
the returns on the FTSE 100 are lower in January than in other months. This is not
35
surprising when studied in depth. An important factor which has been ignored all
along is the size effect. According to the Fama and French op. cit. (1993) 3-factor
model, returns are a function of the market risk premium, the size of the company,
and the book-to-market ratio (value). Moreover, the returns are negatively related to
the size and book-to-market ratios, and so smaller companies and lower book to
market ratio companies outperform those with larger market capitalisation and/or
those with a higher book-to-market ratio. This is building on a paper written by Rozeff
and Kinney (1976).
FTSE 100 has only 100 stocks with the largest market cap. This might explain why
the returns on the FTSE 100 are lower in January than those on the FTSE 250,
which includes the small and mid-cap firms. The result is a negative return on the
FTSE 100, in January. This does not mean that the January effect does not exist. It
simply means that it is empirically evident that it might be a lot less significant if not
negative in indices that have only large-cap stocks traded.
The implication of the January effect for the market is arguably psychological in
nature. People believe “As January goes, so does the year”. A lot of people take this
at face value and if January has positive returns, then they believe that the year will
go well. However, since the dot-com crash in 2000, the January effect has become
even weaker. As per evidence found by Eckett (2015), ever since the bubble burst,
there have only been 5 years in which the FTSE 100 has risen in January, and now,
January ranks 9th among all months in performance.
A small hypothesis test is conducted to check whether or not the saying about the so
called ‘January Barometer’ is true. This can be done by taking the average of all the
January returns, and the average of the mean returns of the remaining 11 months.
Based on these averages, a two-sided test for the difference in means is conducted
to observe whether or not there is a significant difference at a 5% level, between the
January returns and those for the rest of the year, or if the rest of the year actually
does indeed follow January on an average. The results are shown in Table 4.13:
36
TABLE 4.13- COMPARISON OF JANUARY RETURNS TO REST OF THE YEAR AVERAGE RETURNS
AVERAGE 1: AVERAGE 2:
-0.008165751 -0.003094484
test statistic = -0.092986053
t* = -1.96
H0 : Both the averages are ‘not different’ (μ1 = μ2)
H1 : Both averages are different (μ1 ≠ μ2)
To conduct the test and find the value of t, the student applied the following formula:
𝑡 =(�̂�1−�̂�2)
𝑆𝐸(�̂�1)+𝑆𝐸(�̂�2)
Since t < t*, the null hypothesis is not rejected at the 5% significance level.
Thus, it appears to be evident that for stocks on the FTSE 100, “as goes January, so
does the year”. This is consistent with the study conducted by Brown et al. (2004).
Another implication is that if the investor knows that every January stock prices on
the FTSE 100 will be lower, then he can sell in December and buy in January.
However, this links back to the tax-loss selling hypothesis. If this is the case, then in
theory the stock prices should be driven up on the FTSE 100 due to the surge in the
demand. However, it appears that this is not the case, as the small-cap stocks are
the growth stocks and so more of the trading would take place on the indices like the
FTSE 250, and so on, resulting in a relatively dry market in the FTSE 100. Thus,
there is room for speculation in other indices in January, but very little on the FTSE
100. This might be a possible explanation for the negative January returns.
37
According to Investment Week (2013)3, 1989 enjoyed higher returns in January in all
years other than 2013, when it rose 6.43% in January, making it the strongest start
to the year for the period of 1989-2013. Thus, there was a fall in the strength of the
FTSE 100 returns in 1989, which in turn led to much lower returns in January in all
the years to follow. This resulted in positive returns in January becoming a lot lower if
not negative up until 2013. However, unfortunately there is no substantial evidence
to back up why this change occurred in November 1989.
4.2.2) THE JUNE EFFECT ON THE FTSE 100
The June effect is best explained by the old adage “Sell in May and go away”.
According to Zhang and Jacobsen (2013), seasonalities vary with time and depend
on the eyes of the beholder. However, when the year is split into 2 halves- summer
(May-October) and winter (November-April), then the winter months are seen to
greatly outperform the summer months. Eckett op. cit. (2015) explains this theory in
depth in his book on monthly seasonalities. The selling of stocks in May is backed by
this theory of historical underperformance in the 1st half (summer) of the year.
Therefore, an investor who holds stocks for the whole year performs a lot worse than
one who sells in May, and re-invests in November. This sale of stocks drives down
prices significantly. As a result, this weak month leads to an even weaker month with
an illiquid market in June. June has a ranking of 11 in returns in the year, making it
the second worst month of the year. Chart 4.6 shows the results.
3 Investment Week (2013) FTSE 100 enjoys strongest January since 1989 [Online] Available from: http://www.investmentweek.co.uk/investment-week/news/2240734/ftse-100-enjoys-strongest-january-since-1989 [Accessed 1 February 2015]
38
CHART 4.6- RETURNS IN WINTER VS. THOSE IN SUMMER
Source: Eckett (2015)
The question is then, why are there lower returns in summer than in winter?
This might be due to 2 factors. First is the theory of the heterogeneous agent
models, which have constantly been mentioned. People believe that history will
repeat itself and so by doing exactly what people did in the past; it does end up
repeating itself. Secondly, summer is the season for holidays and so none of the
brokers are actually working. So the markets are more or less dormant as the trading
volume is very low (Holiday effect).
It is a great month for bears, and thus for speculators who have knowledge of all
these seasonalities, however investors tend to always find a fall in the value of their
holdings in June. Moreover, this month has a lot of announcements such as the
FTSE 100 quarterly review announcement and the anticipated Monetary Policy
Committee interest rate announcement. In the last 8 years, there has only been one
June in which the market has risen, and since 1982, the market has fallen more than
3% in June. Although the month starts by hitting a high in its first 2-3 trading days
due to the few bulls who believe that they can buy low collectively and drive prices
up before they pull out, there is a gradual drift back down, as even they most likely
sell once they have made their small gain on their trades.
Once again, FTSE 100 is probably more affected as it is made up of the large-cap
stocks which anyways underperform the small and mid-caps. As a result this paper
finds such a significant negative coefficient for DJUN in model 4.
39
The biggest implication of this seasonality is, as already mentioned, for the bears.
They generally sell their shares in May and unlike the long-term investors actually re-
invest in the first few days of June, making a gain on the difference in the prices or
even spreads (for the spread betters). As a result, these speculators drive prices up
again at the start of June, and once again, when the prices reach a peak after 2-3
trading days, they sell, and pocket the difference again, taking their net profits home,
and leaving the market to crash all of a sudden.
Due to the high volatility in this month, there is a lot of risk. Thus, although small
retailers and corporations aren’t too negatively affected, and some such as ‘Synergy
Health’, actually gain in June. The large Financial Institutions tend to have low or
negative returns in June.
4.2.3) THE SEPTEMBER EFFECT ON THE FTSE 100
September still falls in the summer half of the year. Thus, it is expected to have lower
returns than the winter months. Unlike the other seasonalities, there are no concrete
theories, but rather just hunches for why this month has negative returns, and yet it
is the worst month of the year for shares. It has consistently been the worst month of
the year for indices not just in the UK, but all around the world except in Venezuela.
However, this time the large-caps outperform the mid-caps, and therefore in
September, the performance of the FTSE 100 is generally higher than that of the
FTSE 350.
4.3) TESTING CONSISTENCY OF THE NEGATIVE RETURNS The CUSUM tests, only give an idea of the consistency of the model. However,
within the model, to test for how consistent the negative returns are from an
investor’s point of view, it is imperative to look at the relation between the actual,
fitted and residual data.
40
Appendices 4 - 6 show the actual, fitted and residual plots for 3 separate regressions
of returns on the DJAN, then on DJUN and finally on DSEP. The residual graph in
green shows negative returns every January, June and September respectively, as
this represents the effect of the respective dummy that has been created. The red
line represents the actual values of the returns. It can be seen that on average, they
are negative in January, June and September. However, there appear to be some
particularly significant years in which they are positive as well. Therefore, if a
speculator tried to make money by shorting the FTSE 100 in the 3 months, then on
average, he should be able to make money if these trends continue. However, it
could so happen that there would be successive periods of positive returns in one or
more of these months, leading to large losses, as all the tests are based on historical
data; and since nothing is constant in the financial markets, the patterns could
always fade or change.
4.4) SWITCHING STRATEGIES FOR INVESTORS
Chart 4.7 shows the outperformance of the FTSE 100 over the S&P 500 since 1984.
The black bars show data that are unadjusted for currency. The grey bars show the
sterling adjusted returns of both indices.
CHART 4.7- FTSE 100’s MONTHLY OUTPERFORMANCE OVER THE S&P 500
Source: Eckett (2015)
41
It is evident from the chart that the months of January, May and November have a
greater negative return for stocks on the FTSE than they do for the S&P 500 after
taking into account the currency. On the positive side, FTSE 100 outperforms the
S&P 500 significantly in the months of April, July and December.
Thus, these results suggest that it would be profitable to invest in the FTSE 100 in
April, July and December, and in the S&P 500 for the rest of the year. Eckett op. cit.
(2015) describes such a strategy as a ‘Switching’ strategy.
Chart 4.8 shows the implication of such a strategy:
CHART 4.8- RESULTS OF THE ‘SWITCHING’ STRATEGY
Source: Eckett (2015)
As can be seen, the returns under the switching strategy are a lot higher than those
of an investor who is completely invested in either the FTSE 100 or the S&P 500.
Although the September effect does still exist in the UK, it is worse in the US, as is
depicted in Chart 4.7. Thus, the knowledge of these seasonalities helps informed
investors come up with similar strategies, and speculate and arbitrage from-investing
in cross-border markets. If an investor finds that January, June and September are
yielding him/her a higher return net of the cross-border exchange rates, interest
rates, taxes and transaction fees for making such a transaction, then he/she can
invest his/her money in a foreign market till it is safe or comparatively beneficial to
re-invest in the FTSE 100. However, the investor must take into account that the
world does not function in a frictionless market, and so he/she will never get the
42
expected return due to the risks such as interest rate risk, market risk, exchange rate
risk, liquidity risk, credit risk and so on.
Another switching strategy that the investor could employ would be to invest in the
FTSE 250 in January, and then back in the FTSE 100 in February once the prices
fall in January, so as to arbitrage on the differences in the prices. However, this
strategy cannot be used for all that many months as compared to the one involving
the S&P 500, as that was based in differences in undervaluation of the indices due to
exchange rate diferences, rather than one being undervalued at the same time that
the other is overvalued. On the other hand, this strategy does not suffer from
exchange rate risk.
4.5) IMPLICATIONS OF THE SEASONALITIES FOR THE EFFICIENT MARKET HYPOTHESIS (EMH)
The model, which has been created for the returns of the FTSE 100, has identified 3
significant seasonalities- January, June and September. Sections 4.2 and 4.3 have
explained why these seasonalities exist, and what their implications are for the
investors. However, now it is time to look at what these seasonalities imply for the
economy as a whole. To start the discussion, it is important to re-iterate the EMH.
The EMH states that markets are efficient, and that prices reflect all the information
available. There are 3 forms of market efficiency:
Weak form efficiency- the prices reflect all the historical information.
Semi-strong form efficiency- the prices reflect historical data and also public
announcements.
Strong form efficiency- the prices reflect historical data, public information and
also private (insider) information.
The data on the FTSE 100 is only concerned with the semi-strong form of market
efficiency. Since the hypothesis states that any past knowledge should already be
absorbed into the prices, and any new information would ideally be absorbed
immediately, the data on the FTSE 100 is not efficient. This is because there is a drift
in the data. This is consistent with the studies conducted by Basu (1972) which
43
concluded that the available information embedded in P/E ratios did not replicate in
stock prices as fast as was anticipated by the EMH. According to Ball (1978) better
than expected result declarations give higher returns post earnings announcements,
again contrary to the EMH. Findings of Banz (1981) show that businesses with lower
market capitalization had greater value compared to larger organizations, showing
mispricing of the CAPM.
Moreover, if the market was efficient, then knowledge of seasonalities would be
incorporated in the prices and speculators would not be able to gain. However, since
this is not the case and due to the heterogeneous agent model theory every year,
the investors influence the prices by repeatedly acting irrationally simultaneously. As
a result, the prices don’t get a chance to be efficient. Therefore, due to the
seasonalities, the EMH is revelled on the FTSE 100.
44
5) CONCLUSION This paper set out to test whether there were any monthly seasonal patterns in the
FTSE 100; if present then whether or not they have evolved over time; and finally
whether or not these seasonal patterns could be used to make riskless profits by an
investor. It also wanted to test the impact of size on stock returns and seasonalities.
The findings are consistent with several previous studies on the size effect of
companies on their returns such as those by Keim (1983), Gultekin, M. and Gultekin
N. (1983) and Fama and French (1993). Most probably, it is as a result of the size
effect, that the FTSE 100 has negative returns in January, June and September,
causing seasonal patterns that are possibly driven by heterogeneous agent models;
and these seasonalities in turn, revel the efficient market hypothesis (EMH).
Although there may be other seasonalities as well, as the previous studies suggest,
these appear to be insignificant in the FTSE 100. Therefore, although the seasonal
effects might exist, yet it cannot be generalised as to which direction they exist in, as
markets are ever-changing.
There was a break in the pattern of these seasonalities in 1989, before which
there appeared to be a positive, but not very significant January effect, and after
which, there seemed to be a significant reversal to be a negative January, June and
September effect. The most likely cause for this reversal in the trend is the bursting
of the tech-bubble in 2000, which greatly impacted the FTSE 100. However, this
does not explain why 1989 was so significant, as the tech-bubble started in 1994.
One possible explanation is that the January returns in the FTSE 100 reached a
peak in 1989, and haven’t been able to reach the same level till 2013. This is
however, not a satisfactory explanation for this break, and so it is an area that might
be worth exploring, as there is not sufficient evidence to explain the same.
This paper appears to prove the old adage- “As goes January, so goes the year”.
Therefore, for the FTSE 100, there is empirical evidence that January could be used
as a good predictor for the rest of the year. Therefore, this has implications for
international speculators, the government, and the central bank, that can make
investment and policy decisions based on January returns. If the return on the FTSE
45
100 increase relative to the past year, then that implies that the year will be better
than the previous year. This might lead to an increase in FDI. The government could
make changes to its fiscal policy based on the expected returns. It may increase
taxes as the expected earnings may increase, and the central bank may devalue the
currency to encourage more FDI and to increase exports.
Findings suggest that the June and September effects are due to the belief that
returns in summer are always lower than those in winter. Thus people “Sell in May
and go away”, driving prices down.
In terms of methodology, this paper appears to have employed superior tests
compared to those employed in previous papers. To test for stationarity, the PP test
is used rather than the ADF test so as to prevent the lag selection problem, and for
structural breaks the Quandt-Andrews test is used rather than the Chow test, as it
assumes that the break-point is unknown. Finally, recursive stability of the models
has been tested for stability by using the CUSUM test, which has not been employed
in previous studies for testing seasonal patterns.
Finally the study shows that an investor might make money by employing a switching
strategy where he either switches by investing his money in the FTSE 100 in April,
July and December, and investing in the S&P 500 for the rest of the year.
Alternatively, he can switch his investment between the FTSE 100 and the FTSE
250 in January, and any other such month in which the returns on the FTSE 250
outperform those on the FTSE 100. For this the investor must first identify the
months in which the FTSE 100 has consistently outperformed the FTSE 250, and
vice versa. Thus, this paper has created a large niche for further research into the
area of strategies to exploit seasonal patterns on different indices. This is of interest
to asset managers who park investors’ money both in various indices, and in
individual stocks and their derivatives; and for the managers of exchange traded
funds (ETFs). The cross-border switching strategies are also of interest to hedge
funds and risk managers due to the various risks such as interest rate risk, and
exchange rate risk associated with it. Thus, they can earn money in the form of fees
for managing the funds of HNWIs and other small investors who are unaware of how
to manage such risks.
46
The model used in the paper is the Classical Linear Regression Model (CLRM). This
assumes homoscedasticity, normality, and no autocorrelation. However, the model
being tested does suffer from Heteroskedasticity and non-normality. Thus, it might
be a good idea to explore other models such as GARCH in further studies.
Moreover, the paper uses adjusted closing prices at the start of the month. These
types of prices might affect the outcome as well.
Therefore, this paper suggests that as long as the rational investor knows what to
expect from past knowledge, he will do exactly what investors before him did in the
past. The bottom-line is, “History repeats itself”, and if an investor plays his cards
right, seasonalities might just help an investor beat the market. However, it also
shows us that financial markets are highly stochastic, and so no investor should rely
solely on seasonalities and past trends to make money, as trends can fade or
reverse at any time.
47
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APPENDICES
APPENDIX 1- REGRESSION OF RETURNS ON ALL DUMMIES EXCEPT DNOV FROM 1984M01 – 2014M11
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APPENDIX 2- GENERAL REGRESSION (MODEL 1) OF RETURNS ON ALL DUMMIES FOR SAMPLE 1 (USING EQUATION 1)
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APPENDIX 3- GENERAL REGRESSION (MODEL 3) OF RETURNS ON ALL DUMMIES FOR SAMPLE 2 (USING EQUATION 1)
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APPENDIX 4- ACTUAL, FITTED AND RESIDUAL GRAPH FOR THE REGRESSION OF RETURNS ON DJAN FROM 1989M11-2014M11
APPENDIX 5- ACTUAL, FITTED AND RESIDUAL GRAPH FOR THE REGRESSION OF RETURNS ON DJUN FROM 1989M11-2014M11
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APPENDIX 6- ACTUAL, FITTED AND RESIDUAL GRAPH FOR THE REGRESSION OF RETURNS ON DSEP FROM 1989M11-2014M11