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:___________________________________

1

“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

2

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.

3

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

4

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.

5

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

6

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.

7

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

8

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

9

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

10

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

11

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).

12

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

13

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.

14

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.

15

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]

16

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.

17

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

18

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

19

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

REFERENCES

Abraham, A. and Ikenberry, D. L. (1994) ‘The individual investor and the weekend

effect’. Journal of Financial and Quantitative Analysis, 29 (2), pp.263-278.

Aggarwal, R. and Rivoli, P. (1989) ‘Seasonal and Day-of-the-Week effects in Four

Emerging Stock Markets’. The Financial Review, 24, pp. 541-550.

Agrawal, A. and Tandon, K. (1994) ‘Anomalies or Illusions? Evidence from stock

markets in eighteen countries’. Journal of International Money and Finance, 13, pp.

83-106.

Agrawal, R. and Agrawal, T. (2013) ‘Global Capital Flows and its Impact on

Macroeconomic Variables – Evidence from India’. The Macrotheme Review 2(4), pp.

66-86.

Alagidede, P., and Panagiotidis, T. (2006) ‘Calendar Anomalies in a Emerging

African Market: Evidence from the Ghana Stock Exchange’. Discussion Paper Series

2006 (13), Department of Economics, Loughborough University.

Andrews, D. (1993) ‘Tests for Parameter Instability and Structural Change with

Unknown Change Point: A Corrigendum’. Econometrica 61 (4), pp. 821-856.

Ariel, R. A., (1987) ‘A monthly effect in stock returns’. Journal of Financial

Economics, 18, pp. 161–174.

Ball, R. (1978) ‘Anomalies in relationships between securities yields and yield-

surrogates’. Journal of Financial Economics,6, pp.103-26.

Banz, R. (1981) ‘The relationships between return and market value of common

stocks’. Journal of Financial Economics, 9, pp.3-18.

Basu, S. (1972) ‘The information content of price earning ratios’. Financial

Management, Summer 75, 4 (2), pp.53-64.

48

Bodreaux, D.O. (1995) ‘The Monthly Effect in Internatinal Stock Markets: Evidence

and Implications’. Journal of Financial and Strategic Decisions, 8 (1), pp. 15-20.

Breusch, T. (1979) ‘Testing for Autocorrelation in Dynamic Linear Models’. Australian

Economic Papers, 17, pp. 334–355.

Brown, R. L., Durbin, J. and Evans, J. M. (1975) Techniques for Testing the

Constancy of Regression Relationships over Time. JRSS(B) 37:2, 149-163

Brown, Lawrence, D., and Luo, L. (2004) ‘The Predictive value of the Signs of

January Returns: Evidence of a New January Effect’. Available from:

http://ssrn.com/abstract=525162

Chan, K.C. (1986) ‘Can Tax-Loss Selling Explain the January Seasonal in Stock

Returns?’. Journal of Finance, 41, pp. 1115-1128.

Chow, G. (1960) ‘Tests of Equality Between Sets of Coefficients in Two Linear

Regressions’. Econometrica, 28 (3), pp. 591–605.

Dickey, D. and Fuller, W. (1979) ‘Distribution of the Estimators of Autoregressive

Time Series With a Unit Root’. Journal of the American Statistical Association, 74

(366), pp. 427-431.

Doran, James and Jiang, Danling and Peterson, David (2008) ‘Gambling in the New

Year? The January Idiosyncratic Volatility Puzzle’. MPRA Paper 8165, University

Library of Munich, Germany.

Eckett, S. (2015) The UK Stock Market Almanac. (8th ed.) London, United Kingdom,

Harriman House Ltd.

Fama, E. and French, K. (1970)’ Efficient capital markets: A review of Theory and

empirical work’. Journal of Finance, 25 (2), p.383.

49

Fama, E. and French, K. (1993) ‘Common Risk Factors in the Returns on Stocks and

Bonds’. Journal of Financial Economics, 33 (1), pp. 3-56.

Gibbons, M., and P., Hess (1981) ‘Day of the week effects and asset returns’.

Journal of Business, 54, pp.579-596.

Godfrey, L. (1978) ‘Testing Against General Autoregressive and Moving Average

Error Models when the Regressors Include Lagged Dependent Variables’.

Econometrica, 46, pp. 1293–1302.

Gultekin, M.N. and Gultekin, N.B. (1983) ‘Stock Market Seasonality: International

Evidence’. Journal of Financial Economics, 12, pp. 469-481.

Harding, S. (2012) New Academic Study Says Seasonality Triples Market Returns

Over Long Term! [Online] Available at:

http://www.streetsmartreport.com/school/Commentaries/New%20Study%20Says%2

0'Sell%20in%20May'%20Triples%20Markets%20Gains%20Long-Term.html

[Accessed 7 February 2015].

Ho, Y. (1990) ‘Stock Return Seasonalities in Asia Pacific Markets’. Journal of

International Financial Management and Accounting, 2, pp. 47-77.

Ho, R. and Cheung, Y. (1994) ‘Seasonal Patterns in Volatility in Asian Sock

Markets’. Applied Financial Economics, 4, pp. 61-67.

Hommes, C. (2005) ‘Heterogenous Agent Models: two simple examples’. CeNDEF,

Department of Quantitative Economics, University of Amsterdam, Amsterdam, The

Netherlands, pp. 1-36.

Investment Week (2013) FTSE 100 enjoys strongest January since 1989 [Online]

Available from: http://www.investmentweek.co.uk/investment-

50

week/news/2240734/ftse-100-enjoys-strongest-january-since-1989 [Accessed 1

February 2015]

Islam, Anisul, M., Duangploy, O., and Sitchawat, S. (2001) ‘Seasonality in Stock

Returns: An Empirical Study of Thailand’. Global Business and Finance Review, 6

(2), pp. 65-75.

Jaffe, Jeffrey, F., and Westerfield, R. (1989) ‘Is There a Monthly Effect in Stock

Market Returns? Evidence from Foreign Countries’. Journal of Banking and Finance,

13, pp. 237-244.

Jegadeesh, N. and Titman, S. (2001) ‘Momentum’. University of Illinois Working

Paper. Available at SSRN: http://ssrn.com/abstract=299107 or

http://dx.doi.org/10.2139/ssrn.299107

Kamath, R., Chakornpipat, R. and Chatrath, R. (1998) ‘Return Distribution and the

Day-of-the-Week Effects in the Stock Exchange of Thailand’. Journal of Economics

and Finance, 22 (2-3), pp. 97-107.

Kang, J., Pekkala, T., Polk, C., and Ribeiro, M. R., (2011) ‘Stock prices under

pressure: How tax and interest rates drive returns at the turn of the tax year’. LSE

Financial Markets Group, Discussion Paper (671).

Keim, D.B. (1983) ‘Size-Related Anomalies and Stock Return Seasonality: Further

Empirical Evidence’. Journal of Financial Economics, 12 (1), pp. 13-32.

Keim, B. D. and R. F. Stambaugh (1984) ‘A further investigation of the weekend

effect in stock returns’. Journal of Finance, 39, pp.819-840.

Lakonishok, J., and Maberly, E., (1990) ‘The weekend effect: trading patterns of

individual and institutional investors’. Journal of Finance, 45 (1), pp.231-243.

Lakonishok, J., and Smidt, S., (1988) ‘Are seasonal anomalies real? A ninety year

perspective’. The review of financial studies, 1, pp. 403–425.

51

Lazar, D., Priya, Julia, and Jeyapaul, Joseph (2005) ‘SENSEX Monthly Return: Is

there Seasonality?’. Indian Institute of Capital Marthets, 9th Capital Markets

Conference.

Lewis, M. (1989) ‘Stock Market Anomalies: A Re-Assessment Based on The U.K.

Evidence’. Journal of Banking and Finance, 13, pp. 675-696.

Lee, I., Petit, R. and Swankoski, M.V. (1990) ‘Daily Return relationship among Asian

Stock Markets’. Journal of Business Finance and Accounting, 17, pp. 265-283.

Lee, I. (1992) ‘Stock Market Seasonality: Some Evidence From the Pacific-Basin

Countries’. Journal of Business Finance and Accounting, 19, pp. 192-209.

Li, B., Liu, B., Fin, B., and Su, J.J. (2011) ‘Monthly Seasonality in Currency Returns:

1972-2010’. JASSA The Finsia Journal of Applied Finance, 3, pp. 6-11.

Lipsey, R. and Chrystal, A. (2011) Economics. (12th ed.) New York, Oxford University

Press Inc.

Marples, D. J. and Gravelle, J. G., (2011) ‘Tax Cuts on Repatriation Earnings as

Economic Stimulus: An Economic Analysis’. Congressional Research Service, 7-

5700, R40178.

Marsh, T., Brown, P., Keim, D., and Kleidon, A. (1982) ‘Stock Return Seasonalities

and the “Tax-Loss Selling” Hypothesis: Analysis of the Arguments and Australian

Evidence’. Working Paper, Alfred P. Sloan School of Management, Massachusetts

Institute of Technology, Massachussets.

Mills, T.C. and Coutts, J.A. (1995) ‘Calendar Effects in the London Stock Exchange

FTSE Indices’. European Journal of Finance, 1 (1), pp. 79-93.

Nassir, A., & Mohammad, S. (1987). ‘The January effect of stocks traded on the

Kuala Lumpur stock exchange: an empirical analysis’. Hong Kong Journal of

Business Management, 5, pp. 33-50.

52

Officer, R. (1975) ‘Seasonality in Australian Capital Markets : Market efficiency and

empirical issues’. Journal of Financial Economics, 2, pp. 29-51.

Pandey (2002) ‘Is There Seasonality in the Sensex Monthly Returns’. IIMA Working

Paper, IIM Ahmedabad.

Penman, S. H., (1987) ‘The distribution of earnings news over time and seasonalities

in aggregate stock returns’. Journal of Financial Economics, 18, pp. 199–228.

Phillips,P and Perron,P. (1987) ‘Testing for a Unit Root in Time Series Regression’.

Cowles Foundation Discussion Paper. 795-R (1), pp. 335-346.

Quandt, R. (1960) ‘Tests of the Hypothesis that a Linear Regression Obeys Two

Separate Regimes’. Journal of the American Statistical Association, 55 (290), pp.

324-330.

Raj, M. and Thurston, D. (1994) ‘January or April? Tests of the turn-of-the-year effect

in the New Zealand stock market’. Applied Economic Letters, 1, pp. 81-93.

Ray, S. (2012) ‘Investigating Seasonal Behavior in the Monthly Stock Returns:

Evidence from BSE Sensex of India’. Advances in Asian Social Science (AASS), 2

(4), pp. 560-568.

Reinganum, M.R. (1983) ‘The Anomalous Stock Market Behavior of Small Firms in

January: Emiprical Tests for Tax-Loss Selling Effects’. Journal of Financial

Economics, 12 (1), pp. 89-104.

Ritter J. R. (1988) ‘The Buying and Selling Behaviour of Individual Investors at the

turn of the years’. Journal of Finance, 43, pp. 701-717.

Ross, S. A., Westerfield, R. W., and Jaffe, J. F. (2002) Corporate Finance.

(International ed.) Berkshire, McGraw-Hill Education.

53

Rozeff, M.S. and Kinney, W.R. (1976) ‘Capital Market Seasonality: The Case of

Stock Market Returns’. Journal of Financial Economics, 3, pp. 376-402.

Schwert, G. (1989) ‘Tests for Unit Roots: A Monte Carlo Investigation’. Journal of

Business & Economic Statistics, 7(2), pp.147–159.

Schwert, G. (2003) ‘Anomalies and market efficiency’. In: Konstantinides, G., Harris,

M., and Stulz, R. (eds) Handbooks of the Economics of Finance. North-Holland-

Amsterdam, pp. 937-972.

Shiller, R.J. (1981) ‘Do stock prices move too much to be justified by subsequent

changes in dividends?’. American Economic Review, 71, pp. 421-436.

Smirlock, Michael, and Stacks, L. (1986) ‘Day of the Week and Intraday effects in

Stock Returns’. Journal of Financial Economics, 17, pp. 197-210.

Watchel, S.B. (1942) ‘Certain Observation on Seasonal Movement in Stock Prices’.

Journal of Business, 15, pp. 184-193.

Zhang, C. and Jacobsen, B. (2013) ‘Are Monthly Seasonals Real? A Three Century

Perspective’. Review of Finance, 17, pp. 1743-1785.

54

APPENDICES

APPENDIX 1- REGRESSION OF RETURNS ON ALL DUMMIES EXCEPT DNOV FROM 1984M01 – 2014M11

55

APPENDIX 2- GENERAL REGRESSION (MODEL 1) OF RETURNS ON ALL DUMMIES FOR SAMPLE 1 (USING EQUATION 1)

56

APPENDIX 3- GENERAL REGRESSION (MODEL 3) OF RETURNS ON ALL DUMMIES FOR SAMPLE 2 (USING EQUATION 1)

57

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

58

APPENDIX 6- ACTUAL, FITTED AND RESIDUAL GRAPH FOR THE REGRESSION OF RETURNS ON DSEP FROM 1989M11-2014M11