Bear vs Bull Market: The difference in market behavior between the two phases

(1)

Department of Business Administration Bachelor Thesis, 15 Credits, Spring 2020

Supervisor: Anna Thorsell

BEAR VS BULL MARKET

The difference in market behavior between the two

phases

Ludvig Edvall, Jonatan Höjlind

(2)

[Blank page]

(3)

Abstract

The Bear and Bull markets is today frequently used terms amongst practitioners and researchers alike. Despite its lack of a standardised definition it still seemingly means the same thing to the majority of people and the overarching consensus is that a bear market is negative and bull market is positive. Previous research of the bear and bull markets

primarily discusses how it affects the individual investor and not the aggregated market movements. The research was based on a study of the Swedish stock market that suggested that the standard deviation is higher during a bear market and the monthly buy and hold return is higher during a bull market. However, with the lack of statistical support from this study, the basis for the research question was based on their findings. The goal was to test whether their claims held, when their methodology was applied to a different sample from the same market. To categorise the market into bear and bull markets we used a 12-month simple moving average of the OMX Stockholm 30 (OMXS30) to define the trend. Every data point, consisting of daily buy and hold returns from the OMXS30, was then measured against the 12-month simple moving average of the market. We used the definition that when the daily buy and hold return exceeded the 12-month SMA, it is a bull market. When the daily buy and hold return is lower than the 12-month SMA, it is a bear market. The results of Levene’s test and a two-sample t-test showed that the bull market exhibited a higher daily buy and hold return and higher standard deviation when compared to the bear market. This conclusion aligns well previous research and confirmed the conclusion of the study upon this research was built.

Keywords: Bear and Bull market, Trend, Technical analysis, Efficient Market Hypothesis, Behavioural Finance

(4)

Acknowledgement

This thesis was written in collaboration with E2 Trading AB. We would like to sincerely thank the owners, Johan Hellström and Peter Nilsson, for their valuable input and their assistance in forming the research. Thank you for helping us coding the data which saved a lot of time and headaches when performing the statistical tests. We hope that this thesis can act as a reference point in your work of educating other traders in the future.

In addition, we would also like to express our sincere gratitude to our supervisor Anna Thorsell for keeping us on the right track throughout the whole process, and always motivated us to strive for perfection.

Ludvig Edvall & Jonatan Höjlind 2020-06-05

(5)

List of tables

Table 1:Summary of the differences in Daily Buy and Hold Returns, standard deviation and time spent in phase between the Bear and Bull market ... 23

Table 2. Result from Levene’s test ... 24

Table 3. Result from the T-test testing difference in Daily Buy and Hold Returns ... 25

List of figures

Figure 1.Historical Daily Buy- and Hold Returns of the OMXS30 plotted in the same graphs as its 12 month MA... 24

(7)

[Blank page]

(8)

1

1. Introduction

This chapter aims to explain the objective of the thesis and put it into context. The chapter starts with introducing the topic and reviewing some of the conflicting literature on the stock market. Further, we problematise the literature and motivate the study and the gap we aim to fill in the research. We end the chapter with stating the research question and purpose of the study.

1.1 Background

Given the lucrative phenomenon the stock market is, few are surprised by the amount of research attention that it gets. During the past century, few other topics have been studied as exhaustively and multiple theories have been developed with the aim to explain its

behaviour.

In the wake of the burst of the dot com bubble in the early 2000’s and the following sub- prime crisis of 2007-2009 investors worldwide have been exposed to volatile market conditions during the last 25 years. During this period, the market has gone through several bear and bull market phases. The goal of this study is to assess how the market behaves during each of the phases and if there is a difference in market behaviour between them. To do so, we will analyse the daily returns of the OMXS30 for the last 25 years, between January 1995 to the first quarter of 2020.

The research conducted on the stock market is as previously mentioned extensive. The stock market is according to Claesson (1987, p. 2) a fundamental piece of a functional capital market. The stock market acts as a broker that allocates capital from where it exists in excess to where it is scarce. It is, according to Claesson (1987, p. 2) of societal interest to make sure that this capital allocation occurs as efficiently as possible. One consequence of the stock market being so fundamental to the economy is that it has attracted the attention of countless researchers that have made important contributions to the aggregated knowledge we have today.

However, there is far from any consensus in the plethora of literature that exists. For decades, researchers have taken turns developing theories and providing evidence both in favour and against each other. The behaviour of the stock market is a frequently debated topic and there is a lot of research that both contradicts and confirms each other’s

conclusions. In the following section we will review the existing academic landscape of the stock market related to our research.

1.1.1 Efficient market hypothesis (EMH)

The efficient market hypothesis (EMH) is probably the most prominent financial theory and has since its introduction in 1965 by Eugene Fama, held a unique position within the

academic world (Claesson, 1987, p. 1). It has been a central theory since its conception within financial research and has laid the groundwork for a large portion of theoretical development within the area. What Fama (1970, p .383) introduced as an “efficient” market is when every piece of available information is immediately and accurately reflected in the price of the stock. Given the intense scrutiny of the stock market and with its plethora of

(9)

2 information available to the market actors, it is one of the markets that has the highest

chance of being efficient according to this definition (Claesson, 1987, p. 2). However, although the EMH holds a unique status within the academic world, it has been frequently questioned by practitioners and never been fully accepted.

According to Fama (1970, p. 388) there is a strong connection between the efficiency of the market and the availability of information to the market actors. Intuitively, with the rapid progression of IT and the globalised stock markets of today, the markets should be more efficient than they were in 1970. The natural consequence of this assumption is that the EMH should have further established itself amongst financial practitioners. However, that is not the case. The criticism has instead increased since the 1970, the EMH is today arguably more questioned than it ever was before (Shleifer, 2000, p.23).

1.1.2 Anomalies and Criticism to the Efficient Market Hypothesis

The main criticism against EMH is that the assumption it makes is so extreme. The EMH states that all available information is constantly reflected in the price (Fama, 1970, p. 383).

The consequences of this assumption is that there are no trends on the market (Shleifer, 2000. p.1). If the price would always, at every moment reflect all the currently available data, the only cause of a price fluctuation would be an addition of new information. The addition of new information is an unpredictable element and cannot be predicted by

technical trading-based systems. Thus, if the EMH hold, there are no trends and patterns on the market and regardless of the skill of the investor, the market cannot be beaten (Shleifer, 2000, p.1).

This has sparked a debate amongst financial researchers as well as practitioners, who question the validity of the theory. One search on google is sufficient to find a plethora of disagreeing literature that supports the trading market and its potential profitability. The driver behind the resistance to the EMH is founded in the continuous discoveries of the so- called anomalies. Anomalies are occurrences that cannot be explained by the EMH and contradicts the assumption that the market is efficient. (Claesson, 1987, p. 17-18).

One the most famous anomalies, in support of a trending market, considers the stock markets tendency to overreact to new information. This was discovered by Debondt and Thaler in 1985 (p. 804). They studied the New York Stock Exchange (NYSE) between 1926-1982 and found that if they constructed two portfolios, one with stocks of recent poor performance (losers) and one with stocks of recent well performance (winners). The losers outperformed the winners in the long run (Debondt & Thaler, 1985, p .804). They attributed this result to market overreactions and argued that the market overreacted to the positive and negative results respectively which resulted in winners becoming overbought and losers becoming oversold (Debondt & Thaler 1985, p. 804). These findings present a strong argument against the EMH as it suggests that when new information is introduced the market will trend up or down depending on the nature of the information presented. This contradicts the EMH that the price accurately reflects the available information (Fama, 1970, p. 383)

Another anomaly supporting the trending stock market is the so-called momentum effect which suggests that stocks in stronger trends outperform stocks in weaker trends. Evidence in favour of the momentum effect was presented by Jegadeesh and Titman (1993, p. 89-90).

They based their study on De Bondt and Thaler (1985, p .804) and assumed that the market

(10)

3 overreacts. Jegadeesh and Titman (1993, p. 65) argued that if the market overreacts this will give birth to trends that investors should be able to capitalise on. In their study they

constructed two portfolios, one with low relative strength and one with high relative strength. The portfolio with higher relative strength consisted of stocks with strong trends, and the portfolio with low relative strength consisted of stocks with weak trends. They found that the high relative strength portfolio outperformed the low relative strength portfolio (Jegadeesh and Titman 1993, p. 89-90). This is contradictory to the EMH, which implies that prices cannot be predicted by technical investment strategies (Shleifer, 2000, p.

1).

The plethora of anomalies found in the EMH are too many to support the existence of an efficient market. On the other hand, there are many studies confirming EMH and the pool of literature is conflicting. Hence, there should be a consensus amongst financial researchers that the question of efficiency is complex, and it is hard to both accept and reject the EMH without any reservations (Claesson, 1987, p. 27).

1.1.3 Market Trends

The idea of a partially efficient market is interesting. If you adapt the idea that the market is neither fully efficient nor inefficient, you will start to discover a lot of trends and patterns in the market movements, whilst still being able to see the market adapt quickly to new

information. The assumption of partial efficiency implies that the market reflects the available information, but not fully.

Following this assumption, researchers have found that there are, contrary to what the EMH suggests, trends on the stock market that can be exploited by technical analysts to earn excess returns. Studies conducted by Brock et al.(1992, p. 21-23), Ivanovski et al. (2017, p.

117-118) and Shalini et al. (2019, p. 217) all show that by using momentum based

indicators, the investors can capitalise on trends and earn excess returns. This idea seems to be a pervasive trend amongst stock markets as these studies were conducted on the US, Indian and Macedonian stock markets, respectively.

Another interesting finding is that trend is not a new phenomenon. Hurst et al. (2017, p. 15) made an extensive study of 67 markets, spanning across four major asset classes:

commodities, equity indices, bond market and currency pairs. Their data set spanned from January 1880 to December 2016 and found that for over a century, the trend following investing strategy have consistently outperformed the market both across the markets and asset classes (Hurst et al., 2017, p.15).

1.1.4 Bear & Bull markets

With the stock market being subject to both upward and downward trends it is important to make a distinction between the two. The terms Bear and Bull market are frequently used terms both in in academic literature and amongst practitioners and broadly divides the market into two different phases. The term bear market is used to describe the depressed and declining market in a negative trend, and the bull term is used to describe the positive trend (Schultz, 2002, p. 10). Although there are no standardised definition of the bear and bull markets beyond the up and downward trending markets they are still repeatedly used by researcher, who uses their own definitions to apply these terms to their research.

(11)

4 The current literature on the bear and bull market presents a lot of interesting findings.

Research have shown that the state of the market is important as investors tend to act differently between bear and bull markets. Studies conducted by Guidolin and Timmerman (2004, p. 141-142) and Kim and Nofsinger (2007, p.152) have shown that, on the United Kingdom (UK) and Japanese stock markets, the investors makes different investment decisions depending on whether the market is bearish or bullish.

There are, to our knowledge, not any investigations of this kind conducted on the Swedish stock market. However, there are findings that are similar. Nilsson et al. (2011, p. 28-29) conducted a test on bear and bull markets, but instead of testing investor behaviour, they tested market behaviour. They found that the market exhibits higher returns and lower standard deviation during the bull market compared to the bear market (Nilsson et al., 2011, p. 28-29). Although they are not per definition testing the same variables, there are parallels that can be drawn between the studies. The stock market movements are based on how the investors trade, and what prices they are willing to pay for certain stocks. If it is determined that investor behaviour is different between bull and bear market phases, that should in theory result in a difference in market behaviour as well. However, these conclusions are merely an assumption and would require further research to conclude with certainty.

1.1.5 Technical Analysis

Technical analysis is present in all financial markets and if you pay close attention to the financial media you should be familiar with terms such as such as support, resistance, moving average, trendlines, among others. For decades now, technical trading rules have been extremely popular to use amongst investors. Taylor and Allen (1992, p. 311-312) conducted a survey on major Forex dealers in London and found that at least 90% of their respondents placed some weight on technical analysis in their everyday decisions, especially in the short term. Later, Menkhoff (2010, p. 2573) analysed survey evidence from 692 fund managers in five countries and found that the amount of fund managers that put some importance on technical analysis is 87%. The survey indicates that technical analysis is mainly used as a complement to fundamental analysis. But, when concerning forecasting horizons, technical analysis becomes the most important forecasting tool when making short-term decisions.

Since technical analysts monitors prices with the intention of creating profit or help making investment decisions and all available information is already included in the price following the efficient market hypothesis. Therefore, it is useless to use any financial statements to compare a market price of a share with its intrinsic value as done by fundamental analysts (Bodie et al., 2019 p.354-356). Hence fundamental analysis will be excluded in this paper.

1.2 Problem Discussion

When reviewing the literature, we can find overwhelming support for the idea of a trending stock market and the existence of a bear and bull markets. The findings of Guidolini &

Timmerman ( 2004, p. 141-142) and Kim and Nofsinger (2007, p.152) both point in the direction that the behaviour of the investors differed between the bull market and the bear market on the UK and the Japanese stock markets respectively. The conclusion that

investors behave differently during different market phases raises the question whether the behaviour of individual investors impact the market as a whole. Further research by Nilsson

(12)

5 et al. (2011, p. 28-29) argues that it does, as they found that the there is a difference in both the monthly buy and hold return and the standard deviation between the two phases.

There are however reasons to question the results by Nilsson et al. (2011, p.28-29). In their book they provide descriptive statistics of their findings and show that the bull market on average has a higher monthly buy and hold return and lower standard deviation than the bear market. What makes us question their result is that they fail to provide statistical evidence to support this claim. It is unclear from their research whether this result is a predictable pattern or merely a result that can occur by chance. This leaves a gap in the research of the Swedish stock market to fill.

In our study we aim to statistically test whether we can confirm or deny the claim by Nilsson et al. (2011, p.28-29) that the stock market exhibits different behaviour during bear and bull markets. We will partially replicate their study, but with a few changes. These changes and their implications will be further discussed in Chapter 4 below.

The study is motivated by the importance this information has to investors. The active traders on the stock markets all trade according to the opposite premise of the EMH, that the most informed investors can earn the highest returns Bodie et al. (2019, p. 355). If the key to success is based on accessible information, it lies in the interest of the investors to

accumulate as much information as possible. This study provides the Swedish investors with a deeper insight of what they can expect depending on the phase that the market is currently in. When trading strategies are created, they are based on the information the investor currently holds. When the investor knows what to expect from bear and bull markets, they also know how to prepare and protect themselves from potential losses.

From a more academic point of view this research furthers extends existing research on the bear and bull markets. The idea that the investors behave differently during bull and bear markets have been proven on both the UK (Guidolini & Timmerman. 2004, p.141-142) and Japanese (Kim & Nofsinger (2007, p.152) stock markets. There is however not enough research conducted on the Swedish stock market given the lack of statistical support from Nilsson et al. (2011, p. 28-29). This study aims to fill that gap.

1.3 Research question

Is there a significant difference in standard deviation and average daily buy and hold returns of the Swedish stock market during bear and bull markets respectively?

1.4 Purpose

The purpose of the study is to clarify whether the bear and bull market phases impact the behaviour of the Swedish stock market other than simple up and downward movements. The study intends to explain whether Swedish stock market is more volatile during bear markets than during bull markets.

(13)

6

2. Scientific Method

Here we explain our methodological and philosophical worldview when we conducted the research. The ontological and epistemological viewpoints are first explained which acts as a framework for the subsequent data gathering method and research approach used. All parts of the scientific method will be discussed in relation to the thesis.

2.1 Ontology

When conducting an academic study, it is important to define our ontological approach.

This is because the ontological approach taken by the researcher is bound to have an impact on the outcome of the study (MacIntosh & O’Gorman, 2015, p. 56). Ontology explores the science of reality and tries to define what can be considered real (Ryan et al, 2002, p. 13).

Given the fact that reality is hard to define, a common way to simplify the ontological discussions is to divide the assumptions into two fundamentally different categories, subjectivity, and objectivity (MacIntosh & O’Gorman, 2015, p. 56). The objectivist standpoint assumes that the object of research exists independently of the researcher, and that the existence of these objects is not dependent on our capacity to observe them (MacIntosh & O’Gorman, 2015, p. 56). In contrast to the objectivists, the subjective approach perceives reality as a construct of perceptions and interactions of living subjects (MacIntosh & O’Gorman, 2015, p. 56).

When defining our ontological approach as researchers we look back at our research question, and what we aim to answer. The research question is: Is there a significant difference in standard deviation and average daily returns of the Swedish stock market during bear and bull markets respectively? To answer this question, it is logical to, like the studies conducted before us, use established and proven theories and from there form and test our hypotheses. Since we are analysing the OMXS30, an established index, it is reasonable to assume that this data is objective and exists independently from us as researchers and our beliefs and worldviews. Both the hypothesis and the data set are observable and measurable and therefore the objective approach will be applied in this study.

The alternative would be to adopt the subjective approach. However, there are a few

problems with applying the subjective approach to our study. As MacIntosh and O’Gorman (2015, p. 56) argues, the ontological approach taken by the researcher will affect the

research. The main issue we see with applying a subjective approach to this study is that the integrity of our findings could be questioned. According to Bryman and Bell (2002, p. 48) there should be distinction between the research and the researcher when conducting a positivist study. The results should not be affected depending on who is conducting the research. Since a subjectivist approach would allow for conclusions to be drawn out of personal beliefs (MacIntosh & O’Gorman, 2015, p. 56), the subjectivist approach would compromise the integrity of the study and should not be considered in this case.

(14)

7

2.2 Epistemology

Epistemology aims to explain and study what to accept as valid knowledge (MacIntosh &

O’Gorman, 2015, p. 56). To answer this question, researchers examine the relationship between the research conducted and the researcher (Collis & Hussey, 2014, p. 47). To simplify what can be defined as valid knowledge the epistemological studies are divided into two main paradigms, positivism and interpretivism (Collis & Hussey, 2014, p.47).

Positivism is founded on the belief that knowledge is derived from positive data, that can be analysed and proven, statistically and mathematically (Collis and Hussey, 2014, p. 46) Researchers using a positive approach uses logical reasoning and their research is strongly characterised by objectivity and precision rather than intuitively and subjectivity. The underlying assumption in positivism is that reality exists independently from the researcher and that the research conducted does not affect the reality investigated (Collis and Hussey, 2014, p. 46). Positivism is generally associated with quantitative studies as it is assumed that reality can be measured, and these studies relies heavily on the analysis of statistical data (MacIntosh & O’Gorman, 2015, p. 60).

The alternative to the previously discussed positivism is interpretivism, which was

developed due to the perceived inadequacy of the positivist approach. The main difference between these two paradigms stems from the different aim that the interpretivists adopts, understanding instead of explaining a phenomenon (MacIntosh & O’Gorman, 2015, p. 64).

The interpretivists claim that humans act differently depending on the situation, and that their interpretations of the situation heavily influence their behaviour. The interpretivist researcher typically is more subjective in their research and do not distinguish as heavily been the object of research, and the person conducting it (Collis & Hussey, 2014, p. 47).

Interpretivist research therefore uses a smaller sample size and tries to create new theories where the focus is to understand the world and what behaviour it generates (Collis &

Hussey, 2014, p. 50)

According to MacIntosh and O’Gorman (2015, p. 64-65) interpretivism has a more subjective approach compared to positivism, which generally adopts a more objective approach. Further, since positivism assumes that social phenomena can be measured, it is generally associated with quantitative studies as they are based on statistical analysis and quantitative data (Collis & Hussey, 2014, p. 44). The basis of our study consists of established theories and quantitative research data. We aim to statistically test how the market behaves during bear versus bull market. The positivist approach is therefore a better fit to our research as we believe that an interpretivist approach would undermine the

credibility of our conclusions and harm the replicability of the study.

2.3 Data Gathering

The gathering of data can be either classified as quantitative or qualitative. The quantitative method uses statistics to analyse numerical data, which is normally collected from archives, databases, or other published sources (Collis & Hussey, 2014, p. 5-6).

In this study, a quantitative approach was chosen, because it was naturally a progression from the stated research question: ’’Is there a significant difference in standard deviation and average daily returns of the Swedish stock market during bear and bull markets respectively?’’. Since we aim to analyse the OMXS30, an index consisting of quantitative

(15)

8 data to find differences between bear and bull markets, the logical option is to analyse the historical market data. The quantitative approach which consists of producing and analysing large amounts of numerical data, to test the variables against the stated hypothesis is

therefore the most suitable option (Collis & Hussey, 2014, p. 196-197).

The other approach would have been the qualitative one, which produces and analyses non- numerical data. Non-numerical data can be defined as for instance text, figures, diagrams and other images or visual material such as recordings of interviews and focus groups, videos, or broadcasts (Collis & Hussey, 2014, p. 130). The qualitative research tends to require that the researchers are more involved in the study and result creation process.

Therefore, qualitative studies are more subjective (Zikmund et al., 2013, p. 134). This suggests that different researchers tend to interpret the same data differently depending on outside factors. Qualitative research differs from the quantitative study also in regards of the sample size as qualitative studies tend to have a smaller sample size than a quantitative study. This is because there is no need to analyse the view to generalise the sample to the population (Collis & Hussey, 2014, p. 131). Qualitative studies are also more common in exploratory research designs, where the topic needs to be explained and evaluated from a subjective angle (Zikmund et al., 2013, p. 135). This research design would not work when analysing an index. Hence, we would not be able to answer the stated research question to examine the difference between daily buy and hold return and standard deviation between bear and bull markets. One way to utilise a qualitative research is using a similar research question as Kim and Nofsinger (2007, p.138), who evaluated individual asset allocation during bull and bear markets. However, we are interested in overall market trend and not the individual behaviour of the investor, hence the use of qualitative research design.

2.4 Research Approach

The research approach should be developed considering the information and the knowledge of the chosen topic at hand before conducting the research. The pre-existing knowledge is important to consider, as it will influence the choice of method and approach when conducting the research (Collis & Hussey, 2014, p. 3)

Research approach can be divided between the deductive and the inductive approach. We have selected the deductive approach, which is popular among the natural sciences (Saunders et al., 2009, p. 124). In a deductive approach the theories and hypotheses of interest are stated the study is conducted. These hypotheses are then tested against empirical observations (Collis & Hussey, 2014, p. 7-8). The goal is to test the stated research question and to be able to generalise the results to future market behaviour (Saunders et al., 2009, p.

124-125). This is described as moving from the general to the specific (Collis and Hussey, 2014, p. 7).

The alternative would be to use the inductive approach, which is the most relevant to the social sciences (Saunders et al., 2009, p. 125-126). The inductive approach normally does not start with a specific theory in mind that the researchers want to test. The researchers instead collect and analyses the required data and subsequently creates the theory from the results derived (Saunders et al., 2009, p. 126). Collis and Hussey (2014, p.7-8) agrees with (Saunders et al., 2009, p. 125-126) and propose that the inductive approach works in the opposite way compared to the deductive approach. The researcher starts from individual observations and then generalises these observations to new possible theories. In this case there is a lot of research that implies that there is a difference between bear and bull markets. Therefore, it is reasonable to think that it is suitable to apply the deductive

(16)

9 approach to analyse the stated research question as we aim to test whether or not the same behaviour can be observed in Sweden, as in UK or Japan. If the aim were to instead, understand what caused the underlying behaviour of investors during bear and bull markets the inductive approach would have been suitable. Hence, there is no need for an inductive approach in this case, rather, we can expand on current knowledge through the deductive approach.

(17)

10

3. Theoretical Framework

The purpose of this chapter is to introduce the main theories that we base the research on and state the assumptions and their subsequent implications on the research. First, we review EMH, that is central to the construction of the study. Following, we discuss trending following investing and our use of moving average to define Bear & Bull markets. Finally, we discuss modern portfolio theory and behavioural finance to add support to the construction of our hypotheses.

3.1 The Efficient Market hypothesis

The theory for the efficient market is one of the most important of the traditional finance theories. The definition comes from the article The Behaviour of Stock-Market Prices (1965, p. 94) published by Eugene Fama where he defined an efficient market as, a market where prices always represent the best estimates of intrinsic values. This implies that, when the intrinsic value changes, the actual price will adjust "instantaneously".

Since the EMH received a lot of criticism for the assumptions made and its difficulty to empirically test. Fama addressed the issue in Efficient Capital Markets: A Review of Theory and Empirical Work (1970, p. 383). He acknowledged the complexity of the question, and to allow for empirical tests he introduced three forms of EMH. The forms are weak form, semi-strong form and strong form and each reflecting varying amounts of information reflected in the price. The strong form is derived from the original assumption that all information would be fully reflected, from there the degree of reflected information decreases in the weaker forms.

The weak form of the EMH is of interest in this study. It states that all the historical information such as previous prices, volumes and short interests are fully reflected in the price. The weak form has the most evidence presented in its favour. Sodsai and

Suksonghong (2018, p. 235) tested the weak form of EMH on the Thai indices during 2001- 2015. They further divided the period into two sub periods, pre-crisis, and post-crisis, to examine the post-crisis policies implemented after the crash in 2007. The study found evidence in favour of the weak form, primarily on the overall market and the large-cap and mid-cap indices. This is aligning with the research conducted on the Swedish stock market (Claesson, 1987, p. 213). Claesson, found that during the tested time-period, the Swedish market shown signs of weak form efficiency and have been “partially efficient” with some anomalies being reported.

Ţiţan (2015, p. 444-446) summarises the empirical research that has been done since the definition of Fama (1970, p. 383). He starts with presenting the research of EMH in relation to random walk tests (RW). RW assumes that prices do not have memories and an increase today does not forecast a future increase or decrease the following day. Hence, trend cannot exist in the market. From there it gained acceptance from the scientific community until the end of the millennium, when behavioural finance started to gain recognition. This by criticizing the RW by arguing that the investors behaviour is not always rational. Examples of such research were Lo and MacKinley (1999) and Lo, Mamaynski and Wang (2000) who tested the RW by using a variance ratio test that tested if there is a linear relationship between the holding period and the variance. The findings showed that markets are not completely random and that predictable components do exist in recent stock and bond returns.

(18)

11 It is important to assess the implications that that the market does not follow a RW has for the study. Such assumption would entail that the market would only accurately reflect the historical information available. If that is the case as presented by Lo and MacKinley (1999) the investor could look for trends and patterns in the historical data. If trends and recurring patterns are found, it is a reasonable assumption to make that the history will repeat itself.

These two schools of thought show us the EMH is simple in theory but has been proven to be hard to test and to get precise results. This coupled with no overarching consensus regarding any of the three forms of the EMH among economists it continues to be a highly debated topic. Fama (1997, p. 283) himself states that long-term anomalies exist but argues that they are random results. These anomalies can be due to methodology and most long- term return anomalies tend to disappear with changes in technique. Given the plethora of criticism of the EMH and Famas continuous defence, there is hard to see any consensus forming in the foreseeable future.

Even though we do not directly test for the weak form of the EMH, the weak form indirectly states that the existence of trend in the market is not possible by the nature of random walk (Ţiţan, 2015, p. 444-446). Consequently, the weak form of the EMH indirectly contradicts the purpose our research where we are testing the differences between the bear and the bull markets. The underlying assumption in this thesis stems from the three premises of technical analysis that market discounts everything, trends exists, and history repeats itself (Murphy, 1999b, p. 2-5). Since these premises simultaneously confirms and contradicts the EMH, it is essential to understand the weak form of EMH and what it entails. Hence, its inclusion in this paper. The discussion of the correlation between EMH and technical analysis will be further discussed in section 3.2 below.

3.2 Trend following investing

Trend following investment has existed as a trading strategy for a long time and was popularised by Charles Dow in the late 1800’s (Murphy, 1999b, p. 23). The strategy suggests that you should buy an asset when price goes up and subsequently sell it when the trend shifts down again. The underlying expectation is that the trend is more likely to continue than to stop and the investor should hold their position until something indicates a change in the trend (Christensen et al., 2012, p. 366).

To evaluate its applicability, we look at ’’Does Trend Following Work on Stocks?’’ (2020, p. 2-4).This study looks, in retrospect, at how well trend following investing would have worked when deciding when to enter and exit a stock. The results show us that trend

following works well. Buying stocks on a new all-time high and selling when they fallen 10 points from the average true range (ATR) would on average yield significant returns for the investor.

Other research in favour of trend following investment were conducted by Hurst et al.

(2017, p. 15) where they applied trend following investing across global markets between 1880 and 2016. The data used spanned the monthly returns from 67 markets across four major asset classes: commodities, equity indices, bond market and currency pairs. They did not have data on each of the 67 markets during each month in this sample, so a trend-

following strategy was constructed using the set of assets for which return data exist at each point in time. They then created a time series momentum strategy (MOM) and adjusted it by an equal-weighted combination of 1-month, 3-month and 12-month time series MOM

(19)

12 strategies from January 1880 to December 2016. The strategy was consequently rebalanced each month. Using this strategy, they found a consistent performance across markets and asset classes over the full-time frame.

In contrast to what the EMH suggests, trend-following investing has performed well in each decade over more than a century. The research by Hurst et al. (2017, p. 12) indicates that since the beginning of the data examined, trends have been a pervasive feature across global markets. Initially, it appears that technical analysts completely reject the EMH. However, that is not entirely true. The fundamentals premises of technical analysis, as mentioned in 3.1, both confirms and contradict the EMH, simultaneously.

The three premises upon which technical analysis builds is: the market discounts everything, the market moves in trends and that history repeats itself (Murphy. 1999b, p. 4-5). The claim that the market discounts everything states that all the current information is available in the price (Murphy. 1999b, p. 2-3), according to what the EMH suggests (Fama, 1970, p.

383). However, the second claim that the market moves in trends (Murphy. 1999b, p. 3-4) is in direct violation of the consequences of the EMH, stating that in an efficient market, prices move randomly (Ţiţan, 2015, p. 444-446). The third premise, that history repeats itself (Murphy. 1999b, p. 4-5), also contradicts the EMH, that suggests that prices follow a random walk (Ţiţan, 2015, p. 444-446).

These premises are somewhat conflicting since, if the EMH holds, these assumptions cannot simultaneously be true. However, as Menkhoff (2010, p. 2573) found there is consensus amongst fund managers that technical analysis works. In this thesis we will adopt the idea proposed by the technical analysts that the price reflects all the past information but that trends exist, and history repeat itself. This assumption is key as it will allow us to use technical trading tools to categorise the market as bear and bull, and statistically the

difference in daily buy and hold return and standard deviation. Without this assumption, this study cannot be conducted as the existence of trends and predictability is mandatory when testing the difference in market behaviour between two trends.

3.3 Moving Averages

In the discussion above we concluded that one of the fundamental principles of technical analysis is that prices move in trends (Murphy. 1999b, p. 3-4). Traders look to identify these trends to generate profit and minimize losses one of the most popular trend following

investment rule is the moving average (MA) rule (Bodie et al., 2019 p. 401-403).

The MA is defined as an indicator utilised to smooth out the volatile movements that assets or indices exhibits daily (Murphy, 1999a, p. 197). It works as a trend lagging indicator that is calculated based on past price points. The average is then used mainly for two things, to identify the trend direction and to set new support and resistance levels for the asset in question (Murphy, 1999a, p. 201-203).The MA can then be divided up into a multitude of variations. The simplest and most frequently used is the simple moving average (SMA) which gives you an arithmetic average, smoothing the trend accordingly and giving the investor a trendline to base decisions on (Murphy, 1999a, p. 199).

(20)

13 The SMA then calculated as follows:

(EQ1)

SMA= X1+X2+…+Xn/n

X = closing value of the security for each period n = number of periods

The empirical research conducted by Ishfaq Ahmad et al. (2017, p. 353), found that when comparing all their MA portfolios to conventional buy and hold (BH) ones, the return on all the moving average portfolios yielded higher returns and experienced smaller levels of volatility. Glabadanidis (2015, p. 391-394) discussion on profitability, performance, abnormal returns for MA portfolios confirms the results by Ishfaq Ahmad et al. (2017, p.

353) that MA portfolios have higher returns relative to BH the underlying portfolios.

Following these discoveries, Glabadanidis (2015, p. 391-394) argues further that stock returns are predictable to a certain degree. The level of predictability is not perfect but, sufficient to improve forecasts of stock returns and should not be ignored. The findings of Brock el al. (1992, p. 21-23) supports these arguments when they used MA to predict future moments of the Dow Jones Industrial Average.

Additionally, Zakamulin and Giner (2018, p. 31-32) found when they empirically tested the predictability of the MOM and MA rules. MA rules delivered a more robust forecast

accuracy in comparison to the MOM correspondent. Thus, meaning that the MA has a better correlation with predictability on average compared to the MOM rules.

Since we aim to replicate the study of Nilsson et al. (2011, p. 27-28), we use the same definition of the bear and bull market. To identify the different market phases, they used a 12-month SMA (EQ1) of the market to act as a trendline and plotted them in the same graph. When the market is higher than its 12-month SMA, it is in a bull market. When the market is lower than the 12-month SMA, it is a bear market. The SMA is proven to be a successful forecasting tool for trends (Murphy, 1999a, p. 201-203), and since we aim to test the difference between bear and bull markets, it should work well in categorising the sample into two different trends. The definition of the bear and bull market is important, as it will impact the constitution of the samples we will test. The advantages of this definition of the bear and bull market will be further discussed in 3.4 below.

3.4 Trends and Bear & Bull markets

Bear and bull markets are almost financial folklore at this point. The terms are frequently used in academic research and investing literature and the terms seemingly mean the same to the majority of the population. Yet, there is no consistent and universally applicable definition of the phenomena. Since we look to investigate the difference between bull and bear market phases it is important that we clarify what it entails.

Fabozzi and Francis (1977, p. 1094) measures bear and bull markets with the help of monthly data. They deploy two definitions of bear and bull markets. The first is developed by Cohen, Zinbarg and Zekel (1987, p. 464-465), who simply define the bear and bull markets as months with positive (negative) returns to be bull markets (bear markets), unless the preceding and succeeding months were negative (positive). The second, they call Up and

(21)

14 Down Markets (UD). UD is defined as months with negative market returns, independent of the preceding and the succeeding months.

Further, Nilsson et al. (2011, p. 28-29) talks in their studies about positive and negative market phases. They define the positive market phase as being when the market is below a 12-month SMA, and a positive market phase to be when the market is above the 12-month SMA. Their discussion about positive market phases and negative market phases can be translated into bull and bear markets, respectively. With support from the literature there is no standardised definition of what a bear and bull market is. However, the consensus

amongst the authors is that the bear market is associated with negative market performances and the bull market is associated with positive market performances.

Even though different definitions seem to be used by different researchers, the research conducted on the subject shows that there are differences between the two phases. Guidolin and Timmerman (2004, p 141-142) and Kim and Nofsinger (2007, p.152) showed that depending on whether the market is bearish or bullish, both the investors on the UK and Japanese stock markets adjusted their investment behaviour. Further Nilsson et al (2011, p.

28-29) showed that the Swedish stock market exhibited higher monthly buy and hold and lower standard deviation during a bull market compared to a bear market. Since we aim to replicate the study conducted by Nilsson et al. (2011, p. 28-29) we will use the same definition that when the 12-month SMA lies above the market, it is bearish. when the 12- month SMA lies under the market, it is bullish.

The advantages with this definition are that a 12-month SMA can detect major trend changes while still filtering out the day to day fluctuation (Murphy, 1999a, p. 197). These fluctuations are not representative of the overall trend and is more a reflection of the fluctuating prices on the daily basis. Given that our sample consists of daily buy and hold returns, it is important that our definition is not to sensitive short-term fluctuations but captures trends over longer time periods. The SMA accomplishes this.

The reason for excluding the definitions provided by Cohen et al. (1987, p. 464-465) and Fabozzi and Francis (1977, p. 1094) stems from the fact that these definitions are not

applicable to a data set consisting of daily buy and hold returns. Cohen et al. define the Bear and Bull markets as months with positive (negative) returns to be bull markets (bear

markets), unless the preceding and succeeding months were negative (positive). This works well when the data consists of monthly data, but not with daily data as in our case.

If we apply their definitions to the data set, we could theoretically have the market switch between a bear and bull market every third day. Their definitions would be too sensitive to daily fluctuations, and with a set of daily data we would not be able to consistently identify overall patterns in the market. This would compromise in the integrity of the results as the samples would not be drawn from different market phases, but from days with positive returns versus days of negative returns. The definition by Fabozzi (1977, p. 1094), who defined UD as months with negative market returns, independent of the preceding and the succeeding months, presents the same problem. This definition is even more sensitive to the daily fluctuations and instead of changing between bear and bull market every third day it could hypothetically occur every other day. This would result in the same problems

discussed above. If any these definitions were applied to our study, we could not accurately define the two samples and hence not test the difference between them. Consequently, none of the alternative definitions would allow us to answer the research question.

(22)

15

3.5 Modern portfolio management-during different market phases

One of the most influential authors in the field of finance is Markowitz (1952) where he laid the groundwork for the theory. There he explains the role of risk in portfolio allocation, introducing the concept of risk aversion. This shows the trade-off between risk and return where risk is defined as the variance in returns and is considered undesirable. He

subsequently argued that all optimal portfolios should maximize return with the lowest corresponding risk. To achieve this, the portfolio is diversified by allocating the resources across multiple assets (Bodie et al., 2019 p.792-793)

Little research has been conducted regarding individual’s investment behaviour during the different market states. However, Guidolin and Timmermann (2004, p. 141-142) examines whether the presence of bear and bull markets influence portfolio holdings on the UK market. They found that since the risk-return trade-off on UK stocks and bonds varies substantially across the bear and bull market, their presence has the potential to significant affect investors optimal asset allocation. Subsequently, they stated that optimal asset allocations are strongly affected by investors beliefs regarding the underlying state of the market. A buy-and-hold investor who perceives a high probability of being in the bear state will invest very little in stocks and bonds in the short run. This investor will hold a greater portion of stocks at longer investment horizons as the likelihood of shifting to the normal or bull state grows. In contrast, in the persistent bull state, investors hold less in stocks but more in bonds the longer their investment horizon. Weller and Wenger (2008, p. 505-506) follows this same reasoning when arguing about asset allocation of public pension plans, they propose that when the volatility of investment returns increase assuming constant investor risk preferences, the optimal share of equities should decrease.

If the investors change their asset allocation during a bear market by moving their capital away from the stock market in the short run (Guidolin and Timmermann, 2004, p. 141-142), this will theoretically cause the prices to drop and markets decline. However, this cannot fully explain the increased volatility during the stock markets (Guidolin and Timmermann, 2004, p. 141-142) since optimal asset allocation assumes that investors are rational. To explain the observed increase of volatility during the bear market we apply theories from behavioural finance. We discuss this further in 3.6.

3.6 Behavioural finance

Behavioural finance has its roots in the social sciences, where much of the human

irrationality is explored and subsequently defined. The pre-existing research within the field has applied these theories in situations where investors must make decisions during period of uncertainty. These theories heavily criticise the traditional theories that base their

assumptions on the rational investor. Tversky and Kahneman (1974, p. 26-31) has made one of the more influential contributions to the overall development of the field. They assume that humans are not completely rational but base their decisions on heuristic rules, which simplifies the task of making decisions based on chance. The interesting theories from this field, in the context of our study, is prospect theory and heard behaviour.

(23)

16

3.6.1 Prospect theory

Prospect theory (Tversky & Kahneman. 1979, p. 271-273) is of interest because it refutes the utility theory that assumes that humans act strictly rational and choose the option that maximises their utility during uncertain situations. Tversky and Kahneman proved this by using a test of lotteries. With a lottery where you had two options, option 1 had a chance of 25% to win 3000 and option 2 had a 20% chance of winning 4000, they found that 65%

choose option 2. In the second lottery, option 1 had a 100% chance to win 3000 and option 2 had an 80% chance of winning 4000. The results were that 80% choose option 1. This then showed the so called the certainty effect which shows the overall preference for safe results.

3.6.2 Herd behaviour

Herd behaviour describes the innate behaviour of humans to act according to the group. This implies that human actions are highly reflective of their surroundings. This theory was early adopted by Keynes (1936, p.157-158) to describe how investors behave on the stock market.

Keynes (1936, p.157-158) argued that the individual investor assumes that the other actors on the market has knowledge that the individual investor does not possess themselves.

Alternatively, that the others process the information faster. Hence, the investor follows the broader group behaviour, which leads to that every individual, to some degree, reduces their own use of personal information with the belief that other investors know better. This leads to a reduction in the aggregated information, and the markets behaviour can be seen as random (Keynes, 1936, p.157-158)

To further the discussion started in 3.5, these theories are helpful in providing explanation to the observed increase in volatility during bear market phases found by (Guidolin &

Timmermann 2004, p. 141-142) and Nilsson et al. (2011, p. 27-28) The assumptions made in behavioural finance is that investors do not act rationally when uncertainty increases (Tversky & Kahneman, 1974, p. 26-31). The bear market is generally characterised by depression and decline (Schultz, 2002, p. 10), situations where uncertainty generally

increases. This supports the idea that volatility should increase in bear markets. In our study we aim to test whether there is a difference in standard deviation between the bear and bull market. Given that we base our study on testing the validity of the evidence presented by Nilsson et al. (2011, p. 27-28) we have indications of what the outcome of the study might be. However, we do not have explanations to why potential differences between bear and bull market occur. The theories from behavioural finance provides us with a theoretical framework to analyse the results and gives further support to the construction of our hypotheses.

3.7 Hypotheses

Based on the presented theories and past research we have developed two hypotheses to be tested in our aim to answer if there is a difference in mean return or standard deviation between the different market phases. Given that Nilsson et al. (2011, p. 28-29) claims that there is a difference in standard deviation and monthly buy and hold return between the bear and bull markets, the hypotheses will be based on the conclusions of their results and

supported by previous research and theories from other financial fields.

Hypothesis 1

H1: The standard deviation is higher during a Bear market than during a Bull market

(24)

17 With background in Nilsson et al. (2011, p. 28-29) and (Guidolin and Timmermann, 2004, p. 141-142) both stating that, the Swedish and UK stock market respectively, exhibits a higher standard deviation during the bear market, we expect this to hold in our study as well.

To further back the hypothesis, we argue that since the consensus is that bear markets are times of increased uncertainty behavioural finance theories can explain this notion. Both prospect theory and herd behaviour indicate that when the market declines during a bearish phase, the investors amplify this effect by overreacting to the negative information. When a large number of investors follow this behaviour and sell their securities the market becomes increasingly volatile.

This idea is also consistent with modern portfolio theory that states that the investors will move away from the stock market during bear markets. When a big number of investors leave the stock markets in favour of other securities, they sell their stocks and the market becomes increasingly volatile.

Hypothesis 2

H2: The return is higher during a Bull market than during a Bear market

Nilsson et al. (2011, p. 28-29) presents that the monthly buy and hold return is higher during the bull market than in the bear market. Adding to that, the findings of Hurst et al. (2017, p.

15) states that trend is a pervasive feature across global markets and assets classes. Relating this to the consensus that the bull market is associated with positive market performances, as discussed in 3.4, we assume this holds for the time period and different index set in our research.

(25)

18

4. Research method

Below we will present the methods used in conducting the research. Here we discuss the research design, literature search, data collection and sample, choice of variables and operationalization, pretesting and underlying assumptions and data analysis. The focus lies on arguing in favour of our chosen method in context of the thesis.

4.1 Research design

The design of the research is based on the paradigm chosen, which is a guide for how the research should be conducted (Collis & Hussey, 2014, p. 59). Since we adopted a

positivistic view, it is clear on what objective need to be fulfilled regarding the data collection and the stated research question.

The goal with the research is to examine the performance of the market during bear and bull phases during 1995-2020 and test the differences in daily buy and hold and standard

deviation between the two phases. Because of this, the historical research design was

chosen, which collects, verifies, and synthesise evidence from the past to establish facts that defend or refute the stated hypothesis (Savitt, 1980, p. 54). This works well since we are testing historical data.

Other possible designs related to positivism are experimental, surveys, longitude, or cross- sectional studies. These are disregarded since they do not allow us to answer our research question. Experimental research is conducted with the implication of manipulating an independent variable to observe the effect on a dependent variable, this is not applicable in our study. Surveys were then directly disregarded since the data is directly collected from a database and surveys were not needed to collect a data set. Longitudinal design was

disregarded since it requires the researcher follows the phenomenon during the period they wish to research. Finally, cross sectional was disregarded since it needs to compare the sample over the same time-period (Collis & Hussey, 2014, p. 60-64).

4.2 Literature search

The study is primarily based on the study conducted by Nilsson et al. (2011, p. 28-29) published in their book ’’Successful Trading - 10 winning strategies”. To further gain an appropriate theoretical ground for the thesis, a systematic literature search was conducted.

To find relevant literature, databases available to Umeå University students were used. The primary ones consisted of DiVA, Business Source Premier and Scopus, where we

subsequently scanned for peer-reviewed literature. The literature search was conducted in three steps. First, we focused on finding literature related to technical analysis and moving average. This was done to understand the concepts presented in the study by Nilsson et al.

(2011, p. 28-29). Keywords used were: Technical analysis, moving average, market trends.

The second literature search was made in response to what was found in the first literature.

The first literature indicated that the applicability of technical analysis was conflicting which prompted us to investigate the criticism against it. We searched for literature

concerning the EMH and bear and bull markets. Keywords used in the second search were:

efficient market hypothesis, bear and bull markets, finance, returns.

(26)

19 The literature found gave provided us with good theoretical ground and found previous research on both the EMH and the bear and bull markets. Some of the literature found suggested that the established theories associated with technical analysis were insufficient to explain why bear and bull markets occur. This prompted our final search where we scanned for theories trying to explain the behaviour of the stock market. Keywords used were.

behavioural finance, modern portfolio theory, volatility, uncertainty, prospect theory, overconfidence, herd behaviour. However, all the literature found in the searches were not used in the thesis. This is because the majority of literature found was not applicable and relevant to the research. Outside of the systematic literature search many sources were found from cited articles in the previous research.

4.3 Data collection and sample

The goal of the research is to examine the differences in daily buy and hold return and standard deviation between the bear and bull markets. The decision to base the research on the Swedish stock market comes naturally, since we base our research on the study

conducted by Nilsson et al. (2011, p. 27-28). However, we will test a different sample from the Swedish market to see if arrive at the same conclusion.

Nilsson et al. (2011, p. 28-29) conducted their research on Affärsvärldens General Index (AFGX) which is a weighted index covering all the Swedish stock indices. In this study we have chosen to conduct our research on the OMX Stockholm 30 index (OMXS30). The data was gathered by extracting the closing price from the OMXS30 for each trading day during the sample. This index was chosen because it consists of the 30 stocks with the highest turnover on the Swedish stock markets. OMXS30 should therefore act as a proxy for the Swedish market reflecting most of the overall market movements. This is also the most established index on the Swedish stock market and subject to most of the research

conducted by analysts on the Swedish stock market. Given that the index is well researched further motivates its use as we have a lot of other research to compare our results to.

The other difference in the sample is the chosen time-period. The sample in this study is from 11 January, 1995 to 30 March, 2020. The sample used by Nilsson et al. (2011, p. 28) stretches from 1948 to 2011. We believe that since the study conducted by Nilsson et al.

(2011, p. 28) covers all major market movements before 1995, and ends in 2011, it would be interesting to test a more recent set of data. This is because their conclusions only tell that the Swedish stock market is different during bear and bull markets until 2011. The time- period 1995 to 2020 adds 9 more years and includes the recovery after the great recession (2007-2009). The great recession had its roots in the financial markets and in the wake of this economic downturn, the Basel III regulations were introduced forcing the banks to increase their liquidity (Boora & Kavita, 2018, p. 8). Higher liquidity of banks would limit their ability to issue loans which could reduce the amount of capital circulating in the market. It is unclear whether this has affected the behaviour of the stock market, but it is interesting to include potential effects of these new regulations in our data set.

The final difference between our study and the study conducted by Nilsson et al. (2011, p.

28-29) is that we will investigate the daily buy and hold returns instead of the monthly buy and hold returns. The reason for this is that it will provide a more accurate representation of the sample investigated. Trends are not necessarily limited to the turn of the months, by analysing daily buy and hold returns we can capture switches in trend that occur within months and more accurately divide the sample into a bear and bull market.

(27)

20 Findings from the UK (Guidolin & Timmerman, 2004, p.141-142) and Japanese stock market (Kim & Nofsinger, 2007, p.152), suggests that there is a difference in investor behaviour during bear and bull markets. This raises the question whether these results can be generalised over all stocks market or if there is a need to test the Swedish stock market as well. We argue that a test of the Swedish stock market is necessary to draw any conclusion.

There are reasons to believe that the Swedish market might behave differently than the UK and Japanese markets that has previously been examined. This is because there are obvious cultural differences between the nations in question. The cultural differences are enough to argue that the generalisation between markets is difficult. Given that the cultures differ between Sweden, Japan, and the UK it is reasonable to assume that the investor culture does as well, and stock market behaviour should not be generalised across markets. To draw any conclusion about the Swedish stock market with certainty, the Swedish stock market should also be tested.

The data was gathered by extracting the closing price from the OMXS30 for each trading day since 11 January 1995 to 30 March 2020. The data set was then divided into the two samples to define if the Swedish market has been in a bear or bull phase.

4.4 Choice of variables and operationalisation

To answer our research question, we will test the differences in daily buy and hold return and standard deviation between the bear and bull market. In this chapter we explain how these variables are constructed, and how they are measured.

Calculation of return is calculated as follows:

(EQ2)

Daily buy and hold return = Closing value of stock - opening value of stock / opening value of stock

Calculation of standard deviation (SD) is calculated as follows:

(EQ3)

𝑆𝐷 = (𝜒 − 𝜇) /𝑛 − 1 𝜒=sum of the sample 𝜇=mean of the sample 𝑛 =numbers of observations

To operationalise the data for the intended purpose of categorising the sample into bear and bull market we used nominal variables. Nominal variables are defined as variables using numerical to identify named categories (Collis and Hussey, 2014, p. 202).

To identify the bull market, we used a 12-month SMA of the OMXS30 as calculated by EQ1. When the daily buy and hold return (as calculated in EQ2) is higher than the 12-month SMA it is considered a bull market, when the daily buy and hold return is lower than the 12- month SMA it is considered a bear market. This subsequently netted us 4549 days that can be classified as a bull market and 1801 days that can be considered a bear market. These

Bear vs Bull Market: The difference in market behavior between the two phases