Stock market anomalies: The day-of-the-week-effect

Stock market anomalies: The day-of-the-week-effect

An empirical study on the Swedish stock market: A GARCH model analysis

MASTER THESIS WITHIN: Business Administration NUMBER OF CREDITS: 30 ECTS PROGRAMME OF STUDY: Civilekonomprogrammet AUTHORS: Alexander Abrahamsson and Simon Creutz J?NK?PING May 2018

Acknowledgements

This thesis contributed to the authors' deeper knowledge within finance and especially within statistics.

The authors are thankful to their tutor Fredrik Hansen for all the incredible support and much appreciated advice during the thesis writing process. A further thanks to all the other supporting teachers at JIBS for their patience and knowledge in responding to our questions.

The authors are grateful to the members of their thesis writing seminar group and are also grateful for the constructive feedback from the opponents at the final opposition seminar.

The authors would like to devote their appreciation to Robert Van Fossen (enrolled at Fordham University, New York, and employed at Citibank. U.S.A) for reviewing this thesis.

Alexander Abrahamsson

Simon Creutz i

Master Thesis in Business Administration

Title:

Stock market anomalies: The day-of-the-week-effect

Authors: Tutor: Date:

Alexander Abrahamsson and Simon Creutz Fredrik Hansen 2018-05-20

Key terms: Market Efficiency, Day-of-the-week effect, Volatility clustering, Leverage effect, GARCH

Abstract

Background:

The day-of-the-week effect has been a widely studied field ever since the

concept was introduced in the early 1970s. Historically, negative returns on Mondays have been

the most common finding. In line with improved market efficiency, researchers have started to

question the existence of this anomaly.

Purpose:

The purpose of this study is to examine the weak-form efficiency level

within the Swedish stock market by using sophisticated statistical approaches. The authors aim to

investigate if the day-of-the-week effect was demonstrated between 2000 and 2017.

Method:

To properly provide answers to this investigation, a quantitative

study has been conducted on the OMXS30. The data has been analysed by using different

kind of sophisticated statistical methods such as GARCH and TGARCH.

Conclusion:

The results show that the day-of-the-week effect was not

demonstrated within the OMXS30 during this time period, providing evidence for

improved market efficiency.

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Table of Contents

1

1.1 1.2 1.3 1.4 1.5 1.6

2

2.1 2.1.1 2.1.2 2.2 2.2.1 2.2.2 2.3

3

3.1 3.2 3.3

4

4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.1.7 4.1.8 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5

5

Introduction......................................................................... 6

Background ............................................................................................6 Problem ..................................................................................................7 Purpose ..................................................................................................7 Hypothesis .............................................................................................. 7 Delimitations ...........................................................................................8 Abbreviations .......................................................................................... 9

Theoretical background ................................................... 10

Efficient markets...................................................................................10 Samuelson?s dictum .............................................................................11 The random walk hypothesis................................................................12 Market Anomalies.................................................................................12 Leverage effect.....................................................................................14 Volatility Clustering ...............................................................................14 Behavioural finance ..............................................................................14

Literature review ............................................................... 16

Summary of previous findings ..............................................................16 Review of pre-2000 studies ..................................................................17 Review of post-2000 studies ................................................................20

Method............................................................................... 24

Method Summary .................................................................................24 Scientific Philosophy.............................................................................24 Scientific Approach...............................................................................25 Research Method .................................................................................25 Research Purpose................................................................................25 Time Horizon ........................................................................................26 Data Sample Selection .........................................................................26 Data Collection .....................................................................................27 Statistical Theory ..................................................................................27 Computation of Returns........................................................................27 Volatility ................................................................................................27 Comparing mean using T-stat ..............................................................28 Model of the day-of-the-week effect .....................................................28 Test for heteroscedasticity....................................................................29 GARCH (1/1) ........................................................................................29 TGARCH (1/1)......................................................................................30 Quality Criteria......................................................................................31 Reliability ..............................................................................................31 Validity ..................................................................................................31 Replicability ..........................................................................................31 Generalisability .....................................................................................32 Source Criticism ...................................................................................32

Empirical Results.............................................................. 34

iii

5.1 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.4 5.5 5.5.1 5.5.2 5.5.3 5.5.4

6

6.1 6.2 6.3

7

8

9

10

10.1

Descriptive Statistics ............................................................................34 T-test for mean .....................................................................................35 Sample 1 ..............................................................................................35 Sample 2 ..............................................................................................35 Sample 3 ..............................................................................................36 Full Period ............................................................................................36 Ordinary least squares regression........................................................37 Sample 1 ..............................................................................................37 Sample 2 ..............................................................................................38 Sample 3 ..............................................................................................38 Full Period ............................................................................................39 Test for Heteroscedasticity ...................................................................39 ARCH/GARCH/TGARCH .....................................................................41 Sample 1 ..............................................................................................41 Sample 2 ..............................................................................................41 Sample 3 ..............................................................................................41 Full Period ............................................................................................42

Analysis............................................................................. 43

Non-existing day-of-the-week effect .....................................................43 Evidence on Leverage Effect................................................................45 Evidence on Volatility Clustering ..........................................................46

Discussion ........................................................................ 48

Conclusion ........................................................................ 52

References ........................................................................ 53

Appendix ........................................................................... 56

List of companies on DAX30 & OMXS30 ............................................56

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List of Tables

Table 1: Different types of stock market anomalies ................................................................... 13 Table 2: Findings from additional investigations regarding the day-of-the-week effect ............ 16 Table 3: Descriptive statistics for Sample 1................................................................................ 35 Table 4: Descriptive statistics for Sample 2................................................................................ 35 Table 5: Descriptive statistics for Sample 3................................................................................ 36 Table 6: Descriptive statistics for Full Period............................................................................. 36 Table 7: OLS regression for Sample 1. ....................................................................................... 37 Table 8: OLS regression for Sample 2. ....................................................................................... 38 Table 9: OLS regression for Sample 3. ....................................................................................... 38 Table 10: OLS regression for Full Period. .................................................................................. 39 Table 11: Breusch-Pagan test for heteroscedasticity................................................................... 40 Table 12: ARCH/GARCH/TGARCH output for Sample 2. ....................................................... 41 Table 13: ARCH/GARCH/TGARCH output for Sample 3. ....................................................... 41 Table 14: ARCH/GARCH/TGARCH output for Full Period. .................................................... 42

List of Figures

Figure ii: The value function of prospect theory......................................................................... 15 Figure iii: Data sample timeline.................................................................................................. 27 Figure iv: Histogram graphs fit with normal distribution for all weekdays and the full period.. 34 Figure v: OMXS30 daily returns over the period 2000/01/01 to 2017/12/31. ............................ 40

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Introduction

1 Introduction

In this section the authors will give an introduction to their study. First, the background will be presented followed by a problem formulation and purpose. In addition, the hypothesis will also be explained, followed by a list of the delimitations and abbreviations.

1.1 Background

In the 1970, the Efficient Market Hypothesis was established by Eugene Fama. The hypothesis seeks to explain how market efficiency can be described and tested within three categories: the weak-form efficiency, semi-strong efficiency, and strong-form efficiency. However, Fama describes an efficient security market as a market where prices fully reflect all available information. Moreover, Fama argues that prices in an efficient market should follow a random walk and thus making it impossible to predict future security prices using only historical security price data.

Furthermore, evidence from statistical tests contradicts with the efficient market assumptions made by Fama. Seasonal patterns, such as what month or what weekday it is, tend to affect the returns on the stock market. Since the concept of these phenomena is going in the opposite direction of the idea of efficient markets, these are called market anomalies. Therefore, market anomalies have been a well-studied issue in finance, with an emphasis on the day-of-the-week effect beginning in the middle of the 20th century. Pioneers in testing stock markets for anomalies were researchers as: Frank Cross, Kenneth French, Michael R. Gibbon and Patrick Hess, and Donald B. Keim and Robert F. Stambaugh.

Anomalies can be described as unexpected price behaviour in the market. The day-of-the-week effect is one form of a seasonal anomaly and it is one of the most heavily investigated topics. Early studies, like Cross (1973) and French (1980), have shown that there exists a negative Monday effect, meaning essentially that mean returns on Mondays are negative. The existence of this effect contradicts to the EMH, suggesting that there should be no observable pattern of return in the market. Moreover, this could give investors a possibility to earn positive risk-adjusted returns (RAR). More recent studies, like Steeley (2001) and Kohers et al. (2004) suggests that the stock markets are more efficient today, causing the day-of-the-week effect to slowly disappear.

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Introduction

Weighing the evidence for market anomalies against the more recent arguments of Kohers et al. and Steeley; the question remained ? do these aforementioned anomalies exist today in our modern, more efficient markets?

1.2 Problem

Using data from 1978-1984, Claesson (1987) found evidence of a day-of-the-week effect on the Swedish stock market. This is in accordance with the findings of Cross (1973), French (1980), and Gibbon and Hess (1981) regarding the U.S. stock market. Modern studies of market efficiency, like Steeley (2001) and Kohers et al. (2004) suggests that stock markets have become more efficient today. Applying the findings of Steeley and Kohers et al., one might argue that the findings of Claesson on the Swedish stock market are rather outdated. This, therefore, mandates a need for a new investigation explaining the existence of the day-of-the-week effect on the Swedish stock market using more recent data.

This leaves us with the opportunity to adjust a knowledge gap in the research about the stock market efficiency in Sweden. By using recent data, the authors can provide findings regarding a potential day-of-the-week effect in Sweden.

1.3 Purpose

The purpose of this study is to examine the weak-form efficiency level on the Swedish stock market by using sophisticated statistical approaches. Specifically, the authors aim to determine the disappearance of the day-of-the-week effect in Sweden between 2000 and 2017.

1.4 Hypothesis

Testing for daily mean return using t-stat:

H0: = 0 H1: The daily mean return for the weekday is not equal to 0

Where denotes the daily mean return and t represents the weekday. By rejecting the null hypothesis, the authors can conclude that the Swedish stock market is weak-form inefficient.

Testing for daily mean return using OLS-Regression:

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