Excessive trading and
overconfidence
An empirical analysis on excessive trading and overconfidence in the behavior of investors
Sannie Nitters
April 30
th
, 2008
University of Groningen
Faculty of economics and business
MSc BA Finance
Supervisor: Drs M.M. Kramer
Excessive trading and
overconfidence
An empirical analysis on excessive trading and overconfidence in the behavior of investors
ABSTRACT
This paper deals with excessive trading and overconfidence. Excessive trading affects the returns which investors make. A lot of trading can lead to higher trading cost and therefore the returns can be lower. In previous papers it has been hypothized that overconfidence can investors cause to trade excessively. In this study it will be investigated whether the investors trade excessively. Furthermore, the role of overconfidence in this perspective will be determined. Several studies have discussed excessive trading in relationship with overconfidence. However, this has never been studied in the Netherlands before. The dataset consists of 8.750 transactions made from January 1st, 2005 trough June 30th, 2007. The data is provided by a branch of a bank in the Netherlands. The daily returns of the securities bought and securities sold are acquired from DataStream.
Average return to securities bought and the average return to securities sold are used to investigate excessive trading and overconfidence. The Wilcoxon Signed Rank Sum Test is used to test for significance. Moreover, calendar-time portfolios are also used to test the robustness of these results. I find some evidence for excessive trading. On average, the investors in this dataset reduce their returns through trading. The investors in this dataset do trade when their expected gains through trading are not enough to offset the cost of trading. They even lower their returns when trading costs are ignored. This means that the investors are overconfident.
Sannie Nitters Hoofdweg 43 9698 AB Wedde
PREFACE
I have been studying MSc BA Finance at the University of Groningen. The last part of this study is writing a Master Thesis. In my Master Thesis I investigated whether the investors trade excessively. Besides this, I examined whether these investors are subject to overconfidence.
During the process of writing my thesis several people helped me a lot. I would like to thank them for their support. In the first place, my mentor Drs. Marc Kramer. He was always willing to give me some advice and he gave me useful insights in the subject of this thesis. Furthermore, I would thank the company which offered me a student internship. They committed the data of the investors studied in this thesis. My colleagues at this bank provided me with a real-life based advice that ensured that theory and practice stayed in touch. Last, but not least, I would thank my boyfriend and my family for always supporting me.
TABLE OF CONTENTS
1. INTRODUCTION ...6
2. THEORY AND BACKGROUND ...8
2.1. BEHAVIORAL FINANCE VERSUS TRADITIONAL FINANCE... 8
2.2. BOUNDED RATIONALITY... 8
2.3. FOUNDATIONS OF BEHAVIORAL FINANCE... 9
2.3.1. Framing ... 9
2.3.2. Heuristics ... 10
2.3.3. Self-attribution biases ... 11
2.4. TYPICAL INVESTOR BEHAVIOR... 13
2.4.1. Familiarity bias ... 13 2.4.2. Attention-based buying ... 13 2.4.3. Disposition effect... 13 2.4.4. Excessive trading ... 14 2.5. INSTITUTIONAL ENVIRONMENT... 14 2.5.1. Agency problems ... 14 2.5.2. Legal environment... 15
2.6. STOCK MARKET DEVELOPMENTS... 17
2.7. PREVIOUS EMPIRICAL RESULTS ON EXCESSIVE TRADING... 17
2.7.1. Noise trading ... 17
2.7.2. Excessive trading and overconfidence... 18
2.7.3. Excessive trading and overconfidence related to demographics ... 21
2.7.4. Excessive trading and overconfidence related to online trading... 23
2.7.5. Overview of previous empirical results... 24
3. DATA AND METHODOLOGY... 27
3.1. DATASET... 27 3.1.1. Descriptive statistics ... 28 3.1.2. Characteristics of returns ... 29 3.1.3. Subsamples... 30 3.2. METHODOLOGY... 32 3.2.1. Average returns ... 32
3.2.2. Round-trip transaction costs ... 33
3.2.3. Hypotheses ... 33
3.3. SIGNIFICANCE TESTING... 34
3.3.1. Wilcoxon Signed Rank Sum Test... 34
3.3.2. Calendar-time portfolios ... 35
4. EMPIRICAL RESULTS ... 39
4.1. RESULTS FOR THE WHOLE DATASET... 39
4.2. RESULTS FOR THE SUBSAMPLES... 39
4.2.1. Subsample 1 ... 40
4.2.2. Subsample 2 ... 40
4.2.3. Subsample 3 ... 41
4.3. RESULTS FOR THE CALENDAR-TIME PORTFOLIOS... 41
5. CONCLUSION ... 44
5.1. LIMITATIONS... 45
5.2. COMPARISON WITH OTHER STUDIES... 46
5.3. RECOMMENDATIONS FOR FURTHER RESEARCH... 47
1. INTRODUCTION
This paper examines whether individual investors trade excessively and whether they are subject to overconfidence. Excessive trading can reduce the returns of investors. When an investor trades a lot, trading cost will be higher. Consequently, the net returns can be lower. Excessive trading arises when the difference between the securities bought and the securities sold is not enough to offset the cost of trading. It is hypothized that overconfidence can investors cause to trade excessively. Overconfident investors overestimate the precision of their knowledge and their skills relative to other investors. Overconfidence leads to lower returns even when transaction costs are ignored.
In this research I will investigate whether the investors in the dataset trade excessively. Besides, I will investigate whether overconfidence is related to excessive trading.
The main question in this paper is as follow: Is there evidence for excessive trading in the behavior of
investors? Moreover, is there evidence for overconfidence in the behavior of the investors?
This is not the first research on excessive trading. Though, this research is novel in several ways. Many research focused on the investors in the United States. There are also researches like this done in Europe and other continents as well. However, to my knowledge, a research on excessive trading and overconfidence in the behavior of investors in the Netherlands has never been published before. Furthermore, this study includes also a new period. Moreover, a lot of people studied the investors who invest through direct canals. This thesis is about the investors who invest through the help of an investor.
The data which is used in this paper is acquired from an internal database of a branch of a bank in the Netherlands. The dataset consists of transactions of individual investors’ accounts with this bank from 1st, 2005 trough June 30th, 2007. The accounts which are taken into account need to be active. Furthermore, only stock transactions are examined in this study. The dataset contains 8.750 transactions. Moreover, subsamples are created to zoom in on parts of the dataset.
2. THEORY AND BACKGROUND
In this chapter I will discuss the theory and the background with respect to excessive trading and overconfidence. In section 2.1 the concepts of behavioral finance and traditional finance will be explained. Bounded rationality will be discussed in section 2.2. Subsequently, the foundations of behavioral finance will be dealt with in section 2.3. Section 2.4 will go into the behavior of investors and section 2.5 will go into the institutional environment. Furthermore, the developments in the Dutch stock market will be discussed in section 2.6. In section 2.7 several empirical studies are discussed.
2.1. Behavioral finance versus Traditional finance
In traditional finance theory the concepts of perfect and efficient markets are very important. A perfect capital market assumes that there is perfect competition and that the market is frictionless. In such a perfect market arbitrage opportunities will be exploited directly. An efficient market means that the prices fully reflect all available information. Traditional finance assumes also that investors make rational decisions. Arbitrage theory, portfolio theory, asset pricing theory, and option pricing theory are based on these traditional finance ideas. [Nofsinger, 2005]
Alternatively, the field of behavioral finance considers how people actually behave. Psychologists assume that people act in a not so rational manner. People are often subject to behavioral biases. According to Tempelaar [2006] behavioral finance can be defined as follow: “the system of ideas, models, and applications in which insights from psychology are employed for the explanation of phenomena in the fields of corporate finance, portfolio investments and financial markets”. Behavioral finance considers markets and people to be imperfect.
In the next paragraphs, attention will be paid to the foundations of behavioral finance, to typical investor behavior, to the institutional environment, and to empirical results with respect to excessive trading.
2.2. Bounded rationality
less than completely rational in spite of their best intentions and efforts. March defines this as the concept of bounded rationality.
To develop a theory of rational decision making under uncertainty, it is necessary to make some assumptions about the behavior of the individuals. These assumptions are known as the axioms of rational choice under uncertainty. These axioms are comparability, transitivity, strong independence, measurability and ranking. Given the axioms of rational decision making and the assumption that investors prefer more wealth to less, it can be said that investors will always seek to maximize their expected utility of wealth. [Copeland, Weston, and Shastri (2005)] The axioms of rational choice are generally satisfied in transparent situations and often violated in situations which are not transparent. [Tversky and Kahneman (1986)]
2.3. Foundations of behavioral finance
A useful categorization of foundations in behavioral finance can be framing, heuristics and self-attribution biases. These will be discussed in the next three subparagraphs, because these are important in the field of behavioral finance. Furthermore, excessive trading has some links with the phenomena discussed in this section.
2.3.1. Framing
Framing can be defined as the internal processes of developing frames. Frames affect the behavior of decision makers. Two important concepts which are related to framing are mental accounting and prospect theory. These will be examined now.
Mental accounting
Prospect theory
Prospect theory [Tversky and Kahneman (1986)] is a theory which describes how people frame and value a outcomes of decisions involving uncertainty. Firstly, it states that investors frame the choices in terms of potential gains and losses relative to a reference point. Secondly, investors value the gains and losses according to an S-shaped function. This S-shaped function is concave for gains and convex for losses. This is related to the fact that people are usually risk-averse for choices involving gains and risk-seeking for choices involving losses. Furthermore, the function is steeper for losses than for gains, which has to do with loss aversion. Loss aversion refers to the tendency for people to prefer avoiding losses than acquiring gains. Findings that have been related to loss aversion are the endowment effect [Thaler (1980)], the equity premium puzzle [Benartzi and Thaler (1995)], and the status quo bias [Samuelson and Zeckhauser (1988)].
2.3.2. Heuristics
Heuristics means that people recognize patterns and apply rules of appropriate behavior [March (1994)]. Heuristics can contribute to the efficiency of decision behavior and also to its consistency. However, it also has negative effects, because heuristics easily create biases in the process of decision making. Generally, heuristics can be quite useful, however sometimes they lead to severe and systematic errors. Tversky and Kahneman [1974] describe three heuristics; representativeness, availability and the anchoring effect.
Representativeness heuristic
The first heuristic, representativeness, is judgment based on stereotyping. The brain often makes the assumption that things that share similar qualities are quite alike. In the financial markets, for example, people make the error to confuse a good company with a good stock. Another implication from the representativeness heuristic is the gambler’s fallacy, which means that the likelihood of a random event can be affected by other independent events. For example, when someone has observed a long run of red on the roulette wheel, most people believe that black is now due.
Availability heuristic
The availability heuristic, or the salience effect, is about the impact of the ease with which something can be brought to mind. The availability heuristic (maybe together with the anchoring heuristic) causes people to stick to familiar options, which is known as the familiarity bias.
Anchoring heuristic
unwarranted optimism. Furthermore, it generates the tendency to state overly narrow confidence intervals. This means that more certainty is reflected than is justified by one’s knowledge.
2.3.3. Self-attribution biases
In this paragraph attention will be paid to self-deception problems, to overconfidence and to limited self-control.
Self-deception problems
People are often unrealistic optimistic about future events. They expect good things happen more often to them than to others [Weinstein (1980); Kunda (1987)]. For example, De Bondt [1998] surveyed the behavior of the individual investor and found that the investors are optimistic about the expected performance of the stocks they own. However, they are not optimistic about the performance of the DJIA (Dow Jones Industrial Average). Furthermore, most individuals see themselves as better than the average individual [Tayler and Brown (1988)]. People who are subject tot the ‘better-than-average-bias’ rate their abilities and their prospects higher than those of others. Many people think that they are better than they really are. This is known as self-deception. Overconfidence, which is discussed next, is a part of the self-deception problem.
Overconfidence
Overconfidence refers to the tendency of people to be more confident in one’s behavior, attributes and physical characteristics than one should be. Overconfidence causes investors to overestimate the precision of their knowledge, to underestimate the risks, and to exaggerate their ability to control events. Overconfidence can lead to poor investment decisions. Overconfidence may result in excessive trading, excessive risk taking or rising market volatility.
Which factors cause overconfidence? One important factor is the illusion of knowledge. This is related to the tendency for people that the accuracy of their forecasts increases with more information. Another important factor is the illusion of control. People think that they can affect the outcome of uncontrollable events. If the investor does have outstanding skills and knowledge, a lot of trading should result in high returns which could beat a simple buy-and-hold strategy. Moreover, it should also cover the costs of trading. On the other hand, when the investor is subject to overconfidence and does not have these outstanding skills and knowledge, the high frequency of trading will not result in returns large enough to beat the buy-and-hold strategy and will not cover the trading costs. [Nofsinger (2005)]
Furthermore, the self-attribution bias is an important factor which can cause overconfidence. People often attribute successful outcomes to their own skills and unsuccessful outcomes to bad luck or to external forces. People are prone to change their perceptions of successful and unsuccessful outcomes so as to protect or enhance their self esteem [Miller and Ross (1975)]. A lot of people believe they are highly capable to invest. These people think they can time the market and pick the ‘right’ stocks. If the stocks they picked are doing well, they will confirm this to their abilities to invest. Conversely, when their stocks are doing badly, they will confirm this to circumstances which lay behind their control. In the matter of fact, people learn to be overconfident trough their experiences [Gervais and Odean (2001)]. If a person is subject to the self-attribution bias, he will not learn from his mistakes, because he does not see this as a mistake.
Overconfidence appears the most when tasks are complex and when predictability is low. [Griffin and Tversky (1992)]. Investing is very complex and stocks are very unpredictable. Therefore, people are most overconfident with a type of task like investing. Overconfidence exists especially following bull markets [Lin (2005)].
Limited self-control
are used to strengthen their willpower and reduce their desire; rules of thumb and environment control. [Nofsinger (2005)]
2.4. Typical investor behavior
In this paragraph some typical behavior of investors will be discussed. Successively, the familiarity bias, attention-based buying, the disposition effect, and excessive trading pass in review. Excessive trading is where this study is about and therefore the most important in this section. However, some other phenomena are also discussed here shortly to create a complete view.
2.4.1. Familiarity bias
People often refer to things that are familiar to them; they tend to stick to options which they are familiar with. In financial markets investors tend to invest in familiar securities. Looking internationally, investors are often prone to the home-country bias, because companies from their own country usually are more familiar to them than foreign countries. If investors choose foreign firms, they pick large firms with recognizable products which are familiar to them. Moreover, investors prefer securities from local or regional firms. Investors are more bullish on their domestic market. This familiarity bias causes investors too be too confident in stocks that are familiar, judging them too optimistically on expected return and risk. The familiarity bias also plays a role in investing pension money. Generally, people are most familiar with the company they work for. As a result, employees invest their pension money in the stocks of the company they work for, which can result in under diversified portfolios. [Huberman (2001) and Nofsinger (2005)]
2.4.2. Attention-based buying
Attention-based buying means that investors tend to buy stocks which have caught the attention of the investor. Examples are stocks which are in the news, stocks which experience high abnormal trading volumes and stocks which have extreme day returns. The reason for attention-based buying is that it is very difficult for investors to search the thousands of stocks they can potentially buy. This problem does not appear when investors sell stocks, because they tend to sell only stocks they already own. [Barber and Odean (2006b)]
2.4.3. Disposition effect
2.4.4. Excessive trading
In a market with transaction costs and rational investors who have the purpose to increase their returns, it is expected that when investors trade they want to increase their returns by at least the amount of the trading costs. The securities these investors buy will therefore outperform the securities they sell by at least enough to cover these costs [Odean, (1999)]. In my study excessive trading is designed as the difference between the securities bought and the securities sold is not enough to offset the cost of trading. In other words, the investors trade so much that it reduces their returns. As can be seen earlier, the reason why investors trade excessively can be overconfidence.
Previous empirical studies about excessive trading are discussed in section 2.7.
2.5. Institutional environment
Some individual investors invest through securities institutions, for example banks and brokerage firms. The security institution may give the individual investor advice. Because of this advise, the investor could be influenced by the preferences and the interests of the adviser. Consequently, excessive trading could be caused by the adviser. Agency problems and legal environment are related to this. Therefore, this will be discussed next.
2.5.1. Agency problems
In the economic world there are contractual relationships. Individuals have subjective preferences, and hence different interests. Sometimes, these subjective preferences can result in conflicts of interest between contracting parties.
Agency theory deals with agency problems which results from conflicts of interest. This theory explains how the contracting parties can design contracts to minimize costs associated with agency problems. Furthermore, it draws attention to the existence of market and institutional mechanisms that complete contracts to reduce these problems. Agency theory has two key concepts; asymmetric information and creation of incentives. Asymmetric information arises when one party has better or more information than the other party.
[Waldman (2004) and Ross, Westerfield, Jaffe (2002)]
One important advantage of investing with the help of a security institution is that the investor can use the advice, and thereby the expertise, of the consultant. The investor can also be subject to churning. Brown [1996] defined churning as excessive trading by stock brokers in order to generate commissions. [Brown (1996)]
These agency problems are important here, because there can arise a conflict between the investor and the advisor. Excessive trading could be in the interest of the advisor, because he generates more provisions than. However, this is not always in the interest of the investor. In the next section, attention will be paid to the legal backgrounds.
2.5.2. Legal environment
The ‘Autoriteit Financiële Markten’ (henceforth, AFM) is responsible for regulating behavior on the financial markets in the Netherlands. The AFM supervises the conduct of all parties that are active on the savings, lending, investment and insurance markets. Furthermore, the AFM contributes to the proper operation of the financial markets by providing information to professional market players, including norms and standards. So, the AFM controls the parties in the financial market and also develops norms and standards. The AFM is an independent administrative authority.
On January 1st, 2007 the ‘Wet op het financieel toezicht’ (henceforth, Wft) has come into effect. The Wft brings together practically all the rules and conditions that apply to the financial markets and their supervision. The AFM supervises compliance with the ‘Wet financiële dienstverlening’ (henceforth, Wfd). The Financial Services Act lays down rules for providing, mediating in and advising on financial products for consumers. This act sets out requirements that financial service providers must meet in terms of integrity, expertise, sound business operations, financial security, transparency, and the duty to protect their clients' interests (care-duty).
[www.afm.nl]
On November 1st, 2007 the ‘Markets in Financial Instruments Directive’ (henceforth, MiFID) came into force. The MiFID introduces new and more extensive requirements which firms have to comply with. The MiFID has the following goals:
The protection of investors and market integrity by laying down harmonized regulations that govern the activities of licensed intermediaries;
According to the MiFID a securities institution has to retrieve information concerning the knowledge and experience of the investor, the financial situation of the investor and the aim of the investments. Every investor who invests with this branch of a bank has a profile concerning risk and return, which is dependent on the knowledge and experience, the financial situation and the aim of the investments. Before starting to invest such a profile has to be established. The profiles are ‘guarantee of principal’, ‘very defensive’, ‘defensive’, ‘neutral’, ‘offensive’, ‘very offensive’ and ‘speculative’. The investments have to fit in this profile.
[www.afm.nl]
The AFM also developed rules with respect to churning. In the Netherlands it is forbidden to execute transactions in such frequency that it is advantageous for the bank/stock broker. Article 84 of the Bgfo1says that a securities institution should act in the interest of her clients.
Article 6:12 NRgfo2 contains the following provision on disproportionately high transaction frequency, fees and other remuneration:
A securities institution shall refrain form executing transactions for the account of clients with such a frequency or such a size that, given the circumstances, this will obviously only serve to benefit the security institution, unless the transactions are ones for which the client has expressly placed orders on his or her own initiative;
A securities institution shall refrain from charging disproportionately high fees or other remuneration.
This policy rule is published to further clarify the policy of the AFM on provisions in article 6:12 NRgfo. The costs which are charged cannot be so much that it is reasonably expected that it is not possible to obtain a positive investment result.
[www.afm.nl]
It can be seen that there exists a strict legal environment in the Netherlands concerning churning. Because of this strict legal environment it is unlikely that the advisors trade excessively in order to generate commissions.
1Besluit gedragstoezicht financiële ondernemingen 2
2.6. Stock market developments
Developments in the stock market could influence the returns of the investors. In a bull market it is more likely that there will be higher returns than in a bear market. Consequently, transaction costs will be covered more easily in a bull market than in a bear market.
The stock market developments in the Netherlands are described for the period of January 1st2005 to June 30th2007. This period is taken, because this is the same as the return period investigated in this thesis. In the beginning of January 2005 the Amsterdam Exchange Index (henceforth, AEX) was about 350 points. In March 2006 this index quoted 470 points, after which there was a little decrease. On January 2nd 2007, the AEX stated at 500 points. The highest level of 2007 was on July 16th 2007; 561,90 points. At the end of the return period, on June 29th, 2007, the AEX quoted 548,21. On the whole, the AEX increased during the period which is studied here. In figure 1, the development of the AEX from January 2005 to January 2008 is graphical presented.
Figure 1:Development of the AEX from January 2005 to January 2008.
There was a good climate to invest in the period from January 1st, 2005 to June 30th, 2007. Generally, stocks made good returns. In this rising market it is more easily to cover trading costs than in a falling market. On the other side an rising market can cause the sentiment to be very positive and a falling market can cause the sentiment to be negative.
2.7. Previous empirical results on excessive trading
Excessive trading in relation to overconfidence is studied before by other researchers. In this section attention will be paid to these previous empirical results.
2.7.1. Noise trading
believe they can control the market and they have the ‘right’ information. These illusions can be seen as noise.
Fisher Black [1986] was the first who introduced noise trading. He defined it as trading on noise as if it was information. This can be interpreted as trading on ‘rumors’ or on misperceived ‘information’. Black investigated the effects of noise in the trading process. According to Black, noise makes financial markets possible. Although, it also causes the financial markets to be imperfect. The more noise trading there is, the more liquid the markets are. However, noise trading puts noise into the prices.
Willman, Fenton-O’Creevy, Nicholson, and Soane [2006] also did research on noise trading. Efficient market models cannot explain the high level of trading in financial markets. Much of this excessive trading is irrational ‘noise’ trading. Traders must be irrational or traders are rational with irrational aberrations.
Barber, Odean and Zhu [2006] examined whether small noise traders significantly distort asset prices. Noise traders trade systematically as a group due to psychological biases and sentiment. If these conditions are met and asset prices have the tendency to return towards their underlying value eventually, the buying and selling activities of noise traders will also predict future asset returns. The results of Barber, Odean and Zhu are consistent with noise trader theory. In this theory it is stated that concentrated buying (selling) of uniformed investors pushes prices too high (low), which eventually leads the subsequent reversals. So, noise traders do move markets.
2.7.2. Excessive trading and overconfidence
Odean [1999] showed in his paper that the trading volume of investors with discount brokerage accounts is excessive. The data used by Odean were provided by a nation wide discount brokerage house. To test overconfidence-based excessive trading Odean first measured the average return to securities bought and the average return to securities sold. The CRSP daily return is used to calculate this return. Then he calculated the total average commission for the sale and purchase when one security is sold and the sale proceeds are used to buy another. The average commission when a security is purchased is 2,23 percent of the purchase price and the average commission when a security sold is 2,76 percent of the purchase price. After that, the effective bid-ask spread is estimated, which is 0,94 percent.. Next, the average total cost of round-trip trade is the sum of the average commission for and the effective bid-ask spread. Odean found a round-trip trading costs of 5,9 percent.
The first hypothesis tested here implies that the average returns to securities bought minus the average returns to securities sold are less than the average round-trip transaction costs. The second hypothesis is that the average returns to securities bought are less than those to securities sold, ignoring trading costs. In this study statistical significance is estimated by bootstrapping an empirical distribution for differences in returns to purchased and sold securities. In the sample period there were 49.948 purchases and 47.535 sales. The first null hypothesis as well as the second null hypothesis is rejected with significance levels of 1 percent and 2 percent. All excess returns found using the bootstrap methodology are negative. For example, the difference between average returns following purchases and sales for the whole dataset is -1,36 for 84 trading days. For 252 trading days this is -3,31 and for 504 trading days this is -3,32.
there is some evidence that, compared to the stocks they sell, these investors tend to buy smaller, growth stocks. However, after adjusting for size and book-to-market effects, there is no evidence of systematic differences in the market risk (β) of the stocks they buy and sell.
Odean concluded that the investors with discount brokerage accounts trade excessively in the sense that their returns are on average reduced through trading. Besides, Odean examined whether investors trade excessively because of overconfidence. He found that overconfident investors may trade even when their expected gains through trading are not enough to cover the trading costs. Even when trading costs are ignored, the investors lower their returns trough trading.
Barber and Odean [2000] investigated the returns earned on common stock investments of 66.465 (active) households at a large discount brokerage firm. In this research is focused on common stock investments of households. The sample period is from January 1991 trough December 1996. In the sample period there were 1.082.107 purchases and 887.594 sales. For each trade they estimated the bid-ask spread component of the transaction costs for purchases and sales. Then, the round-trip trading cost is estimated. On average, the round-trip transaction cost is about 1 percent for the bid-ask spread and about 3 percent in commissions. Furthermore, the monthly portfolio turnover for each household is calculated; a monthly purchase turnover and a monthly sales turnover. Also, the gross monthly returns on the household’s portfolios and the net monthly returns on the household’s portfolios are calculated. Furthermore, Barber and Odean calculate four measures of risk-adjusted performance; the own-benchmark abnormal return for the individual investors, the mean monthly market-adjusted abnormal return for individual investors, Jensen’s alpha (to employ the theoretical framework of the Capital Asset Pricing Model), the three-factor model developed by Fama and French [1993].
the difference in the net performance of the 20 percent of households that trade frequently and the 20 percent that trade infrequently is quite larger. The net average monthly returns are 1,009 and 1,470, representatively. When they looked at the 20 percent of households that trade most often, they found that these households turn their common stock portfolios over more than twice annually. Small portfolios have slightly higher monthly turnover than large portfolios, 6,68 percent and 6,33 percent respectively. The net returns of these households are not well; 1,478 percent for the smallest quintile and 1,279 percent for the largest quintile. The average household underperforms the value-weighted market index by about 1,1 percent annually. The central message of this study is that trading is hazardous to the wealth of investors. They believe that excessive trading can be at least partly explained by overconfidence.
Gervais and Odean [2001] developed a multiperiod market model describing both the process by which traders learn about their ability and how a bias in this learning can create overconfident traders. Most investors tend too have too much credit for their own successes, which can lead to overconfidence. The model is dynamic, which means that it changes with success and failure. The model that Gervais and Odean have developed, predicts that overconfident traders will increase their trading volume and consequently lower their expected returns. They found also that investors are most overconfident in an early stage of their career.
Barber and Odean [2006a] investigated the fact that actually observed trading volumes cannot be explained by rational motives. This study is based on earlier studies: Barber and Odean [1999], Barber and Odean [2000], Odean [1999] and Barber and Odean [2002]. The explanation they gave in this study for excessive trading is overconfidence, which results in increasing heterogeneity in the opinions of investors and which generates excessive trading. They found that the investors do not even earn their transaction costs. They also concluded that investors not only burn money on commissions, but they also sell a good performing stock in order to purchase a poorer one.
2.7.3. Excessive trading and overconfidence related to demographics
Barber and Odean estimated for each trade the bid-ask spread component of the transaction costs for purchases and for sales. Subsequently, the round-trip transaction costs are estimated. The monthly portfolio purchase turnover as well ass the monthly sales turnover for each household is calculated then. Also, the own-benchmark abnormal return is calculated. This abnormal return represents the return that a household would have earned if it had merely held it’s portfolio that it had at the beginning of the year. Barber and Odean found that women hold slightly smaller common stock portfolios than men do, $18,371 versus $21,975. Women turn over their portfolios approximately 53 percent annually, whereas men turn over their portfolios approximately 77 percent annually. This means that men trade 45 percent more than women do. Moreover, trading reduces men’s net returns by 2,65 percentage point a year as opposed to 1,72 percentage points for women. They also examined whether there is a difference between married and single people. They found that single men trade the most (85 percent annual turnover). Married men have an annual turnover of 73 percent. Married and single women trade 53 percent and 51 percent in annually turnover, respectively.
Shu, Chiu, Chen and Yeh [2004] investigated whether the individual investors of a Taiwanese brokerage house trade excessively. The data is obtained from a large securities brokerage firm in Taiwan. 52.649 customer accounts are randomly selected from all active accounts from January 1998 through September 2001. They only investigate the stock investments of individual investors. Looking at the dataset, Shu et al. found that individual investors purchase 73,4 percent and sell 64,5 percent of their stock portfolio each month. This is more than ten times the statistics surveyed by Odean [2000]. The aggregate purchase turnover is 70,53 percent and the aggregate sales turnover is 63,30 percent. The average purchase and sale commission are 0,1452 percent and 0,1465 percent respectively. On average, a round-trip transaction incurs 0,3 percent in commission and 0,5 percent for the bid-ask spread. The transaction costs in Taiwan are significantly lower than in the United States. Furthermore, they calculated the gross monthly returns and the net monthly return for the average account and for the aggregate accounts. Hereby, they took account of commissions, the bid-ask spread and the market price impact. Also risk-adjusted return measures are established by the own-benchmark abnormal return for the individual investors, the mean monthly market-adjusted abnormal return for individual investors, Jensen’s alpha (to employ the theoretical framework of the Capital Asset Pricing Model) and the three-factor model developed by Fama and French [1993].
factors. Shu, Chiu, Chen and Yeh investigated also the relationship between overconfidence and gender. They found that men hold significantly larger common stock portfolios then women do; NT$2,5 million for men and NT$2,0 million for women. They also concluded that men also trade more excessively than women do. The mean monthly turnover rate for men is 78,11% and 60,24% for women. Furthermore, the proportion of men involved in margin trades is slightly higher than that of women, 29,18% and 24,75% respectively. Men (56,16%) also trade more through electronic accounts than women (53,58%) do.
Bhandari and Deaves [2006] looked in their research at the demographics of overconfidence. They used a dataset of 2.000 defined contribution plan members. They not only looked at overconfidence, but they also explored the demographics of this. Overconfidence is split into certainty and knowledge. Two five-option multiple-choice questions were asked in order to test the knowledge level of respondents. Furthermore, each question had a second part which asked how certain they were in their answers. Bhandari and Deaves found that men who have a high education, who are nearly to their retirement, who have received investment advice, and who have experience investing for themselves, tend to be more certain. They concluded that highly-educated males are more subject to overconfidence, because they do not have higher levels of knowledge.
2.7.4. Excessive trading and overconfidence related to online trading
Barber and Odean [2002] analyzed 1.607 investors who switched from phone-based trading to online trading. These investors were made out a dataset of 78.000 households with brokerage accounts at a large discount brokerage firm. All trades and monthly positions in common stock are used from January 1991 through December 1996. The methodology used in this study is similar to that of Barber and Odean [2000]. The gross monthly return is 1,649 percent for online households before they went trading online. This gross monthly return is 1,198 after trading online. Moreover, the net monthly return is 1,492 percent for online households before the trade online. When they trade online, this figure is 1,002 percent. The total turnover of online households before they trade online is 73,7 percent. After trading online this total turnover becomes 95, 5 percent. Barber and Odean also used calendar-time portfolios. Here, there are positive excess returns for all the measures except for the own-benchmark return. These are negative. The gross monthly return for the market adjusted return is significant with a level of 10 percent. Furthermore, net monthly return for the own benchmark return is significant with 1-percent level. The conclusion of this study is that the investors trade more actively, and less profitable than before going online. The explanation for this can be overconfidence, in coherence with the self-attribution bias and the illusion of knowledge.
2001. This study uses a combination of three datasets. The first contains 563.104 transactions of 3.079 individual investors. The second dataset consists of demographic and other self-reported information that was collected when the investor opened the account. The third dataset consists of answers to an online questionnaire to measure overconfidence. A questionnaire is used to test for overconfidence. To test empirically, they correlate the scores of overconfidence with the performance of the investor in the past. The measures of trading volume were calculated by the trades of 215 individual investors who answered the questionnaire. Glaser and Weber found that investors, who trade more, do not have higher monthly gross returns. The mean monthly gross portfolio return of the dataset is 0,54%. The gross returns varies from -16% to +24% per month. Furthermore, they did not find evidence for the learning-to-be-overconfident hypothesis. This hypothesis means that a high degree of overconfidence is a result of past investment successes. Moreover, they discovered that investors who think that they are above average in terms of investment skills or past performance trade more.
The internet has brought changes to investing that may strengthen the overconfidence of online investors. This is because the internet provides an illusion of knowledge and illusion of control. Additional information can lead to an illusion of knowledge and an illusion of control. Online traders have access to vast data. Therefore, online traders are more likely to become overconfident. [Barber and Odean (2006a)]
2.7.5. Overview of previous empirical results
In the next table the empirical results are showed. Table 1:Literature review
Country Author(s)/Title Sample Time period Method Main results
United States BARBER, B.M. AND ODEAN, T. [1999] ‘Boys will be boys: gender, overconfidence, and common stock investment’ 37.664 households (portfolios) Account data of households from a large discount brokerage is used in this study. February 1991 -January 1997 Returns to securities bought and returns to securities sold, effective bid-ask spread, round-trip transaction costs.
Men trade 45 percent more than women do. Trading reduces men’s net returns by 2,65 percentage points a year as opposed to 1,72 percentage points for women. United States BARBER, B.M. AND ODEAN, T. [2000] ‘Trading is hazardous to your wealth: the common stock investment performance of 66.465 households (portfolios) Common stock investments of (active) households at large discount firm January 1991 – December 1996 Effective bid-ask spread, round-trip transaction costs, return performance and adjusted return performance. Creating portfolios.
individual investors’ United States BARBER, B.M. AND ODEAN, T. [2002] ‘Online investors: Do the slow die first?’
1.607 investors who changed from phone-based trading to online trading January 1991 – December 1996 Effective bid-ask spread, round-trip transaction costs, return performance and adjusted return performance.
The investors trade more actively, and less profitable than before going online. The explanation for this can be overconfidence, in coherence with the self-attribution bias and the illusion of knowledge. United States BARBER, B.M. AND ODEAN, T. [2006a] ‘Individual investors’
n/a n/a This paper is based
on earlier studies: Barber and Odean [1999], Barber and Odean [2000], Odean [1999] and Barber and Odean [2002]
Investors do not even earn their trading costs. The explanation they gave in this study for excessive trading is overconfidence, which results in increasing heterogeneity in the opinions of investors and which generates excessive trading. They not only sell winners too soon, they buy the wrong stock instead. United States BHANDARI, G. AND DEAVES, R. [2006] ‘The demographics of overconfidence’ 2.000 defined contribution pension members
n/a Two five-option
multiple-choice questions and a second part in which is asked how certain the
respondents are about their answer.
Men who have a high education, who are nearly to their retirement, who have received investment advice, and who have experience investing for themselves, tend to be more certain. United States GERVAIS, S. AND ODEAN, T. [2001] ‘Learning to be overconfident’
n/a n/a They developed a
multiperiod market model. This model describes the process by which traders learn about their ability. The model shows also how a bias in this learning can create overconfident traders.
Overconfident traders will increase their trading volume and consequently lower their expected returns. Investors are most overconfident in an early stage of their career. Germany GLASER, M. AND WEBER, M. [2003] ‘Overconfidence 3.079 investors of a German online broker. 563.104 transactions. January 1997 – April 2001 A questionnaire and gross portfolio returns.
and trading volume’
who think that they are above average in terms of investment skills or past performance trade more. United States ODEAN, T. [1998] ‘Volume, volatility, price and profit when all traders are above average’
n/a n/a For each of the three
market settings, price-taking traders, a strategic-trading insider, and risk-averse marketmakers, a model is developed. Overconfidence increases expected trading volume, increases market depth, and decreases the expected utility of overconfident traders. United States ODEAN, T. [1999] ‘Do investors trade too much?’
162.948 trade records and 1.258.135 position records. Randomly selected 10.000 accounts form a nationwide discount brokerage house. January 1987 – December 1993 Returns to securities bought and returns to securities sold, effective bid-ask spread, round-trip transaction costs. Bootstrap methodology and calendar-time portfolios: performance measures. A particular group of investors trade
excessively in the sense that their returns are reduced trough trading. Moreover, he found that overconfident investors may trade even when their expected gains through trading are not enough to cover the trading costs.
Taiwan SHU, P.G. et al. [2004] ‘Does trading improve individual investor performance’ 52.649 accounts, 10.615.117 transaction records. January 1998 – September 2001 Effective bid-ask spread, round-trip transaction costs, return performance and adjusted return performance.
3. DATA AND METHODOLOGY
First, the data used in this study will be examined in section 3.1. Furthermore, the methodology which is applied in this study will be discussed in this chapter. Section 3.2 will go into the methodology. Then, the significance is tested in section 3.3 .
3.1. Dataset
The dataset contains trading records of individual investors from January 1st, 2005 trough June 30th, 2007 (30 months). The data is provided by a branch of a bank in the Netherlands. This is all the trading data that is available by this bank. The daily returns and closing prices of the securities bought and sold are acquired from DataStream.
The dataset consists of investors who invest with the help of a consultant. On the contrary, investors can also invest through direct canals. Allen [2001] found that in the United States 64 percent of the investors rely on professional investment advice. Fisher and Gerhardt [2007] found that roughly 80 percent of the individual investors in Germany rely on financial advice for their investment decisions. In the Netherlands 49% of the investors invest with the help of a consultant [Millward Brown (2005)]. These figures show that almost half of the investors in the Netherlands rely on financial advice. In the United States and Germany this is even more. Examining the investors who invest with the help of a consultant is not done often before by other researchers, while a lot of investors rely on financial advice. Therefore, I choose for this group of investors. In this study there is not chosen to compare the investors who invest with the help of a consultant with the investors who invest through direct canals. In this study, I did not take into account the investors who invest through direct canals, because the data of the investors who invest through direct canals was difficult to acquire.
securities are purchased, with a market value of €38.013.758,29 and 3.022.165 securities sold, with a market value of €51.167.019,41.
3.1.1. Descriptive statistics
In table 2 the characteristics of the trade size, the price per share, the closing price, the transaction cost and the number of transactions are given for the whole dataset, the securities bought and the securities sold. From table 2 it can be concluded that the average trade size for the whole dataset is €10.193,24 and the median trade size for the whole dataset is €7.280,00. It can also be seen that the average trade size when purchasing (€9.845,57) is smaller than the average trade size when selling (€10.467,88). The average price per share is €24,56 when the whole dataset is taken and the median price per share is €22,75. The average closing price for the whole dataset is €24,53. For he whole dataset as well as for the securities bought the average closing price is slightly smaller than the average price per share. However, for the sales it is the other way around. Here, the average closing price is slightly greater than the average price per share. The average price per share when purchasing (€23,43) is smaller than the average price per share when selling (€25,45). If the average transaction cost of the securities bought and the securities sold are compared, it can be seen that there is only a slight difference. The average transaction costs for the purchases and sales are €93,20 and €95,37, representatively. If we take a look at relative transaction cost, we can see that the maximum transaction cost are 500 percent of the value of the trade. The reason for this is that the bank charges a minimum amount for each transaction plus a percentage of the market value of the trade. Finally, table 2 shows the number of transactions made in one portfolio. The average number of transactions an investor made is 11. Furthermore, the average number of purchases is 6 and the average number of sales is 5. In the histogram presented in figure 2 it can be easily seen that most of the investors make few transactions.
The dataset consist of 227 different securities, of which 92 securities of Dutch companies. 7.011 transaction in Dutch securities are made (80,13 percent). Furthermore, 1.739 transactions are done in foreign securities (19,87 percent). Appendix A gives an overview of the different securities which are taken into account in this study.
Table 2:Descriptive statistics
Mean First
percentile
Median Third
percentile
Minimum Maximum Standard
Deviation Whole dataset
Trade size (€) 10.193,24 3.919,80 7.280,00 12.171,13 4,02 171.465,00 11.411,66
Price per share (€) 24,56 12,76 22,75 32,00 0,12 713,25 20,76
Closing price (€) 24,53 12,80 22,68 31,91 0,12 711,81 20,58 Transaction cost (€) 94,41 37,12 77,20 119,50 0,00 1551,20 93,23 Transaction cost 0,0093 0,007 0,01 0,01 0,00 5,30 0,09 Transactions (#) 11 2 5 13 1 225 17,35 Purchases Trade size (€) 9.845,57 4.168,75 7.360,00 11.262,00 16,50 150.100,00 10.391,56
Price per share (€) 23,43 13,15 22,02 31,66 0,12 157,95 15,55
Closing price (€) 23,31 13,08 21,94 31,44 0,12 158,35 15,40 Transaction cost (€) 93,20 40,62 78,50 115,45 0,00 1.185,34 89,77 Transaction cost 0,0095 0,007 0,01 0,01 0,00 0,41 0,18 Transactions (#) 6 0 2 6 0 132 9,26 Sales Trade size (€) 10.467,88 3.576,64 7.216,84 12.845,79 4,02 171.465,00 12.152,19
Price per share (€) 25,45 12,63 23,36 32,18 0,18 713,25 24,06
Closing price (€) 25,49 12,68 23,40 32,14 0,16 711,81 23,85
Transaction cost (€) 95,37 33,63 76,38 123,10 0,00 1.551,20 95,89
Transaction cost 0,0091 0,007 0,01 0,01 0,00 5,30 0,12
Transactions (#) 5 1 3 7 0 97 8,86
Notes: The transaction costs are calculated as the transaction cost paid divided by the value of the trade. Transactions (#) stands for the number of transactions made in one portfolio.
3.1.2. Characteristics of returns
To test whether the returns are normally distributed Jarque-Bera is used. Jarque-Bera is a descriptive statistic which is composed of skewness and kurtosis. Jarque-Bera can be calculated with the following formula:
W = T [(skewness²/6) + (kurtosis – 3)²/24] [3]
where T is the sample size.
In table 3 the descriptive statistics for the returns are given.
Table 3:Skewness, kurtosis and Jarque-Bera for the returns.
Skewness Kurtosis Jarque-Bera
0,2606 3,4843 89,6289
From table 3 can be concluded that the data is not normally distributed. Therefore, a non-parametric test has to be used here. The return data is positively skewed. Moreover, the distribution of the return data is peaked relative to a normal distribution. [Brooks (2002)]
Furthermore, the data is not independent here, because the securities in the dataset can be bought or sold on more than one date. Moreover, the securities can be bought or sold by different investors on the same date. This can cause the return horizons to overlap. Suppose, for example, that one investor purchases a particular stock and that two months later another investor buys the same stock. If the return horizon is three months, the periods overlap for one month. Because of this overlap, the returns earned by this security over the three-month periods subsequent to each of these purchases are not independent. Consequently, statistical tests which require independence cannot be used here.
3.1.3. Subsamples
Three subsample are formed to look at the data more detailed. The three subsamples made in this study are as follow:
Subsample 1: Transactions made form January 1st, 2005 to June 30th, 2006.
Subsample 2: Purchases within five trading days subsequent to a sale - sales and purchases
where the purchase security is from the same amount as the security sold or from a smaller amount.
Subsample 3: investors who trade the most (10 percent) and the investors who trade the least
(90 percent).
These three subsamples will be discussed now.
A subsample is made from January 1st, 2005 to June 30th, 2006, because more return data is available for this period. Therefore, testing for significance can be done more accurate here. This subsample consists of 4.445 transactions; 2.070 purchases and 2.375 sales.
borrow cheaper than the cost of selling the securities and later buying them. Furthermore, the assumption is made that the proceeds of a sale are used to buy another security. Therefore, this subsample only contains sales and purchases where the purchase security is from the same decile as the security sold or from a smaller amount than the security sold. So, when a security position is sold for amount x the buy transaction can be maximal this amount x. Moreover, this subsample only examines sales and purchases where the purchased security is from the same size decile or from a smaller size decile as the security sold. It is widely accepted that size is a risk factor. Therefore, this restriction is intended to eliminate most cases where an investor buys a security of lower expected return and smaller size than the one he sells because he wants to reduce the risk of his portfolio. Market capitalization is used as a proxy for size. Market capitalization stands for the share price times the number of shares outstanding. To get an estimate of the market capitalization for the different securities, figures of market capitalization are acquired from Amadeus and from DataStream.
When all restrictions are taken into account this subsample contains 1.873 transactions; 893 purchases and 980 sales.
Furthermore, the dataset is split up in the investors who trade the most and the investors who trade the least. The ten percent of the investors who trade the most are taken. The investors who trade the most have done minimal 25 transactions from January 1st 2005 to June 30th 2007. This study is about excessive trading, therefore the investors who trade the most are examined separately. There could be a difference in excessively trading between the investors who trade the most and who trade the least. In table 4 the distribution of these two subsamples is given.
Table 4:Distribution of the transactions subsample 3.
Whole dataset 10% of investors who
trade the most
90% of investors who trade the least
Portfolios (#) 812 82 730
Transactions (#) 8.750 3.835 4.915
Transactions per portfolio (mean) (median) 11 5 47 35 7 5 Purchases (#) 3.862 1.843 2.019
Purchases per portfolio (mean) (median) 6 2 22 18 3 1 Sales (#) 4.888 1.992 2.896
3.2. Methodology
In this section the methodology is discussed.
3.2.1. Average returns
To test whether the investors are subject to excessive trading, I will determine whether the securities which the investors in the dataset have bought outperform those they have sold by enough to cover the trading cost. It is first established whether the securities the investors bought outperform or underperform those they sold, without taking notice of the trading costs. The return horizons are established at 21 trading days (1 month) and 84 trading days (4 months) following a transaction. These horizons are chosen, because more data is not available for the whole dataset. For the subsample from January 1st, 2005 to June 30th, 2006 there is also a return horizon set at 252 trading days (1 year) following a transaction. This is also the maximal available data for this subsample.
The average returns to securities bought or sold will be calculated next. It is possible that the same security is bought or sold on the same day. If this is the case, each transaction will be treated as a separate transaction. Each transaction will be indexed with a subscript i, where i stands for 1 to N.
The average return to the securities bought (RB) over T trading days subsequent to the purchase is:
[1]
In formula [1] Rj,tis the daily return (from DataStream) for security j on date t, T stands for the number
of trading days and N is the number of purchases.
The average return to the securities sold (RS) over T trading days subsequent to the sale is:
[2]
Formula [2] is in basis the same as formula [1]; Rj,tis the daily return for security j on date t, T stands
The return calculations begin the day after the purchase or the sale. This is done to avoid incorporating the bid-ask spread into the returns.
3.2.2. Round-trip transaction costs
The round-trip transaction costs are all of the costs associated with completing a round-trip transaction, so with completing a sale and a purchase. The round-trip transaction costs consists of the average total transaction costs when one security is sold and the proceeds of the sale are used to buy another security and the effective bid-ask spread.
The average transaction costs paid when a security is purchased is 0,95 percent of the purchase price. This is calculated as the average transaction cost (€) divided by the average trade size (€). The average transaction costs paid when a security is sold is 0,91 percent of the sale price. Hence, if one security is sold and the proceeds of the sale are used to buy another security the average total transaction costs are about 1,86 percent.
The bid-ask spread measures the difference between the ask price and the bid price of a security. It is the amount by which the ask price exceeds the bid price. The bid-ask spread can be approximated using real bid-ask spreads. The bid prices and the ask prices are obtained from DataStream. Then, a weighted average is taken for all the transactions made in this dataset. When taking the weighted average of the real bid-ask spreads, an accurate reflection of the bid-ask spread is acquired.
The weighted average for the bid-ask spread is 0,02 percent.
So, the round-trip transaction costs becomes about 1,88 percent. If an investor sells securities and buys others because he thinks the securities bought will outperform those sold, the return on the securities bought has to be 1,88 percent higher just to cover trading costs.
3.2.3. Hypotheses
Now, the hypotheses can be formulated. The first null hypothesis (H01) is that the difference in returns
is greater than or equal to the round-trip transaction costs (1,88 percent). Consequently, the alternative (H11) hypothesis is that the difference in returns is less than the round-trip transaction costs (1,88
percent).
H01: RB– RS≥ round-trip transaction costs.
H11: RB– RS< round-trip transaction costs.
where RBis the average returns to securities bought and where RSis the average returns to securities
The second null hypothesis (H02) in this study is that the average returns to securities bought are
greater than or equal to those sold ignoring trading costs. The alternative hypothesis (H12) is that the
average returns to securities bought are less than those sold ignoring trading costs.
H02: RB≥ RS (ignoring trading costs).
H12: RB< RS(ignoring trading costs).
where RBis the average returns to securities bought and where RSis the average returns to securities
sold.
3.3. Significance testing
In this section of this empirical study methods are discussed which can be used for significance testing. In this study, the Wilcoxon Signed Rank Sum test is used to test the hypotheses. Furthermore, calendar-time portfolios are formed.
3.3.1. Wilcoxon Signed Rank Sum Test
In this study the Wilcoxon Signed Rank Sum Test is used to test the hypotheses. This statistical test can be used if two populations have to be compared. In this study this is the case; the returns to the securities bought have to be compared with the returns to the securities sold. Furthermore, the difference between the securities bought and the securities sold has to be compared with the round-trip transaction cost. The Wilcoxon Signed Rank Sum Test is applicable for data which is non-normal and not independent. As can be seen in section 3.1.2 this is the case in this study.
The Wilcoxon Signed Rank Sum Test compares the returns of the securities bought to the returns of the securities sold. This test also relates the excess returns with the round-trip transaction cost. The positive and negative ranks are added up. If the securities bought and securities sold are equal to each other, the sum of the positive and negative ranks should be zero.
The formula for the Wilcoxon Signed Rank Sum Test is as follow. T+is labeled as T here.
E(T) = [n(n+1)]/4 [3]
σT= √ [n(n+1)(2n+1)]/24 [4]
z = [T – E(T)]/σT [5]
There cannot be determined whether there will be a positive or a negative difference beforehand. Therefore, testing will be done two-sided here. The rejection regions for the Wilcoxon Signed Rank Sum Test are given in table 5. For example, if the z-value is larger than 2,575 the result is significant at a 1-percent level.
Table 5:Rejection regions.
Significance level Rejection region
1% +/-2,575
5% +/-1,96
10% +/-1,645
To perform the Wilcoxon Signed Rank Sum Test, SPSS is used.
3.3.2. Calendar-time portfolios
Three measures of performance are used to measure the returns of calendar-time portfolios of the securities bought and the securities sold. Calendar-time portfolios are formed, because the problem of cross-sectional dependence among stocks is eliminated then. The second null hypothesis is tested here, because transaction cost are ignored when using calendar-time portfolios. The second null hypothesis is that the average returns to securities bought are greater than or equal to those sold ignoring trading costs.
Calendar-time returns for the securities purchased have been estimated as follow. For each calendar month t, the return is calculated on a portfolio with one position in a security for each occasion of a purchase in the formation period (one month or four months) preceding this calendar month. Each purchase causes a separate position in the portfolio, because there can be different occasions when a security may have been purchased. Each position is weighted equally in the portfolio. The same is done for the securities sold.
There are three risk-adjusted measures of performance used here. The first measure which is calculated is the average monthly calendar-time return on the buy-portfolio minus that on the sell-portfolio.
The following regression can be employed:
RBpt– Rspt= αp+ βp(Rmt– Rft) + εpt [6]
where RBpt= the monthly return on the calendar-time portfolio based on purchases.
RSpt= the monthly return on the calendar-time portfolio based on sales.
Rmt= the monthly return on a value-based market index.
Rft= the monthly return on a risk-free asset.
βp= the beta.
εpt= the error term.
The coefficients αpand βpdetermine the factors.
To compose a proxy for the monthly return on the value-based market index (Rmt), a weighted average
is made of two indices. 80,13 percent of the transactions in this dataset is done in Dutch securities. The other 19,87 percent of the transactions is done in foreign securities. Therefore, a weighted average is made of the MSCI Netherlands Index (80,13%) and the MSCI World Index (19,87%). The MSCI Netherlands Index consists of stocks traded primarily on the Amsterdam Stock Exchange and it seeks to measure the performance of the Dutch stock market. The MSCI Netherlands Index is a broad index. This index is chosen, because is represents the Dutch market in a precise way. The MSCI World index includes a collection of stocks of all the developed markets in the world. It contains amply 1.700 stocks. This index is a common benchmark for investments all over the world. The MSCI World Index is chosen in this study, because it gives a good representation of the stock market in the world. To get a good estimate of the market index in the case of the investors in this dataset, a weighted average of the MSCI Netherlands Index (80,13%) and the MSCI World Index (19,87%) is made.
The monthly return on a risk-free asset (Rft) is the return an investor would receive with an investment
with zero risk. In practice there does not exist a complete free investment. To estimate the risk-free rate in this study, 1-month Euribor is used. Euribor is the rate at which Euro interbank term deposits within the Euro zone are offered by one prime bank to another prime bank. Generally, investing in a bank is quite safe. Therefore, it can be used as an approximation for the risk-free rate.
Beta can be calculated as follow:
βi= [cov(Ri,Rm)/σ²(Rm)] [7]
The beta of the portfolio (βp) is a weighted average of the betas of the individual securities.
The third measure which is used is the three-factor model developed by Fama and French [1993]. This three-factor model consists of an overall market factor and factors related to firm size and book-to-market equity. The following monthly times-series regression in determined:
RBpt– Rspt= αp+ βp(Rmt– Rft) + zpSMBt+ hpHMLt+ εpt [8]
where RBpt= the monthly return on the calendar-time portfolio based on purchases.
RSpt= the monthly return on the calendar-time portfolio based on sales.
Rmt= the monthly return on a value-based market index.
Rft= the monthly return on a risk-free asset.
βp= the beta.
SMBt= the return on a weighted portfolio of small stocks minus the return on a
value-weighted portfolios of big stocks.
HMLt= the return on a value-weighted portfolio of high book-to-market stocks minus the
return on a value-weighted portfolio of low book-to market stocks. zp= coefficient which determines SMBt.
hp= coefficient which determines HMLt.
εpt= the error term.
αp, βp, zp, and hpare coefficients which determine the factors (‘Rmt– Rft’, SMBtand HMLt). Rmt, Rftand
βpare the same as for the CAPM intercept.
The book-to-market ratio is used to find the value of a company by dividing the book value of a firm by its market value. The book value is determined by looking at a firm’s historical cost or accounting value. The total value of the equity on the balance sheet is used to determine the book value. This data is obtained from Amadeus and from DataStream. Market value is established through its market capitalization. The figures for the market capitalization are obtained from Amadeus and from DataStream. The average book-to-market ratio is 0,3289 and the median book-to-market ratio is 0,2646. Like Fama and French did in their study, the dataset is split into three groups; a group with the 30 percent lowest book-to-market value, a group with the 40 percent middle book-to-market value and a group with the 30 percent highest book-to-market value. The 30%-percentile and the 70%-percentile are used to split the dataset. These are 0,1279 and 0,4023, representatively.
Then, six portfolios are constructed:
Small size/low book-to-market value (SL)
Small size/medium book-to-market value (SM)
Small size/high book-to-market value (SH)
Big size/low book-to-market value (BL)
Big size/medium book-to-market value (BM)
Big size/high book-to-market value (BH)
For example, the BH portfolio contains stocks in the big size group that are also in the high book-to-market value group. Furthermore, the monthly returns on these six portfolios are calculated. The two portfolios SMBtand HMLtare created then. The SMBtportfolio is used to mimic the risk factors in the
returns related to size. The return on this portfolio is calculated by the difference between the average of the returns on the three small-stock portfolios (SL/SM/SH) and the average of the returns on the three big-stock portfolios (BL/BM/BH). Moreover, the HMLt portfolios are used to mimic the risk
factors in returns in relation with the book-to-market value. The return on this portfolios is estimated by the difference between the average of the two high book-to-market portfolios (SH/BH) and the average of the two low book-to-market portfolios (SL/BL).
An approximate of α offers a test of the second null hypothesis. This second null hypothesis states that the difference in the mean monthly excess return of the buy-portfolio and sell-portfolio is zero. So, if this null hypothesis holds, α should be zero for all of the three performance measures.
