Evaluation of the Momentum Strategy on the German Stock Exchange

An empirical analysis of the DAX and MDAX

Master's Thesis, 2013

92 Pages, Grade: 1.3


Table of Contents

Executive Summary

Table of Contents

List of Abbreviations

List of Figures

1 Introduction

2 Traditional Financial Market Theory vs. Newly Developed Financial Behavior Theory
2.1 Market efficiency and “noisy inverter”
2.2 Behavioral Finance
2.2.1 Overconfidence
2.2.2 Representativeness
2.2.3 Other behavioral biases and models

3 Momentum Effect and Momentum Strategy as Part of Market Anomalies
3.1 CAPM and “abnormal return”
3.2 Contrarian strategy
3.3 Momentum strategy: initial evidence from the United States
3.4 Empirical evidence of momentum strategy from other countries

4 Data and Methodology
4.1 Data
4.2 Methodology

5 Results
5.1 DAX
5.2 MDAX
5.3 Summary

6 Outlook

7 Conclusion




Executive Summary

This work covers the momentum effect on financial markets and a trading strategy based on this effect. The research focuses on the German Stock Exchange data from the last decade. The data are divided into two sections in order to build two different types of vir­tual portfolios. One section contains the data of the DAX index, and the second section is filled with securities from the MDAX. Two hypotheses are to be verified. First, is momen­tum still available in a time of mass internet availability, like during the past decade? And second, is momentum stronger in MDAX due to smaller firm sizes and corresponding lower market efficiency?

This work is divided into five parts. The first part describes the research results on behav­ioral financial theory. Several biases like representativeness, overconfidence, availability, and disposition effect are introduced. Their root causes and influences on trading behavior are also discussed. The evidence documented and presented in several financial journals concludes this chapter.

The second chapter handles abnormal stock returns and the CAPM model. Several defini­tions and the background of CAPM are introduced. Momentum and the contrarian trading strategy are introduced. The momentum effect discovered initially by JAGADEESH and TITMAN (1993) is explained in detail. In contrast, the contrarian strategy idea by DEBONDT and THALER (1985) is introduced. Evidence that justifies both trading strat­egies is discussed. The time frame that different strategies use is pointed out. The contrari­an strategy uses the long term and the momentum strategy uses the middle term.

The third chapter explains the database and methodology used for this research. The main data are derived from a Bloomberg terminal. The time frame of the used data is limited to the last decade, beginning in February 2001. The main tool used for data analysis is Mi­crosoft Excel. The algorithm written in VBA language and its functions are briefly ex­plained. The output data and their dependency on input variables are described. The algo­rithm itself is available in the appendix. The portfolio consists of 10 securities. The portfo­lio creation was done “dynamically.” One of the strongest or weakest securities is selected for the portfolio. Next the security selection for the portfolio is done periodically. This period depends on the share-keeping time of the portfolio. The period is adjusted in order to keep the number of securities in the portfolio equal to 10. Theoretically the portfolio can contain 10 equal shares in case this share was strong or weak over a relatively long time period. This approach is new compared to the “static portfolio” approaches used in the initial paper by JAGADEESH and TITMAN (1993).

The results are documented in chapter four. The momentum effect is clearly visible in portfolios built on MDAX securities. Especially portfolios with a long stock-monitoring time J and short stock-keeping time K bring high abnormal returns of approximately 3% per month. The t-statistic figures in MDAX portfolio are high, between 4 and 7. These results are in line with the results provided in the initial paper byJAGADEESH and TIT- MAN (1993). However, the results of the DAX portfolio does not show a clear momen­tum effect. In addition, t-statistic values are low, close to 2. Furthermore, the contrarian strategy does not show negative returns in a time frame of 12 months. This is in contradic­tion to the literature sources.

The last chapter (chapter five) explains how to use the written software to verify the results by using additional calculations. Some suggestions are made in order to increase the confi­dence level of the statistics.

List of Abbreviations

Abbildung in dieser Leseprobe nicht enthalten

List of Figures

Figure 1. SML/CML. Source: SHARPE (1964)

Figure 2. Input data format. Own source

Figure 3. Internet users in Germany. Source: Initiative D2 2012

Figure 4. Internet users in the United States. Source: ITU 2012

Figure 5. Development of online banking users in Germany. Source: Statista and

Federation of German banks

Figure 6. Online banking users in Europe. Source: EUROSTAT

Figure 7. Share ordering cost for 1,000 Euro. Source: FINANCEADS 2013

Figure 8. Changes in DAX between 1990 and 2001. Source: Deutsche Borse

Figure 9. Changes in DAX starting in the year 2001. Source: Deutsche Borse

Figure 10. DAX securities used for momentum calculation. Own source

Figure 11. MDAX securities used for calculation. Own source

Figure 12. Share of Aareal Bank. Source: Bloomberg terminal

Figure 13. Share of BAYWA. Source: Bloomberg Terminal

Figure 14. Input window in calculation software. Own source

Figure 15. Visual explanation forj and K parameters. Own source

Figure 16. Output window after the monitoring process. Own source

Figure 17. Output window after “keeping” calculation process. Own source

Figure 18. Matrix of final results. Own source

Figure 19. Example of calculation results in portfolio formation. Own source

Figure 20. Visual example of portfolio handling where K=90. Own source

Figure 21. Evaluation results of best shares in DAX. Own source

Figure 22. Evaluation results of worst shares in DAX. Own source

Figure 23. Evaluation results of DAX index. Own source

Figure 24. Evaluation results of best shares in MDAX. Own source

Figure 25. Evaluation results of the worst MDAX shares. Own source

Figure 26. Evaluation results of the MDAX index. Own source

Figure 27. Proposal for a “switching” button. Own source

Figure 28. Best and worst DAX shares in past 12 months and past one week in percent. Source: FAZ 04 Feb 2013 Citation

“Those who have knowledge don’t predict. Those who predict don’t have knowledge.”

Laoze, philosopher of ancient China

1 Introduction

For decades the discussion about market efficiency and its strength has been the subject of many publications in financial journals. This trend seems to continue in the near future. Since discovering that the price of investment is not solely related to its risk and dividends, the search for market anomalies and their root cause becomes intense. The anomalies are used for developing certain trading strategies by several funds and private persons.

Two strategies that use market anomalies are the contrarian and momentum strategies. The strategies are completely opposite, but both use the past stock quotes in order to predict stock quotes in the future. The idea behind the contrarian strategy is to purchase stocks that performed worst in the past, and the idea behind the momentum strategy is to buy stocks that performed best in the past. Both strategies believe that the resulting portfolio will bring abnormal returns. The literature provides much evidence to justify both ap­proaches.

The goal of this work is to investigate the momentum strategy on the German stock ex­change in the past decade and its potential usability. Additionally, the portfolios are to be built based on separate stocks: stocks from the DAX and stocks from the MDAX. The first part of this work handles the classical financial theory and behavioral financial theory. The initial studies and modern outcomes are discussed. The momentum and contrarian strategies are introduced in the second part. Some evidence based on stock exchanges from different countries are presented and briefly discussed. In the third part of this work the methodology for investigating the momentum effect in both the DAX and MDAX is in­troduced. The time frame used is the last decade and the stock population is divided into two groups: stocks from the DAX and stocks from the MDAX. The results of this investi­gation and outlook are presented in the final chapters.

2 Traditional Financial Market Theory vs. Newly Developed Financial Behavior Theory

2.1 Market efficiency and “noisy inverter”

Not too many non-regulated markets are driven by offer and demand only. One example is the financial market or stock exchange. The financial market is famous for its pure rational­ity, where the price of securities mirrors its properties. According to SAMUELSON (1965) the stock prices will follow a random walk if rational investors expect a fixed amount of return. FAMA (1965) proved that the market should follow a random walk rule if it is effi­cient. Two separate hypotheses were examined: successive price is independent and the price changes conform to some probability distribution (FAMA 1965; 35). As evidence, JENSEN (1978) positively tested the market efficiency hypothesis.

Nevertheless, bubbles pop up during the history of stock exchange. There are several em­pirical facts for such bubbles, beginning with “tulip mania” (SORNETTE 2003: 9) in the 17th century and following even during modern stock exchange culture (SHILLER 2000: 3—11). The stock run-up of 1920 is interrupted by a crash in 1929, the new run-up during the late 1950s and beginning of 1960 end with a new crash in 1974. But the bubble in 1999 was not comparable with last two (SHILLER 2000: 5). By end of 1999 the average of NASDAQ securities showed price to earning ratios of 200. At the same time, the S&P in­dex ratio was approximately 30 (OECD 2000: 47). The crash in 2002 reduced the NASDAQ index to one-fourth of its value reached by end of 1999 (FIDLEY and ROT- NEY 2011: 430). How do we understand such hot run-ups and dramatic declines?

According to the classical theory about financial market places, the share price must be the exact mirror of its fundamental value. The financial market is structured to be bubble free. The price movement must be caused by fresh information only. The market must be ra­tional by its own definition. This rationality is based on and permanently supported by market efficiency. Market efficiency is “the general notion that price fully reflect available information” (FAMA 1970: 383). There are three levels of market efficiency: weak, semi, and strong (ROBERTS 1967). According to ROBERTS (1967), the weak form of efficien­cy prohibits the prediction of further returns based on past returns. The semi-strong level of market efficiency prohibits the prediction of returns in the future based on public in­formation only. The strong level does not allow for predicting future returns based on any information received on relatively confidential information. In a market with strong effi­ciency, an investor cannot beat this market; he or she can be only lucky or unlucky (BREALEY and MYERS 2003). SHILLER (1981) shows that volatility of the stock ex­change cannot be explained by the arrival of fresh information only (SHILLER 1981: 421). The author confirms that the volatility of share prices in an analyzed time frame (past cen­tury) was 5 to 13 times higher as attributed to the arrival of new information (SHILLER 1981: 434). How do we understand such big deviations between expected and real value?

One way to explain the huge volatility rates of the stock exchange is by introducing the “noise investor” concept. Such a concept was introduced by BLACK (1986). This work underlines that “noise causes markets to be somewhat inefficient” and that “noise in the sense of a large number of small events is often a causal factor much more powerful than a small number of large events can be” (BLACK 1986: 529). A noise trader is defined as a trader who just likes to trade; he or she trades even under circumstances when it is best not to trade (BLACK 1986: 529). In contrast, information traders exist, who trade based on information only. According to BLACK (1986) and to pure human logic, the noise trader will lose money and the information trader will make money. The amount increased by the noise traders will increase the profitability of information traders (BLACK 1986: 529—530). With other words, the market discipline and its efficiency cannot accept noise investors for the long term. The “noise theory” was developed by De LONG, SUMMERS, SHLEIFER & WALDMANN (1990). The authors agreed that noise investors could cause the large divergence between market prices and fundamental values.

This “noise trading” has an interesting effect. Due to the unpredictability of “noise invest­ments” there is a risk in the price of assets. The price can be different compared to the fair value even if the fundamental risk does not exist. Such noise risk requires a higher premi­um for the rational market participator like an arbitrageur (De LONG et al. 1990: 734— 736). The arbitrage is “the simultaneous purchase and sale of the same.. .security in two different markets for advantageously different prices” (SHARPE and ALEXANDER 1990). The arbitrage is not risk-free due to the effect of volatility caused by “noise trading.” The arbitrageur is more aggressive in the case of a security price moving away from its fun­damental value. If the market is quite volatile due to the power of “noise investors,” the arbitrage can bring loss, which is one of the arbitrage limits (SCHLEIFER and VISHNY 1997: 54). This means that the “noise inverter” must not lose money by definition only.

The fact that security prices always correspond to their fundamental values was doubted by several financial researchers at the end of the 1980th, beginning of the 1990th. Research re­sults in experimental psychology were combined with stock exchange data in order to ex­plain the bubbles and market overreaction as well under reaction.

As first DE BONDT and THALER (1985) provided evidence that the Bayes Rule is also valid on the market level. What is the Bayes Rule? Thomas Beyes, an English mathemati­cian and priest, provided 300 years ago in his letter “Essay Towards Solving a Problem in the Doctrine of Chances” the mathematical rule as well as theory for explaining how new evidence can affect our belief or expectations for similar events in the future (BAYES 1763). This rule is part of today’s probability theory. It allows researchers to observe future events based on existing conservative knowledge when considering new, fresh data (LEE 2012). Recently this 300-year-old Beyes Rule was used by network and communication engineers in high-end email technology for spam filtering (EASLEY and KLEINBERG 2010: 434). KAHNEMANN and TVERSKY (1982) provided evidence that individuals do not respond to new data or fresh facts according to the Beyes Rule. Individuals tend to accept more fresh information and to forget the base information gain before the new data arise. Individuals simply ignore the base data. Authors introduced the term “representa­tiveness heuristic.” The heuristic neglects the principle that extremeness of prediction must be moderated by consideration of predictability (KAHNEMANN and TVERSKY 1982: 16). One important outcome is that “intuitive judgment is often biased on predictable manner.” So, some decisions of individuals can be debased and improved (KAHNE­MANN and TVERSKY 1982: 5—1). Based on psychological research of previous authors, DE BONDT and THALER (1985: 12) provide validity on the market level. Individuals overreact to unexpected and dramatic news events. BERNARD (1993, ch. 11) argues that price overreactions to information is generally logically consistent with price under reac­tions to quarterly earnings. Both of these statements contradict the rationality of the mar­ket, as well as the rationality of the financial market.

SHLEIFER and SUMMERS (1990) show an alternative to the classical efficient market paradigm. As assumed before, in reality the arbitrage on the market is limited and not per­fect. In such circumstances the noise trading has a big effect on asset pricing. The price development depends on the behavior of both market participants: arbitrageur and noise trader. The noise must be considered seriously as the advantage for arbitrageur as well as the cost accrued through it. Costs can be a social opportunity cost for resources in order to separate the noise trader from the money, as well the private cost, because the noise makes the return on assets risky (SHLEIFER and SUMMERS 1990: 31). The noise can also nega­tively affect society and the rest of the market participators. The capital stock and con­sumption of economy can be reduced if the magnitude of “noise trading” is relatively high. (De LONG, SHLEIFERS, SUMMERS & WALDMANN 1989: 683). In order to reduce the “noise trading” effect, two actions are proposed: introducing taxes on short-term trad­ing operations and open market operations. However, authors have assumed that such actions could hit the financial market itself more than “noise traders” (De LONG, SHLEIFERS, SUMMERS & WALDMANN 1989: 694).

In the last 1980th the theory of Mean Reversion was introduced. This theory, again, con­tradicts the classical market efficiency theory. Market prices tend to be exaggerated; this trend will be corrected over time. Some exaggerations can lead to the extremes, like the NASDAQ bubble in 2000. POTERBA and SUMMERS (1988) introduced this effect on financial markets and produced evidence of mean reverting behavior. The consistency of this theory was proved two years later by CECCHETTI, LAM & MARK (1990). These authors show that asset returns have a negative autocorrelation caused by fundamental differences in capital availability of market players. Except for price or return, the volume and volatility can show the Mean Reversal behavior as well. STEIN (1989) analyzed the volatility of the S&P index options. The options were selected due to stronger arbitrage control compared with the pure securities (STEIN 1989: 1011). The result of this investiga­tion is that volatility expectations do not form rationally. The investor tends to overreact in the short term, thus the mispricing is not economically significant (STEIN 1989: 1022).

JEGADEESH and TITMAN (1993) report strategies that buy past winners and sell past losers realize significant abnormal returns over the 1965—1989 period. In this work the stock was ranked into deciles. If the stocks were ranked into deciles based on past returns in a medium-term period, the winner portfolio from the top decile continued to outper­form the loser portfolio from the bottom decile in a medium-term period, 6—12 months. This effect, which authors called “momentum,” was derived from physics. In physics, mo­mentum is defined as the product of mass and velocity (MYERS, 2006). The physical mass corresponds to the security volume and velocity of the price movement. The presence of the momentum effect on the stock exchange contradicts the classical rationality theory too. The paper of JEGADEESH and TITMAN (1993) and their momentum theory provided initial motivation for this work and will be discussed later in more detail.

2.2 Behavioral Finance

Further overreaction is documented in the works of ROUWENHORST (1998) and DAN­IEL & TITMAN (1999). From their works a new theory was born, the Financial Behavior Theory. This theory is rooted in decision theory and in social psychology. Several invest­ment strategies exist based on today’s outcome of the behavioral finance MONTIER. One of the sources for overreaction is the overconfidence.

2.2.1 Overconfidence

Humans are naturally overconfident. As an example, “94% of college professors [in the United States] think they do above average work.” From a statistic point of view, this is nonsense (ANDERSON et al. 2012). People overvalue their own experience and knowledge and underestimate their possible failures and troubles. Overconfidence is de­fined as “an overestimation of probabilities for a set of events” (MAHAJAN 1992: p. 330). Overconfidence is present in all of us; as a single factor it will not lead to success in any decision process, but “it is usually celebrated and encouraged” (DITTRICH 2001). The availability of overconfidence also has a positive effect. One hypothesis suggests that it can improve our health (PLOUS 1993).

Another example of human overconfidence is the daily behavior of Swedish drivers. SVENSON (1981) analyzed drivers for their feeling of their own competence versus the average driver. The result is a strong tendency toward overconfidence, being more skillful and less risky than the rest of the group (SVENSON 1981: 146). Similar investigations about U.S. students’ driving capability shows that 82% of students think their driving capa­bility is within the top third of all drivers (DE BONDT and THALER 1995: 389). Most tests prove this overconfidence bias provided by PALLIER et al. (2002) and by ALPERT et al. (1982). The financial market players are not immune to this overconfidence bias. The experiment of DITTRICH et al. (2001) shows that in an investor group at least two thirds of the participants exhibit overconfidence behavior.

Overconfidence is often increased in persons who have a relatively higher information level or more data for analyzing than the average person. However, evidence exists that the same higher level of information does not significantly increase the accuracy (OSKAMP 1965). This notion of more information leading to increased confidence but not to increased ac­curacy was confirmed by the use of the linear model in social decision making by DAWES (1979). Further evidence was provided in a large study by PAESE and SNIEZEIK (1991).

If the information level does not lead to a decrease in overconfidence, how can the meth­odology be improved? PAESE and SNIEZEIK (1991) suggest how overconfidence can be reduced: “An interesting question for future research concerns whether provision of feed­back after each judgment trial would reduce or eliminate the increase in confidence due to practice” (PAESE and SNIEZEIK 1991). Evidence of a positive effect on the decreasing level of overconfidence is provided by DANIEL, HIRSHLEIFER & SUBRAHMANYAM (1999). These authors took meteorology as an example. In meteorology some feedback is expected and is one factor to improve the methodology. Feedback from the financial mar­ket is often unclear, so the overconfidence bias cannot be improved as in meteorology. Without any feedback, investors act inertially (DANIEL, HIRSHLEIFER & SUBRAH­MANYAM: 1998). Such behavior is one of the root causes for the momentum effect on wordwide stock exchanges. According to the work of DANIEL, HIRSHLEIFER & SUBRAHMANYAM (1999), one factor can reduce overconfidence in the financial market: repetitiveness of human tasks. That repetitive tasks can replace the feedback is reported by KAHNEMAN and RIEPE (1998). Bridge players (KEREN: 1987) and racetrack bettors (HAUSCH and ZIEMBA: 1995) benefit from this approach.

In addition to the amount of information, there is one more factor that increases human overconfidence: the degree of difficulty of the question. In the case of a simple question, under confidence was observed (ODEAN 1998) and in the case of difficult questions, people tended to show overconfidence (YATES 1990). The interesting proposal of ODEAN (1998) is the hypothesis that overconfidence is the reason why people trade. Therefore the logical effects of overconfidence are increased market volume and increased market depth. On the flip side, the overconfident trader increases the market volatility and, as importantly, decreases the market efficiency (ODEAN 1998: 1916). Overconfidence will drive an investor to ignore or at least to underestimate the unexpected market signals. In­vestors interpret such signals as failure. On other hand, the expected signals from the mar­ket, even the repetitive signals, will increase the self-attributed bias. Investors overreact in this case. Market signals will not lead to rational behavior anyway, but they will increase the acting, the trading (DANIEL, HIRSHLEIFER & SUBRAHMANYAM: 1999).

Another factor that can potentially increase overconfidence is the capability of humans. Here another positive correlation is observed. More capable humans tend to be overconfi­dent. This fact significantly affects the financial market. Most traders are professional. Their qualification can be judged as above average, which means that not only “noise in­vestors” but also “professional investors” can reduce the market efficiency (ODEAN 1998: 1896). The contributions of professional investors to the volatility and to the reduction of market efficiency was confirmed by SHEFRIN (2000). Even when some investors perform weakly they do not lose their overconfidence; in some it even increases it, as confirmed during experiments provided one year later by DITTRICH et al. (2001).

Survivorship can also potentially influence overconfidence (ODEAN 1998a: 1896). The weak market player must give up and the successful player stays in the market. The success­ful market player tends to feel that his or her success is 100% based on his or her knowledge, qualifications, and capability. Successful players can completely neglect such success factors as luck or chance. The survivorship bias and the resulting absorption in the market was more deeply investigated and discussed in work of GARCIA and GOULD (1993). Additionally, these survivorship biases include investors who look only at the per­formance of a stock index like DAX. The value of the index does not consider the shares of companies that are declaring bankruptcy. The securities that do not perform well are exchanged with better running papers. An example is Deutsche Babcock AG. The securi­ties of this company belonged initially to the DAX index. Today the share price of Babcock Borsig as a follower is 0.01 Euro (BECK 2012). The danger caused by survivorship is the ignoring of failures, which leads to wrong conclusions, and to overconfidence.

Underconfidence probably does not exist because no scientific evidence can be found. However, there is evidence that women act with less overconfidence than men (BAUMEISTER 2010).

2.2.2 Representativeness

In addition to overconfidence, representativeness is another important part of financial behavior theory, and is responsible for market overreaction and for reducing market effi­ciency.

The basic gist of this theory is the human tendency to segregate people, events, or process­es into different groups. Our brains act this way in order to be effective during the deci­sion-making process. Usually we check the attributes of other people, events, or processes and compare them with typical attributes of corresponding groups. If some attributes are similar, we usually judge that other unknown attributes will be close to typical properties of the chosen group.

KAHNEMAN and TVERSKY (1972) introduced the representativeness heuristic. The representativeness heuristic can be used for judging some event possibility. The authors defined representativeness as “the degree to which [an event] is similar in essential charac­teristics to its parent population, and reflects the salient features of the process by which it is generated.” By using different examples the authors found out that by using this heuris­tic, wrong expectations of probability can occur (KAHNEMAN and TVERSKY 1972, 1973). Further evidence that “people commonly violate basic rule of probability” is provid­ed by GAVANSKI and ROSKOS-EWALDSEN (1991). According to these authors, even the combination of events instead of a single event will not lead to higher probability.

Representativeness can also affect the stock exchange. When the majority of traders believe that a security belongs to the group of securities acting in the growth market, the price of that security can jump within a short time. The fundamental values and prospective figures like future cash flow are often neglected. The same effect can occur with securities that came from an IPO. The expectation that securities from IPOs will perform better in the short term was present in end of 1990. Based on experience, the relevant group performed well in the past (GUO 2002: 67). The first assumption is that heuristic representativeness can lead to irrational decision making in the financial market was provided by ARROW (1982: 5). The “illusion of validity” is a property, not an attitude, only of temporary actors in the financial market. This property also belongs to the professional investors like from JP MORGANS (SHEFRIN 200: 14).

The representativeness bias can have both a positive and negative affect on the stock ex­change. Investors interpret the short-term stock movement as representative of a trend, so the momentum effect can be easy initiated. In addition, permanently changed stock direc­tion is interpreted as reverting. The positive, negative, or neutral sentiment of investors can push or pull the stock price The Investor-Sentiment model was developed in order to ex­plain the market over- and under reaction (BARBERIS et al. 1998). The Sentiment Index and different sentiment indicators were introduced. The sentiment of investors is consid­ered to be a systematic risk and is responsible for the volatility of the stock exchange (VLAD 2008).

Interestingly, an investigation shows that “representativeness has no place in describing stock return behavior (and also perhaps investor behavior)” (CHAN et al. 2002: 22). These authors state that the multi-month momentum exists but this effect does not reflect behav­ior theory, and the existing predictability of returns is “an interesting and problematic phe­nomenon.”

2.2.3 Other behavioral biases and models


The availability bias is the possibility of judging certain events based on experience or events being imagined as examples. Event examples are quickly and easily imagined and can be extrapolated for similar event probabilities in the future (TVERSKY and KAHNEMANN, 1973). An example of availability bias is often demonstrated in conversa­tions among fishermen. To answer the question about what kind of fish is most prevalent in a certain lake, a fisherman normally recalls all of his catches and information from his friends in order to produce a conclusion. The conclusion could be close to the real proba­bility, but in most of cases the judgment is not accurate enough. Availability bias in the financial market can be distinguished by two aspects (KLINGER and KUDRYAVTSEV 2010): outcome availability and risk availability. Authors find out the availability bias in investors’ behavior when they react to analyst recommendations. The positive (negative) price reaction of a security based on an analyst recommendation upgrades (downgrades) more strongly when accompanied with a positive (negative) market index return. The fact that investors forecast and their investments are affected by the availability bias was also shown by LEE et al. (2008).

Disposition Effect

This effect describes the willingness of investors to sell their winning investment quicker than a losing investment. The first analysis and evidence of this effect was provided by SHEFRIN and STATMAN (1985). The result of the analysis is that the long-term hold of losers in a portfolio is not related to taxation. Additionally, the authors provide evidence that more redemption occurs during the months when the financial market over performed than during the under-performing months. ODEAN (1998b) confirmed the hypothesis of the disposition effect and developed a system for measuring the disposition effect. Today’s famous terms “paper gain” and “paper loss” were introduced. Investors sometimes need assurance when their investment decisions are not successful. The “only paper loss” is just a term to satisfy own’s ego. The self-justification factor as a basis for the disposition effect was documented by WEBER and CAMERER (1998) in an experiment. In the laboratory experiment investors were separated into two groups. One group could trade freely but the other group was restricted to selling all stocks at the end of the investment round. After selling the same members of the second group were able to buy all of their securities back. Transaction costs were zero. According to the conventional economic theory the behavior of both groups can be judged as similar. But significant differences were found. The group with the automatically sell restriction was reluctant to buy the “loser stock” back in order to keep the same balance as the free traded group (WEBER and CAMERER 1998). The con­clusion of the authors is: “It appears that while subject are reluctant to have their hopes of getting their money back extinguished, they are especially reluctant to blow out the flame of hope with their own breath” (page 177).

Feedback Model

The “feedback model” was investigated using several samples by SHILLER (2003). The feedback model explains the housing bubbles as a process of positive or negative price movements that generate expectations of continuous trend. This expectation pushes the price again with a similar feedback loop. Such feedback mechanisms can create “informa­tional cascades” explained by WEIMANN (2012). The investors who interpret the availa­ble facts as negative for a certain investment are ready to invest anyway if they see other individuals who invest or tend to invest. This behavior is called “herding,” taken from bi- sons’ behavior during peregrination. The herding in economics was introduced by MAC- KAY (1841) using the South Sea Company bubble in 1711—1720 as an example. Even the effect of herding looks quite irrational; the “herding” behavior in its basic form is not irra­tional (DEVENOW and WELCH 1996). The feedback models and herding can be consid­ered more a root cause for the momentum effect on financial markets. The positive feed­back model, first mentioned by De LONG (1990), can explain the strong momentum ef­fect during a bullish market. VLAD (2008) confirmed the finding of De LONG et al. (1990) and the positive feedback effect and its influence on the long-term asset pricing model.

The consideration of herding today is important due to the behavior of fund managers. The institution of long-term companies increased from 7.2% to over 50% in 2012 (NYSE 2012). The fund managers tend to imitate the trading decisions of other managers. The reason for this behavior is risk. It is better to be wrong with something than to take a risk and fail when the majority will celebrate its success. Copies of investment patterns will rein­force the positive and negative trends (DASGUPTA 2006).


People judge some results based on initial figures, first calculations, even using a problem definition. The initial data can be different. Different available data for several groups of people can lead to different judgments of the final result (TVERSKY and KAHNEMAN 1974). This heuristic helps to find a quick next action but is insufficient for problem solv­ing because some adjustments during the actual process are needed. In some cases adjust­ments are not sufficient (SLOVIC and LICHTENSTEIN 1971). Some initial information can be irrelevant for the final result. In the case of losses, an investor will tend to wait for a “break even” price instead to realize the losses. The anchor is the initial investment. An­choring is also a property of the simple consumer. When selecting a used car, some people simply look at the price versus the production year, without paying attention to the quality and maintenance of the engine. Here, the production year is the anchoring value that will sometimes not influence the quality of the offered car.

Other biases that can potentially influence investor behavior and reduce market efficiency are gamblers fallacy, framing, loss aversion, regret aversion, mental accounting, and self­control. The details will be not described here; the roots are in the theory of psychology.

Many works have covered the relatively new field of behavior theory in the past decades. Experience from psychology, social science, and economics are needed in order to con­struct a framework for the new theory. The process could be long in order to complete the theory, but the non-perfect theory might find a market pattern promising abnormal re­turns. When constructing behavior theory, investment decisions become more predictable. As a result, the abnormal returns would disappear.

The next few chapters will discuss one of the effects of behavior theory: the momentum effect and a strategy based on this effect.

3 Momentum Effect and Momentum Strategy as Part of Market Anomalies

All previously discussed biases based on simple human psychology can lead to a momen­tum effect on the stock exchange. Momentum effect means that the past winner performs well in the near future and the past loser shows low performance (JEGADEESH and TITMAN 1993). Some people follow the herd instinct without any consideration of fun­damental values or news. The only factor they focus on is performance in the past months. The initiator of such herd behavior could be initiated even by fundamental data (CUTLER, POTERBA and SUMMERS 1990). A human’s well-being is reinforced if his or her in­vestment decision corresponds to the majority in that particular market. The decision to investment or uninvest is always done with some amount of uncertainty. This uncertainty can be reduced if decisions are made in line with current trends.

3.1 CAPM and “abnormal return”

The following momentum strategy or contrarian strategy promises to earn abnormal re­turn. Before going into a detailed explanation of each investment strategy, the definition of “abnormal return” is necessary.

After the introduction of the Markowitz Diversification Theory (MARKOWITZ 1952), in the decades that followed the so-called Capital Asset Pricing Model (CAPM) was devel­oped by SHARPE (1962), LINTNER (1965), and BLACK (1972).

In his both fundamental works, Harry MARKOWITZ (1952, 1959) introduced the “mean variance efficient portfolio.” This work was awarded the Alfred Nobel memorial prize in Economic Science in 1990 by the Swedish Academy of Science (BADGE 2007: 472). The theory describes the weight of a portfolio in order to reach the optimum tradeoff between mean and variance. The mean is a figure corresponding to the portfolio’s profit, and the variance is a figure reproducing the investment risk. This tradeoff allows investors to real­ize their target of maximizing their investment return by considering certain investment risks.

CAPM makes a mathematical expression of “mean variance efficient portfolio” in order to predict or to calculate the price of an asset with consideration of its market risk. This pre­diction is possible due to so-called “equilibrium of all risky assets” as a function of covari­ance of these assets (JONES 2010: 221).

The core of CAPM is SML or CML, the Security Market Line or Capital Market Line. The mathematical expression of SML/CML is as follows (LASHER 2008: 398):

Abbildung in dieser Leseprobe nicht enthalten

The term [Abbildung in dieser Leseprobe nicht enthalten] is called Stock X’s Risk Premium and term [Abbildung in dieser Leseprobe nicht enthalten] is Market Risk Premium. The Market Risk Premium indicates the average degree of risk acceptance by investors. The Stock X’s Risk Premium shows Risk Premium multiplied by beta factor of X securities (LASHER 2008: 398).

The visual understanding of SML/CML as a direct correlation between Risk and Return is provided in Figure 1. This figure was provided by one of the fathers of the Capital Asset Pricing Model, SHARPE (1964).

Abbildung in dieser Leseprobe nicht enthalten

Figure 1. SML/CML. Source: SHARPE (1964)

The sharp ratio, often called Si of SML/CML, is often using to compare and evaluate dif­ferent portfolios. The portfolio with highest sharp value normally performs better. The standard deviation of such portfolios is smaller (mathematical denominator) and the differ­ence between return of portfolio and risk free return is higher (mathematical numerator) (WILKENS and ZHU 2001).

As the “abnormal returns,” which can be called the returns, the expected value exceeds the amount calculated by CAPM.

Note that CAPM is an abstraction of reality because it simplifies the investor and asset by several assumptions, imperfection of market excluded (GRINBLATT and TITMAN 2002):

a) Information has no cost and is distributed to all players in the market, investors, homogeneously. Therefore investors have similar expectations on the return of their investments.
b) Transactions have no cost. Additionally, no restrictions on transactions exist: long- and short-term positions are possible, time is unlimited, quantity of assets is unlim­ited, and taxes are not available.
c) CAPM allows for the existence of risk-free assets. By using these types of assets, investors can borrow or lend money.
d) Individuals tend to expect the maximum out of their investments and at the same time a minimum amount of investment risk.
e) All assets contain sub-assets.

The assumption of market perfection and similar expectations and behaviors of investors excludes any possibility to bite the market performance.

CAPM is popular because the model is simple. Everyone can intuitive understand the rela­tionship between return and investment risk. However, how far the CAPM is from real market dynamics is described in the work of FAMA and FRENCH (1992). These authors analyzed the historical data and found no correlation between returns and beta factors (risk). Therefore, FAMA and FRENCH (1992) introduced the so-called “three-factor mod­el.” The three-factor model considers not only risk but also size and value of an individual stock in order to predict its pricing.

Note also that a more realistic model called Arbitrage Pricing Theory (APT) was developed by ROSS (1976). Some simplifications and restrictions introduced by CAPM are neglected in APT. One example is that investors potentially hold only tradable and available securi­ties. APT is considered a “supply side model” because the risk or beta factors of securities depend on economic factors. CAPM is considered a “demand side” model. In this model, investors are considered “consumers” of assets (VARIAN 1993).

3.2 Contrarian strategy

“It is impossible to produce a superior performance unless you do something different from the majority” (KRASS 1999). This is one of the best investment maxims of Sir John Templeton that describes the contrarian investment strategy. The dream of all investors is to beat the index, to get the so-called “abnormal return,” to earn money. One relatively simple but working strategy is the contrarian strategy.

The contrarian strategy is opposite to the momentum strategy. This strategy, like the mo­mentum strategy, considers the past performance of a certain security in order to derive the future price development. Contrarian strategy contradicts, just like the momentum strategy, the classical market efficiency theory and the random walking model.

The first publications about the contrarian strategy appear in 1970 when the financial be­havior theory was born. First, DEBONDT and THALER in 1985 provided evidence that the contrarian strategy can earn abnormal profits. The data used came from the NYSE from January 1926 until December 1982. The formation period proposed in this paper is three to five years and a holding time of 3 years. The result of this investigation found that the securities that underperformed in the past years earned 19.6% more than the market average. The past winners showed 5%o lower performance than the market average. Most of the returns are realized in January (DEBONDT and THALER 1987). This effect be­came known as the “January Anomaly.” The “January Anomaly” works every year; it also worked injanuary 2013 (SCHULZ 2013). Additionally, the authors found that the contrar­ian strategy works only in the long term. In the short term, within a one-year time frame, the contrarian strategy shows no abnormal returns (DEBONDT and THALER 1985).

When writing about the seasonable effect of the “January Anomaly,” the “Good Day Sun­shine” anomaly must also be mentioned here. HIRSHLEIFER and SHUMWAY (2001) investigated stock shares in the time frame of 1982 and 1997 and their potential dependen­cy on weather conditions: sun, rain, or snow. The results were stunning. In the case of sun­shine during the morning hours, the possibility for positive stock development was high. These results remain in contradiction to rational price setting theory.

Similar findings confirming the contrarian strategy were reported by CHOPRA, LAKONISHOK & RITTER (1992). The authors confirmed the long-term frame for this strategy and the January seasonal dependency of returns. Additional studies found that such overreaction is more available for securities of smaller companies than for larger ones. This fact validates the hypothesis that market efficiency is higher in markets with higher volume and lower in markets with lower volume.

The return of contrarian investment is significantly lower in case of using non-January months. BALL et al. (1995) used end of June data instead of proposed January data. The result was crushing: return becomes negative. The problem is the using of low price looser stock. The discrepancy in rates of such securities is huge.

The statistical significance of long-term investigations is critical for misunderstanding be­cause the significance is not always observable. KOTHARI and WARNER (1996) pro­posed to use the bootstrap procedure in order to describe the reliability of long-term stud­ies. The authors offered the hypothesis of misspecification in previous studies. Extreme caution must be used in long-term investigations. The cause of statistical misspecification and big discrepancy of long-term returns is survival bias, as explained earlier.

KRYZANOWSKI and ZHANG (1992) applied the suggested contrarian strategy to the Canadian financial market. The result was that no significant returns can be accumulated. No price reversal was found, but price continuation was discovered. The authors proposed a hypothesis that the contrarian strategy works only in the U.S. stock market.

CONRAD and KAUL (1993) suggested a new measurement proposal of abnormal returns by using the contrarian method. The authors found an upward bias in the previous studies. These calculations were done by cumulating the returns in single periods (monthly). Not only were “true” returns cumulated, “but also the upward bias in single period returns in­duced by measurement errors.” Instead of the cumulative method, CONRAD and KAUL proposed using the holding period return method. Next, more evidence based on interna­tional stock data were shown by BAYTAS and CAKICI (1999). Data from seven industrial countries were analyzed using the holding period return method proposed by CONRAD and KAUL (1993): United States, Canada, United Kingdom, Germany, France, Japan, and Italy. Except for the United States, the overreaction was found in all countries. The evi­dence from Canada was notably weak.

One interesting finding was documented by CONRAD and KAUL (1993). The initial find­ings of DEBONDT and THALER (1985) were confirmed with comments that such ab­normal returns are based on special situation in the U.S. stock market during the years 1926—1947. During other periods no reversal returns can be detected. The special situation of the time before and during World War II on U.S. stock was also documented in the work of JONES (1993). JONES (1993) used for his investigation the non-overlapping nine-year period.


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Evaluation of the Momentum Strategy on the German Stock Exchange
An empirical analysis of the DAX and MDAX
University of Applied Sciences Essen
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evaluation, momentum, strategy, german, stock, exchange, mdax
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Eugen Stumpf (Author), 2013, Evaluation of the Momentum Strategy on the German Stock Exchange, Munich, GRIN Verlag, https://www.grin.com/document/230538


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