This thesis focuses on fractal analysis of economic time series. Chapter One introduces fractal analysis as a method of exploring time series and gathers information about progress and current state of understanding in this field. Chapter Two focuses on design and development of computer software, which will calculate selected fractal indices. Chapter Three is experimental and shows the results and discussion of economic time series (popular stock market indexes and currency exchange rate) analysis that have been obtained from the software developed in Chapter Two.

The Turtle Trading Rules was a successful trend-following trading strategy for commodities in the 1980s but has lost recognition in recent days. The strategy revolved around rules for entering and exiting trades as well as position sizing for each trade. The rules was based on the fundamental aim to capture market trends while at the same time maintaining a controlled risk exposure. This thesis aims to revise the Turtle Trading Rules, here applied on major market indexes, and to examine its viability through different financial metrics. This is done by first implementing the aforementioned trading strategy to the indexes, and later by synthesizing market data through Geometric Brownian Motions. The latter primarily to examine how the strategy perform in different financial environments, what market traits favor the strategy, and to complement the previous examination without altering the core principles of the Turtle Trading Rules. The results suggest that the revised rules for major market indexes is not viable. This because of the poor return, the highest achieved 20-year return and average annual return was 25.1 % and 1.4% respectively (without taking trading fees into account). Furthermore, the strategy applied on synthetic data suggests that favorable traits are highly cyclical data with low volatility, which seldom is the case for real financial time series. The results further indicate that the main issue lies in the rules not being able to distinguish noise from actual entry and exit triggers. Moreover, the drawdown further suggest that it is the exit rather than the entry rules that are to blame for the poor performance during the cycle of a trade. / Turtle Trading-reglerna var en framgångsrik trendföljande handelsstrategi för råvaror på 1980- talet men har sedan dess tappat i populäritet. Strategin kretsade kring regler för inträde och utträde ur ordrar samt kring positionsstorleken för varje order. Reglerna byggde på det grundläggande syftet att fånga marknadstrender och samtidigt upprätthålla en kontrollerad riskexponering. Den här avhandlingen syftar till att revidera Turtle Trading-reglerna, som här tillämpas på utvalda marknadsindex, och att undersöka dess lönsamhet genom olika finansiella mått. Detta görs genom att först implementera den tidigare nämnda handelsstrategin till indexen, och senare genom att syntetisera marknadsdata genom geometriska brownska rörelser (Geometric Brownian Motions). Det senare för att i första hand undersöka hur strategin fungerar i olika finansiella miljöer, vilka marknadsdrag som gynnar strategin, och för att komplettera den tidigare granskningen utan att ändra grundprinciperna i Turtle Trading-reglerna. Resultaten tyder på att de reviderade reglerna för marknadsindexen inte är tillräckligt lönsamma. Detta på grund av den låga avkastningen, den högst observerade 20-årsavkastningen och den genomsnittliga årliga avkastningen var 25,1 % respektive 1,4% (utan hänsyn till handelsavgifter). Dessutom antyds när strategin tillämpas på syntetiska data att tydliga cykliska variationer samt låg volatilitet är fördelaktiga egenskaper, vilket sällan är fallet för reella finansiella tidsserier. Resultatet indikerade vidare att grundproblemet ligger i att reglerna inte kan skilja brus i datan från faktiska inträde och exit triggers. Dessutom tyder drawdown-graferna på att det är exit snarare än inträdesreglerna som är orsaken till det dåliga resultatet i utförandet av köp- och säljprocessen.

Titel: Portföljförvaltarens kamp mot index Syftet: Syftet med denna studie är att beskriva och analysera aktiv fondförvaltning genomriskjusterad avkastning. Metod: En kvantitativ studie har genomförts för att uppfylla syftet och besvara studiensfrågeställning för undersökningsperioden 2018–2022. Riskjusterade prestationsmåtten somanvänds är jensens alfa, sharpe- och treynorkvoten. Empiriskt resultat: Studien är baserad på 21 aktivt förvaltade fonder som är registrerad iSverige. Vidare har dessa fonder placeringsinriktning på industrisektorn samt har 80% av sittinnehav på svenska aktier. Slutsats: Mer än hälften av alla fonder genererade ett positivt jensens alfa. Dock visar etttvåsidigt t-test att inget alfavärde var statistiskt signifikant med både 90% och 95%konfidensgrad.Nyckelord: Riskjusterad avkastning, Aktiv fondförvaltning, Treynokvot, Sharpekvot, Jensensalfa, Marknadsindex, Capital Asset Pricing Model (CAPM) och Modern Portföljteori. / Title: Fund manager’s battle against index. Purpose: The purpose of this study is to describe and analyze active funds through riskadjusted returns. Methodology: The study uses a quantitative research method with data from secondarysources that contains fund’s net asset value (NAV). The research period of this study is 2018 to 2022. The study uses jensens alpha, treynor- and sharperatio as risk adjusted measurements. Empirical foundation: This study uses 21 active mutual funds that are registered in Sweden.The mutual funds that were obtained has an investment strategy that focuses on industry.Furthermore, these mutual funds have 80% holdings in Swedish stocks. Conclusion: More than half of the active mutual funds generated a positive jensens alpha.However, according to a two-sided t-test of a 90% and 95% confidence level, none of themutual fund’s alpha showed to be statistically significant and therefore no conclusions weremade.

Diese Dissertation zielt darauf ab, ein besseres Verständnis für Anomalien und Insiderhandel zu schaffen, sowie die Verfügbarkeit von qualitativ hochwertigen Daten für den deutschen Aktienmarkt zu verbessern. Der erste Aufsatz beinhaltet eine verzerrungsfreie Zeitreihe von monatlichen Renditen deutscher Aktien für die Jahre 1954 bis 2013, die auf der Basis stabiler Regeln berechnet und gut dokumentiert ist. Im Weiteren enthält der Aufsatz eine detaillierte Beschreibung des deutschen Aktienmarktes und dessen Besonderheiten, insbesondere im Vergleich zu den USA. Der zweite Aufsatz zeigt am Beispiel des Fama/French Drei-Faktoren-Modells die Probleme auf, die Anbieter und Nutzer von Faktorendaten haben, die sich nicht auf die USA beziehen. Die empirische Analyse von sieben Faktorensets für Deutschland zeigt, dass die Übernahme von Faktormodellen in einen anderen Kapitalmarkt eine komplexe Thematik ist. Der Aufsatz gibt Anregungen für Nutzer und Anbieter von Faktorensets und zeigt, wie die Wahl des Faktorensets das Ergebnis einer Studie beeinflussen kann. Im dritten Aufsatz werden verschiedene zyklische und antizyklische Handelsstrategien hinsichtlich ihrer Performance im deutschen Aktienmarkt untersucht. Von den untersuchten Strategien erscheint nur Momentum konsequent abnormale Renditen zu erzielen, dies auch nach Transaktionskosten. Die vierte Arbeit untersucht öffentlich bekannt gegebene Aktientransaktionen von Insidern börsennotierter deutscher Unternehmen. Der Aufsatz zeigt, dass Insider von TecDAX-Unternehmen und ihre Imitatoren hohe und statistisch signifikante abnormale Renditen erzielen. Insgesamt zeigt die Dissertation, dass methodische Variationen, die Verwendung verschiedener Untersuchungsdesigns, die Datenqualität und die Sorgfalt beim Erstellen von empirischen Analysen zur Beurteilung der Robustheit und der Stabilität der Ergebnisse unerlässlich sind. Der deutsche Aktienmarkt scheint effizienter zu sein als bisherigere Studien typischerweise nahelegen. / This doctoral thesis aims to contribute to a better understanding of stock market anomalies and insider trading as well as to improve the availability of high quality data for the German stock market. The first paper provides a sixty-year time series of monthly returns on German stocks that is constructed on the basis of stable rules, is well documented, includes all return components, and is free of biases. The paper also contains a detailed description of the German stock market, its peculiarities, regulation and differences as compared to the U.S. The second paper uses the Fama/French three-factor model as an example to point out the problems that providers and users of non-U.S factor data sets face. The empirical analysis of seven different factor data sets available for Germany shows that exporting a specific factor model from the U.S. to another capital market is neither an easy nor well-defined task. The paper gives suggestions to users and creators of factor sets and shows how the choice of a factor set affects the result of an empirical study. The third paper provides evidence on how various contrarian, momentum and seasonality strategies perform in the German stock market. Among these strategies, only momentum investing appears to earn persistently non-zero returns, even after transaction costs. The fourth paper studies publicly disclosed stock transactions by insiders of listed German firms. The paper finds that insiders of TecDAX firms earn large and statistically significant abnormal returns net of transaction costs; for DAX insiders they are indistinguishable from zero. Overall, this thesis illustrates that methodological variations, the use of different specifications, data quality and care when preparing empirical analyses is essential in the assessment of the robustness and stability of results. In sum, the German stock market appears to be more efficient than previous studies have typically suggested.

Investors constantly seek information that provides an edge over the market. One of the conventional methods is to find factors which can predict asset returns. In this study we improve the Fama and French Five-Factor model with Regime-Switches, student's t distributions and copula dependencies. We also add price momentum as a sixth factor and add a one-day lag to the factors. The Regime-Switches are obtained from a Hidden Markov Model with conditional Student's t distributions. For the return process we use factor data as input, Student's t distributed residuals, and Student's t copula dependencies. To fit the copulas, we develop a novel approach based on the Expectation-Maximisation algorithm. The results are promising as the quantiles for most of the portfolios show a good fit to the theoretical quantiles. Using a sophisticated Stochastic Programming model, we back-test the predictive power over a 26 year period out-of-sample. Furthermore we analyse the performance of different factors during different market regimes.