This paper shows the existence of the size effect in the cryptocurrency market. The size effect is a market phenomenon observed in the stock market in which smaller assets outperform larger assets. Recent literature has revealed the size effect in other financial markets as well. In order to explain the size effect, this paper proposes a general quantitative theory that supports its existence in any financial markets under specific conditions. Furthermore, the paper tests for the size effect in the cryptocurrency market using daily price data from April 2013 to April 2018. The paper finds a statistically significant size effect across the cryptocurrency market during the sample period. In the process, we test a profitable pair-trading strategy that involves opening a short position on the higher rank (larger assets) and opening a long position on the lower rank (smaller assets) of the cryptocurrency market. Based on our findings, we discuss the implications on modern finance, specifically on the subjects of Efficient Market Hypothesis and asset pricing models.

Bakgrund: Målet med de flesta investeringar är att nå en hög avkastning till låg risk. Tidigare forskning har identifierat möjligheter till att överträffa marknaden vilket motsäger hypotesen om den effektiva marknaden. Investeringar i småbolag har blivit alltmer attraktivt de senaste åren vilket lyfter frågan angående hur en investering i dessa aktier kan genomföras på ett framgångsrikt sätt. Småbolagsaktier, och framförallt de allra minsta aktierna sett till marknadsvärde, förknippas ofta med högre risk. Detta medför att det är av relevans att undersöka huruvida en riskjusterad överavkastning är möjlig vid en applicering av dessa med befintliga investeringsstrategier. Syfte: Syftet med denna uppsats är att analysera huruvida det existerar en småbolagseffekt på den svenska aktiemarknaden mellan 2007-2019. Studien syftar även till att undersöka om det går att generera riskjusterad överavkastning vid investeringar i småbolagsaktier genom att kombinera dessa med alternativa investeringsstrategier som momentumeffekten samt relativvärdering i form av bolag med låga EV/EBITDA- multiplar. Metod: Studien har genomförts med en kvantitativ metod och en deduktiv ansats. Nio portföljer har konstruerats utefter olika bolagsstorlekar samt olika investeringsstrategier under tidsperioden 2007-2019 på den svenska aktiemarknaden. Dessa portföljer har sedan utvärderats sett till både avkastning samt riskjusterad avkastning för att slutligen testas statistiskt genom parata t-test. Slutsats: En småbolagseffekt kunde inte observeras på den svenska aktiemarknaden under den studerade tidsperioden. De portföljer som baserades på bolagen med lägst marknadsvärde presterade en signifikant lägre avkastning än jämförelseindexet. Vid en applicering av momentumeffekten samt låga EV/EBITDA- multiplar på småbolag kunde däremot fyra av fyra portföljer observeras generera en riskjusterad överavkastning relativt jämförelseindexet. Denna överavkastning kunde dock inte säkerställas statistiskt och skulle därmed kunna vara slumpmässig. / Background: The goal of most investments is to achieve a high return at a low risk. Previous research has identified opportunities to exceed the market, which contradicts the efficient-market hypothesis. Investments in small enterprises have become increasingly popular in recent years, which raises the question of how an investment on these markets can be done successfully. Small company shares, and especially the smallest shares in terms of market value, are often associated with higher risk. This means that a study that investigates whether a risk-adjusted excess return is possible with the application of existing investment strategies is of relevance. Purpose: The aim of this study is to analyze whether there exists a small firm effect on the Swedish stock market between the years 2007-2019. The study also aims to investigate whether it is possible to generate risk-adjusted excess returns when investing in small companies and combine these investments with alternative strategies such as the momentum effect and relative valuation in terms of companies with low EV / EBITDA multiples. Methodology: The study was conducted with a quantitative methodology and a deductive design. Nine portfolios were designed with different company sizes and based on different investment strategies during the period 2007-2019 on the Swedish stock market. These portfolios have then been evaluated in terms of both returns and risk-adjusted returns and the results were then finally statistically tested through the implement of parwise t-tests. Conclusion: A small firm effect could not be observed on the Swedish stock market during the examined time period. The portfolios based on the companies with the lowest market value generated a significantly lower return than the benchmark index. Meanwhile, when applying the momentum effect and the strategy of low EV/EBITDA multiples on small companies, four out of four portfolios were found to generate a risk-adjusted excess return relative to the benchmark index. However, this excess return could not be statistically proven and could thus be the result of randomness.

Bakgrund: Småbolagseffekten påvisades först av Banz (1981) och Reinganum (1981) som kom fram tillatt småbolag genererade högre avkastning än stora bolag under samma period. Effekten syntes även stabil över tiden vilket ej är förenligt med Capital Asset Pricing Model (CAPM) och den effektiva marknadshypotesen (EMH). Syfte: Syftet med denna uppsats är att undersöka om det finns någon påvisbar småbolagseffekt påNasdaq OMX Stockholm och huruvida den i så fall har varit konstant under studieperioden. Vidare syftar studien till att undersöka huruvida relativvärdering av småbolagsaktier framgångsrikt kan användas för att generera överavkastning. Metod: Studien baseras på en kvantitativ metodansats med ett deduktivt angreppssätt. Behövd datasamlas in och sammanställs för att sedan användas för att skapa portföljer som studeras och analyseras baserat på prestation. Slutsats: Studien  har  ej  kunnat  påvisa  en  småbolagseffekt  under  hela  studieperioden.  Underhögkonjunktur har dock en småbolagseffekt kunnat påvisas. Vidare har studien kunnat visa att relativvärdering av småbolagsaktier genererar både absolut och riskjusterad överavkastning jämfört med studiens småbolagsportfölj och marknadsindex (AFGX). Så kallade värdebolag, det vill säga bolag med låga värden på P/BV-, P/E- och P/S-talen, är de som genererat högstavkastning. / Background: The small firm-effect was first demonstrated by Banz (1981) and Reinganum (1981) who found that small caps generated higher returns than large companies during the same period. The effect also seemed stable over time, which is not compatible with the Capital Asset Pricing Model (CAPM) and the efficient market hypothesis (EMH). Aim: The purpose of this study is to examine whether there is any evidence of a small firm-effect on Nasdaq OMX Stockholm and whether it in such case has been constant over the study period. Furthermore, the study aims to examine whether relative valuation of small caps can be successfully used to generate excess returns. Methodology: The study is based on a quantitative method with a deductive approach. The required data is collected and compiled and then used to create portfolios which are then studied and analyzed based on their respective performance. Results: The study has not been able to detect a small firm-effect throughout the study period. During the boom, however, a small firm-effect could be detected. Furthermore, this study has shown that relative valuation of small caps generates both absolute and risk adjusted excess returns compared to the market index (AFGX). So called value stocks, companies with low values on the P/BV, P/E and P/S multiples, are the ones that generated the highest returns.

En god inblick i den ekonomiska marknaden leder till ett gynnsamt läge från vilket vi kan maximera avkastningen på våra investeringar. Är det möjligt att genomföra en sådan typ av investering sett till endast bolagens storlek? Ett flertal studier har genomförts kring småbolagseffekten som en anomali på kapitalmarknaden. Effekten innebär att småbolag skulle generera en högre procentuell avkastning än storbolag under samma tidsperiod, vilket inte går i linje med vad den effektiva marknadshypotesen påstår kring kapitalmarknaden. Avsikten med denna undersökning är att analysera huruvida detta stämmer eller ej. Syftet med studien är att analysera om det förekommer en mikrobolagseffekt på den svenska aktiemarknaden under åren 2005-2014, det vill säga en anomali med extremare utfall av småbolagseffekten. Vi har använt oss av en kvantitativ statistisk analys för att mäta de genomsnittliga avkastningarna mellan de tre olika portföljer vi skapat bestående av bolag från Large Cap, Small Cap och Aktietorget. Tre hypoteser är testade och resultatet är analyserat med hjälp utav ett statistiskt t-test i programmet SPSS. Studiens resultat är att det inte går att påvisa någon signifikant skillnad i avkastningen mellan storbolag, småbolag och mikrobolag under den givna tidsperioden. Inte heller under delperioder har det kunnat påvisas någon statistisk skillnad. / A good insight in the economic market leads to a favorable position from which we can maximize the profits of our investments. Is it possible to make such investments with regards only to the size of the companies we are considering? Numerous studies have been made on the small firm effect as an anomaly of the capital market. The effect supposedly tells us that, given the same period of time, small companies generates a higher percentage return than large companies. This contradicts the Efficient-market hypothesis, and the purpose of this research is to analyze whether this could be true, or not. The research study is made with regards to micro-size companies in the Swedish capital market during the years 2005-2014, thus, this is an extreme version of the small firm effect. A quantitative statistical analysis is used to measure the average return of three different stock portfolios; Large Cap, Small Cap and Aktietorget. Three different hypothesis are tested and the results analyzed with the help of statistical T-tests in SPSS are used. The results of the study is that there is no solid statistical proof that there is a difference in profit between the three different markets during the time period. Nor could an effect be seen during any smaller time period within the given time frame.

The question many investors ask is whether or not it is possible to beat the market andearn money by being active on the stock market. In efficient markets this should not be possible, but several researches have come up with strategies that prove the opposite. There are certain market movements that cannot be explained by the arguments of the traditional efficient market hypothesis and such market movements are in the standard finance theory called anomalies. Two well-known anomalies are the P/E effect and the small firm effect. The P/E effect means that portfolios with low P/E stocks attain higher average risk-adjusted returns than portfolios with high P/E stocks. Similarly, the small firm effect means that companies with small market capitalization earn higher return than those with large market capitalization. Even though these anomalies were discovered in the US, they occur on other markets as well. However, most of the studies regarding these have focused on developed markets. Therefore, the focus in this study has been on emerging markets, more specifically the Baltic market. The problem we aimed to answer with this study is whether or not it is possible to attain abnormal returns on the Baltic stock market by using the P/E effect or the small firm effect. Further on, we found it interesting to investigate which one of the two anomalies that is the best investment strategy. By doing this, we have also been able examine if the Baltic market is efficient or not. The study investigates all listed firms (both active and dead) with available data on Nasdaq OMX Baltic between the years 2000-2014. There are two different samples, a P/E sample and a market capitalization sample. The firms in the samples are ranked and grouped into portfolios and then tested to see if there is significant evidence of the existence of the P/E effect and the small firm effect. The results of the tests show that the Baltic market is not completely efficient, since statistical support was found for the small firm effect. This implies that it is possible to attain abnormal returns on the Baltic market by investing in small capitalization stocks. However, the tests showed no significant evidence of the P/E effect. For this reason, with the assumptions made, we recommend the small firm effect as an investment strategy on the Baltic stock market.

One could argue that the most discussed topic in finance is whether or not it is possible to “beat the market”. Even though many people claim to do this, there is little evidence to support the idea that one can consistently beat the market over a long period of time. There are indeed several examples of investors who have managed to outperform the market consistently for a long time, but the efforts of these individuals or institutions could by many be considered to be pure luck. One of the many strategies that have been evaluated by several researchers and is said to generate a risk adjusted return greater than that of the market, is one based on the P/E-effect. This strategy is based on the financial ratio P/E – price divided by earnings – and used by constructing portfolios consisting of stocks with low P/E ratios. Several studies have confirmed the existence of the P/E-effect on various stock markets around the world and over different time periods. On the Swedish market, however, few studies have generated the same results. Most of these studies can be considered to be insufficient with regards to sample sizes and methods, spawning a need for more extensive studies. We have examined the P/E strategy on the Swedish Stock Exchange (SSE) between 2004 and 2012. The sample included 358 companies (excluding financial companies) with available necessary data. The stocks were divided into five portfolios based on their yearly P/E ratios (low to high), upon which the monthly returns of the individual stocks were calculated using a logarithmic formula. The returns were also risk adjusted using the Capital Asset Pricing Model (CAPM), followed by a regression analysis to see if possible abnormal returns could be considered to be statistically significant for the examined time period. The results of our study indicate that the P/E effect is not present on the Swedish Stock Exchange during the examined time period, and we therefore conclude that it was not possible to utilize a strategy based on the P/E effect between 2004 and 2012 in order to achieve an abnormal return. The results can be used to argue that the Swedish stock market is more efficient than for example the U.S. stock market where the P/E effect has been found to exist.

Bakgrund: En av de vanligaste aspekterna vid investeringar är att åstadkomma hög avkastning samtidigt som risken hålls på en låg nivå. Risker kopplade till bolag beror på flera olika faktorer varaven anses vara bolagsstorleken. För att vidare nå önskad avkastning har flertalet investeringsstrategier presenterats som sägs ska kunna överavkasta marknaden och vilket kontrasterar den effektiva marknadshypotesen. Genom investeringar i bolag med låga börsvärden, samt i kombination medinvesteringsstrategier, är det av intresse att undersöka huruvida överträffande av marknaden kan ske. Syfte: Denna uppsats har som syfte att analysera om det, på Spotlight Stock Market och First North, under åren 2007–2019, har gått att påvisa existensen av en SBE och huruvida det går att generera en riskjusterad överavkastning i småbolag med hjälp av investeringsstrategier. Metod: För att genomföra denna uppsats användes en kvantitativ design i kombination med endeduktiv ansats. Åtta olika portföljer sammanställdes baserat på storleken hos bolagen samt en investeringsstrategi baserad på låga P/BV-multiplar. Urvalen skedde utifrån Spotlight Stock Market, Large Cap och First North. Resultaten som genererades analyserades utifrån avkastning och riskjusterad avkastning samt statistiska tester i from av t-tester genomfördes. Slutsats: Utifrån resultaten kunde en småbolagseffekt inte påvisas. Portföljerna enbart baserade påbolagsstorlek för Spotlight Stock Market och First North presterade avkastningar som alla var lägre änOMXSPI, dock kunde detta inte säkerställas statistiskt. När investeringsstrategin utifrån låga P/BVmultiplar användes kunde portföljen utifrån Spotlight Stock Market påvisa en högre avkastning än OMXSPI, dock kunde denna inte heller statistiskt säkerställas. Gällande den riskjusterade avkastningen kunde enbart en av portföljerna baserade på Spotlight Stock Market och First Northpåvisa en riskjusterad överavkastning. Portföljerna baserade på Large Cap påvisade både högre avkastning än småbolagsportföljerna samt riskjusterad överavkastning. / Background: One of the most common aspects when investing is to achieve high returns while maintaining the risk at low levels. Risks associated with firms vary due to different factors of which oneis the size. In order to reach satisfactory returns many investment strategies have been presented with the goal of outperforming the market and thus contrasts the efficient market hypothesis. Through investments in firms with low market value of equity, and in combination with other investment strategies, it is of interest to investigate whether outperforming the market is possible. Purpose: The purpose of this study is to analyze whether a Small firm effect on the Spotlight Stock Market and First North during the years 2007-2019 could be proven and if it is possible in combination with investment strategies to generate risk-adjusted returns. Methodology: In order to complete the study a quantitative design in combination with a deductive design was used. Eight different portfolios were compiled based on the size of the companies as well as an investment strategy based on low P/BV-multiples. The samples were chosen from Spotlight StockMarket, Large Cap and First North. The results that were generated were analyzed based on return, risk-adjusted return and statistical test in the form of t-tests. Conclusion: The results from this study show that a Small Firm effect could not be established. The portfolios solely based on company size for Spotlight Stock Market and First North all performed a lower return than OMXSPI, though this could not be statistically confirmed. When an investment strategy based on low P/BV-multiples was used the portfolio based on Spotlight Stock Market showed a return higher than OMXSPI, though this could not be statistically confirmed either. Regarding the risk-adjusted excess return only one of the portfolios based on Spotlight Stock Market and First North could prove a risk-adjusted excess return. The portfolios based on Large Cap both proved a higher return than the small firm portfolios as well as risk-adjusted excess return.

Bakgrund: Denna studie är ett test av investeringsstrategi baserad på relativvärdering av multiplar. Den multipel som kommer att studeras som investeringsstrategi är Price-to-Book (P/B). Valet av multipel på P/B beror på att det är en väl omskriven multipel som fortfarande väcker frågeställningar avseende betydelsen av bokfört värde i kombination med marknadsvärde. Syfte: Syftet med denna studie är att undersöka och analysera multipeln P/B som investeringsstrategi för aktier. Vidare syftar studien till att undersöka aktier med låga respektive höga P/B från de olika börslistorna Small, Mid och Large Cap på Stockholmsbörsen. Genomförande: Sex portföljer skapas baserat på låga respektive höga P/B från de marknadsvärdemässiga börslistorna Small, Mid och Large Cap på Stockholmsbörsen. Portföljerna ombalanseras årligen och följs mellan 2006 och 2016. Resultat: Fyra av sex portföljer har högre ackumulerad avkastning än jämförelseindex före och efter riskjustering. Dock hindrar svag statistisk evidens påvisande av överavkastning över tid. På motsvarande vis finnes svaga säkerställda skillnader i avkastning mellan låga och höga P/B. Ej heller förefaller det förekomma signifikanta skillnader i avkastning och risk mellan portföljer på Small, Mid och Large Cap. / Background: This study is a test of an investment strategy based on relative valuation of multiples. The multiple to be studied is Price-to-Book (P/B). P/B is chosen because although previously researched, the implications of book values paired with market values are still not well understood. Aim: The aim of this study is to examine and analyze the multiple P/B as an investment strategy for stocks. Moreover, this study intends to examine stocks with low and high P/B: s from the Small, Mid and Large Cap on the Stockholm Stock Exchange. Completion: Six portfolios are created based on low and high P/B: s respectively from the market value-based stock exchange lists Small, Mid and Large Cap on the Stockholm Stock Exchange. The portfolios are rebalanced annually and are followed between 2006 and 2016. Results: Four out of six portfolios exhibit higher levels of cumulative returns than the chosen stock index before and after adjusting for risk. However, weak statistical evidence prevent conclusive showings of excess returns over time. Similarly, we find weak support for differences in returns between low and high P/B: s. Neither does there seem to exist significant differences in return and risk between the Small, Mid and Large Cap.