Momentum, or the basic idea of the momentum effect in finance, is that there is a tendency for rising asset prices to continue rising, while the falling prices continue to fall. As such, a momentum strategy is based on the idea that previous returns will predict future returns. In order to follow this line of thought, a momentum strategy is generally based on buying past winners and taking short positions in past losers. This quantitative study addresses the phenomenon of momentum crashes, which is a moment in time when a momentum strategy fails, and past losers outperform past winners. In our study we are setting out to study the momentum crash phenomenon during the years of 2006-2012 on NASDAQ OMX Stockholm, focusing specifically on the Small- and Large Cap segments. As we intend to explore the concept of momentum crashes as thoroughly as possible, we will also be researching momentum itself during this time period, as these two concepts are inevitably intertwined. In order to do this, we will be applying commonly used portfolio construction methods used in previous momentum research. These portfolios will be based on past winners and past losers, and their performance will then be tracked for different lengths of time, which will allow us to identify points in time where momentum crashes have occurred. What we found in our research was that, while we gathered data indicative of momentum trends during our chosen time period, we could not prove that momentum existed to any statistically meaningful degree. As for momentum crashes, we identified many different points in time where the past-loser portfolios outperformed the past-winner portfolios, thus resulting in negative winner-minus-loser portfolios and momentum crashes. The most interesting aspect of these findings was that the highest frequencies of momentum crashes were found in the years of 2008 and 2009, where we made the most negative winner-minus-loser portfolio observations. This finding is in line with similar research on other populations, as momentum crashes are theorized to occur at a higher frequency during times of market stress and high volatility. Furthermore, we also made some interesting connections between our findings and behavioral finance; we identified certain patterns which could be indicative of a relationship between the two. As for the research gap and the ultimate contribution of this study, we have increased the knowledge, understanding and awareness of momentum crashes in Sweden, and we have shown during which times these are likely to occur in a Swedish context. Additionally, we have also increased the general knowledge of momentum by exploring it from a Swedish perspective.

Stationarity is an essential property to portfolio return in the past statistical arbitrage strategy, this article uses Neo-75 rule, momentum effect, properties as independent and identically distribution and stationarity in error term, in one asset and in the very short holding period. The result in out sample period owning positive cumulative return. The finding suggests individual investors use this strategy in higher efficiency market to avoid invalidation in our model. This article surveyed CAC40, DJI, HangSeng, NASDAQ, Nikkei225, Shanghai and TWII indices. All the excess returns in out sample periods indicate they are exclude weak form of efficient market.

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.

O trabalho tem como objetivo identificar a existência do efeito momento, de comprar ações com alto desempenho relativo no passado e vender as de baixo desempenho relativo no passado, e do efeito contrário, de comprar ações com baixo desempenho relativo no passado e vender as de alto desempenho relativo no passado. A análise considerou 662 ações negociadas na BM&FBOVESPA entre julho de 1994 e junho de 2015, considerando quatro períodos de formação (3, 6, 9 e 12 meses) e seis de manutenção (3, 6, 9 e 12, 18 e 24 meses) das carteiras. A metodologia adotada para o efeito momento utiliza a abordagem de Jegadeesh e Titman (1993) e, para o efeito contrário, optou-se por De Bondt e Thaler (1985). A partir da identificação das carteiras vencedoras e perdedoras, passou-se a calcular as diferenças dos retornos acumulados mensais com uma janela móvel para expurgar o viés de seleção. Das 24 estratégias analisadas, verificou-se que apenas uma não apresentou significância para o efeito momento e rejeitou-se a hipótese de existência do efeito contrário. Constatou-se o efeito momento em 23 estratégias, sendo que duas apresentaram desempenho médio mensal superior ao Ibovespa no mesmo período, nas carteiras \"12x3\" e \"9x6\", respectivamente, de 1,60% e 1,48%. As principais contribuições do trabalho foram a adoção de uma carteira móvel para a avaliação do desempenho das carteiras, o amplo período utilizado na análise e o grande número de ativos, o que proporciona maior robustez aos resultados encontrados. / The work aims to find momentum effect, that buys stocks with relative high return in the past and sells stocks with relative poor return in the past, and the contrarian effect, that buys stocks with relative poor return in the past and sells stocks with relative high performance in the past. The analysis included 662 stocks traded on BM&FBOVESPA between July 1994 and June 2015, considering four formation periods (3, 6, 9 and 12 months) and six holding periods (3, 6, 9 and 12, 18 and 24 months) for the portfolios. The methodology adopted for momentum effect uses the theory of Jegadeesh and Titman (1993) and the contrarian effect uses De Bondt and Thaler (1985) theory. From the identification of winners\' portfolios and losers\' portfolios, it was calculated the differences in monthly cumulative returns with a rolling window to purge the selection bias. Of the 24 strategies analyzed, it was found that only one has no significance for momentum effect, and the hypothesis of contrarian effect was rejected. Momentum effect was found in 23 strategies, and two had average monthly performance superior to Ibovespa in the same period in the \"12x3\" portfolios and \"9x6\" portfolios, respectively, 1.60% and 1.48%. The main contributions of this study was to adopt a rolling window for evaluating the performance of the portfolios, the extended period used in the analysis and the large number of stocks, which provides greater robustness to the results found

O trabalho tem como objetivo identificar a existência do efeito momento, de comprar ações com alto desempenho relativo no passado e vender as de baixo desempenho relativo no passado, e do efeito contrário, de comprar ações com baixo desempenho relativo no passado e vender as de alto desempenho relativo no passado. A análise considerou 662 ações negociadas na BM&FBOVESPA entre julho de 1994 e junho de 2015, considerando quatro períodos de formação (3, 6, 9 e 12 meses) e seis de manutenção (3, 6, 9 e 12, 18 e 24 meses) das carteiras. A metodologia adotada para o efeito momento utiliza a abordagem de Jegadeesh e Titman (1993) e, para o efeito contrário, optou-se por De Bondt e Thaler (1985). A partir da identificação das carteiras vencedoras e perdedoras, passou-se a calcular as diferenças dos retornos acumulados mensais com uma janela móvel para expurgar o viés de seleção. Das 24 estratégias analisadas, verificou-se que apenas uma não apresentou significância para o efeito momento e rejeitou-se a hipótese de existência do efeito contrário. Constatou-se o efeito momento em 23 estratégias, sendo que duas apresentaram desempenho médio mensal superior ao Ibovespa no mesmo período, nas carteiras \"12x3\" e \"9x6\", respectivamente, de 1,60% e 1,48%. As principais contribuições do trabalho foram a adoção de uma carteira móvel para a avaliação do desempenho das carteiras, o amplo período utilizado na análise e o grande número de ativos, o que proporciona maior robustez aos resultados encontrados. / The work aims to find momentum effect, that buys stocks with relative high return in the past and sells stocks with relative poor return in the past, and the contrarian effect, that buys stocks with relative poor return in the past and sells stocks with relative high performance in the past. The analysis included 662 stocks traded on BM&FBOVESPA between July 1994 and June 2015, considering four formation periods (3, 6, 9 and 12 months) and six holding periods (3, 6, 9 and 12, 18 and 24 months) for the portfolios. The methodology adopted for momentum effect uses the theory of Jegadeesh and Titman (1993) and the contrarian effect uses De Bondt and Thaler (1985) theory. From the identification of winners\' portfolios and losers\' portfolios, it was calculated the differences in monthly cumulative returns with a rolling window to purge the selection bias. Of the 24 strategies analyzed, it was found that only one has no significance for momentum effect, and the hypothesis of contrarian effect was rejected. Momentum effect was found in 23 strategies, and two had average monthly performance superior to Ibovespa in the same period in the \"12x3\" portfolios and \"9x6\" portfolios, respectively, 1.60% and 1.48%. The main contributions of this study was to adopt a rolling window for evaluating the performance of the portfolios, the extended period used in the analysis and the large number of stocks, which provides greater robustness to the results found

The thesis addresses two areas of research within financial economics: empirical asset pricing and the borderline area between finance and economics with emphasis on econometrical methods. The empirical asset pricing section considers the effects of short-sale constraints on both the stock market as well as the derivatives market. Many arbitrage relations in the economy are intimately tied to the possibility to go short. One such arbitrage relation is the put-call-parity (PCP) relation that dictates a pricing relation between several derivative instruments and their underlying assets. During the latter part of the 1980s stock options could be traded in Sweden, while at the same time shorting was not permitted. The main contribution of the paper is to show that this shorting prohibition indeed implied larger deviations from PCP. Furthermore, this effect is only relevant for firms with stocks that were not shortable abroad, as firms with stocks shortable abroad did not show any deviations from PCP. The second paper investigates the asymmetries found in the momentum effect. Previous studies have found that the momentum effect is mostly due to the fact that a portfolio of loser firms tend to continue perform poorly, rather than because a portfolio of winner firms continue to do well. The explanation for this phenomenon investigated in the paper is based on the theoretical work by Diamond and Verrecchia (1985). In this model they demonstrate that the effects of restrictions on the ability to go short will have as a result that negative news are incorporated more slowly than positive news. The main contribution of my paper is to explore this hypothesis, and provide a link to the momentum effect. This has been achieved by considering Sweden during the 1980s during which the rare situation of a complete shorting prohibition was enforced. The second section of the thesis foremost addresses the CCAPM model. In the third paper the joint effect of market frictions, different utility specifications, as well as more stringent econometrical analysis, on the CCAPM are considered. Since all these remedies tend to co-exist and should not be considered on a stand alone basis, as has been the case in the previous literature. The paper also shows how several measures of misspecification available in the literature are implemented when market frictions are present. In particular, the paper presents the Hansen and Jagannathan measure with market frictions. The final paper considers L1-norm-based alternatives to the L2-norm-based Hansen and Jagannathan (1997) measure. It is well known that L1-norm methods may show good properties in the presence of non-normal distributions, for instance, with respect to heavy-tailed and/or asymmetric distributions. These methods provide more robust estimators, since they are less easily influenced by outliers or other extreme observations. The basic intuition for this is that L2-norm methods involve squaring errors, which magnifies large deviations, while L1-norm methods are based on absolute deviations. Since financial data are known to frequently display non-normal properties, L1-norm methods have found considerable use in financial economics. / Diss. Stockholm : Handelshögskolan, 2005

Bakgrund & Problemformulering: Momentumeffekten på fondmarknaden är ett relativt outforskat område där dess existens på senare tid har blivit omtvistad. Eftersom kunskapen om pensionssparande och det svenska pensionssystemet är låg, samtidigt som de sociala skyddsnäten i samhället minskar är det viktigt att undersöka om momentumstrategier kan ge överavkastning för privatpersoners pensionssparande. Således ställs frågan: Kan momentumstrategier skapa överavkastning på fondmarknaden? Syfte: Syftet med uppsatsen är att undersöka momentumeffekten på fondmarknaden och om momentumstrategier kan utnyttjas av svenska pensionssparare för att skapa överavkastning i PPM-systemet. Metod: Uppsatsen har ett kvantitativt tillvägagångssätt och en deduktiv utgångspunkt tillämpas. För att undersöka momentumeffekten på fondmarknaden tillämpas en multipel regressionsanalys med Fama French-Trefaktormodell, samt Sharpekvot. Uppsatsens urval är PPM-fonder under perioden 2010-2017. Slutsatser: Uppsatsen finner inget statistiskt stöd för en momentumeffekt på fondmarknaden genom Fama French-Trefaktormodell. Detta är ett tecken på att fondmarknaden kan vara svagt effektiv då historisk information inte har kunnat användas för att skapa riskjusterad överavkastning. Uppsatsen finner således ingen momentumeffekt för fondmarknaden efter finanskrisen 2008, trots att en momentumeffekt har kunnat påvisas dessförinnan inom tidigare forskning. Med hänsyn till det har författarna anledning att misstänka att marknadens effektivitet kan variera, vilket skulle kunna förklaras av den Adaptiva Marknadshypotesen. / Background & Problem: The momentum effect in the fund market is relatively unexplored were its existence has been controversial. Due to the lack of knowledge in retirement savings and the Swedish Premium Pension Agency system, alongside the weakening of a social safety net, it is important to examine if momentum strategies give excess returns and can be used for retirement savings. Therefore, the authors question: Do momentum strategies give excess returns in the fund market? Purpose: The aim of the thesis is to examine the momentum effect in the fund market and if momentum strategies can be used to create excess return in the Premium Pension Agency system. Method: The thesis takes a deductive research approach with a quantitative methodology. To examine the momentum effect in the fund market, a multiple regression analysis model from Fama French-Three factor model is applied, and the Sharpe ratio. The sample for the study is Swedish Premium Pension Agency funds, which is examined over the period of 2010-2017. Conclusions: The thesis does not find support for a momentum effect in the fund market through the Fama French-Three factor model. This indicates that the fund market is weak form efficient, as historical information cannot be used to create risk adjusted excess return. Thus, the thesis does not find a momentum effect for the fund market after the financial crisis in 2008, even though a momentum effect is proven to exist before then. In view of this, the authors have reason to suspect the market efficiency to vary, which could be explained by the Adaptive Market Hypothesis.

The present thesis is focused on speculative behavior of investors in financial markets. More precisely, the thesis consists of five papers and takes a closer look at two speculation driven financial market anomalies, the overreaction hypothesis and the momentum effect, and considers them in two financial markets, cryptocurrency and commodity markets.

動能效果是各國股票市場中最常見的異常現象，Sharpe (1964)提出資本資產定價模型(CAPM)，認為股票報酬與系統風險之間呈現正相關，而和其他非系統性風險無關，因此投資人透過投資所能獲得的超額報酬皆因承擔系統風險而得到的補償。然而近來許多實證研究的結果皆發現了一些非系統性風險能夠解釋股票報酬的異常現象，例如規模效應、本益比效應等等。若股票市場是具有效率的，那麼市場上所有已公開資訊皆應已充分反應在股價上，因此透過各種投資策略皆應無法獲得超額報酬，然而Jegadeesh and Titman (1993)卻發現利用買進過去報酬相對較佳之股票和賣出過去報酬表現相對較差之股票可獲得顯著的超額報酬，即所謂的動能投資策略，這種策略的獲利性很顯然的違背了效率市場假說，因此許多學者相繼提出理論來解釋造成此種現象之原因，其中有某些行為財務理論將此現象歸因於投資人對市場上之新訊息反應不足所致。 本文研究係以Grinblatt and Han (2005)的實證方法，透過建立資本利得與損失的代理變數來衡量由於處分效果造成股價反應不足之程度，並利用Fama-Macbeth橫斷面分析法來探討台灣股市的動能效果是否是因市場上存在處分效果，導致股價反應不足所引起。實證結果發現台灣股市在中長期(過去27到52週)存在顯著的動能效果，然而利用資本利得與損失的代理變數並無法成功的將該動能效果消除，顯示處分效果無法有效的解釋台灣股市中動能效果的來源。

In financial markets, momentum effect can be defined as the tendency of prices to maintain their short term movements. On the other hand, reversal effect is usually understood to be the change in direction of long term price movements. This paper examines whether momentum and reversal effects were in evidence in the Brazilian stock market between January 1999 and June 2012. After calculating 1296 trading strategies, no evidence of reversal effect is found. With regard to momentum effect, some weak evidence is presented for the very short term. Exposure to risk factors can explain returns on strategies, including returns on momentum strategies. The results are borne out with different market proxy specifications and size subsamples. When compared to previous studies, the results raise the question of whether the reversal effect is vanishing from the Brazilian stock market and whether the traces of momentum are sufficient to confirm its existence. Furthermore, evidence of seasonality is found for June in momentum strategies and for November in both reversal and momentum strategies. Subsequent tests reveal that the effects of seasonality are limited to small stocks. / Nos mercados financeiros, o efeito momento pode ser definido como a tendência dos preços em manter seus movimentos de curto prazo. Por outro lado, o efeito contrário é geralmente entendido como a mudança na direção dos movimentos de longo prazo dos preços. O presente trabalho examina a existência dos efeitos momento e contrário no mercado acionário brasileiro no período compreendido entre janeiro de 1999 e junho de 2012. A partir do cálculo de 1296 estratégias de investimento, nenhuma evidência de efeito contrário é encontrada. Com relação ao efeito momento, observou-se apenas uma fraca evidência no curtíssimo prazo. A exposição aos fatores de risco é capaz de explicar os retornos das estratégias, inclusive os retornos das estratégias de momento. Os resultados são robustos ao se utilizar diferentes especificações de proxy de mercado e subamostras de valor de mercado. Quando comparados a trabalhos anteriores, os resultados colocam em questão se o efeito contrário está desaparecendo no mercado acionário brasileiro e se as fracas evidências do efeito momento são suficientes para confirmar sua existência. Ademais, são observadas evidências de sazonalidade no mês de junho nas estratégias de momento e, no mês de novembro, em ambas as estratégias. Testes posteriores revelam que esses efeitos de sazonalidade estão restritos à subamostra de baixo valor de mercado.