Avsikten med studien är att undersöka den magiska formelns prestation på den svenska aktiemarknaden mellan åren 2017–2021. Syftet är att undersöka om denmagiska formeln kan uppnå en högre riskjusterad avkastning än OMXS30 underundersökningsperioden. I denna studie tillämpas backtesting med hjälp av historiska data hämtat från Refinitv Eikons databas för att utforska strategins prestation under undersökningsperioden. Målet med denna studie var att undersöka om den magiska formeln kan användas av investerare med mindre erfarenhet för att uppnå en högre riskjusterad avkastning än OMXS30-index. Med hjälp av två variabler, return on capital och earnings yield fick vi fram ett resultat för att besvara studiens syfte. Under hela undersökningsperioden uppnådde den magiska formeln en genomsnittlig avkastning på 15,32% medan OMXS30 portföljen uppnådde en avkastning på 10,78%. Resultatet från denna studie visade att den magiska formeln kunde uppnå en högre avkastning än OMXS30 under undersökningsperioden men eftersom Sharpekvoten för OMXS30 var högre än den magiska formeln formas indikationer att OMXS30 presterade bättre än den magiska formeln på en genomsnittlig riskjusterad nivå under undersökningsperioden. / This study examines the performance of the magic formula by Joel Greenblatt on the Swedish stock market. A back test was performed to see if the magic formula could generate a higher risk adjusted return and outperform the OMXS30 index between the years 2017 and 2021. The study constructed portfolios for each year for the magic formula and OMXS30 with the ambition to compare the two results. The results show that the magic formula achieved a higher return at a higher risk rate so therefore, it was not able to beat the OMXS30 index on a risk adjusted level.

No description available.

Yes / This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

A dissertação aborda e compara as características dos índices de Sharpe (SR) e suas variantes, SRc e SRd, Sharpe generalizado (GSR ) e potencial de investimento (IP), sendo os índices GSR e IP associados a alguma função de utilidade. Pelo fato de o GSR e o IP serem idênticos, testes empíricos foram realizados entre SRc e o GSR. Ambos foram avaliados teoricamente sob dois aspectos, o que definimos de análise retrospectiva, i.e., análise de séries de log-retornos mensais observados, e a análise prospectiva, i.e., séries a ocorrer. No âmbito prospectivo, ex ante facto, o SRc (índice de Sharpe com variável de estado normal) e o SRd (índice de Sharpe com variável de estado lognormal), por estarem associados à função de utilidade quadrática, apresentam distorções como o ponto bliss e o agente econômico bomba de dinheiro. O mesmo ocorre no âmbito retrospectivo, ex post facto, com o GSR (potencial de desempenho de ativos de risco para indivíduos com função de utilidade HARA) quando o coeficiente de aversão ao risco é igual a um negativo, gama=-1. No entanto, o GSR pode ser associado a funções de utilidade diferentes da quadrática evitando seus efeitos indesejáveis. Sob a suposição de movimento browniano geométrico (MBG) e da utilidade HARA para o preço mensal ajustado de ações brasileiras e americanas e para pontos mensais de índices brasileiros e americanos, entre janeiro de 2000 e março de 2008, obtivemos os seguintes resultados: (1) o índice GSR para utilidade quadrática apresentou elevada correlação com o SRc; (2) a menor correlação de GSR com SRc ocorreu para utilidade logarítmica; (3) para a utilidade exponencial, o GSR apresenta elevado grau de correlação com o SRc. Os resultados mostraram que o GSR com utilidade exponencial é o índice que menos se aproxima do comportamento do GSR com utilidade quadrática. Sabendo-se das distorções da utilidade quadrática, a adoção do GSR com gama=1 parece mais adequado para a classificação de ativos de risco. / This master dissertation studies and compares the characteristics of Sharpe ratio and its variants, SRc and SRd, generalized Sharpe ratio (GSR) and investment potential (IP), both GSR and IP associated to any utility function. By the fact that GSR and IP are identical indexes, empiric tests were conducted between SRc and GSR. The indexes were evaluated theoretically under two different aspects: retrospective analysis, i.e., analyze the observed monthly log-returns, and prospective analysis, i.e., series to occur. Under prospective view, ex ante facto, SRc (Sharpe ratio with normal state variable) and SRd (Sharpe ratio with lognormal state variable), for being associated to the quadratic utility function, show the inherent problems to utility functions such as the bliss point and the pump money economic agent. The same happens in a retrospective view, ex post facto, with the GSR (performance potential with HARA utility function family) when the risk aversion coefficient equals minus one, gama=-1. Therefore, the GSR can be associated to different utility functions avoiding the undesirable effects. Under the GBM (geometric Brownian motion) condition and HARA utility function for the Brazilian and American adjusted monthly stock prices and indexes monthly points during January 2000 and March 2008, we reached the following: (1) results indicate that GSR for quadratic utility has high correlation level with SRc; (2) while the logarithmic utility showed lowest correlation level between GSR and SRc; (3) exponential utilities showed a high level of correlation between GSR and SRc. The results showed that GSR with exponential utility kept the biggest behavior difference for the GSR with quadratic utility. Based on the knowing problems of the quadratic utility, GSR with gama=1 seems to be a better index choice for risk assets classification.

A dissertação aborda e compara as características dos índices de Sharpe (SR) e suas variantes, SRc e SRd, Sharpe generalizado (GSR ) e potencial de investimento (IP), sendo os índices GSR e IP associados a alguma função de utilidade. Pelo fato de o GSR e o IP serem idênticos, testes empíricos foram realizados entre SRc e o GSR. Ambos foram avaliados teoricamente sob dois aspectos, o que definimos de análise retrospectiva, i.e., análise de séries de log-retornos mensais observados, e a análise prospectiva, i.e., séries a ocorrer. No âmbito prospectivo, ex ante facto, o SRc (índice de Sharpe com variável de estado normal) e o SRd (índice de Sharpe com variável de estado lognormal), por estarem associados à função de utilidade quadrática, apresentam distorções como o ponto bliss e o agente econômico bomba de dinheiro. O mesmo ocorre no âmbito retrospectivo, ex post facto, com o GSR (potencial de desempenho de ativos de risco para indivíduos com função de utilidade HARA) quando o coeficiente de aversão ao risco é igual a um negativo, gama=-1. No entanto, o GSR pode ser associado a funções de utilidade diferentes da quadrática evitando seus efeitos indesejáveis. Sob a suposição de movimento browniano geométrico (MBG) e da utilidade HARA para o preço mensal ajustado de ações brasileiras e americanas e para pontos mensais de índices brasileiros e americanos, entre janeiro de 2000 e março de 2008, obtivemos os seguintes resultados: (1) o índice GSR para utilidade quadrática apresentou elevada correlação com o SRc; (2) a menor correlação de GSR com SRc ocorreu para utilidade logarítmica; (3) para a utilidade exponencial, o GSR apresenta elevado grau de correlação com o SRc. Os resultados mostraram que o GSR com utilidade exponencial é o índice que menos se aproxima do comportamento do GSR com utilidade quadrática. Sabendo-se das distorções da utilidade quadrática, a adoção do GSR com gama=1 parece mais adequado para a classificação de ativos de risco. / This master dissertation studies and compares the characteristics of Sharpe ratio and its variants, SRc and SRd, generalized Sharpe ratio (GSR) and investment potential (IP), both GSR and IP associated to any utility function. By the fact that GSR and IP are identical indexes, empiric tests were conducted between SRc and GSR. The indexes were evaluated theoretically under two different aspects: retrospective analysis, i.e., analyze the observed monthly log-returns, and prospective analysis, i.e., series to occur. Under prospective view, ex ante facto, SRc (Sharpe ratio with normal state variable) and SRd (Sharpe ratio with lognormal state variable), for being associated to the quadratic utility function, show the inherent problems to utility functions such as the bliss point and the pump money economic agent. The same happens in a retrospective view, ex post facto, with the GSR (performance potential with HARA utility function family) when the risk aversion coefficient equals minus one, gama=-1. Therefore, the GSR can be associated to different utility functions avoiding the undesirable effects. Under the GBM (geometric Brownian motion) condition and HARA utility function for the Brazilian and American adjusted monthly stock prices and indexes monthly points during January 2000 and March 2008, we reached the following: (1) results indicate that GSR for quadratic utility has high correlation level with SRc; (2) while the logarithmic utility showed lowest correlation level between GSR and SRc; (3) exponential utilities showed a high level of correlation between GSR and SRc. The results showed that GSR with exponential utility kept the biggest behavior difference for the GSR with quadratic utility. Based on the knowing problems of the quadratic utility, GSR with gama=1 seems to be a better index choice for risk assets classification.

在投資無國界的全球化金融市場下，國際市場的開放與整合平台的建立，使國內投資人可選擇更多的金融工具。傳統的投資項目多為股票、債券或平衡型商品，在獲利狀況不甚理想下，便開始尋求其他國際的投資管道或是金融商品加入其資產配置中，希望獲取穩定的報酬下，又能降低所承擔的投資風險將投資所需承擔的風險減低。 近年避險基金的投資績效及資產規模成長搶眼，挾著法令寬鬆與靈活運用的操作策略，以及投資範疇廣與市場連動性低等特性，創造出日益壯大的規模。我國積極致力於金融改革，除了監督管理制度面的改善，對於新興金融工具的開放，也是國內投資環境必須跟進的方向。未來在台灣若能開放設立避險基金之前，國內投資人與監管機關所擔負職責，皆應該對此種金融工具有深入的認識。 本研究透過四個概念的架構，去評估避險基金加入投資組合後，是否可以幫助投資人達成降低風險以及增加報酬之目標，以及身為資產管理者如何將避險基金納入其資產配置決策等相關考量；對國內金融主管機關而言，避險基金的開放或是投資限制的放寬是否是正確的金融政策方向，才能配以完善的監理機制與法令規範，使國內投資大眾在投資理財工具上更加完備。 實證結果分析發現，在研究期間避險基金的確可以幫助投資組合之效益提升，但是加入總體情境時，其對投資組合的幫助卻不一致，只有在空頭期間的效果明顯。另外發現沒有避險基金相關之投資限制下的投資組合，其夏普指數高於有限制的投資組合；在避險基金限制放寬下，效率前緣往左上角移動，推論放寬避險基金限制該是正確的金融政策。最後，本研究也發現以機構投資法人而言，避險基金加入投資組合能幫助達到絕對報酬。 / Under the global financial market, which has broken the boundaries between nations, domestic investors now have more choices of financial instruments than they did before. Therefore, besides traditional domestic investment vehicles, such as stocks or mutual funds, domestic investors have started seeking other instruments to enhance their portfolio, pursuing better risk-return profile. In recent years, hedge fund’s performance and assets size have both grew impressively by capitalizing on deregulations and various trading strategies of its own. Besides the improvement in financial supervision system, deregulation and capitalizing on newly innovated financial instruments are also important to the reformation of Taiwan’s financial market. Before hedge funds can be legally raised in Taiwan, both domestic investors and market supervisors should equip themselves with adequate knowledge about this important instrument. By analyzing the four concepts in the third chapter, the research intends to evaluate whether investors can enjoy better risk-return profile by adding hedge funds into their portfolios. Also, the research objective is to provide suggestions to fund managers as they consider their assets allocation. Finally, we want to evaluate whether it is correct for Taiwan to open up to hedge funds, therefore the government can establish feasible supervision system to protect domestic investors’ rights. The research has found that hedge funds could indeed benefit the portfolio during the time period under consideration. However, hedge funds did not have significant effect on the portfolio as macroeconomic scenario was taken into consideration. In the scenario, hedge funds have significantly positive effect on the portfolio only under a bearing market. Furthermore, the research found that the portfolios with less limitation on hedge fund investment can enjoy better Sharp Ratios than those with striker limitation on hedge fund investment. Since the efficiency frontier moved upper left as we reduced the limitation on hedge fund investment in the research, we may conclude that an open-up to hedge funds should be the correct direction for our financial policy. At last, the research also found that institutional investors can get absolute return by adopting hedge funds in their portfolios.

<p>Hedge funds are a debated subject in today’s financial industry. During 2008, despite hedge funds absolute return target, the global hedge fund industry showed a negative performance whilst the Swedish hedge fund market performed relatively well in comparison. Many studies have been made investigating the effect on incorporating hedge funds in a traditional portfolio though none focused separately on the Swedish market. In a global perspective it is quite easy to invest in hedge fund portfolios due to the existence of investable indices. To invest on the Swedish market is a more complex matter. SIX Harcourt HFXS Index is a Swedish hedge fund index representing the Swedish hedge fund market though it is not investable. Hence it would be interesting to see if it is possible to create an investable version of SIX Harcourt HFXS. When creating an investable index, several administrative costs will arise and in order to cover these costs it would be interesting to see whether or not it possible to optimize SIX Harcourt HFXS Index in purpose of achieving a outperformance which could cover any administrative costs for setting up the investable version. Also, since the optimized version must replicate the standard SIX Harcourt HFXS Index it must maintain a certain level of correlation.</p><p>This thesis, which is based on a positivistic epistemology, is built upon a quantitative case study where SIX Harcourt HFXS Index is optimized in purpose of achieving an outperformance in terms of the risk-adjusted return. The optimization uses an adjusted mean-variance methodology and is limited to a maintained correlation above 0,9 towards the standard SIX Harcourt HFXS Index. The optimization is created through the use of an Excel application created by Harcourt Investment Consulting.</p><p>Also, based on the outperformance by Swedish hedge funds compared to global hedge funds, this study aims to show the effect of incorporating Swedish hedge funds in a traditional portfolio consisting of equities and bonds. This effect is analyzed by the use of several performance-and risk measures.</p><p>The study shows that it is possible to optimize SIX Harcourt HFXS Index and produce an outperformance of approximately 1,5% per annum with a maintained correlation above 0,9. It also shows that the effect of incorporating Swedish hedge funds to a traditional portfolio is positive in regards to both risk and return.</p>

Hedge funds are a debated subject in today’s financial industry. During 2008, despite hedge funds absolute return target, the global hedge fund industry showed a negative performance whilst the Swedish hedge fund market performed relatively well in comparison. Many studies have been made investigating the effect on incorporating hedge funds in a traditional portfolio though none focused separately on the Swedish market. In a global perspective it is quite easy to invest in hedge fund portfolios due to the existence of investable indices. To invest on the Swedish market is a more complex matter. SIX Harcourt HFXS Index is a Swedish hedge fund index representing the Swedish hedge fund market though it is not investable. Hence it would be interesting to see if it is possible to create an investable version of SIX Harcourt HFXS. When creating an investable index, several administrative costs will arise and in order to cover these costs it would be interesting to see whether or not it possible to optimize SIX Harcourt HFXS Index in purpose of achieving a outperformance which could cover any administrative costs for setting up the investable version. Also, since the optimized version must replicate the standard SIX Harcourt HFXS Index it must maintain a certain level of correlation. This thesis, which is based on a positivistic epistemology, is built upon a quantitative case study where SIX Harcourt HFXS Index is optimized in purpose of achieving an outperformance in terms of the risk-adjusted return. The optimization uses an adjusted mean-variance methodology and is limited to a maintained correlation above 0,9 towards the standard SIX Harcourt HFXS Index. The optimization is created through the use of an Excel application created by Harcourt Investment Consulting. Also, based on the outperformance by Swedish hedge funds compared to global hedge funds, this study aims to show the effect of incorporating Swedish hedge funds in a traditional portfolio consisting of equities and bonds. This effect is analyzed by the use of several performance-and risk measures. The study shows that it is possible to optimize SIX Harcourt HFXS Index and produce an outperformance of approximately 1,5% per annum with a maintained correlation above 0,9. It also shows that the effect of incorporating Swedish hedge funds to a traditional portfolio is positive in regards to both risk and return.

Recently, the selections of ethical funds are increased; at the same time investors with social and moral preferences have increased in the capital market. There are currently debates on whether ethical funds perform better or worse than funds without ethical criteria. This also involves a vivid discussion on whether investors know about the consequences of investing in ethical funds. Therefore, this study involves theories about the rationality and decision theory, in addition to what mainly control the investment decisions. The study also discusses portfolio theory since this is one of the underlying theories behind fund management and its development. The purpose of this study is to explain if ethical limitations in the selection of securities affect risk and return in the fund portfolio. This study has positivistic research approach and a quantitative method. The method involves some calculations and equations used that will be presented. The study indicates that ethical funds actually deliver better risk adjusted returns than its Swedish benchmark index. It also indicates a trend that ethical funds deliver better excess returns than funds without ethical preferences. Furthermore, the study concludes that no statistical difference between the ethical funds and the benchmark in terms of risk in investment can be demonstrated. One limitation of the study is that the survey mainly includes the Swedish market with Swedish company stakeholders. This means that there may be a need for research in a global market where also cultural aspects need to be considered. It has not previously been quite clear how ethical fund performance in the Swedish market, and at a time when demand for ethical choice increases, the goal of this study was to clarify the performance of ethical funds. / På senare tid har urvalet av etiska fonder ökat, samtidigt som investerare med sociala och moraliska preferenser har blivit allt vanligare på kapitalmarknaden. Det finns idag diskussioner om huruvida etiska fonder presterar bättre eller sämre än fonder utan de etiska kriterierna. Detta innefattar också en livlig diskussion om huruvida investerare är medvetna om konsekvenserna av att investera i etiska fonder. Därför berör studien teorierna kring den rationella- och beslutsteorin, för vilka huvudsakligen styr investeringsbesluten. Studien behandlar också portföljvalsteori då detta är en av de bakomliggande teorierna för fondförvaltning och dess uppkomst. Syftet med denna studie är förklara om de etiska begränsningar i urvalet av värdepapper påverkar risk och avkastning i fondportföljen. I studien kommer en positivistisk forskningssats användas samt en kvantitativ metod. Metoden innefattar en del beräkningar och ekvationer som används och som presenteras. Studien pekar på att de etiska fonderna faktiskt levererar en bättre  riskjusterad  excessavkastning än sitt jämförelseindex på den svenska marknaden. Den visar också tendenser att de etiska fonderna levererar en bättre excessavkastning än de fonderna utan etiska preferenser. Vidare kommer studien fram till att det inte kan påvisas någon statistisk skillnad mellan de etiska fonderna och jämförelseindexet vad det gäller risken i investeringar. En begränsning med studien är att undersökningen huvudsakligen innefattar den svenska marknaden med svenska företagsaktörer. Detta gör att det kan finns behov av forskning på en global marknad där även de kulturella aspekterna behöver bejakas. Eftersom det tidigare har varit ganska oklart vad det gäller etiska fondernas prestanda på den svenska marknaden, och i en tid då efterfrågan på etiska urvalet ökar, är målet med denna studie att bringa klarhet om etiska fonders prestation.

Syfte: Studera sju portföljer och notera den bästa typen av portfölj med högst avkastning till lägst risk. Metod: Sekundärdata är grunden för uträkning av samtliga portföljers avkastningar, risker och korrelation. Studien är deduktiv med kvantitativa inslag av kända teorier av nobelpristagare i ekonomisk vetenskap.  Slutsats: Studien visar att stora bolag i olika branscher är ett vinnande portföljinnehåll för denna studie. Stora bolags aktier har visat högre avkastning till lägre risk jämfört med små bolag under studiens tid då ekonomiska kriser drabbade marknaden. Den mest presterande portföljen var därför storbolagsportföljen. Vidare forskning: Längre tidsperspektiv och nya teorier som Jensens alfa samt Treynorkvot är av intresse för vidare forskning för att styrka vår slutsats. / Intention: To study seven portfolios and note the best type of portfolio with the maximum return at a minimum risk. Method: Secondary data is the basis for calculation of the total portfolio returns, risk and correlation. This study is deductive based using a quantitative method of world-known theories of Nobel laureates in economic sciences. Conclusion: The study shows that the best efficient portfolio contains large companies in different lines of business. Large companies' shares have higher returns at lower risk compared to small companies in circumstances to difficult economic situations globally. The best performed portfolio was the portfolio with large companies.                                       Further Research: Longer period of time study and a study of new theories such as Jensens Alfa and Tretnor ratio would be interesting for further research.