In this thesis we consider three different problems in the domain of portfolio optimisation. The first problem we consider is that of selecting an Absolute Return Portfolio (ARP). ARPs are usually seen as financial portfolios that aim to produce a good return regardless of how the underlying market performs, but our literature review shows that there is little agreement on what constitutes an ARP. We present a clear definition via a three-stage mixed-integer zero-one program for the problem of selecting an ARP. The second problem considered is that of designing a Market Neutral Portfolio (MNP). MNPs are generally defined as financial portfolios that (ideally)exhibit performance independent from that of an underlying market, but, once again, the existing literature is very fragmented. We consider the problem of constructing a MNP as a mixed-integer non-linear program (MINLP) which minimises the absolute value of the correlation between portfolio return and underlying benchmark return. The third problem is related to Exchange-Traded Funds (ETFs). ETFs are funds traded on the open market which typically have their performance tied to a benchmark index. They are composed of a basket of assets; most attempt to reproduce the returns of an index, but a growing number try to achieve a multiple of the benchmark return, such as two times or the negative of the return. We present a detailed performance study of the current ETF market and we find, among other conclusions, constant underperformance among ETFs that aim to do more than simply track an index. We present a MINLP for the problem of selecting the basket of assets that compose an ETF, which, to the best of our knowledge, is the first in the literature. For all three models we present extensive computational results for portfolios derived from universes defined by S&P international equity indices with up to 1200 stocks. We use CPLEX to solve the ARP problem and the software package Minotaur for both our MINLPs for MNP and an ETF.

This study examines the performance of long-short equity trading strategies from January 1990 to December 2010. This study combines two financial screens that will yield candidates for both long and short positions for each month during the aforementioned time period. Two long-short strategies are tested: (1) perfectly-hedged, or equal allocation to long and short positions, and (2) net-long. The results of this thesis reveal that if a long-short equity manager is able to successfully determine what companies are overvalued and undervalued and actively rebalance their portfolio, perfectly-hedged and net-long strategies can generate superior risk-adjusted alpha.

This Thesis attempts to construct a Taiwan equity multi-factor model using fundamental cross-sectional approach step by step. It is found that the model involves 28 explanatory factors (including 20 industry factors) and its explanatory power is 58.6% on average. The results of the estimations can be considered very satisfactory. Moreover, based on MFM, this study simulates applications of equity market neutral strategies through quantitative techniques over the period Jan.2003 ¡V Dec.2003. The results verified that the three major characteristics of equity market neutral portfolio performance are: 1) providing absolute return; 2) lack of correlation to the equity benchmark; and 3) low volatility due to hedged portfolio structures.

I compared various MIDAS (mixed data sampling) regression models to predict volatility from one week to one month with different regressors based on the records of Chinese Shanghai composite index. The main regressors are in 2 types, one is the realized power (involving 5-min absolute returns), the other is the quadratic variation, computed by squared returns. And realized power performs best at all the forecast horizons. I also compare the effect of lag numbers in regression, form 1 to 200, and it doesn’t change much after 50. In 3 week and month predict horizons, the fitness result with different lag numbers has a waving type among all the regressors, that implies there exists a seasonal effect which is the same as predict horizons in the lagged variables. At last,the out-of -sample and in-sample result of RV and RAV are quite similar, but in sometimes, out-of sample performs better.

An alternative form of investing that has grown steadily during turbulent economic conditions is the decision to invest in Hedge funds. Hedge funds differ from mutual funds by achieving absolute returns, meaning that the funds use complex investment strategies in order to achieve positive returns regardless of the performance of the stock market. The hedge fund market has grown significantly since the mid-1990s in the Nordic countries. Sweden has dominated the hedge fund scene in terms of pure numbers and is also in a dominant position in terms of hedge fund assets under management. Despite this growth, Swedish investors generally have a lack of knowledge about hedge funds as an alternative form of investment, which makes it difficult to assess its advantages and drawbacks. The purpose of the report is to study what hedge fund strategies on the Swedish market are able to generate absolute return over a given period. The purpose is also to compare the performance of the hedge fund strategies with the performance of the Swedish stock market over the given period. The strategies have been compared with the Swedish Stock Market Index SIXRX which reflects the performance of the Stockholm Stock Exchange, adjusted for dividends. The results show that all the hedge fund strategies had a lower volatility and generated a higher return relative to risk compared to the Stockholm Stock Exchange, over the given period. However, only three out of five hedge fund strategies managed to generate absolute return over the total period. / Ett investeringsalternativ som har vuxit sig starkare under turbulenta ekonomiska förhållanden är möjligheten att investera i hedgefonder. Hedgefonder skiljer sig från traditionellt förvaltade fonder genom möjligheten att utvinna s.k. absolut avkastning. Detta innebär att fonden använder komplexa investeringsstrategier i syfte att generera en positiv avkastning oberoende av aktiemarknadens utveckling. Hedgefonder har sedan mitten av 1990- talet vuxit sig allt starkare bland nordiska länder och Sverige är idag det land i Norden som dominerar avseende både antalet hedgefonder och förvaltat hedgefondkapital. Trots denna tillväxt har svenska investerare generellt sett låg kännedom om hedgefonder som placeringsalternativ, vilket gör det svårt att bedöma dess för- och nackdelar. Rapportens syfte är att undersöka vilka hedgefondstrategier på den svenska marknaden som klarar att generera absolut avkastning över en bestämd tidsperiod. Syftet är även att under samma period jämföra hedgefondstrategiernas utveckling med den svenska aktiemarknadens utveckling som helhet. Jämförelsen har gjorts med det svenska aktieindexet SIXRX som speglar Stockholmsbörsens utveckling, justerat för aktieutdelningar. Slutresultatet visar att samtliga hedgefondstrategier hade en lägre volatilitet samt genererade en högre avkastning i förhållande till risk jämfört med Stockholmsbörsen som helhet, under vald tidsperiod. Endast tre av fem strategier klarade dock att generera en absolut avkastning under tidsperiodens samtliga år.

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.

Förvaltning och avkastning hos fonder har forskats om i flera studier runt om i världen. Tidigare forskning har gett varierande resultat, där vissa studier visar på att det föreligger ett samband mellan en fonds avgift och avkastning, medan andra inte kan säkerställa ett sådant resultat. Då de svenska hushållen idag sparar mer än någonsin, visar det på att fondsparande är ett aktuellt ämne för ytterligare forskning. Statistik från 2020 visar att fondförmögenheten i Sverige totalt uppgick till 4 554 miljarder kronor och har visat på en fortsatt ökande trend de senaste åren. Dock har endast få studier genomförts på den svenska kapitalmarknaden och de har i huvudsak analyserat ämnet på kort sikt, med en tidsperiod om fem år. Eftersom avgifternas påverkan på fonder är tydligast på lång sikt, ger det utrymme för fortsatt forskning inom ämnet. Syftet med följande forskning är att studera sambandet mellan svenska aktiefonders avkastning och avgift på lång sikt i förhållande till fondernas risk. Studien avgränsas till att undersöka svenska aktiefonder som har varit verksamma i minst tio år, mellan åren 2011-2020. Forskningen antar en kvantitativ forskningsmetod, vilket syftar till att testa teorier. Tillvägagångssätt sker genom en analys av urvalets regression och korrelation i samband med hypotesprövning, där variabler undersöks för att ge underlag till studiens analys av resultat. Studiens resultat visar att svenska aktiefonder i genomsnitt underpresterar den svenska marknaden på lång sikt. Forskningen visar även varierande resultat gällande korrelation mellan riskjusterad avkastning och avgift på lång sikt. Resultaten indikerar att den svenska kapitalmarknaden har en relativ marknadseffektivitet av svag form. I tillägg verkar aktivt förvaltade fonder kunna utnyttja tillfällig trendidentifiering och informationsasymmetri för att uppnå en överavkastning. Forskningen avslutas med slutsatsen att högavgiftsfonder, vilka är mer aktivt förvaltade, indikeras vara ett bättre investeringsalternativ för att uppnå en god långsiktig prestation i jämförelse med passiva fonder. / The management and return of funds have been researched in many studies around the world. Previous research has yielded varied results, with some studies showing that there is a link between a fund's fee and return, while others cannot ensure such a result. As Swedish households save more today than ever, it shows that fund saving is a current topic for further research. Statistics from 2020 show that fund assets in Sweden are 4 554 billion swedish crowns in total, a number that has continuously grown in the past years. However, only a few studies have been conducted on the Swedish capital market where the existing studies have mainly analyzed the subject in the short term, with a time period of five years. Since the impact of fund fees is most noticeable in the long term, the subject can be further explored.  The aim of this research is to study the correlation between returns and fees of Swedish equity funds in the long term in relation to the funds risk. The study is limited to examining Swedish equity funds that have been active for at least ten years, between the years 2011-2020. The study adopts a quantitative research method, which aims to test theories. This research utilizes a regression and correlation analysis in conjunction with hypothesis testing, where variables are examined to provide a basis for the study's analysis of results. The results of this study show that Swedish equity funds on average underperform the Swedish market in the long term. The research also shows varying results regarding the correlation between risk-adjusted return and fee in the long term. The results of this study indicate that the Swedish capital market has a relative weak form of market efficiency. In addition, actively managed funds seem to be able to utilize occasional trend identification and information asymmetry to achieve an excess return. The research concludes that high-fee funds, which are more actively managed, indicate to be a better investment alternative for achieving long-term performance in comparison to passive funds.