This study examines whether modern portfolio theory can be used to improve the Magic Formula investment strategy. With the assets picked by the investment strategy we modify the portfolios by weighting the portfolios in accordance with modern portfolio theory. Through the process of creating efficient frontiers and weighting the portfolios differently we create two alternative portfolios each year. One portfolio that aimsfor maximum Sharpe ratio and one that aims for minimum variance. These weighted portfolios produce higher risk-adjusted returns consistently during the examined period of 2010-2020. We conclude that the Magic Formula can be improved by using modern portfolio theory.

Valet mellan aktiv respektive passiv fondförvaltning har sedan länge varit en omdiskuterad fråga inom privata fondsparandet. På senare tid har frågan kommit att återaktualiserat efter att de aktivt förvaltade storfonderna Allemansfond komplett och Kapitalinvest anklagats för vilseledande marknadsföring, då de inte har generat en högre avkastning än den generella marknaden. Inom den akademiska världen har erkända forskare och sedermera pristagare av Sveriges Riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne, påvisat att aktivt förvaltade fonder inte kan generera en högre avkastning med hänsyn till förvaltningsavgifterna. Utifrån förvaltningsavgifterna påvisade betydelse har vi valt att studera effekten av de rabatterade förvaltningsavgifterna, inom Premiepensionssystemet. Studiens syfte är således att under tidsperioden, 1 januari 2004 till 31 december 2013, analysera om aktiv förvaltade fonder har genererat en högre riskjusterad avkastning än passivt förvaltade fonder, då hänsyn tagits till de rabatterade förvaltningsavgifterna. Studien baserades på dagliga marknadsnoteringar av 174 aktivt förvaltade premiepensionsfonder och årliga förvaltningsavgifter.  Vidare använde vi oss av ett globalt aktiemarknadsindex, MSCI World, som utifrån definitionen av passivt förvaltade fonder var synonymt med studiens jämförelseindex. I enlighet med studiens syfte använde vi oss av det riskjusterade avkastningsmåttet Sharpekvot för att kunna besvara studiens frågeställning.  Resultatet av studien påvisade att aktivt förvaltade fonder har genererat en högre avkastning än passivt förvaltade fonder då hänsyn tagits till förvaltningsavgifter. Då även fondernas risktagande togs i anspråk blev resultatet det motsatta och vi kan därigenom konstatera att aktivt förvaltade fonder har generat en lägre riskjusterad avkastning är passivt förvaltade fonder. Vidare har vi även kunnat konstatera att aktivt förvaltade fonder med låga förvaltningsavgifter har generat en högre såväl avkastning som riskjusterad avkastning än aktivt förvaltade fonder med höga förvaltningsavgifter. / The choice between active and passive fund management has long been a contentious issue within the private mutual fund investments. Lately, the issue has been widely discussed since the actively managed funds Allemansfond komplett and Kapitalinvest was accused of misleading marketing, since their performance has not overachieved the return of the general market. In the academic world, recognized scholars and later Laureate of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, has demonstrated that actively managed funds cannot generate a higher return with regard to management fees. Based on the importance of the management fees, we have chosen to study the effect of the discount management fees, within the Premiepensionssystemet. Therefore the study's objective is to analyse whether active managed funds have generated higher risk-adjusted returns than passively managed funds, reduced for the discounted management fees. The study will be limited to analyse the period between the 1st January 2004 to 31th December 20103 The study was based on daily market quotations of 174 actively managed Premiepensionsfonder and annual management fees. Furthermore, we used a global stock market index, MSCI World, by the definition of passively managed funds that was synonymous with the study's benchmark. In accordance with the study’s purpose, we used the risk-adjusted performance measure Sharpe ratio in order to answer the research question. The results of this study demonstrated that actively managed funds have generated higher returns than passively managed funds, reduced for the discounted management fees. When the funds' risk taking was committed, the result is the opposite, and we can thus conclude that actively managed funds have yield a lower risk-adjusted returns than passively managed funds. Furthermore, we also noted that actively managed funds with low management fees has generated higher returns as well as risk-adjusted returns than actively managed funds with high management fees.

Background: The Swedish fund savings have developed strongly over the past two decades. Together with this development, the knowledge that the earth's population is facing an extensive climate challenge has also increased. For many people today, living sustainably has become a central aspect of everyday life, and when it comes to investing their savings, the majority of Sweden's fund savers state that sustainability is something that is taken into account when choosing an investment. Investments in funds that based on measuring tools, show a high degree of sustainability have thus increased. This raises the question of whether these sustainable funds can generate a higher alpha and thus a better risk-adjusted return than the less sustainable alternatives available on the market. Previous studies have shown differences of opinion, which means that it is relevant to examine how these different types of funds perform against each other in the Swedish market.   Purpose: The aim of this study is to analyze whether fund savers that are investing in sustainable funds can generate a higher alpha and thereby a better risk adjusted return than fund savers that invests in less sustainable alternatives.   Methodology: The study was conducted with a quantitative method and a deductive approach. Sustainability ratings have been collected for 253 funds from a measuring institute. For these 253 funds, data in the form of net asset value have been collected between the period 2016 - 2020 monthly. These funds have then been evaluated based on risk-adjusted returns where regression analysis has been the groundwork for finding answers to whether alpha has been achieved compared to the market or not. Results obtained have then been statistically examined through various tests.   Conclusion: After completed study, there were no signs that studied sustainable funds have given rise to a better risk-adjusted return than the less sustainable alternatives available on the market. Of the 253 funds included in the study, only five funds showed a risk-adjusted return statistically different from zero, where three had a negative return and two a positive return. When the 253 funds were divided into four different quartiles based on sustainability ratings, it appeared that the funds with a positive risk-adjusted return were placed in quartile four, which was the one with the highest sustainability rating. However, this may be based on chance and a result of two in a sample of 253 gives clear indications that efficiency prevails in the market.