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.