The increasing practice of using social media as the basis for decision-making has made social media an important alternative information source. This is, in particular, true for investors in the stock market due to their needs to gain dynamic, real-time information and strategic persons’ views. It is therefore very interesting to investigate the relationships between the sentiments of the text as published on social media and how they may influence investors’ minds. In this paper, we selected several influential Twitter accounts, inc. Bloomberg, Forbes, Reuters, WSJ and Donald Trump, for sentiment analysis using SentiStrength. We found a fair amount of agreement between the sentiments as generated by the tool and those assigned from investors’ point of view, esp. when plenty of positive words have been used in Tweets. However, we also discovered that not all Tweets with many positive words may generate positive sentiments in investors’ minds. Furthermore, we identified interesting differentiated sentiments expressed in different Tweeter accounts that may indicate the stance of their holders, e.g. using an upbeat tone thus to promote economic growth; or being conservative, thus maintaining one’s authority. Overall, we found many Tweets scored a neutral sentiment, as many of them contain references that their views cannot be determined without examining additional sources.