This study attempts to group investors (individuals and professionals) into different segments based on their level of overconfidence (as a psychological bias) and, then, to examine whether, and to what extent, specific personality trait drive investors' trading behaviour. This study performing a cluster analysis, and using a representative survey of 345 investors in Greece, identified two main segments of investors: Overconfident investors and Underconfident investors. A comparative analysis between these two segments identified some differences in the trading behaviour of investors, depending on the segment they belong to. Moreover, a statistical association between investors' clusters and various demographic, socioeconomic characteristics and trading behaviour is also found.