I have a confession. I once had a psychopath boss. His nickname in the office was 'silent assassin'. He wasn't the CEO but did hold a senior position as Head of Department for a big consultancy I worked at.
Self awareness is the first and most influential aspect of EI: the few who are gifted with true self awareness have a realistic understanding of how what they feel affects what they do. They also understand which situations trigger certain emotional responses in themselves and others.