According to the American Psychiatric Association's Diagnostic and Statistical Manual,
Egocentric
Sociopaths indulge in bragging about themselves like there's no tomorrow. They firmly believe that what they are doing is absolutely right and there's no way they can do anything wrong. They are highly self-assured and this leads them to making highly preposterous and unrealistic plans about life, marriage, earning money and general living. Sociopaths fail to understand why others around them are so against them.
Is this trait common in all sociopaths? I don't remember reading about this being a common trait.