I believe that we are born with some personality traits that we inherit. But in spite of that we can be "modeled" depending on our surrondings. For example: a person inherits a trait that makes him/her easily react with violence. If he's raised in USA (taking El Wray's example) he'll then not hesitate in reacting violently. However if he's raised in Japan he might get used to think twice before doing something violent.
So it's kind of a mixture of nature and nurture: we are born with a personality that can be changed to a certain extent by society.