Baruch Cohen, better known as Billy Joe Cobra, is a former world-famous rock star. The Wright family moved into his home not long after Billy died, and led him to meet Spencer Wright, his distant relative. Together, the two of them get prank-style revenge on people who hurt Spencer, work to improve Spencer's image at Beverly Beverly High, and enjoy some quality "bro time" (usually resulting in hilarity).
Overall, Billy's main goal seems to be to have as much fun as possible, which causes enough problems for Spencer to clean up. Billy never turns his back on a friend though, and helps Spencer when he can.
Billy Joe is pretty well up on the hottie-scales and the popularity charts, and he knows it -- to the point of blatant narcissism. This, along with his other achievements, gives him a huge ego, good for the stroking. However, he can usually put his self-absorption aside if his bro is in danger or needs help. He also seems to be an understanding individual, being able to put personal grievances aside for important situations, such as an event where Spencer wants to impress a girl. (Still, Billy doesn't seem to understand the concept of "tact".)
He isn't particularly street smart, since all his life people have been doing things in his stead and kissing up to him. As a result, he hasn't had much experience living as an ordinary person. He's also gullible, evidenced by his being fooled by Sam Hoover's disguises and getting hoodwinked into doing Spencer's homework for him. In addition, Billy is incredibly easily distracted and has a short attention span that only serves to get him and his homebods in trouble.
Despite this, he is shown to be relatively intelligent, and has surprisingly good memory. He knows some school material incredibly well because he has personal experience with the subjects covered, and completely understands Beverly Beverly celeb scene's unusual and convoluted social rules.
Billy is incredibly prone to throwing diva tantrums if Spencer either doesn't stop him or makes him start them. He doesn't seem to regret them afterwards, suggesting that he is used to them and constantly had them while he was alive. This may have caused several movie directors to despise him.
He seems to crave attention from Spencer, (as well as attention in general) as well as want to appease him. When scared, Billy clings to Spencer like a lifeline. Only Spencer can talk him into doing things like letting crazed tourists into his mansion or hanging out with a geeky, "unchill" ghost. In addition, Billy is always willing to make it up to Spencer whenever he wrongs him.