As tempting as that would be, and as satisfying as it may seem in the short term, don't touch that kid. No one will benefit and you may just make it worse by escalating the name calling to physical violence against your sister. Get adults involved. Tell a school counselor, parents, or if this jerk is threatening her call the cops. Don't get yourself arrested for assault by beating this bully up.
I wouldn't beat him up, but I would take him down. Someone picked on my little brother once and by the time I got done telling them and everyone else around about all their faults that were glaringly obvious because they were picking on a smaller kid. If they were so perfect why weren't they picking on someone their own size or better yet someone bigger? Why? Because they were small minded. Then I started talking baby talk to them so they could understand what I was saying. You know I didn't want to go above their level of understanding. In other words, bully the bully! Of course this works best if you have some friends with you and they start laughing at the idiot.
They need to be able to take what they dish out, so if you've earned them...you gave them a chance to stop it, therefore you have no choice but to take care of it yourself. On the other hand, I don't think this is the best advice I have given. But if you're SURE you've tried EVERYTHING ELSE, his parents, school, filed a report with the police, then I'm sure you can "convince" him to make him stop. Protect your sister.
When I was a kid samething happened and my big bro picked him up by the neck against a tree the guy was two years older than me and my bro di not kick the snot out of him by he scared him shitless. It worked
Think logically. I would want to do that to. Still, what are the consequences? Yes, you get the satisfaction of punching the kid and the guy leaving you alone, but now that means YOU are also in trouble. Bullying is a big problem, and the kid should know that. He/she has probably been bullied before. If your own family member is the bully, that can be a serious problem, and it is also very depressing. The kid is only trying to make himself/herself feel better. Sometimes, you can just ask them why they are being jerks, and that will shut them up. What really annoys them is when you pay no attention to them, so don't do that. Just stare at the kid with a look that says you don't know why their doing it and tell them they sound like an idiot when they bully you like that. Now, saying that may fire the bully off. This is the time to ignore them. Try to shut the bully out. Don't do any of that "Did you hear something?" stuff. They'll only get louder and more obnoxious. Always remember: Violence results in consequence.
I hope you get rid of your bully. They are such a pain!