Why is my unneutered cat randomly aggressive after coming in from the balcony?

Your cat has obviously seen something that is invading “his” territory, probably a stray cat (or dog) out there and is exhibiting “misplaced aggression” since he can’t get to whatever is upsetting him, so he’s taking it out on you. Cats are very territorial most especially unneutered males. You have to be worried that he may try to get off the balcony if he becomes upset enough. Cats, if powered by adrenaline, can jump pretty high even if you have a solid railing. Having him neutered is a wonderful idea since this will cut down on the aggression and improve his life in so many other ways. There isn’t much you can do at the moment so just keep him in and away from whatever is upsetting him.