Cannot use instance member within property initializer
So if we decode the error message you can figure out whats wrong. It says property initializers run before self is available so we need to adjust what we're doing since our property depends on bounds which belongs to self. Lets try a lazy variable. You can't use bounds in a let because it doesn't exist when that property is created because it belongs to self. So at init self isn't complete yet. But if you use a lazy var, then self and its property bounds will be ready by the time you need it.
lazy var arrowPath = UIBezierPath.bezierPathWithArrowFromPoint(startPoint: CGPoint(x: self.bounds.size.width/2,y: self.bounds.size.height/3), endPoint: CGPoint(x: self.bounds.size.width/2, y: self.bounds.size.height/3*2), tailWidth: 8, headWidth: 24, headLength: 18)