[quote=dumbrenter]Isn’t the volatility defined relative to an index? If the market goes down 10% and your stock does the same, then there is no volatility at all.[/quote]

Beta is (in theory) a correlative indicator. If the index and the target both move the same, then the correlation would be 1, whether the delta is 1%, 10% or 50%. (And a 10% move IS the volatility.)