None of altcoin can be independent from bitcoin price, the huge drop from the price of bitcoin affected the value of altcoins as a result many investors couldn't realize 10% of initial amount of money invested.
Even all altcoins are depending on bitcoin price movement, we can see some coins are trading on its own time to time. Ethereum must be the good example here and recently waves is doing on its own regardless of where bitcoin is trading. It means we have to choose altcoins after some study, so that we can save our capital even all other cryptos are performing poorer. Also if you are choosing only major altcoins then you do not need to worry about.
Moreover, those investors who are all getting panic on seeing bitcoin markets is falling down may face looses and then may become poor. But, for those investors who are very confident about the future of bitcoins will not get panic hence they will not pull off their bitcoin holding now. They must be choosing to continue their bitcoin stash for the future.
Bitcoin is only good for long term. People who are understanding this fact are making good profits and people are not ready to accept this fact may become poor on their attempts to test the potential of bitcoins.