While any Altcoin is swayed by the overall market, finding an Altcoin with a large market cap and large trading volume should be a good estimator of stability. For the cheap mid-price Altcoins, something like Ripple is pretty stable. For the even cheaper coins, you can never go wrong with Dogecoin.
Even most of those altcoins with the high marker cap were red for some days together with bitcoin. The goal is to find an altcoin where I can hide my money from those dumps. Ripple performed greate this time but I see no guarantees that this coin will do the same at the next time.
Actually there is no stable altcoin. Changing of value is natural in this digital money world. We all know that cryptocurrency is volatile. I think some of cryptos remains at the high price because of their platform or investors. Thats what I think. It is not being pulled also by the dumped of bitcoin.