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.
You are talking about correlations. They are not stable anyway. You can predict it with some % chance. For example LTC was good hedge against BTC for a long time in the past. But right now there are a lot of strong and interesting coins that looks more stable than other: EOS for example. You can watch the charts from the past few weeks and analyse by yourself. Dash is also interesting and correlating with BTC sometimes. But doing it by the hands isn't best option. People who are good at the correlation using algorithms to analyse it in % together. Just looking the charts isn't best option imho.