It showed some stability at that price but then it fell to the lower of 3000$ and I dont think bitcoin is going to be stable at a price for a longer time. The trading keeps happening and people buy and sell at support and resistance points so we cannot expect the price of bitcoin to be stable especially with such low market cap.
Marketcap of bitcoin is 67 billion dollars and I do not think it is at lower side for manipulation. I mean its marketcap is not a criteria for being volatile. Like any commodity, bitcoin's price level also being determined by supply and demand. Even we have calculated supply, the demand is at lower side to match the supply and already existing coins. When people dump their bitcoins, if there are more buyers then we will have rising markets still there will be less possibilities for stable prices.
Only after bitcoin will become as a mainstream payment system and people buy and use bitcoins for transacting like fiats, we may have stable prices for bitcoins.