Bitcoin is already more stable than certain fiat currencies and has been more stable than the crashing Euro on a weekly basis from March to June 2015(Daily BTC is slightly more volatile). The BTC token is both a currency and an asset and will likely become more stable as market capitalization grows. I wouldn't be surprised if it becomes more stable than all fiat currencies in 20-40 years.
You can always find time periods to satisfy your hypothesis. On an overall basis, there is no denying the fact that Bitcoin is volatile. Of course, this is to be expected in its initial stages. Give it time, and it will find its stable level.