It is a common wisdom in Bitcoin circles that volatility of the price will diminish as market grows. The logic is based in the fact that, for a given value of a trade, the larger (or deeper) market moves less in response to that trade than a smaller market. An opposing – and often overlooked – argument is that smaller market capitalization results in more participants being able to move the market. If diversity of strategies prevails over herd mentality, the average result may be decreased volatility compared to a larger market where only few participants can cause significant moves, including intentional manipulation. Whatever the case may be, it is not quite simple.
Volatility was calculated for each day as a standard deviation of logarithmic returns in a 7-day moving window. Alternatively, and more simply, volatility for each day was calculated in a 7-day moving window as the ratio of the difference between the high and low and the volume-weighted average price. It should be noted that bitcoin markets are generally open 24/7. The two methods lead to the same conclusion discussed below. Bitstamp market data were obtained from Bitcoin Charts. Data on the total bitcoin supply over time was obtained from Blockchain.info via Quandl.
The total valuation of bitcoin supply has increased hundredfold over the past two years. The volatility does not appear to show correlation with the dramatic growth of bitcoin economy in the same period. If we get lucky (or work hard), we might see another hundredfold increase in the valuation, enabling us to answer the question with much more certainty. Until then, the volatility of bitcoin prices will need to be understood in terms of something other than the market size.