Revisiting the volatility of bitcoin with approximate entropy

Two distinct and non-redundant understandings of volatility, as deviation from consistency, exist for a time-series: (1) exhibiting high standard deviation and, closer to the dictionary definition of the term, (2) appearing highly irregular and unpredictable. We find that Bitcoin is a prime example of an asset for which the two concepts of volatility diverge. We show that, historically, Bitcoin combines high Standard Deviation and low Approximate Entropy, relative to Gold and S&P 500. Moreover, subsample analysis for different time-scales (daily, weekly, monthly) shows that lower sampling frequencies drastically reduce the Kurtosis of the distribution of log-returns of Bitcoin. The opposite effect is observed for Gold and S&P 500. These properties suggest that, contrary to the volatility of the two traditional assets, Bitcoin’s high volatility is essentially an intra-day phenomenon that is strongly attenuated for a weekly or monthly time-preference.