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A reputation of high volatility accompanies the emergence of Bitcoin as afinancial asset. This paper intends to nuance this reputation and clarify ourunderstanding of Bitcoin's volatility. Using daily, weekly, and monthly closingprices and log-returns data going from September 2014 to January 2021, we findthat Bitcoin is a prime example of an asset for which the two conceptions ofvolatility diverge. We show that, historically, Bitcoin allies both highvolatility (high Standard Deviation) and high predictability (low ApproximateEntropy), relative to Gold and S&P 500.  Moreover, using tools from Extreme Value Theory, we analyze the convergenceof moments, and the mean excess functions of both the closing prices and thelog-returns of the three assets. We find that the closing price of Bitcoin isconsistent with a generalized Pareto distribution, when the closing prices ofthe two other assets (Gold and S&P 500) present thin-tailed distributions.However, returns for all three assets are heavy tailed and second moments(variance, standard deviation) non-convergent. In the case of Bitcoin, lowersampling frequencies (monthly vs weekly, weekly vs daily) drastically reducethe Kurtosis of log-returns and increase the convergence of empirical momentsto their true value. The opposite effect is observed for Gold and S&P 500.These properties suggest that Bitcoin's volatility is essentially an intra-dayand intra-week phenomenon that is strongly attenuated on a weekly time-scale,and make it an attractive store of value to investors and speculators, but itshigh standard deviation excludes its use a currency.

Scale matters: The daily, weekly and monthly volatility and predictability of Bitcoin, Gold, and the S&P 500