  A reputation of high volatility accompanies the emergence of Bitcoin as a
financial asset. This paper intends to nuance this reputation and clarify our
understanding of Bitcoin's volatility. Using daily, weekly, and monthly closing
prices and log-returns data going from September 2014 to January 2021, we find
that Bitcoin is a prime example of an asset for which the two conceptions of
volatility diverge. We show that, historically, Bitcoin allies both high
volatility (high Standard Deviation) and high predictability (low Approximate
Entropy), relative to Gold and S&P 500.
  Moreover, using tools from Extreme Value Theory, we analyze the convergence
of moments, and the mean excess functions of both the closing prices and the
log-returns of the three assets. We find that the closing price of Bitcoin is
consistent with a generalized Pareto distribution, when the closing prices of
the 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, lower
sampling frequencies (monthly vs weekly, weekly vs daily) drastically reduce
the Kurtosis of log-returns and increase the convergence of empirical moments
to 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-day
and 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 its
high standard deviation excludes its use a currency.
