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

Nassim Dehouche
2021 arXiv   pre-print
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)
more » ... d 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.
arXiv:2103.00395v1 fatcat:hcrfqxcqrnbetmyysyiyb3iuwm