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

TL;DR

This paper examines Bitcoin's volatility across different time scales, revealing that while Bitcoin exhibits high volatility and predictability, its heavy-tailed returns and distributional properties differ from traditional assets like Gold and S&P 500.

Contribution

It provides a nuanced analysis of Bitcoin's volatility and distributional characteristics across multiple time scales using advanced statistical methods.

Findings

Bitcoin's volatility is high but predictability is also high.

Bitcoin's returns are heavy-tailed with non-convergent moments.

Lower sampling frequencies reduce kurtosis in Bitcoin's returns.

Abstract

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.