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Bitcoin, Gold, and S&P 500 Volatility Across Sampling Scales

Article arXiv papers · Author: Nassim Dehouche
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Summary

The study compares Bitcoin with gold and the S&P 500 using daily, weekly, and monthly closing prices and log returns from September 2014 to January 2021. It distinguishes volatility measured by standard deviation from predictability measured by approximate entropy, and applies extreme value methods to examine tail behavior and whether empirical moments converge.

Bitcoin shows both higher standard deviation and greater predictability than the two comparison assets. Closing prices for Bitcoin fit a generalized Pareto distribution, while gold and S&P 500 prices have thinner tails; returns for all three assets are heavy tailed, with non-convergent second moments. Aggregating Bitcoin returns to lower frequencies reduces kurtosis and improves moment convergence, whereas the reverse pattern appears for gold and the S&P 500. The authors infer that Bitcoin's volatility is concentrated within days and weeks. These historical findings do not establish future behavior, and the reported high standard deviation limits Bitcoin's suitability as a currency.

Key ideas

  • The study compares volatility and predictability at daily, weekly, and monthly frequencies.
  • Bitcoin displays both high standard deviation and low approximate entropy relative to gold and the S&P 500.
  • Returns for all three assets are heavy tailed, and their second moments do not converge in the analysis.
  • Lower sampling frequencies reduce Bitcoin return kurtosis but have the opposite effect for gold and the S&P 500.
  • The findings suggest Bitcoin volatility is concentrated at intraday and intraweek horizons.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.