Revisiting the volatility of bitcoin with approximate entropy

Abstract

Two distinct and non-redundant understandings of volatility, as deviation from consistency, exist for a time-series: (1) exhibiting high standard deviation and, closer to the dictionary definition of the term, (2) appearing highly irregular and unpredictable. We find that Bitcoin is a prime example of an asset for which the two concepts of volatility diverge. We show that, historically, Bitcoin combines high Standard Deviation and low Approximate Entropy, relative to Gold and S&P 500. Moreover, subsample analysis for different time-scales (daily, weekly, monthly) shows that lower sampling frequencies drastically reduce the Kurtosis of the distribution of log-returns of Bitcoin. The opposite effect is observed for Gold and S&P 500. These properties suggest that, contrary to the volatility of the two traditional assets, Bitcoin’s high volatility is essentially an intra-day phenomenon that is strongly attenuated for a weekly or monthly time-preference.

Keywords:

• Time-Series Analysis
• Information Theory
• Approximate Entropy
• Volatility
• Extreme Value Theory
• Cryptocurrency
• Bitcoin

PUBLIC INTEREST STATEMENT

This paper nuances the reputation of high volatility of Bitcoin relative to traditional financial assets (Gold and the S&P 500). We show that, although the variations in the price and returns of the cryptocurrency are wider, they are more regular and predictable. Moreover, the volatility of Bitcoin decreases at lower time-frequencies (monthly vs weekly vs daily), whereas it increases in the case of Gold and the S&P 500.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Pound, J. (2021, February) Bitcoin hits $1 trillion in market value as cryptocurrency surge continues, CNBC. Retrieved on 20/05/2021 from https://www.cnbc.com/2021/02/19/bitcoin-hits-1-trillion-in-market-value-as-cryptocurrency-surge-continues.html

2. Fidelity Learning Center (2020) Standard Deviation, Technical Indicator Guide. https://www.fidelity.com/learning-center/trading-investing/technical-analysis/technical-indicator-guide/standard-deviation on 25/05/2021

3. Commodity Futures Trading Commission (2021) Bitcoin. Retrieved on 20/05/2021 from https://www.cftc.gov/Bitcoin/index.htm

4. Yahoo Finance, Bitcoin-US Dollar quotes. Retrieved on 20/01/2021 from https://finance.yahoo.com/quote/BTC-USD/history?p=BTC-USD

Yahoo Finance, COMEX—COMEX Delayed Price. Retrieved on 20/01/2021 from https://finance.yahoo.com/quote/GC%3DF/history?p=GC%3DF

Yahoo Finance, SNP—SNP Real Time Price. Retrieved on 20/01/2021 from https://finance.yahoo.com/quote/%5EGSPC/history?p=%5EGSPC

Additional information

Funding

The author received no direct funding for this research.

Notes on contributors

Nassim Dehouche

Nassim Dehouche holds a Ph.D. and M.Sc. in Operations Research from Paris-Dauphine University, and a State Engineer degree from Houari Boumedienne University of Science and Technology. His research interests revolve around Operations Research, Combinatorial Optimization, and Data Analysis. In a career spanning three continents, he has had the opportunity to undertake or participate in different projects in the fields of Energy, Non-Profit Project Management, Healthcare Management and Transportation.