As cryptocurrencies become mainstream, researchers have begun examining their statistical properties, particularly volatility, which represents the second moment of the return distribution. However, limited attention has been given to higher-order moments, specifically skewness and kurtosis. Given that cryptocurrencies are highly volatile and exhibit heavy-tail risks, their return distributions are not log-normal, making the study of skewness and kurtosis essential.
Reference [1] effectively analyzes the volatility, skewness, and kurtosis of Bitcoin and their relationships with Bitcoin returns. The authors use 5-minute high-frequency trading data from 2013 to 2024 to study these properties. They pointed out,
This paper employs 5-minute high-frequency data and quantile regression to examine the relationships between returns and higher-order moments in the Bitcoin market. These findings reveal significant asymmetric relationships between returns and higher-order moments in the Bitcoin market. Specifically: First, Bitcoin returns exhibit significant impacts on higher-order moments (namely volatility, skewness, and kurtosis), with contemporaneous returns demonstrating stronger effects than lagged returns. Second, negative returns show significantly negative correlations with changes in volatility and kurtosis, but significantly positive correlations with skewness changes. Third, at the upper quantiles of volatility and kurtosis changes, as well as the lower quantiles of skewness changes, the impact of negative returns on higher-order moments exceeds that of positive returns. Behavioural finance theories help explain these mechanisms.
The paper also provides insights for both investors and regulators
… investors should enhance risk awareness and optimize asset allocation. Investors must fully recognize Bitcoin’s unique risk structure, particularly the tail risks reflected by higher-order moments. When making investment decisions, they should consider not only volatility but also skewness and kurtosis to comprehensively assess risks. Diversification across Bitcoin and traditional assets can mitigate portfolio risks. Investors should also develop science-based strategies aligned with their risk tolerance and investment objectives, avoiding herd behaviour and excessive speculation.
We find this article particularly interesting and important, especially the conclusion that the correlation between Bitcoin returns and volatility is negative. However, we have observed that the options market has not yet priced in this negative correlation. Further research is warranted.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Can Yang and Zhen Fang, The asymmetric relationships between returns and higher-order moments: evidence from the Bitcoin market, Applied Economics, 2025
Article Source Here: Volatility, Skewness, and Kurtosis in Bitcoin Returns: An Empirical Analysis
source https://harbourfronts.com/volatility-skewness-kurtosis-bitcoin-returns-empirical-analysis/
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