The normal distribution is widely used in finance, particularly in financial modeling, derivative pricing, and risk management. However, it is well recognized that asset return distributions are often non-normal and exhibit fat tails. Understanding these distributions is therefore important for derivative pricing, risk management, and even the development of trend-following strategies.
In this context, Reference [1] studies the unconditional return distributions of gold and Bitcoin before, during, and after two major crises: COVID-19 and the Russia–Ukraine war. The authors use daily closing prices from Yahoo Finance for COMEX gold futures and Bitcoin, covering selected periods between January 2019 and December 2023. They test ten probability distributions, including Student's t, Laplace, and others.
The authors pointed out,
Gold demonstrates relative stability across all crises: volatility rises modestly during high-stress periods but remains contained relative to Bitcoin. Its return distributions are best captured by heavy-tailed but near-symmetric specifications, most often the Laplace and, in the calmest sub-period, the normal. These results indicate that gold departs from normality mainly through heavier tails and a sharper central peak, with little role for asymmetry, and that the two-parameter Laplace provides a reliable baseline across the sub-periods considered.
Bitcoin exhibits heightened regime sensitivity. Across the COVID-19 and Russia-Ukraine crises, its best-fitting model shifts with market stress, but the leading specifications are predominantly the Laplace and, at the crisis peak, the Student’s t, both of which capture heavy tails without requiring asymmetry. Scale-mixture models such as the ASLSM become competitive only in the single post-crisis Bitcoin sub-period with the most extreme tails, where the additional mixture component is justified. In all sub-periods Bitcoin retains heavier tails than gold, reinforcing its greater susceptibility to regime shifts.
In short, the paper finds that Bitcoin's return distribution changes substantially across crises, whereas gold is relatively stable. Simple heavy-tailed distributions, particularly Laplace and Student's t, generally provide better in-sample fits than the normal distribution, without consistently requiring additional skewness parameters.
The study makes an important contribution, although the analysis itself is not overly complicated. In fact, this type of analysis can and should be performed by portfolio and risk managers, given its significant implications for investment decisions and risk management.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Nagar, P., Gabin, L. A., & Mandona, K. (2027), Distributional properties of gold and Bitcoin returns across crisis regimes: A comparative analysis, Journal of Statistical Theory and Practice.
Article Source Here: Gold and Bitcoin Return Distributions During Market Crises
source https://harbourfronts.com/gold-bitcoin-return-distributions-market-crises/
