Distributional Properties of Gold and Bitcoin Returns Across Crisis Regimes: A Comparative Analysis

Abstract Financial crises often amplify the limitations of standard return models, which often underestimate the probability of extreme price movements. This paper investigates the distributional properties of daily log-returns for gold and Bitcoin across two major crises: the COVID-19 pandemic and the Russia–Ukraine war, using pre-crisis, crisis, and post-crisis sub-periods to capture regime-specific behaviour. Ten candidate distributions are considered, including normal and Laplace families, their skewed extensions, and contaminated variants to accommodate heavy tails and asymmetry. The evaluated distributional fit across assets and regimes, provides insights into tail thickness and skewness under varying market conditions. Results reveal pronounced differences: gold demonstrates a comparatively stable distributional structure across regimes, while Bitcoin exhibits heightened sensitivity to market stress, with high kurtosis and regime-dependent skewness. These findings underscore the importance of flexible heavy-tailed models for accurate risk quantification and portfolio construction during periods of extreme volatility. By identifying which models best capture return behaviour under crisis conditions, this paper contributes to improving risk management strategies and reconciling mixed evidence on the distributional behaviour of these assets under market stress.