Bitcoin and portfolio diversification during crises: Evidence from the French market with mean–variance and stochastic dominance analysis

This study explores the diversification potential of Bitcoin in a French investment portfolio comprising oil, currency, and gold across three distinct market regimes: a pre-crisis stable period, the COVID-19 pandemic, and the Russia–Ukraine conflict. The purpose is to assess whether Bitcoin can enhance portfolio efficiency and provide hedging opportunities under varying market conditions. The analysis is conducted using daily data for Bitcoin, gold, oil, currency, and the CAC40 index from January 1, 2019, to April 22, 2022. Portfolio performance is evaluated through the Mean–Variance (MV) framework and Stochastic Dominance (SD) analysis, allowing for a robust comparison of risk–return trade-offs and investor preferences. The MV results show that including Bitcoin consistently improves the portfolio’s risk–return profile, evidenced by an upward shift in the efficient frontier across all sub-periods. However, the SD analysis yields more nuanced insights. Before and during the COVID-19 crisis, the portfolio excluding Bitcoin dominates the Bitcoin-inclusive portfolio under second- and third-order stochastic dominance criteria, suggesting that risk-averse investors would prefer the traditional asset mix. In contrast, during the Russia–Ukraine war, no clear stochastic dominance is detected between Bitcoin-inclusive and Bitcoin-exclusive portfolios. These findings emphasize that Bitcoin’s diversification role is highly context- and framework-dependent.