Environmental Constraints in Cryptocurrency Portfolio Optimization: A Mean-CVaR Analysis

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Sustainable investing raises an important question: do environmental restrictions affect the risk–return characteristics of cryptocurrency portfolios? This study compares Mean-CVaR optimal portfolios across Green, Dirty, and Mixed cryptocurrency universes using daily returns for 12 cryptocurrencies from January 2022 to September 2025. Ethereum (ETH) was classified as Dirty before its transition from Proof-of-Work to Proof-of-Stake in September 2022 and as Green thereafter. Each universe is optimized independently using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2), and Particle Swarm Optimization (PSO), with CVaR measured at the 95% confidence level. The results show that, in the Post-Merge period, the Green universe exhibits a higher CVaR than the Dirty and Mixed universes under all three algorithms. This result remains consistent across the main robustness analyses and is confirmed by an exact optimization benchmark. The asset-exclusion analysis further shows that excluding Bitcoin (BTC) increases CVaR under all three algorithms, whereas excluding ETH does not produce the same effect. These findings indicate that environmental screening can alter portfolio risk by changing the assets available for investment. For sustainability-oriented investors, the financial effect of such restrictions therefore depends on the assets excluded from the portfolio.