The green, the dirty and the stable: Diversifying equity portfolios by adding tokens of different nature

•BRICS equities and dirty/green cryptos exhibit lower correlations than their peers (G7-dirty/green)•The correlation between equities and stablecoins is always scarce and even negative.•All cryptos analyzed provide diversification benefits, but stablecoins may be also considered as safe havens.•Some strategies reduce their risk due to low correlations and others rely on their residual intrinsic volatility.•Almost all strategies enhance their performance. In this study we propose to empirically assess the potential diversification benefits of three types of cryptocurrencies (traditional: Bitcoin, green: Cardano and stablecoins: Tether) by including them in equity-based asset allocation strategies. We build monthly rebalanced minimum VaR portfolios based on different wavelet scales or investment horizons. We use the ADCC-GARCH model to fit the dynamic dependence structure. We find that traditional and green cryptocurrencies provide diversification opportunities when considering portfolio strategies based on short-term investment horizons. We also demonstrate that stablecoins may play the role of safe haven assets for those portfolio strategies based on long-term investment horizons.