To augment the relative prices of carbon content emeries to green energies, many governments have imposed carbon prices and proved subsidies to green energy production. Given the imperative role of green finance for global energy transitions, we investigate whether oil equity transmits any significant signal to green investments and vice-versa as substitute commodities. To this end, we apply three novel time-series methods; namely, the Cross-Quantilogram, Time-frequency connectedness and Cross-spectral quantile coherency approaches to analyze daily return series of green bonds, green equity, and selected oil companies' equity returns as dirty investments ranging 30th August 2014 till 9th November 2021. Our empirical investigation demonstrates that dirty investments (oil equity) transmit negative volatility spillovers to green investments (both bond and equity). On the contrary, dirty investment returns respond positively to both green bonds and green equity returns. The co-movement between green and dirty markets is more pronounced in the short time. We also confirm that oil equities induce higher volatility on green markets than vice versa, with green bonds being more vulnerable to this impact. The paper provides policy implications for investors' decision-making making process on risk hedging. © 2023 Elsevier B.V.