The idea of green economy, which was placed on the global agenda by the Rio+20 conference, claims to serve as a bridge between the demands of global capitalism and the vision of sustainability. In the corporate social responsibility (CSR) literature, writers such as Michael Porter and Mark Kramer have made a similar claim, arguing that there is a positive correlation between corporate social performance and corporate financial performance. I argue that the claim underlying the green economy thesis, whereby the goals of (classical) economic growth and sustainable development can be achieved concurrently, is highly problematic. First, the claim disregards the extent to which the web of ideas and institutional structures that underpin the global capitalist system constrains the capacity of agents to commit themselves to sustainable policies. Second, it understates the difficult tradeoffs involved in implementing green growth policies. This critique ties in with the debate over the capacity of CSR instruments to promote sustainable development. I examine this general critique in the context the two leading global sustainability indexes: the FTSE4Good Index Series (FTSE4Good) and the Dow Jones Sustainability Indices (DJSI). Sustainability indexes epitomize the green economy thesis because they claim to positively affect the sustainability profile of firms despite the fact that (or precisely because) they are situated at the heart of modern capitalism: the stock exchange. I demonstrate how the paradox at the heart of the green economy thesis manifests in sustainable indexes. In particular, I highlight the tension between the indexes' dual role as financial products (tracking the firms'share values) and as CSR instruments. I also show that both indexes suffer from a deep democratic deficit, which is inconsistent with their public function. I conclude with policy recommendations that could bring the indexes closer to a more meaningful understanding of the concept of green economy.