Abstract: According to the “portfolio primacy” theory, large asset managers, and in particular large index funds, can and will undertake the role of “climate stewards” and will push corporations to reduce their carbon footprint. This theory is based on the view that index fund portfolios mirror the entire market and therefore have strong financial incentives to reduce market-wide threats, such as climate change. But how much can we rely on portfolio primacy to mitigate the effects of climate change? In this Article, I provide a conceptual and empirical assessment of the potential impact of portfolio primacy on climate change mitigation by examining the scope of action, economic incentives, and fiduciary conflicts of index fund managers. The analysis reveals three major limits, each reinforcing the others, that undermine the promise of portfolio primacy. First, the potential scope of index fund stewardship is narrow, as most companies around the world, including most carbon emitters, are private or controlled companies. Second, index funds internalize only a fraction of the social cost of climate change and therefore have very weak incentives to engage in ambitious climate stewardship. Third, index fund managers advise dozens of index funds with conflicting interests with respect to climate mitigation and therefore face serious fiduciary conflicts that would hamper any ambitious mitigation strategy. This analysis shows that we should have very modest expectations about the role of portfolio primacy in the fight against climate change.