Fossil fuel market dynamics will have a significant impact on the effectiveness of climate policies. Both fossil fuel owners and investors in fossil fuel infrastructure are sensitive to climate policies that threaten their natural resource endowments and production capacities, which will consequently affect their near-term behaviour. Although weak in near-term policy commitments, the Paris Agreement on climate signalled strong ambitions in climate change stabilization. Many studies emphasize that the 2 °C target can still be achieved even if strong climate policies are delayed until 2030. However, sudden implementation will have severe consequences for fossil fuel markets and beyond and these studies ignore the anticipation effects of owners and investors. The authors use two energy–economy models to study the collective influence of the two central but opposing anticipation arguments, the green paradox and the divestment effect, which have, to date, been discussed only separately. For a wide range of future climate policies, they find that anticipation effects, on balance, reduce CO2 emissions during the implementation lag. This is because of strong divestment in coal power plants starting ten years ahead of policy implementation. The green paradox effect is identified, but is small under reasonable assumptions. The full article is available on the Nature website.