In this paper we analyze whether and how a central bank can pursue the objective to lower its exposure to climate-related financial risks in its asset purchase programs while meeting the criteria that define the eligible universe of assets, including market neutrality. Despite focusing on the analysis of European Central Bank (ECB)’s asset purchase program and its exposure to climate transition risk, our approach and results can be applied to other central banks. We first prove analytically that under a strict market neutrality principle, the ECB’s corporate bonds’ portfolio is completely determined and climate transition risk cannot be reduced. We then show that under a weaker market neutrality principle, it is possible to construct a portfolio with lower exposure to climate transition risk than the current one. We provide a simple algorithm to produce examples of such portfolios. Our results contribute to support central banks in the assessment of their exposure to climate-related financial risks, and in the introduction of climate change considerations in their assets purchase programs.