The world’s financial sector is making significant strides to account for both transition and physical climate risks in investments. The latter holds promise for increasing resilience. But effective frameworks for characterising physical risks for different types of investors and investments are as yet missing or often not used, and avoidance of investments in high-risk areas may counter the positive effects. This short commentary starts to characterise the promises and pitfalls of climate risk assessment in the financial sector and proposes a conceptual framework to capture the main dimensions. A stronger and collaborative role for public and private climate service providers is suggested to upgrade climate risk assessments for financial actors.