The distribution of ownership of transition risk associated with stranded fossil-fuel assets remains poorly understood. We compute global stranded assets of US$1.4 trillion in the upstream oil and gas sector as expectations change to be consistent with stated climate policies. We trace the equity risk ownership from these 43,439 assets through a global equity network of 1.8 million companies to their ultimate owners. Most of the market risk falls on private investors, overwhelmingly in OECD countries, including substantial exposure through pension funds. Financial markets are exposed to a US$690 billion correction, comparable to the mispricing that triggered the 2007-08 crisis. The ownership distribution also shows the large stake OECD investors have in the continued operation of fossil-fuel facilities incompatible with climate change mitigation goals.