Uncertainty regarding Chinese and American economic policies impacts major investable asset classes in politically contestable geographic regions such as Southeast Asia. Our objective is to examine the dependence structure of Chinese and American Economic Policy Uncertainty (EPU) and returns on six Association of Southeast Asian Nations (ASEAN) stock indices and to assess the impact of a significant statecraft consideration, the One Belt One Road (OBOR) Initiative, and an exogenous shock, the COVID-19 crisis, on the connectedness between EPU and ASEAN stock returns. We do so by employing novel connectedness and copula approaches. We find that American and Chinese EPU influence ASEAN equity indices differently across countries, with the connectedness of US EPU and ASEAN stock markets exceeding that of Chinese EPU post-2002. Further, we find that the introduction of the OBOR Initiative by China in 2013 coincided with a slight change in the dependence structure for several individual ASEAN stock indices, and show that the impact of the COVID-19 pandemic on the relationship between American and Chinese EPU and individual ASEAN stock index returns was not homogenous across countries. In doing so, we shed new light on the vulnerability of ASEAN member capital markets to statecraft considerations and exogenous shocks, as well as to economic policy decision-making in China and the United States.