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While respiratory diseases such as chronic obstructive pulmonary disease (COPD) and asthma share many risk factors, most studies investigate them in isolation and in predominantly European-ancestry populations. Here, we conducted the most powerful multi-trait and multi-ancestry genetic analysis of respiratory diseases and auxiliary traits to date, identifying 25 new loci associated with lung function in individuals of East Asian ancestry. Using these results, we developed PRSxtra (cross-trait and cross-ancestry), a multi-trait and multi-ancestry polygenic risk score (PRS) approach that leverages shared components of heritable risk via pleiotropic effects. PRSxtra significantly improved the prediction of asthma, COPD and lung cancer compared to trait- and ancestry-matched PRSs in a multi-ancestry cohort from the All of Us Research Program, especially in diverse populations. Our results present a new framework for multi-trait and multi-ancestry studies of respiratory diseases to improve genetic discovery and polygenic prediction.