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Polygenic scores (PGS) have been widely used to predict disease risk using variants identified from genome-wide association studies (GWAS). To date, most GWAS have been conducted in populations of European ancestry, which limits the use of GWAS-derived PGS in non-European ancestry populations. Here, we derive a theoretical model of the relative accuracy (RA) of PGS across ancestries. We show through extensive simulations that the RA of PGS based on genome-wide significant SNPs can be predicted accurately from modelling linkage disequilibrium (LD), minor allele frequencies (MAF), cross-population correlations of causal SNP effects and heritability. We find that LD and MAF differences between ancestries can explain between 70 and 80% of the loss of RA of European-based PGS in African ancestry for traits like body mass index and type 2 diabetes. Our results suggest that causal variants underlying common genetic variation identified in European ancestry GWAS are mostly shared across continents.