The vast majority of genome-wide association studies are performed in Europeans, and their transferability to other populations is dependent on many factors (e.g. linkage disequilibrium, allele frequencies, genetic architecture). As medical genomics studies become increasingly large and diverse, gaining insights into population history and consequently the transferability of disease risk measurement is critical. Here, we disentangle recent population history in the widely-used 1000 Genomes Project reference panel, with an emphasis on populations underrepresented in medical studies. To examine the transferability of single-ancestry GWAS, we used published summary statistics to calculate polygenic risk scores for six well-studied traits and diseases. We identified directional inconsistencies in all scores; for example, height is predicted to decrease with genetic distance from Europeans, despite robust anthropological evidence that West Africans are as tall as Europeans on average. To gain deeper quantitative insights into GWAS transferability, we developed a complex trait coalescent-based simulation framework considering effects of polygenicity, causal allele frequency divergence, and heritability. As expected, correlations between true and inferred risk were typically highest in the population from which summary statistics were derived. We demonstrated that scores inferred from European GWAS were biased by genetic drift in other populations even when choosing the same causal variants, and that biases in any direction were possible and unpredictable. This work cautions that summarizing findings from large-scale GWAS may have limited portability to other populations using standard approaches, and highlights the need for generalized risk prediction methods and the inclusion of more diverse individuals in medical genomics.