Polygenic risk scores (PRSs) are weighted sums of risk allele counts of single-nucleotide polymorphisms (SNPs) associated with a disease or trait. PRSs are typically constructed based on published results from Genome-Wide Association Studies (GWASs), and the majority of which has been performed in large populations of European ancestry (EA) individuals. Although many genotype-trait associations have generalized across populations, the optimal choice of SNPs and weights for PRSs may differ between populations due to different linkage disequilibrium (LD) and allele frequency patterns. We compare various approaches for PRS construction, using GWAS results from both large EA studies and a smaller study in Hispanics/Latinos: The Hispanic Community Health Study/Study of Latinos (HCHS/SOL, n=12,803 ). We consider multiple approaches for selecting SNPs and for computing SNP weights. We study the performance of the resulting PRSs in an independent study of Hispanics/Latinos from the Women's Health Initiative (WHI, n=3,582 ). We support our investigation with simulation studies of potential genetic architectures in a single locus. We observed that selecting variants based on EA GWASs generally performs well, except for blood pressure trait. However, the use of EA GWASs for weight estimation was suboptimal. Using non-EA GWAS results to estimate weights improved results.