Here we overcome this limitation by developing a framework that combines publically available GWAS summary statistics across multiple studies of different traits together in a weighted index to generate approximate multi-trait summary statistic BLUP (wMT-SBLUP) predictors (Supplementary Table 1). We show through theory and simulation study that MT-BLUP predictors, which traditionally require individual-level phenotype–genotype data for all traits, can be approximated accurately by wMT-SBLUP predictors in a computationally efficient manner using only summary statistic data and an independent genomic reference sample. We also show how multi-trait summary statistic predictors can be created directly from GWAS summary statistics (wMT-GWAS) or from predictors obtained using the software LDPred18 that extends a single-trait summary statistic BLUP model (SBLUP) by assuming that marker effects come from a mixture of distributions. We apply our approach to multiple phenotypes in the Psychiatric Genomics Consortium (PGC) to compare summary statistic approaches to direct estimation on individual-level data. We further apply our approach to summary statistics of several other phenotypes to create predictors that we evaluate using the UK Biobank data. We show that, for most traits, our multi-trait predictors improve prediction accuracy as compared to a single-trait predictors.