Both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_k^2$$\end{document}hk2 and rG can be estimated from GWAS summary statistics using LD score regression22,23. Following20, individual-level genetic predictors with BLUP properties can also be obtained from GWAS summary statistics (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{g}}_{{\mathrm{SBLUP}}_k}$$\end{document}g^SBLUPk, where SBLUP represents summary statistic approximate BLUP). Therefore, for any given trait, genetic predictors with BLUP properties \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{g}}_{{\mathrm{SBLUP}}_k}} \right)$$\end{document}g^SBLUPk can be created from GWAS summary statistics and these can then be placed in a weighted index to produce approximate multi-trait summary statistic BLUP (wMT-SBLUP) predictors, using only LD score regression and an independent reference sample. This approach, provided in the freely available software SMTPred (see Code availability section), approximates MT-BLUP predictors without the need for individual-level phenotype–genotype data for all traits, enabling prediction accuracy to be improved by fully utilising all of the publically available GWAS summary statistic data. We also show how weighted indices can be calculated for GWAS summary statistics (wMT-GWAS) or from predictors obtained using the software LDPred18 (wMT-LDPred), therefore depending upon the genetic architecture of the trait approximate multi-trait summary statistics can be created to maximise genomic prediction accuracy.