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Personalised medicine, in which genetic testing is the basis for informing future health status and determining intervention, is effectively applied for a number of monogenic disorders 1. For six additional phenotypes in the UK Biobank data, we find increases in prediction accuracy ranging from 0.7% for height to 47% for type 2 diabetes, when using a multi-trait predictor that combines published summary statistics from multiple traits, as compared to a predictor based only on one trait. We apply this framework to predict risk of schizophrenia and bipolar disorder in the Psychiatric Genomics consortium data, finding substantial heterogeneity in prediction accuracy increases across cohorts. We show how a genetic predictor can be created as a weighted index that combines published genome-wide association study (GWAS) summary statistics across many different traits. Here theory and simulation study are used to demonstrate that widespread pleiotropy among phenotypes can be utilised to improve genomic risk prediction. However, to date, the utility of such predictors is limited due to low accuracy for most traits. Genomic prediction has the potential to contribute to precision medicine.