Polygenic risk models have led to significant advances in understanding complex diseases and their clinical presentation. While traditional models of genetic risk like polygenic risk scores (PRS) can effectively predict outcomes, they do not generally account for disease subtypes or pathways which underlie within-trait diversity. Here, we introduce a latent factor model of genetic risk based on components from Decomposition of Genetic Associations (DeGAs), which we call the DeGAs polygenic risk score (dPRS). We compute DeGAs on associations from 1,905 traits in the UK Biobank and find that dPRS performs comparably to standard PRS while offering greater interpretability. We highlight results for body mass index (BMI), myocardial infarction (heart attack), and gout in 337,151 white British individuals (spilt 70/10/20 for training, validation, and testing), with replication in a further set of 25,486 non-British whites from the Biobank. We show how to decompose an individual's genetic risk for a trait across these latent components. For example, we find that BMI polygenic risk factorizes into distinct components relating to fat-free mass, fat mass, and overall health indicators like sleep duration and alcohol and water intake. Most individuals with high dPRS for BMI have strong contributions from both a fat mass component and a fat-free mass component, whereas a few 'outlier' individuals have strong contributions from only one of the two components. Our methods enable fine-scale interpretation of the drivers of genetic risk for complex traits. +Correspondence to Manuel A. Rivas ( mrivas@stanford.edu ).