The heart muscle diseases hypertrophic (HCM) and dilated (DCM) cardiomyopathies are leading causes of sudden death and heart failure in young otherwise healthy individuals. We conducted genome-wide association studies (GWAS) and multi-trait analyses in HCM (1,733 cases), DCM (5,521 cases), and nine left ventricular (LV) traits in 19,260 UK Biobank participants with structurally-normal hearts. We identified 16 loci associated with HCM, 13 with DCM, and 23 with LV traits. We show strong genetic correlations between LV traits and cardiomyopathies, with opposing effects in HCM and DCM. Two-sample Mendelian randomization supports a causal association linking increased contractility with HCM risk. A polygenic risk score (PRS) explains a significant portion of phenotypic variability in carriers of HCM-causing rare variants. Our findings thus provide evidence that PRS may account for variability in Mendelian diseases. More broadly, we provide insights into how genetic pathways may lead to distinct disorders through opposing genetic effects.