Genetic studies in psychiatry have primarily focused on the effects of common genetic variants, but few have investigated the role of rare genetic variants, particularly for major depression. In order to explore the role of rare variants in the gap between estimates of single nucleotide polymorphism (SNP) heritability and twin study heritability, we examined the contribution of common and rare genetic variants to latent traits underlying psychiatric disorders using high-quality imputed genotype data from the UK Biobank. Using a pre-registered analysis, we used items from the UK Biobank Mental Health Questionnaire relevant to three psychiatric disorders: major depression (N = 134,463), bipolar disorder (N = 117,376) and schizophrenia (N = 130,013) and identified a general hierarchical factor for each that described participants' responses. We calculated participants' scores on these latent traits and conducted single-variant genetic association testing (MAF > 0.05%), gene-based burden testing and pathway association testing associations with these latent traits. We tested for enrichment of rare variants (MAF 0.05-1%) in genes that had been previously identified by common variant genome-wide association studies, and genes previously associated with Mendelian disorders having relevant symptoms. We found moderate genetic correlations between the latent traits in our study and case-control phenotypes in previous genome-wide association studies, and identified one common genetic variant (rs72657988, minor allele frequency = 8.23%, p = 1.01 × 10-9) associated with the general factor of schizophrenia, but no other single variants, genes or pathways passed significance thresholds in this analysis, and we did not find enrichment in previously identified genes.