MOTIVATION: A typical genome-wide association study searches for associations between single nucleotide polymorphisms (SNPs) and a univariate phenotype. However, there is a growing interest to investigate associations between genomics data and multivariate phenotypes, for example, in gene expression or metabolomics studies. A common approach is to perform a univariate test between each genotype-phenotype pair, and then to apply a stringent significance cutoff to account for the large number of tests performed. However, this approach has limited ability to uncover dependencies involving multiple variables. Another trend in the current genetics is the investigation of the impact of rare variants on the phenotype, where the standard methods often fail owing to lack of power when the minor allele is present in only a limited number of individuals. RESULTS: We propose a new statistical approach based on Bayesian reduced rank regression to assess the impact of multiple SNPs on a high-dimensional phenotype. Because of the method's ability to combine information over multiple SNPs and phenotypes, it is particularly suitable for detecting associations involving rare variants. We demonstrate the potential of our method and compare it with alternatives using the Northern Finland Birth Cohort with 4702 individuals, for whom genome-wide SNP data along with lipoprotein profiles comprising 74 traits are available. We discovered two genes (XRCC4 and MTHFD2L) without previously reported associations, which replicated in a combined analysis of two additional cohorts: 2390 individuals from the Cardiovascular Risk in Young Finns study and 3659 individuals from the FINRISK study.