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While lipid traits are known essential mediators of cardiovascular disease, few approaches have taken advantage of their shared genetic effects. We apply a Bayesian multivariate size estimator, mash, to GWAS of four lipid traits in the Million Veterans Program (MVP) and provide posterior mean and local false sign rates for all effects. These estimates borrow information across traits to improve effect size accuracy. We show that controlling local false sign rates accurately and powerfully identifies replicable genetic associations and that multivariate control furthers the ability to explain complex diseases. Our application yields high concordance between independent datasets, more accurately prioritizes causal genes, and significantly improves polygenic prediction beyond state-of-the-art methods by up to 59% for lipid traits. The use of Bayesian multivariate genetic shrinkage has yet to be applied to human quantitative trait GWAS results, and we present a staged approach to prediction on a polygenic scale.