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Most autoimmune-disease-risk effects identified by genome-wide association studies (GWAS) localize to open chromatin with gene-regulatory activity. GWAS loci are also enriched in expression quantitative trait loci (eQTLs), thus suggesting that most risk variants alter gene expression. However, because causal variants are difficult to identify, and cis-eQTLs occur frequently, it remains challenging to identify specific instances of disease-relevant changes to gene regulation. Here, we used a novel joint likelihood framework with higher resolution than that of previous methods to identify loci where autoimmune-disease risk and an eQTL are driven by a single shared genetic effect. Using eQTLs from three major immune subpopulations, we found shared effects in only ∼25% of the loci examined. Thus, we show that a fraction of gene-regulatory changes suggest strong mechanistic hypotheses for disease risk, but we conclude that most risk mechanisms are not likely to involve changes in basal gene expression.