In recent years, genome-wide association studies (GWAS) have identified many loci that are shared among common disorders and this has raised interest in pleiotropy. For performing appropriate analysis, several methods have been proposed, e.g. conducting a look-up in external sources or exploiting GWAS results by meta-analysis based methods. We recently proposed the Compare & Contrast Meta-Analysis (CCMA) approach where significance thresholds were obtained by simulation. Here we present analytical formulae for the density and cumulative distribution function of the CCMA test statistic under the null hypothesis of no pleiotropy and no association, which, conveniently for practical reasons, turns out to be exponentially distributed. This allows researchers to apply the CCMA method without having to rely on simulations. Finally, we show that CCMA demonstrates power to detect disease-specific, agonistic and antagonistic loci comparable to the frequently used Subset-Based Meta-Analysis approach, while better controlling the type I error rate.