One surprising feature of the recently completed waves of genome-wide association studies is the limited impact of common genetic variation in individually detectable polymorphisms on many human traits. This has been particularly pronounced for studies on psychiatric conditions, which have failed to produce clear, replicable associations for common variants. One popular explanation for these negative findings is that many of these traits may be genetically heterogeneous, leading to the idea that relevant endophenotypes may be more genetically tractable. Aspects of cognition may be the most important endophenotypes for psychiatric conditions such as schizophrenia, leading many researchers to pursue large-scale studies on the genetic contributors of cognitive performance in the normal population as a surrogate for aspects of liability to disease. Here, we perform a genome-wide association study with two tests of executive function, Digit Symbol and Stroop Color-Word, in 1086 healthy volunteers and with an expanded cognitive battery in 514 of these volunteers. We show that, consistent with published studies of the psychiatric conditions themselves, no single common variant has a large effect (explaining >4-8% of the population variation) on the performance of healthy individuals on standardized cognitive tests. Given that these are important endophenotypes, our work is consistent with the idea that identifying rare genetic causes of psychiatric conditions may be more important for future research than identifying genetically homogenous endophenotypes.