Sensory and cognitive processing relies on the concerted activity of large populations of neurons. The advent of modern experimental techniques like two-photon population calcium imaging makes it possible to monitor the spiking activity of multiple neurons as they are participating in specific cognitive tasks. The development of appropriate theoretical tools to quantify and interpret the spiking activity of multiple neurons, however, is still in its infancy. One of the simplest and widely used measures of correlated activity is the pairwise correlation coefficient. While spike correlation coefficients are easy to compute using the available numerical toolboxes, it has remained largely an open question whether they are indeed a reliable measure of synchrony. Surprisingly, despite the intense use of correlation coefficients in the design of synthetic spike trains, the construction of population models and the assessment of the synchrony level in live neuronal networks very little was known about their computational properties. We showed that many features of pairwise spike correlations can be studied analytically in a tractable threshold model. Importantly, we demonstrated that under some circumstances the correlation coefficients can vanish, even though input and also pairwise spike cross correlations are present. This finding suggests that the most popular and frequently used measures can, by design, fail to capture the neuronal synchrony.