The James Webb Space telescope has discovered an abundant population of broad line emitters, typical signposts for Active Galactic Nuclei (AGN). Many of these sources have red colors and a compact appearance that has led to naming them `Little Red Dots'. In this paper we develop a detailed framework to estimate the photometry of AGN embedded in galaxies extracted from the Obelisk cosmological simulation to understand the properties of color-selected Little Red Dots (cLRDs) in the context of the full AGN and massive black hole population. We find that using realistic spectral energy distributions (SEDs) and attenuation for AGN we can explain the shape of the cLRD SED as long as galaxies host a sufficiently luminous AGN that is not too much or too little attenuated. When attenuation is too low or too high, AGN do not enter the cLRD selection, because the AGN dominates over the host galaxy too much in blue filters, or it does not contribute to photometry anywhere, respectively. cLRDs are also characterized by high Eddington ratios, possibility super-Eddington, and/or high ratios between black hole and stellar mass.