Researchers applying clustering methods have found that the five most commonly studied personality traits (the ‘Big Five’) appear to form three prototypes, known as resilient, undercontrolled, and overcontrolled (RUO) personality types. The analysis has been replicated cross‐nationally, and the results have been reasonably robust. However, these findings do not necessarily imply discontinuities or non‐linearities in the Big Five data. We study whether the RUO types can arise from typical Big Five intercorrelations alone. We used data from a previous meta‐analysis of inter‐trait correlations (N = 144 117 participants) and simulated normally distributed observations with this correlation structure. Applying three different clustering algorithms (k‐means, hierarchical agglomerative, and model based) with three‐cluster solutions to the simulated data, we examined whether the known correlations alone can give rise to the RUO typology. The simulated results were compared with previous empirical findings. A simple multivariate normal distribution with the Big Five correlation structure was sufficient to generate the RUO typology in three‐cluster solutions for all the three clustering methods. Contrary to the RUO typology ‘carving personality description at its joints’, linear correlations typical for correlations among Big Five traits can create RUO types even in the absence of any points of discontinuity. Copyright © 2017 European Association of Personality Psychology