Personality traits and their correlations have been shown to be linked with life history strategies and fitness in various species. Among-individual correlations (i.e. behavioural syndromes) between personality traits can affect the evolutionary responses of these traits to environmental variation. Understanding the genetic and ecological determinants of personality traits and their interactions as behavioural syndromes in the wild is thus needed to shed light on the mechanisms shaping their evolution. Partitioning the observed (co)variance in these traits, however, requires large numbers of repeated behavioural measures on many individuals of known relatedness level. In the absence of such data, it is thus often assumed that phenotypic (co)variances inform about (i) underlying among-individual (co)variances (i.e. ignoring within-individual (co)variances) and (2) underlying genetic (co)variances. We tested these assumptions using three personality traits collected during 3 years on a long-term monitored breeding population of collared flycatchers, Ficedula albicollis. We partitioned the observed phenotypic (co)variance of aggressiveness, boldness and neophobia into genetic, permanent environment and parental components, and we estimated the repeatability, and heritability of these traits and their among-individual correlations. All three traits were repeatable between years (at least on the latent scale) but none were heritable. Permanent environment effects explained 15% of the phenotypic variance in aggressiveness, and parental effects explained 25% of the phenotypic variance in neophobia, in line with previous studies in wild populations. The three traits showed phenotypic correlations but no among-individual correlations and no additive genetic covariance. Thus, our results did not support the assumptions that phenotypic covariance reflects behavioural syndromes and genetic covariance. We discuss the reasons for the absence of heritability and among-individual and genetic covariance between these three personality traits in light of the possible selective pressures acting on this population.