Abstract Sea bass is a major species in Mediterranean aquaculture, and is now being subject to selective breeding programmes for faster growth. In terrestrial species, it was demonstrated that fast growth may be linked to a correlated degradation of fitness traits. In this experiment, we evaluated 600 young sea bass from a factorial mating of 76 sires and 13 dams. The sires were from four genetic groups, wild (W), domesticated (D), and selected for growth (2 groups, M and P). The 600 offspring were submitted to two acute confinement stress challenges at 6 weeks intervals, and plasma cortisol at one hour post stress was measured. The same fish were also submitted to two swimming challenges at a 5 days interval, where the maximum sustained swimming speed ( U max ) of each fish was evaluated. Parentage was assessed by genotyping of 12 microsatellites. 554 fish had both valid parentage and phenotypes. Cortisol had a low repeatability (r = 0.30 between the two successive measurements) while repeatability was moderate for U max (r = 0.62). However, genetic correlations between successive measurements were very high (> 0.96) for both traits, indicating that successive measurements were related to the same trait. Heritability was moderate for mean post-stress cortisol (h 2 = 0.34 ± 0.09) and U max (h 2 = 0.48 ± 0.08). When U max was expressed in m.s − 1 , it was negatively correlated to cortisol (r A = − 0.48 ± 0.08) and weakly correlated to body weight (r A = 0.12 ± 0.16), but figures changed when it was expressed in Body Lengths.s − 1 (h 2 = 0.55 ± 0.08, r A = − 0.10 ± 0.19 with cortisol and r A = − 0.64 ± 0.07 with body weight, respectively). Cortisol was moderately negatively correlated with body weight (r A = − 0.36 ± 0.18). The four lines did not differ for cortisol or U max , but when U max was expressed in BL.s − 1 it tended to be lower in the two selected lines — which were also significantly larger. However, this is likely due to a phenotypic decrease of relative U max with increasing body size. We conclude that selection for growth and/or domestication should not impact maximum sustained swimming speed in the European sea bass, but may tend to favour animals with low cortisol responsiveness. These traits could be used to orientate functional capabilities other than productivity in sea bass. Statement of relevance We estimate heritability of cortisol stress response and (for the first time) in European sea bass, as well as their correlations with growth. We show moderate correlations, and no correlated response to selection for growth. We also provide methods to evaluate these traits on large number of fishes. This can be useful to monitor and design breeding programmes.