Due to the much larger luminance and contrast characteristics of high dynamic range (HDR) images, well-known objective quality metrics, widely used for the assessment of low dynamic range (LDR) content, cannot be directly applied to HDR images in order to predict their perceptual fidelity. To overcome this limitation, advanced fidelity metrics, such as the HDR-VDP, have been proposed to accurately predict visually significant differences. However, their complex calibration may make them difficult to use in practice. A simpler approach consists in computing arithmetic or structural fidelity metrics, such as PSNR and SSIM, on perceptually encoded luminance values but the performance of quality prediction in this case has not been clearly studied. In this paper, we aim at providing a better comprehension of the limits and the potentialities of this approach, by means of a subjective study. We compare the performance of HDR-VDP to that of PSNR and SSIM computed on perceptually encoded luminance values, when considering compressed HDR images. Our results show that these simpler metrics can be effectively employed to assess image fidelity for applications such as HDR image compression.