Early-type galaxies (ellipticals and lenticulars) are considered to be the end-products of the formation of massive galaxies. Spectroscopic studies of early-type galaxies using optical features reveal an early (z>2) and fast (<1Gyr) formation process, but are insensitive to small episodes of recent star formation. This can be tackled in the ultraviolet (UV) spectral range, which provides a unique window to disentangle such small contributions from young populations. I will show a detailed study comprising high-quality stacked spectra from the SDSS/BOSS survey at redshift z~0.4, producing unambiguous constraints on the fraction of very young stellar populations in massive early-type galaxies thanks to their near-UV features. We constrain the young stellar mass fraction (<2Gyr) with unprecedented sensitivity (~0.1-0.6%), finding a decreasing trend with galaxy mass, consistent with a down-sizing scenario. We apply a similar methodology to synthetic galaxies from state-of-the-art cosmological numerical simulations and find that these models significantly overproduce both intermediate and young stellar populations. Our results pose stringent constraints on numerical simulations of galaxy formation.