  We present the first photometric redshift distribution for a large unbiased
sample of 870um selected submillimeter galaxies (SMGs) with robust
identifications based on observations with the Atacama Large Millimeter Array
(ALMA). In our analysis we consider 96 SMGs in the Extended Chandra Deep Field
South, 77 of which have 4-19 band, optical-near-infrared, photometry. We model
the Spectral Energy Distributions (SEDs) for these 77 SMGs, deriving a median
photometric redshift of z=2.3+/-0.1. The remaining 19 SMGs have insufficient
optical or near-infrared photometry to derive photometric redshifts, but a
stacking analysis of IRAC and Herschel observations confirms they are not
spurious. Assuming these sources have an absolute H-band magnitude distribution
comparable to that of a complete sample of z~1-2 SMGs, we demonstrate that the
undetected SMGs lie at higher redshifts, raising the median redshift for SMGs
to z=2.5+/-0.2. More critically we show that the proportion of galaxies
undergoing an SMG phase at z>3 is 35+/-5% of the total population. We derive a
median stellar mass for SMGs of Mstar=(8+/-1)x10^10Mo, but caution that there
are significant systematic uncertainties in our stellar mass estimate, up to x5
for individual sources. We compare our sample of SMGs to a volume-limited,
morphologically classified sample of ellipticals in the local Universe.
Assuming the star formation activity in SMGs has a timescale of ~100Myr we show
that their descendants at z~0 would have a space density and M_H distribution
which are in good agreement with those of local ellipticals. In addition the
inferred mass-weighted ages of the local ellipticals broadly agree with the
look-back times of the SMG events. Taken together, these results are consistent
with a simple model that identifies SMGs as events that form most of the stars
seen in the majority of luminous elliptical galaxies at the present day.
