  The optimization of a large random portfolio under the Expected Shortfall
risk measure with an $\ell_2$ regularizer is carried out by analytical
calculation. The regularizer reins in the large sample fluctuations and the
concomitant divergent estimation error, and eliminates the phase transition
where this error would otherwise blow up. In the data-dominated region, where
the number $N$ of different assets in the portfolio is much less than the
length $T$ of the available time series, the regularizer plays a negligible
role even if its strength $\eta$ is large, while in the opposite limit, where
the size of samples is comparable to, or even smaller than the number of
assets, the optimum is almost entirely determined by the regularizer. We
construct the contour map of estimation error on the $N/T$ vs. $\eta$ plane and
find that for a given value of the estimation error the gain in $N/T$ due to
the regularizer can reach a factor of about 4 for a sufficiently strong
regularizer.
