  The ``small'' black ring in 5D obtained by giving angular momentum to the
D1-D5 system compactified on S^1 x K3 is a very interesting object in the sense
that it does not have an event horizon in the supergravity limit whereas it
microscopically has a finite entropy. The microscopic origin of this small
black ring can be analyzed in detail since it is constructed by adding angular
momentum to the well-studied D1-D5 system. On the other hand, its macroscopic,
geometrical picture is difficult to study directly. In this note, by duality
transformations and the 4D-5D connection, we relate this 5D small black ring to
a 4D small non-rotating black hole, where the latter is known to develop a
non-vanishing horizon due to stringy R^2 corrections to the supergravity
action. This gives an indirect evidence that a non-vanishing horizon is formed
for the 5D small black ring. We also show that the entropy of the 4D small
black hole agrees with the microscopic entropy of the 5D small black ring,
which supports that the 4D-5D connection is indeed valid even for small black
objects.
