  This paper studies a distributionally robust portfolio optimization model
with a cardinality constraint for limiting the number of invested assets. We
formulate this model as a mixed-integer semidefinite optimization (MISDO)
problem by means of the moment-based ambiguity set of probability distributions
of asset returns. To exactly solve large-scale problems, we propose a
specialized cutting-plane algorithm that is based on bilevel optimization
reformulation. We prove the finite convergence of the algorithm. We also apply
a matrix completion technique to lower-level SDO problems to make their problem
sizes much smaller. Numerical experiments demonstrate that our cutting-plane
algorithm is significantly faster than the state-of-the-art MISDO solver
SCIP-SDP. We also show that our portfolio optimization model can achieve good
investment performance compared with the conventional robust optimization model
based on the ellipsoidal uncertainty set.
