  In this paper, we consider the basic problem of portfolio construction in
financial engineering, and analyze how market-based and analytical approaches
can be combined to obtain efficient portfolios. As a first step in our
analysis, we model the asset returns as a random variable distributed according
to a mixture of normal random variables. We then discuss how to construct
portfolios that minimize the Conditional Value-at-Risk (CVaR) under this
probabilistic model via a convex program. We also construct a second-order cone
representable approximation of the CVaR under the mixture model, and
demonstrate its theoretical and empirical accuracy. Furthermore, we incorporate
the market equilibrium information into this procedure through the well-known
Black-Litterman approach via an inverse optimization framework by utilizing the
proposed approximation. Our computational experiments on a real dataset show
that this approach with an emphasis on the market equilibrium typically yields
less risky portfolios than a purely market-based portfolio while producing
similar returns on average.
