In this paper, a portfolio selection model with a combined
Worst-case Conditional Value-at-Risk (WCVaR) and Multi-Factor Model is proposed.
It is shown that the probability
distributions in the definition of WCVaR can be determined by specifying
the mean vectors under the assumption of multivariate normal distribution
with a fixed variance-covariance matrix. The WCVaR minimization problem is then
reformulated as a linear programming problem. In our numerical experiments,
to compare the proposed model with the traditional mean variance model,
we solve the two models using the real market data in Japan and present
the efficient frontiers to illustrate the difference. The comparison reveals
that the WCVaR minimization model is more robust than the traditional
one in a market recession period.