Doctoral Dissertation Defense: Hyekyung Park
Advisor: Drs. Weining Kang and Florian Potra
The robust portfolio selection problem considers the worst case of return under uncertainty sets of parameters, such as mean return and covariance of return. Goldfarb and Iyengar define the return of assets by a factor model and provide the `Separable' uncertainty sets for mean return and covariance of factor returns. However the sets are too conservative and construct a non-diversified portfolio. To overcome the drawbacks, Lu defines the `Joint' ellipsoidal uncertainty set for mean return and covariance of factor returns.
In this research I derive a robust portfolio under the `Joint' ellipsoidal uncertainty set. The problem is to maximize expected return on a portfolio while restricting loss to exceed an investor's specific acceptable loss on a specified degree of confidence, called the robust Value-at-Risk (VaR) constraint problem. The constraint establishes an upper bound on the probability of losing a given percentage on the investment. The constraint under the uncertainty set is a non-convex function, so I use two reasonable estimations, which can be derived as semidefinite and second order cone constraint, so that the problem with the estimations can be easily solved. The computational results on real market data shows why the estimations are reasonable and compare to the problem under the `Separable' uncertainty sets.
Additionally I extend the robust VaR constraint problem under the `joint' uncertainty set to the problem in the presence of transaction costs, which are expenses incurred when buying or selling stocks. The idea is from the multi-period portfolio management problem and uses the same notations. The problem is to maximize transaction-cost adjusted return with the VaR constraint under the ellipsoidal uncertainty set. The real market simulation examines the impact of transaction cost consideration in the model.