We consider a problem where an investment manager must allocate an available budget among a set of fund managers, whose asset allocations are not precisely known to the investment manager. In this paper, we propose a robust framework that takes into account the uncertainty stemming from the fund managers' allocation, as well as the more traditional uncertainty due to uncertain asset returns, in the context of manager selection and portfolio management. We assume that only bounds on the fund managers' holdings (expressed as fractions of the portfolio) are available, and fractions must sum to 1 for each fund manager. We define worst-case risk as the largest variance attainable by the investment manager's portfolio over that uncertainty set. We propose two exact approaches (of different complexity) and an heuristic one to solve the problem efficiently. Numerical experiments suggest that our robust model provides better protection against risk than the nominal model when the fund managers' allocations are not known precisely.
Technical report, Lehigh University, Industrial and Systems Engineering, April 2014