Robust Investment Management with Uncertainty in Fund Managers’ Asset Allocation

We consider a problem where an investment manager must allocate an available budget among a set of fund managers, whose asset class 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 class returns, in the context of manager selection and portfolio management when short sales are not allowed. A key application area is university endowments funds. 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 a 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.