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. 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. 1 Motivation and Literature Review Institutional investors, such as pension funds, university endowments and insurance companies, actively manage their portfolio by investing money in outside fund managers with the expectation of generating superior returns while keeping risk at an acceptable level. Fund managers might have quite different risk and return profiles regarding their strategy and investment process, and the investment manager (institutional investor) must decide how to allocate his budget among them given a high-level idea of each fund’s strategy, ∗Senior Quantitative Analyst, JP Morgan, New York, NY [email protected] This research was done while the first author was a doctoral student at Lehigh University. †Visiting Associate Professor, M.I.T. Sloan School of Management, Cambridge, MA, USA and Associate Professor, Lehigh University, Department of Industrial and Systems Engineering, Bethlehem, PA, USA [email protected]