Mean–variance portfolio optimization with parameter sensitivity control

Abstract

The mean–variance (MV) portfolio selection model, which aims to maximize the expected return while minimizing the risk measured by the variance, has been studied extensively in the literature and regarded as a powerful guiding principle in investment practice. Recognizing the importance to reduce the impact of parameter estimation error on the optimal portfolio strategy, we integrate a set of parameter sensitivity constraints into the traditional MV model, which can also be interpreted as a model with marginal risk control on assets. The resulted optimization framework is a quadratic programming problem with non-convex quadratic constraints. By exploiting the special structure of the non-convex constraints, we propose a convex quadratic programming relaxation and develop a branch-and-bound global optimization algorithm. A significant feature of our algorithm is its special branching rule applied to the imposed auxiliary variables, which are of lower dimension than the original decision variables. Our simulation analysis and empirical test demonstrate the pros and cons of the proposed MV model with sensitivity control and indicate the cases where sensitivity control is necessary and beneficial. Our branch-and-bound procedure is shown to be favourable in computational efficiency compared with the commercial global optimization software BARON.