Portfolio selection with the effect of systematic risk diversification: formulation and accelerated gradient algorithm

Abstract

In this paper, we propose an optimal trade-off model for portfolio selection with the effect of systematic risk diversification, measured by the maximum marginal systematic risk of all the risk contributors. First, the classical portfolio selection model with constraints on allocation of systematic risk is shown to be equivalent to our trade-off model under certain conditions. Then, we transform the trade-off model into a special non-convex and non-smooth composite problem equivalently. Thus a modified accelerated gradient (AG) algorithm can be introduced to solve the composite problem. The efficiency of the algorithm for solving the composite problem is demonstrated by theoretical results on both the convergence rate and the iteration complexity bound. Finally, empirical analysis demonstrates that the proposed model is a preferred tool for active portfolio risk management when compared with the existing models. We also carry out a series of numerical experiments to compare the performance of the modified AG algorithm with the other three first-order algorithms.