An optimization–diversification approach to portfolio selection

The classical approaches to optimal portfolio selection call for finding a feasible portfolio that optimizes a risk measure, or a gain measure, or a combination thereof by means of a utility function or of a performance measure. However, the optimization approach tends to amplify the estimation errors on the parameters required by the model, such as expected returns and covariances. For this reason, the Risk Parity model, a novel risk diversification approach to portfolio selection, has been recently theoretically developed and used in practice, mainly for the case of the volatility risk measure. Here we first provide new theoretical results for the Risk Parity approach for general risk measures. Then we propose a novel framework for portfolio selection that combines the diversification and the optimization approaches through the global solution of a hard nonlinear mixed integer or pseudo Boolean problem. For the latter problem we propose an efficient and accurate Multi-Greedy heuristic that extends the classical single-threaded greedy approach to a multiple-threaded setting. Finally, we provide empirical results on real-world data showing that the diversified optimal portfolios are only slightly suboptimal in-sample with respect to optimal portfolios, and generally show improved out-of-sample performance with respect to their purely diversified or purely optimized counterparts.