Intelligent Black–Litterman Portfolio Optimization Using a Decomposition-Based Multi-Objective DIRECT Algorithm

Abstract

It is agreed that portfolio optimization is of great importance for the financial market. However, input sensitivity and highly-concentrated portfolios have posed a challenge. In this paper, a random forest-based Black–Litterman model is developed, aiming to further enhance the portfolio performance, which adopts a novel method for generating investor views on the basis of random forests. More specifically, the view vector is generated based on the predicted asset returns obtained by random forests, and the confidence matrix which contains the uncertainty of each view is measured by the difference in the predicted values of multiple trees. Furthermore, motivated by decomposition strategy, a novel multi-objective DIRECT algorithm is introduced to effectively resolve the proposed model. Through the construction of a unique indicator, the algorithm possesses the capacity to select potentially-optimal hyperrectangles in all reference directions simultaneously, which will further improve the exploratory nature. Experimental results have demonstrated that the proposed algorithm achieves a better performance over NSGA-II and MOEA/D on the MOP and DTLZ benchmark problems. It is also experimentally verified that the random forest-based Black–Litterman model can obtain higher cumulative returns and Sharpe ratios in the application of Chinese stock markets when compared to the classic MV model.

Keywords

• portfolio selection
• Black–Litterman model
• random forests
• DIRECT
• multi-objective optimization