Building Diversified Portfolios that Outperform Out of Sample
提出层次风险平价方法，利用图论和机器学习构建多元化投资组合，解决传统二次优化器的不稳定、集中和表现不佳问题，蒙特卡洛实验显示其样本外方差低于关键线算法。
In this article, the author introduces the Hierarchical Risk Parity (HRP) approach to address three major concerns of quadratic optimizers, in general, and Markowitz’s critical line algorithm (CLA), in particular: instability, concentration, and underperformance. HRP applies modern mathematics (graph theory and machine-learning techniques) to build a diversified portfolio based on the information contained in the covariance matrix. However, unlike quadratic optimizers, HRP does not require the invertibility of the covariance matrix. In fact, HRP can compute a portfolio on an ill-degenerated or even a singular covariance matrix—an impossible feat for quadratic optimizers. Monte Carlo experiments show that HRP delivers lower out-ofsample variance than CLA, even though minimum variance is CLA’s optimization objective. HRP also produces less risky portfolios out of sample compared to traditional risk parity methods. <b>TOPICS:</b>Statistical methods, portfolio construction