%0 Journal Article %A Marcos López de Prado %T Building Diversified Portfolios that Outperform Out of Sample %D 2016 %R 10.3905/jpm.2016.42.4.059 %J The Journal of Portfolio Management %P 59-69 %V 42 %N 4 %X 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.TOPICS: Statistical methods, portfolio construction %U https://jpm.pm-research.com/content/iijpormgmt/42/4/59.full.pdf