I'll introduce the Hierarchical Risk Parity (HRP) approach. HRP portfolios address three major concerns of quadratic optimizers in general and Markowitz's CLA in particular: instability, concentration and under-performance. 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.