Cleaning correlation matrices

The determination of correlation matrices is typically affected by in-sample noise. Joël Bun, Jean-Philippe Bouchaud and Marc Potters propose a simple, yet optimal, estimator of the true underlying correlation matrix and show that this new cleaning recipe outperforms all existing estimators in terms of the out-of-sample risk of synthetic portfolios

The concept of correlations between different assets is a cornerstone of Markowitz's optimal portfolio theory, especially for risk management purposes (Markowitz 1968). In a nutshell, correlations measure the tendency of different assets to vary together, and it is well known that large losses at a portfolio level are indeed mostly due to correlated moves of its constituents (see, for example, Bouchaud & Potters 2003). Efficient and robust diversification is needed to alleviate such events.

CLI