Abstract: Portfolio risk, introduced by Markowitz in 1952 and defined as the standard deviation of the portfolio return, is an important metric in the modern portfolio theory (MPT). A popular method for portfolio selection is to manage the risk and return of a portfolio according to the cross-correlations of returns for various financial assets. In a real-world scenario, estimated empirical financial correlation matrix contains significant level of intrinsic noise that needs to be filtered prior to risk calculations.