Portfolio Risk in Multiple Frequencies

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.