Risk has always played a very large role in the world of finance with the performance of a large number of investment and trading strategies being dependent on the efficient estimation of underlying market risk. The covariance matrix is one of the most popular and widely used estimator of risk but due to its sensitivity to market conditions and dependence on historical data, it produces an unreliable estimation of true market risk. In this post, we go over some important methods of estimating covariance matrices which can be used in practice to remove noise from empirical estimates and produce better and reliable risk estimations.