Random Matrix Theory may be applied to clean the covariance matrix from the statistical noise. This is especially important for short time series and has practical relevance to risk management in portfolio optimisation. In this talk, the relation between spectral densities of empirical covariance matrix and exact correlation matrix will be discussed. The presented method is able to capture heavy tails in the probability density functions of indivudual stocks returns. Furthermore it enables dealing with both temporal and inter-asset correlations. It makes use of a fact that spectrum of the corresponding correlated Wishart ensemble is known. The method may be applied to a broad class of distributions, and an example of multivariate Student distribution will be shown here.

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