We derive the exact form of the eigenvalue spectrum of correlation matrices obtained from a set of N time-shifted, iid Gaussian time-series of length T. These matrices are random, real and asymmetric matrices with a superimposed structure due to the time-lag. We demonstrate that the associated (complex) eigenvalue spectrum is circular symmetric for large matrices (\lim N \to \infty ). This fact allows to exactly compute the eigenvalue density via the inverse Abel-transform of the density of the  symmetrized problem. The validity of the approach is demonstrated by comparison to numerical realizations of random time-series. As an example, spectra of correlation matrices from time-lagged financial data are presented.

PACS numbers: 02.50.--r, 02.10.Yn, 05.40.--a, 87.10.+e