  Signatures of universality are detected by comparing individual eigenvalue
distributions and level spacings from financial covariance matrices to random
matrix predictions. A chopping procedure is devised in order to produce a
statistical ensemble of asset-price covariances from a single instance of
financial data sets. Local results for the smallest eigenvalue and individual
spacings are very stable upon reshuffling the time windows and assets. They are
in good agreement with the universal Tracy-Widom distribution and Wigner
surmise, respectively. This suggests a strong degree of robustness especially
in the low-lying sector of the spectra, most relevant for portfolio selections.
Conversely, the global spectral density of a single covariance matrix as well
as the average over all unfolded nearest-neighbour spacing distributions
deviate from standard Gaussian random matrix predictions. The data are in fair
agreement with a recently introduced generalised random matrix model, with
correlations showing a power-law decay.
