In this talk we will discuss how the top eigenvalue/eigenvector pair evolves through time for estimators of covariance and correlation matrices of equity return type data. By this we mean that the matrices have a top eigenvalue which is well separated from the others. Our main results are that both the eigenvalue and eigenvector of a correlation matrix has an extra stability effect, which has previously been observed empirically but to our knowledge never previously studied theoretically. Because of this, one has to use different methods for determining and studying the stationarity of correlations than what is used for covariances. The results are also interesting from a practical aspect, as they give intuition on how to check for non-stationaries and how to adapt the estimator to them. They can also be used as a tool to more exactly quantify the correlation risk versus the volatility risk of a portfolio or for fine-tuning of estimators.