We present a completely automated optimization strategy which combines the classical Markowitz mean-variance portfolio theory with a recently proposed test for structural breaks in co- variance matrices. With respect to equity portfolios, global minimum-variance optimizations, which base solely on the covariance matrix, yield considerable results in previous studies. However, nancial assets cannot be assumed to have a constant covariance matrix over longer periods of time. Hence, we estimate the covariance matrix of the assets by respecting potential change points. The resulting approach resolves issues like timing or determining a sample for parameter estimation. Moreover, we apply the approach to two datasets and compare the results to relevant benchmark techniques by means of an out-of-sample study. It is shown that the new approach outperforms equally weighted portfolios and plain minimum-variance portfolios on average.