It was already talked much about portfolio optimization in the early 60?s, whereby the topic risk and the measure for risk was the primary discussed issue. The biggest challenge lay in the quantification of the risk variables. After the publication of the well-known essay ?portfolio selection? from Markowitz, advanced models developed. This work contains the theoretical bases of the portfolio theory form Markowitz, the basis assumptions for the models, the description of the variables such as standard deviation, variance and covariance, the description of an efficient portfolio, the theory of estimation error and the estimators of Bayes, Stein, James, Frost, Savarino, Ledoit and Wolf. The empirical study contains an investigation on basis of Ledoit and Wolf to reduce the error estimation in the portfolio optimization. The article of Ledoit and wolf ?Honey, I shunk the sample covariance matrix? describes the theoretically basis for the empirical investigation, whereby the computations, in particular the computation of the estimators for theta exceed the framework of the master work, therefore the shrinkage level is fixed on three levels. The shrinkagesystem is accomplished in the empirical part with the procedure by Frost and Savarino. The results are affected by the financial crisis 2008, because the used historical data in this thesis is from 2001-2011. Two of the three calculated shrunked portfolios end before 2011 because the fictitious value becomes negative. Immense outliers let assume, that the past financial crisis made the historical data possibly useless. Due to the historical data and results of the investigation, no definite result can be confirmed over the decrease of error estimation, because since the last quarter 2008 two shrunked optimization test developed negatively and no comparison can be made over the running time.