We have tested the stability of parameters loading the asymmetric behaviour of the correlation and the importance of this behavior on the portfolio selection. In this paper, we have analyzed the following time series S&P index, gold and CME 5-Year Treasury Note Futures during the most important crisis from 1992 to 2009. The methodology is based on the dynamic conditional correlation model and its asymmetric volatility and asymmetric correlation extensions. The stability of parameters was tested

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... by t-test applied on the rol ling windows data. The information importance of asymmetric volatility and correlation was tested by global minimum variance portfolio. The results suggest that the parameters loading the asymmetric behavior of the correlation are not stable for the analyzed time series during the financial crisis. With one exception we have found out that global minimum variance portfolio based on the dynamic conditional correlation model with asymmetric volatility is significantly less volatile than the global minimum variance portfolio based on the asymmetric dynamic conditional correlation model.