||This thesis focuses on two methods for optimum portfolio selection. We compare Mean-Variance method with Mean-VaR method by the means of investment simulation, based on Czech financial market data from turbulent market periods of the year 2007 and the year 2008. We theoretically describe various approaches of optimum portfolio selection within a frame of Mean-Variance as well as Mean-VaR method. Furthermore, we highlight the similarities and differences of both strategies. Finally, we compare both strategies, basing on measurements of relative and absolute profitability of both strategies in crisis periods.