This paper presents a method for constructing alternative constraints for the Markowitz model. Three models with modification and one standard Markowitz problem give four structures of stock portfolios with different coefficients of extreme risk aversion. The structure of the investment space of each portfolio depends on the coefficient of extreme risk aversion, the shape of the utility function for the selected investment, the ratio of stocks in the portfolio to stocks on the exchange during the selected periods, and the number of stocks. The date sets for the analysis are taken from the WSJ and refer to a planning horizon of 49 months: December 2000 to December 2004.