Since January 2005, pensions in Slovakia are operated by a three-pillar system. This paper concentrates on the mandatory, fully funded second pillar. In their analysis authors follow the dynamic stochastic accumulation model proposed by the authors in (Kilianova et al., 2006). Recently pension asset managers tend to be very cautious and they hold low stock to bond proportions in the pension funds. The authors discuss the sensitivity of the level of savings with respect to the proportion of stocks in the portfolios. Furthermore, they perform the sensitivity analysis with respect to correlation between stock and bond returns and risk aversion. Finally, authors prove linearity of the level of savings with respect to the contribution rate.