The relevance of the article is due to the introduction since 01.01.2024 in the Russian Federation of a long-term savings program for citizens as a substitute for the funded part of pension frozen since 2014. The main reason for the freeze was inefficiency of the saving system, namely negative real investment returns. In the article, we consider the activities of state regulator for regulating investment activities of pension funds and its contribution to the effectiveness of long-term saving program being introduced for citizens and whether the created system will be resistant to external shocks such as COVID-19. Applying Markovitz portfolio modeling to leading international stock indices and comparing the results with the data of pension savings investment in the Russian Federation, the article provides findings concerning the need to change the principles of state regulation of pension savings investment in terms of easing geographical and instrumental restrictions. Building on the findings of Nepp et al. (2022) on short-term nature of COVID-19 impact on financial markets, we apply a differential equation in the Cauchy form, used in physical processes for the research impulse effects, to determine the impact of a short-term external shock on the example of the coronavirus pandemic on funded pension systems. It is proved that in case of a long saving period, significantly exceeding the duration of the influence of an external shock, its impact on funded pension systems can be neglected.