Financial unsustainability of pension systems in developed economies looms large on the horizon due to increasing life expectancy and continuous drop in fertility. In spite of a broad discussion, there has been but a little consensus on appropriate remedy. One aspect partially neglected in the literature is vulnerability of pension systems to market imperfections and economic shocks. I present three basic types of pension schemes adopted across all developed countries - pure PAYG, fully-funded, and mixed (multipillar) scheme - and examine effects of various risks -- particularly market risk, interest rate risk, investment risk, and longevity risk -- on their functioning. The analysis shows that while no pension scheme is immune to external influences, the multipillar scheme provides the best results thanks to appropriate risk diversification.