In an analysis of the risk-sharing properties of different types of pension systems, we show that only a fixed-fee pay-as-you-go (PAYG) pension systems can provide intergenerational risk sharing for living individuals. Under some circumstances, however, other PAYG pension systems can enhance the expected welfare of all generations by reducing intergenerational income variability. We derive conditions for this to occur. We also analyze the stability of actuarially fair PAYG pension systems. It is shown that if an actuarially fair pension with a non-balanced budget system is dynamically stable, its accumulated surpluses will converge to the same fund as in a fully funded system. We also show that the welfare loss due to labor market distortions will, surprisingly, increase if the implicit marginal return in a compulsory system is raised above the average return.