Insurance effects of biodiversity can stabilize the functioning of multispecies ecosystems against environmental variability when differential species' responses lead to asynchronous population dynamics. When responses are not perfectly positively correlated, declines in some populations are compensated by increases in others, smoothing variability in ecosystem productivity. This variance reduction effect of biodiversity is analogous to the risk-spreading benefits of diverse investment portfolios in financial markets. We use data from the BIODEPTH network of grassland biodiversity experiments to perform a general test for stabilizing effects of plant diversity on the temporal variability of individual species, functional groups, and aggregate communities. We tested three potential mechanisms: reduction of temporal variability through population asynchrony; enhancement of long-term average performance through positive selection effects; and increases in the temporal mean due to overyielding. Our results support a stabilizing effect of diversity on the temporal variability of grassland aboveground annual net primary production through two mechanisms. Two-species communities with greater population asynchrony were more stable in their average production over time due to compensatory fluctuations. Overyielding also stabilized productivity by increasing levels of average biomass production relative to temporal variability. However, there was no evidence for a performance-enhancing effect on the temporal mean through positive selection effects. In combination with previous work, our results suggest that stabilizing effects of diversity on community productivity through population asynchrony and overyielding appear to be general in grassland ecosystems.