Innovations in volatility constitute a potentially important asset pricing risk factor that can be tested using the return on variance swaps. We characterize the exposures of returns on equities, bonds and currencies in all regions of the world to U.S. based equity variance risk. We explore implications for global risk premiums and asset return comovements using developed and emerging markets. Regional portfolios across all three asset classes and practically all countries exhibit negative loadings on the variance risk factor. These exposures, combined with the average return to the variance swap, provide statistically and economically significant risk premiums, representing around 50% of the overall risk premiums implied by a simple three-factor model with global equity, bond, and variance risks. This simple three-factor model also explains a substantive fraction of the comovements between international assets. The fit is best for equity correlations and is worse for currency and across asset class correlations.