The average investor in the variance swap market is indifferent to news about future variance at horizons ranging from 1 month to 14 years. It is only purely transitory and unexpected realized variance that is priced. These results present a challenge to most structural models of the variance risk premium, such as the intertemporal CAPM, recent models with Epstein-Zin preferences and long-run risks, and models where institutional investors have value-at-risk constraints. A rare disaster model

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... th constant disaster probability and time-varying exposure of equities to the disaster can match the stylized facts, suggesting that investors use the variance swap market to hedge against disasters. Finally, our results also have strong implications for macro models where volatility affects investment decisions, suggesting that investors are not willing to pay to hedge shocks in expected economic uncertainty.