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We propose a model of volatility tail behavior in which investors display aversion to both low-volatility and high-volatility states, and hence, the derived pricing kernel exhibits an increasing and decreasing region in the volatility dimension. The model features investors who have heterogeneity in beliefs about volatility outcomes and maximize their utility by choosing volatility-contingent cash flows. Our empirical examination suggests that the model is better suited to reproduce data features in the left tail of the volatility distribution, both qualitatively and quantitatively. [ABSTRACT FROM AUTHOR]