This article examines whether investors receive compensation for holding crash-sensitive stocks. We capture the crash sensitivity of stocks by their lower-tail dependence (LTD) with the market based on copulas. We find that stocks with strong LTD have higher average future returns than stocks with weak LTD. This effect cannot be explained by traditional risk factors and is different from the impact of beta, downside beta, coskewness, cokurtosis, and Kelly and Jiang’s (2014) tail risk beta. Hence, our findings are consistent with the notion that investors are crash-averse.

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In this online appendix, I first provide a brief comparison of the small noise expansion series and the Taylor expansion series. I then use separably Taylor expansion series and the small noise expansion series to derive the pricing kernel in a one-market model with two dates, and the pricing kernel in a two-market model with three dates. I thereafter, investigate whether one obtains a pricing kernel that depends on the market co-skewness and the market volatility in a long run risk model and also in a model where the representative investor chooses his optimal allocation in the presence of the market equity and the variance swap contracts. The remaining part of the appendix contains additional tables and figures used in the paper.