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Extreme Dependence Structures and the Cross-Section of Expected Stock Returns

There is strong empirical support for the notion that investors are crash-averse. The option pricing literature documents that deep out-of-the-money index puts, i.e. instruments that o er protection against extreme market downturns, have a high implied volatility, i.e. they are relatively expensive. Garleanu, Pedersen, and Poteshman (2009) show that this e ect is driven by high demand for out of the money puts, which drives up their price.

This strong demand is typically interpreted as investors being crash-averse or showing signs of 'crasho phobia' (Rubinstein (1994)). Surprisingly, the potential impact of crash-aversion has not caught much attention in the empirical asset pricing literature on common stocks. Our study addresses this issue by investigating the impact of individual stock crash sensitivity on the cross-section of returns.

We capture the crash-sensitivity of a stock based on copula methods. We examine the in uence of extreme dependence between individual stocks and the market on the cross section of asset returns. Standard asset pricing models since Sharpe (1964) and Lintner (1965) argue that the joint distribution of individual stock returns and the market portfolio return determines the cross-section of expected stock returns. According to the empirical interpretation of the traditional CAPM, a stock whose return has a high linear correlation with the market return must earn a higher return than securities that are less correlated with the market to induce risk averse investors to hold the security.

In the context of bivariate normal distributions, the linear correlation is the appropriate dependence concept. However, the linear correlation is not able to characterize the full dependence structure of non-normally distributed random variables such as realized stock returns (Embrechts, McNeil, and Straumann (2002)). Particularly, it is not able to capture clustering in the tails of the bivariate return distribution between individual securities and the market.

Extreme Dependence Structures and the Cross-Section of Expected Stock Returns