We study whether prices of traded options contain information about future extreme market events. Our option-implied conditional expectation of market loss due to tail events, or tail loss measure, predicts future market returns, magnitude, and probability of the market crashes, beyond and above other option-implied variables. Stock-specific tail loss measure predicts individual expected returns and magnitude of realized stock-specific crashes in the cross-section of stocks. An investor that cares about the left tail of her wealth distribution benefits from using the tail loss measure as an information variable to construct managed portfolios of a risk-free asset and market index.
extreme value theory tail measure implied correlation variance risk premium option-implied distribution predictability portfolio optimization