-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 … cares about the left tail of her wealth distribution benefits from using the tail loss measure as an information variable to …

risk capital allocation with the average value-at-risk measure (AVaR). AVaR is the average loss provided that the loss is …