Option-Implied Information and Predictability of Extreme Returns

Abstract

We study whether option-implied conditional expectation of market loss due to tail events, or tail loss measure, contains information about future returns, especially the negative ones. Our 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, especially the one who cares about the left tail of her wealth distribution (e.g., disappointment-averse), benefits from using the tail loss measure as an information variable to construct managed portfolios of a risk-free asset and market index. The tail loss measure is motivated by the results of the extreme value theory, and it is computed from observed prices of out-of-the-money put as the risk-neutral expected value of a loss beyond a given relative threshold.

Keywords: extreme value theory, tail measure, implied correlation, variance risk premium, option-implied distribution, predictability, portfolio optimization

JEL Classification: G11, G12, G13, G17