Volatility measures as predictors of extreme returns

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book-to-market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E-GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.