  Being able to predict the occurrence of extreme returns is important in
financial risk management. Using the distribution of recurrence intervals---the
waiting time between consecutive extremes---we show that these extreme returns
are predictable on the short term. Examining a range of different types of
returns and thresholds we find that recurrence intervals follow a
$q$-exponential distribution, which we then use to theoretically derive the
hazard probability $W(\Delta t |t)$. Maximizing the usefulness of extreme
forecasts to define an optimized hazard threshold, we indicates a financial
extreme occurring within the next day when the hazard probability is greater
than the optimized threshold. Both in-sample tests and out-of-sample
predictions indicate that these forecasts are more accurate than a benchmark
that ignores the predictive signals. This recurrence interval finding deepens
our understanding of reoccurring extreme returns and can be applied to forecast
extremes in risk management.
