Tail risk and the prediction of stock returns

This paper compares the ability of three tail risk variables to forecast stock returns. One tail risk variable is calculated with the Hill estimator, one with the threshold exceeding method and one is calculated with the price of out-of-the-money European put options. The variables are calculated for two data samples, one with small companies and one with large companies. The forecasts are evaluated using in-sample predictive regressions and out-of-sample regressions with an expanding window. For both the large and the small companies, the variable constructed with the price of out-of-the-money European put options is the best in predicting future stock returns of the three tail risk variables. Some of the benchmark variables, however, perform equally well or even better.