Testing for differences in the tails of stock-market returns

In this paper, we use a database consisting of daily stock-market returns for 20 countries to test for similarities between the left and right tails of returns, as well as across countries. We estimate and test using the distribution of extreme returns over subsamples approach. Via Monte-Carlo simulations, we show that maximum-likelihood estimators are essentially unbiased, provided the size of subsamples is correctly chosen, and that the likelihood-ratio tests on parameters characterizing the behavior of extremes are correctly sized. For actual returns, we find that left and right tails behave very similarly. Across countries, we find that extremes are located at different levels and that their dispersion varies. The tail index, characterizing large extreme realizations, is found to be constant within each geographical group. We verify that the perception that left tails are heavier than right ones is not due to clustering of extremes. The failure to detect statistical significant differences is likely to be due to the relative infrequency of large extremes.