DISCUSSION PAPERS IN STATISTICS AND ECONOMETRICS SEMINAR OF ECONOMIC AND SOCIAL STATISTICS UNIVERSITY OF COLOGNE No. 9/07 Dependence of Stock Returns in Bull and Bear Markets

Pearson’s correlation coefficient is typically used for measuring the dependence structure of stock returns. Nevertheless, it has many shortcomings often documented in the literature. We suggest to use a conditional version of Spearman’s rho as an alternative dependence measure. Our approach is purely nonparametric and we avoid any kind of model misspecification. We derive hypothesis tests for the conditional Spearman’s rho in bull and bear markets and verify the tests by Monte Carlo simulation. Further, we study the daily returns of stocks contained in the German stock index DAX 30. We find some significant differences in dependence of stock returns in bull and bear markets. On the other hand the differences are not so strong as one might expect.