A New Tail-based Correlation

The dependence between assets tends to increase when the market declines. This paper develops a correlation measure focusing on market declines using the expected shortfall (ES), referred to as the ES-implied correlation, to improve the existing value at risk (VaR)-implied correlation. Simulations which define period-by-period true correlations show that the ESimplied correlation is much closer to true correlations than is the VaR-implied correlation with respect to average bias, standard deviation and root-mean-squared error. More importantly, this paper develops a series of test statistics to measure and test correlation asymmetries, as well as to evaluate the impact of weights on the VaR-implied correlation and the ES-implied correlation. The test statistics indicate that the linear correlation significantly underestimates correlations between US and other G7 countries during market downturns, and the choice of weights does not have significant impact on the VaR-implied correlation or the ES-implied correlation.