The current subprime crisis has prompted us to look again into the nature of risk at the tail of the distribution. In particular, we investigate the risk contribution of an asset, which has infrequent but huge losses, to a portfolio using two risk measures, namely Value-at-Risk (VaR) and...

Since Value-at-Risk (VaR) disregards tail losses beyond the VaR boundary, the expected shortfall (ES), which measures the average loss when a VaR is exceeded, and the tail-risk-of-VaR (TR), which sums the sizes of tail losses, are used to investigate risks at the tails of distributions for major...