This article extends the variance ratio test of Lo and MacKinlay (1988) to tests of skewness and kurtosis ratios. The proposed tests are based on generalized methods of moments. In particular, overlapping observations are used and their dependencies (under the IID assumption) are explicitly...

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...

Extreme losses caused by leverage and financial derivatives highlight the need to backtest Value-at-Risk (VaR) based on sizes of tail losses, for the risk measure disregards losses beyond the VaR boundary and there is no formal statistical analysis required for stress testing. While Basel II...

The US dollar is the most widely held currency in the world. In recent years, however, it suffered huge depreciation. In this paper, various risk models are used to forecast the Value-at-Risk (VaR) in holding the currency. Being a quantile measure, VaR disregards valuable information conveyed by...