Studying the correlation structure of risk measures

The aim of this paper is to study the correlation structure of different risk measures. These measures include idiosyncratic skewness (IS), idiosyncratic kurtosis (IK), volatility, idiosyncratic volatility (IV), Cornish-Fisher VaR(CFVaR), extreme downside risk (EDR) and right tail index. The GARCH(p,q) model is estimated by Fama-French regression innovations and then using the residuals to calculate the EDR and other measures for 175 stocks in TSE. In this research, Extreme Value Theory (EVT) is used to estimate Extreme downside risk and Cornish-Fisher expansion of value at risk. The results show that the IS and CFVaR methods have the highest correlation coefficient with the EDR method, but given the low correlation values, this implies that the EDR effect cannot be completely subsumed by other risk measures. Only the EDR and CFVaR measures focus on left tail of distribution and are comparable to each other. Back testing results for Cornish-Fisher expansion of value at risk and Extreme downside risk approaches show Extreme downside risk has a better prediction in compare with Cornish-Fisher expansion of value at risk.