The Infiniti Four Moment Risk Decomposition introduces the concept of ‘modified Volatility’ and associated modified correlation and modified covariance matrices that allow you attribute the impact of higher moments (Skewness and Kurtosis) to your portfolio VaR and CVaR for a given set of weights using the normal RiskMetrics framework rather than having to work with the co-skewness and co-kurtosis matrices. The linked PowerPoint file and Excel Spreadsheet show a worked example of the uni-variate Normal and Cornish Fisher ‘Modified’ VaR and CVaR and their multivariate Risk decomposition using this method. As you can see we step back through the Cornish Fisher expansion to arrive at ‘Modified’ Correlation and Covariance Matrices. These are satisfying and not globally optimal matrices but have been constructed on an ‘as if’ basis to allow the end user to use the matrices in the ‘Normal’ RiskMetrics manner to get to the implied ‘modified’ portfolio volatility that would give you the correct Cornish Fisher modified VaR using the Normal VaR method. In this manner we are able to make the problem more tractable to the end user by reducing it back to a simpler paradigm where the impact of the co-skewness ( N x N x N ) and co-kurtosis ( N x N x N x N ) matrices are combined into a single value represented by the ‘modified’ volatility without the end user needing to see or understand the use of these higher moment matrices.Unfortunately this method is correct only for a given set of weights ( is not weight invariant ) and cannot be used in a portfolio optimisation sense because the impact of the weights is embedded in the matrices and they will change for each set of weights. However it does help the end user understand the contribution of individual assets within their portfolio’s skewness and kurtosis to their overall risk.My question for the forum is if anyone can think of a way in which these matrices could be made weight invariant ?

Correction to Infiniti Multivariate 4 Moment Risk DecompositionHi AllPlease note that we discovered an error in this presentation. We were mixing sample and population measures which although it was giving the correct global answer was incorrect at component level. This has now been rectified and :Modified VaR at both portfolio and component level can now be calculated as Modified VaR = Mean + ( Z score x Population ‘Modified Volatility’ x SQRT(n/(n-1))) as in the Normal case whereNormal VaR = Mean + ( Z score x Sample Volatility ) Similarly the population ‘modified’ vols can now be recovered by taking the square root of the diagonal of the ‘modified’ variance covariance matrix.Where Modified = Cornish Fisher ‘expanded’No change to the IAS software where it is all correct just to our Excel testing model Please note: This method embeds both the portfolio weights and the confidence level so cannot be used for optimisation purposes in the same way a normal correlation matrix can be. However, it does provide useful insights as to the contribution of the higher moments of individual component assets to your portfolio’s VaR and CVaR over some historic time-period.The correct version here

Hi,I'd be interested in this ppt and xls file. Is it still available?It somehow is related to my latest post on portfolio skewness and portfolio kurtosis