Business Principles, Tools, and Techniques in Participating in Various Types...
Four moment risk decomposition presentation
1. Introduction to the Infiniti Capital Four Moment Risk Decomposition By Peter Urbani and Mitchell Bristow
2.
3. Normal versus Modified VaR In the case of a standard normal distribution (Mean=0, Std Dev=1, Skew=0, Kurt=3) both the Normal Var and Cornish Fisher Modified VaR give the same answer. Note this assumes Raw Kurtosis – Excels formula assumes Excess Kurtosis > 3 and subtracts 3 automatically. This is why Kurtosis is not 0 in the above example.
4. Normal versus Modified VaR In the case of a slightly positive skewness and slightly higher than normal kurtosis (Mean=0, Std Dev=1, Skew=0.5, Kurt=4) the Cornish Fisher Modified VaR is lower (less negative) than that given by the Normal VaR calculation.
5. Normal versus Modified VaR In the case of a slightly negative skewness and slightly higher than normal kurtosis (Mean=0, Std Dev=1, Skew=-0.5, Kurt=4) the Cornish Fisher Modified VaR is higher (more negative) than that given by the Normal VaR calculation.
6. The Cornish Fisher Modification In Excel for use with Excess Kurtosis = (Skew*(ZScore^2-1)/6)+(Kurt*(ZScore^3-3*ZScore)/24)-((Skew^2)*(2*ZScore^3-5*ZScore)/36) for use with Raw Kurtosis =(1/6)*(ZScore^2-1)*Skew+(1/24)*((ZScore^3)-3*ZScore)*(Kurt-3)-(1/36)*(2*Zscore^3-5*ZScore)*Skew^2
7. Moving from the Univariate to the Multivariate (normal) Variance Covariance Matrix Std Devs (normal) Correlation Matrix Weights (normal) VaR (normal) Variance Covariance Matrix Std Devs Co-Skewn ess Co-Kurtosis (modified) Correlation Matrix Weights (modified) VaR Mod Std Devs