1. Introduction to the Infiniti Capital Four Moment Risk Decomposition By Peter Urbani and Mitchell Bristow

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

8. Infiniti Capital Modified VaR Decomposition

9. Normal & Modified VaR for a portfolio

10. Basic Portfolio Statistics

11. Covariance Matrix

12. ‘ Modified’ Covariance Matrix

13. Correlation Matrix

14. ‘ Modified’ Correlation Matrix

15. ‘ Modified’ Volatility

16. Normal & Modified VaR from these Matrices

17. Infiniti Capital Four Moment Risk Decomposition http://www.infiniti-analytics.com