This presentation on Why Distributions Matter
may be of interest. In it I highlight the deficiencies of the Cornish Fisher expansion to the Normal Distribution - now widely used by Hedge Funds to include the impact of excess skewness and kurtosis in their Value at Risk (VaR) calculations in the form of 'modified' Value at Risk or mVaR. I show that for just under 50% of all Hedge Funds tested the Cornish Fisher expansion is not appropriate and may give misleading and potentially dangerous VaR estimates. These problems are not unknown and have been reported by Mina and Ulmer in Delta Gamma Four Ways
. However I believe I am the first to quantify the size of the problem with respect to hedge funds and to provide a small VBA test of the bounds of the feasible region within which the expansion is 'well behaved'. I also use some 'best fit' distribution fitting methods to arrive at the bi-variate copula correlation which can be used for example for pairs trading. These 'best fit' methods identify different lowest correlated pairs than the standard product moment or Pearson correlation coefficient widely in use approximately 1/3 of the time.
+64 21 0255 2816