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, Jaschke and Stoyanov. 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.
Kind regards,
Peter Urbani
Comments
This is an extremely interesting and well put together presentation. Certainly, we can confirm that net asset returns in some of these funds are far from normally distributed after reading this.
I was aware of modified VaR having bad tail behavior but WOW the difference between the 95% quartile and the 99% is seriously non-monotonic you are right there. Something else I notice is Chi-Squared normality testing is also popular with a lot of analysts because of its simplicity and again it is questionable whether it should be used at all.
This is brilliant and thanks for sharing this paper.