portfolio skewness / kurtosis now with Excel file

roomer · May 1st, 2012, 9:38 am

Here is the file!

purbani · May 2nd, 2012, 10:28 pm

You do not have enough information to be able to calculate the portfolio skewness and kurtosis. Need the time series of returns for the underlying Asset Classes plus the weights which you do have. Currently you only have information about the first two moments ( mean and standard deviation ). The higher order third and fourth ( skewness and kurtosis ) moments require information about the inter-relationships between the assets and the weights. This can be calculated directly from the p&l or time series of portfolio returns or from a co-Skewness and co-Kurtosis tensor matrix ( see attached )

roomer · May 3rd, 2012, 6:41 am

Thank you for the file.I attached my original file with time the correspondent series now. I can reproduce the portfolio skewness and kurtosis by referring to the historic portfolio return time series like you did in your file for double check. I saw in your VBA code that you have also two functions calcportskew() and calcportkurt() where you refer to another pair of functions called coskewness() and cokurtosis() that are necessary to calculate portfolio skewness and kurtosis in a parametric way in one step. Could you apply these to my file attached - I already copied your functions into the file. Would be great! Thanks!

purbani · May 24th, 2012, 9:20 pm

Here you go roomer. The spreadsheet now includes the VBA code to calculate the CoSkewness and CoKurtosis tensor matrices which can be used to decompose portfolio risk for the Cornish Fisher (Modified) VaR and CVaR. Please note this is not the most efficient way to calculate these matrices as only the unique elements need be stored in practice see Fowler (2005). They also scale very poorly as the number of assets (n) gets large so it should really only be used for illustrative purposes. Moreover, the Cornish Fisher modification to the normal distribution, although attractive because of its ease of calculation, is subject to a number of problems including a lack of monotonicity and tail instability even at low levels of skewness and kurtosis see my recent presentation on Why Distributions Matter for more on this.

purbani · June 5th, 2012, 10:02 pm

For the sake of completeness herewith Some further revisions to my Excel demo of CoSkewness and CoKurtosis tensor matrices used for 4 Moment Risk Decomposition of Normal and Cornish Fisher ( Modified ) VaR and CVaR. Now includes univariate CoSkewness, CoKurtsosis, CoVolatility and CoDrawdown VBA and the closed form approximation to CVaR ( Modified ) of Maillard