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Multi-asset portfolio skewness&kurtosis formulae
4 messages · aito araki, Brian G. Peterson, David Lüthi
aito araki wrote:
I do face some difficulties trying to set up a mean-modified-VaR optimization in excel, using the SOLVER function. I use a parametric approach in calculating the MVaR and the cornish-fisher expansion to account for skewness and leptokurtosis. So far i just could not find any general formula to calculate the s&k on a portfolio level only the well known formulae for individual assets. Does anyone know how i can calculate the s&k for the portfolio that enter my MVaR measure? I would very much appreciate some advice from anyone familiar with this.. Thanks a lot!
This is a list for R in finance, not Excel in finance. As such, I am happy to report that the functions you need are all available in the R package PerformanceAnalytics. You can find all the formulae and proofs in our paper: /Estimation and Decomposition of Downside Risk for Portfolios with Non-normal Returns/. Kris Boudt and Brian Peterson and Christophe Croux. Journal of Risk. Winter 2008 11(2) **p. 79-103. Regards, - Brian
Brian G. Peterson http://braverock.com/brian/ Ph: 773-459-4973 IM: bgpbraverock
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Dear Aito If you want to tackle your problem in a fully parametric way you might also consider to use the package 'ghyp'. This package provides code to fit a multivariate generalized hyperbolic distribution (or one of its many special cases) which allows for skewness and excess-kurtosis to your return series and subsequently use 'portfolio.optimize' to optimize the portfolio with respect to different risk-measures as VaR, Conditional VaR, and variance. Best regards, David L?thi
aito araki wrote:
Hi everyone, I do face some difficulties trying to set up a mean-modified-VaR optimization in excel, using the SOLVER function. I use a parametric approach in calculating the MVaR and the cornish-fisher expansion to account for skewness and leptokurtosis. So far i just could not find any general formula to calculate the s&k on a portfolio level only the well known formulae for individual assets. Does anyone know how i can calculate the s&k for the portfolio that enter my MVaR measure? I would very much appreciate some advice from anyone familiar with this.. Thanks a lot! [[alternative HTML version deleted]]
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