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Making Cornish–Fisher fit for risk measurement

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posted on 05.07.2018, 13:08 authored by John D. Lamb, Maura E. Monville, Kai-Hong TeeKai-Hong Tee
The truncated Cornish–Fisher inverse expansion is well known and has been used to approximate value-at-risk and conditional value-at-risk. The following are also known. The expansion is available only for a limited range of skewness and kurtosis. The distribution approximation it gives is poor for larger values of skewness or kurtosis. We develop a computational method to find a unique corrected Cornish–Fisher distribution efficiently for a wide range of skewness and kurtosis. We show it has a unimodal density and a quantile function that is twice continuously differentiable as a function of mean, variance, skewness and kurtosis. We extend the univariate distribution to a multivariate Cornish–Fisher distribution and show it can be used together with estimation-error reduction methods to improve risk estimation. We show how to test goodness-of-fit. We apply the Cornish–Fisher distribution to fit hedge-fund returns and estimate conditional value-at-risk. We conclude that the Cornish–Fisher distribution is useful in estimating risk, especially in the multivariate case where we must deal with estimation error.



  • Business and Economics


  • Business

Published in

Journal of Risk


LAMB, J.D., MONVILLE, M.E. and TEE, K-H., 2018. Making Cornish–Fisher fit for risk measurement. Journal of Risk, 21 (5), pp.53-81.


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