Making Cornish–Fisher Distributions Fit

John Douglas Lamb, M.E. Monville, Kai-Hong Tee

Research output: Working paper

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Abstract

The truncated Cornish–Fisher inverse expansion is well known. It is used, for example, to approximate value-at-risk and conditional value-at-risk. It is known that this expansion gives a distribution for limited skewness and kurtosis and that the distribution may be a poor fit. drawing on Maillard (2012) we show how 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 show how to obtain random variates efficiently and how to test goodness-of-fit. We apply the Cornish–Fisher distribution to fit hedge-fund returns and estimate conditional value-at risk. Finally, we investigate various generalisations of the Cornish–Fisher distributions and show they do not have the same desirable properties.
Original languageEnglish
Number of pages59
Publication statusPublished - 2016

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Skewness
Kurtosis
Conditional value at risk
Mean-variance
Goodness of fit test
Value at risk
Hedge funds
Quantile

Keywords

  • Conditional value-at-risk
  • Goodness-of-fit
  • Kurtosis
  • Random variates
  • Skewness

Cite this

Lamb, J. D., Monville, M. E., & Tee, K-H. (2016). Making Cornish–Fisher Distributions Fit.

Making Cornish–Fisher Distributions Fit. / Lamb, John Douglas; Monville, M.E.; Tee, Kai-Hong.

2016.

Research output: Working paper

Lamb, JD, Monville, ME & Tee, K-H 2016 'Making Cornish–Fisher Distributions Fit'.
Lamb, John Douglas ; Monville, M.E. ; Tee, Kai-Hong. / Making Cornish–Fisher Distributions Fit. 2016.
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AB - The truncated Cornish–Fisher inverse expansion is well known. It is used, for example, to approximate value-at-risk and conditional value-at-risk. It is known that this expansion gives a distribution for limited skewness and kurtosis and that the distribution may be a poor fit. drawing on Maillard (2012) we show how 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 show how to obtain random variates efficiently and how to test goodness-of-fit. We apply the Cornish–Fisher distribution to fit hedge-fund returns and estimate conditional value-at risk. Finally, we investigate various generalisations of the Cornish–Fisher distributions and show they do not have the same desirable properties.

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