Making Cornish–Fisher Fit for Risk Measurement

30 Pages Posted: 19 Jun 2019

See all articles by John D. Lamb

John D. Lamb

University of Aberdeen - Business School

Maura E. Monville

University of Surrey

Kai-Hong Tee

Loughborough University - School of Business and Economics

Date Written: June 18, 2019

Abstract

The truncated Cornish–Fisher inverse expansion is well known and has been used to approximate value-at-risk (VaR) and conditional value-at-risk (CVaR). The following are also known: the expansion is available only for a limited range of skewnesses and kurtoses, and the distribution approximation it gives is poor for larger values of skewness and kurtosis. We develop a computational method to find a unique, corrected Cornish–Fisher distribution efficiently for a wide range of skewnesses and kurtoses. We show that it has a unimodal density and a quantile function which 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 that it can be used together with estimation-error reduction methods to improve risk estimation. We show how to test the goodness-of-fit. We apply the Cornish–Fisher distribution to fit hedge-fund returns and estimate CVaR. We conclude that the Cornish–Fisher distribution is useful in estimating risk, especially in the multivariate case where we must deal with estimation error.

Keywords: conditional value-at-risk (CVaR), estimation error, goodness-of-fit, kurtosis, skewness

Suggested Citation

Lamb, John D. and Monville, Maura E. and Tee, Kai-Hong, Making Cornish–Fisher Fit for Risk Measurement (June 18, 2019). Journal of Risk, Vol. 21, No. 5, 2019, Available at SSRN: https://ssrn.com/abstract=3406086

John D. Lamb (Contact Author)

University of Aberdeen - Business School ( email )

Edward Wright Building
Dunbar Street
Aberdeen, Scotland AB24 3QY
United Kingdom

Maura E. Monville

University of Surrey ( email )

Guildford
Guildford, Surrey GU2 5XH
United Kingdom

Kai-Hong Tee

Loughborough University - School of Business and Economics ( email )

Epinal Way
Leics LE11 3TU
Leicestershire
United Kingdom

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