Journal of Risk

Risk.net

Making Cornish–Fisher fit for risk measurement

John D. Lamb, Maura E. Monville and Kai-Hong Tee

  • We show how to fit a Cornish–Fisher distribution with exact skewness and kurtosis.
  • The method extends to multivariate distribution fitting.
  • The distributions fit financial data well.
  • They combine with estimation-error reduction and improve estimates of VaR and CVaR.

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.

To continue reading...

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here: