Fitting Non-Normal Distributions With Calibrated Cornish-Fisher Expansions

8 Pages Posted: 1 Jul 2013

Date Written: June 30, 2013


The Cornish-Fisher expansion is a popular method to adjust value-at-risk calculations for the skewness and kurtosis of non-normal return distribution. On the other hand, it is an open secret that “modified value-at-risk” calculations produce “strange” results from time to time, under certain parameter constellations. But the phenomenon was poorly understood, and no guidance was available from academia. In this research note, we illustrate the shortcomings of the traditional Cornish-Fisher expansion, by analyzing the distribution of S&P 500 price returns. We apply insights from recent research, which turns the Cornish-Fisher expansion into a well-behaved and accurate tool for modelling empirical non-normal return distributions.

Keywords: Cornish-Fisher, modified value-at-risk, risk measurement, investment risk analysis

Suggested Citation

Steiner, Andreas, Fitting Non-Normal Distributions With Calibrated Cornish-Fisher Expansions (June 30, 2013). Available at SSRN: or

Andreas Steiner (Contact Author)

Andreas Steiner Consulting GmbH ( email )

Walderstrasse 43c
Hinwil, 8340


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