Cornish-Fisher Expansion for Commercial Real Estate
Value at Risk
Charles-Olivier Am´ed´ee-Manesme ·
Fabrice Barth´el´emy · Donald Keenan
Published online: 5 July 2014

Abstract

The computation of Value at Risk has traditionally been a troublesome
issue in commercial real estate. Difficulties mainly arise from the lack of appropriate
data, the non-normality of returns, and the inapplicability of many of the traditional
methodologies. As a result, calculation of this risk measure has rarely been done in
the real estate field. However, following a spate of new regulations such as Basel
II, Basel III, NAIC and Solvency II, financial institutions have increasingly been
required to estimate and control their exposure to market risk. As a result, financial
institutions now commonly use “internal” Value at Risk (VaR) models in order
to assess their market risk exposure. The purpose of this paper is to estimate distribution
functions of real estate VaR while taking into account non-normality in
the distribution of returns. This is accomplished by the combination of the Cornish-
Fisher expansion with a certain rearrangement procedure. We demonstrate that this
combination allows superior estimation, and thus a better VaR estimate, than has
previously been obtainable. We also show how the use of a rearrangement procedure
solves well-known issues arising from the monotonicity assumption required for the
Cornish-Fisher expansion to be applicable, a difficulty which has previously limited the useful of this expansion technique. Thus, practitioners can find a methodology
here to quickly assess Value at Risk without suffering loss of relevancy due to any
non-normality in their actual return distribution. The originality of this paper lies
in our particular combination