Cornish-Fisher Expansion for Commercial Real Estate Value at Risk

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 (V a R) models in order to assess their market risk exposure. The purpose of this paper is to estimate distribution functions of real estate V a R 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 V a R 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 of Cornish-Fisher expansions and the rearrangement procedure.