Cornish-Fisher Expansion for Commercial Real Estate Value at Risk

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 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 of Cornish-Fisher expansions and the rearrangement procedure.

Keywords: Value at risk; Risk measurement; Real estate finance; Cornish-Fisher expansion; Risk management; Rearrangement procedures