Cornish-Fisher expansion for real estate value at risk

Value at risk is a convenient and popular risk measurement tool. It represents the maximum potential loss on a specific portfolio of financial assets given a specific time horizon and a confidence interval. Principally value at risk is used in finance for risk management, financial reporting and capital requirement. In real estate, the calculation of this risk measurement is still rare even if it is now common to compute and disclose it in numerous other fields of finance. Indeed nowadays, financial institutions are facing the important task of estimating and controlling their exposure to market risk following a scope of new regulation such as Basel II, Basel III or Solvency II. It is in this context that financial institution may use internal models for estimating their market risk. The purpose of this paper is to investigate the possibility to use Cornish-Fisher expansion to assess real estate value at risk. Despite strong assumptions, we show how Cornish-Fisher approximation can give quickly accurate measurements. In addition, practitioners can find here a methodology to assess quickly value at risk without too many loss of relevancy due to normal hypothesis. After a review of literature on value at risk and of the existing methodologies, the paper describes the Cornish-Fisher expansion and how the expansion is used to compute value at risk. Then, we apply the proposed model to a set of real estate indices and compare the results obtained with the traditional variance-covariance method.

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