Modified Sharpe Ratios in Real Estate Performance Measurement: Beyond the Standard Cornish Fisher Expansion

An important component in the analysis of real estate performance and allocation is the efficient calibration of the distribution of returns. The classical method is to compute market or sub-market returns and volatilities, and to then calculate the standard performance measure, namely the Sharpe ratio. This measure is only based on the first two moments of the return distribution. Therefore, a significant weakness of this method is that it implicitly assumes that this distribution is Gaussian (if not, the approach may lead to a bad fit for the distribution). In fact, risk comes not only from volatility but from higher moments of the distribution, such as skewness and kurtosis. In order to resolve this issue, we focus on another risk-adjusted performance measure, one that takes the Value-at-Risk (VaR) as the risk measure, as was adopted by the Basel II regulation directive. This criterion is based on specific quantiles of the distribution of returns. When the VaR is computed from the Cornish Fisher expansion, the corresponding risk-adjusted performance measure is called the modified Sharpe ratio. Usually, its computation is based on the first four moments of the return’s distribution. However, this methodology can exhibit several pitfalls, and thus, this paper shows how to make proper use of this tool. The usefulness of the proposed methodology is illustrated through an empirical application to optimal portfolio allocation in commercial real estate, using the IPD database. We find that markets that appear more desirable using simple Sharpe ratios bear, in reality, higher risk when the distribution of returns is taken into account in a more appropriate manner. Institutional investors may find that the technique proposed here is useful in that it allows them to consider non-normality in real estate performance analysis.