Smoothing in appraisal-based returns

Abstract

This article presents a conceptual analysis of smoothing in the second moments of appraisal-based returns series in commercial real estate. The intent of the article is to lay the groundwork necessary for the more scientific use of appraisal-based returns time series for the purpose of inferring the true second moments. Formal smoothing models are presented together with their theoretical implications for smoothing in various second moments of interest to investment analysts. Empirical estimators for inferring true moments from appraisal-based data are described. Limited empirical findings from previous literature are also briefly discussed in the light of the theoretical findings of this study. The overall conclusion is that appraisal-based returns can be very useful in studying the risk characteristics of commercial real estate assets, provided that this type of data is corrected for smoothing as discussed in the article.The ever-growing quantity of appraisal-based time series of real estate returns represents an increasingly important database for the study of the risk and returns characteristics of investment grade commercial real estate. But while such data are a rich source of information, they are a source that must be used carefully. The differences must be recognized between appraisal-based returns and the true market returns which represent the fundamental economic opportunity costs to investors and which are more directly comparable to the returns studied for alternative investments such as stocks and bonds. These differences drastically affect the risk characteristics of the returns so that the direct unadjusted use of appraisal-based data can be quite misleading. The differences between appraisal-based and true returns bias not only the volatility but virtually all the statistics about the returns that are of interest to investment and portfolio analysts, including the mean of the return, the systematic risk or hedging ability measured by covariances with exogenous indices, and the intraportfolio covariance or "heterogeneity" among real estate assets.While the problems in appraisal-based returns data have been recognized in much of the past literature, attempts to deal effectively with these problems have been less than successful. Many studies have simply presented analyses of appraisal-based returns without correcting for the effect of smoothing (e.g., Brueggeman, Chen, and Thibodeau, 1984;Miles and McCue, 1984; Miles, 1986, 1987;Hartzell, Shulman, and Wurtzebach, 1987). Other studies have attempted to correct for appraisal smoothing by developing simulated returns series, either by applying cap rate time series to real estate income time series (e.g.

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“…This leads to several authors using some form of unsmoothing procedure to extract the market information out of the appraisal index with Blundell and Ward (1987) and Geltner (1991) among the first applications. The underlying assumption used in the unsmoothing filter is that appraisers form opinions about current values using some mix of current market information and past appraisal values.…”

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