Real Estate Return Distributions with New NCREIF Data Series

Abstract

The accuracy of real estate return distribution parameter estimation is affected by the tools used to do the work as well as the data sets employed. Consistent with previous studies, investment risk models with infinite variance describe distributions of individual property returns in the new NCREIF Indicators: Capital Performance and Property Operations individual property database over the period 1990–2021. Applying Maximum Likelihood Estimation (MLE) to historic data shows real estate investment risk to be heteroscedastic, but the Characteristic Exponent of the investment risk function varies more among property types than previously reported whether computed by MLE or other estimation techniques.

Keywords:

• Asset-specific risk
• Maximum Likelihood Estimation
• Non-normality
• Diversification
• NCREIF

Acknowledgements

The authors wish to thank Jeffrey D. Fisher, John P. Nolan, Marlyn L. Hicks, and Kenneth M. Lusht for their considerable support in this project. All errors remain solely those of the authors.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The implementation of other analytical techniques up until the availability of Maximum Likelihood Estimators (MLE) for Levy-stable distributions is related in Young and Graff (1995).

2 Less frequently there are problems with market value estimates in a quarter such as recording a downpayment as the initial market value followed by the balance of the purchase price as the market value in the subsequent quarter. These cause extreme distortion of quarterly returns for individual properties, but are largely obscured in the aggregate NPI returns commonly cited as representative of the asset class. However, when working with individual property returns or smaller aggregations of property returns as in this study, these problems would necessarily distort the return distribution statistics as they unfortunately did in earlier NPI-based studies.

3 Perhaps it should be noted that there have been other attempts to test the null hypothesis that real estate return distributions are Gaussian Normal using more conventional statistical techniques. The authors know of no cases that resulted in failing to reject the null. For example, there have been studies in the U.S. and even more in the U.K. using Chi-Square, Kolmogorov-Smirnov, or Anderson-Darling tests of common distributions like Logistic, Normal, Student’s t, or Extreme Value. For a summary of these studies pre-2000, see Lizieri and Ward (2001).

4 It may be worth noting that the numerators of the Price and Cash Flow formulas are those originally proposed by Young et al. (1995, 1996) as replacements for the so-called Capital and Income Returns. Since NCREIF did not adopt the changes and retained the original formulation of Capital and Income Returns, the new Price and Cash Flow formulas were introduced for researchers interested in the Young, Geltner, McIntosh, and Poutasse concept. Notice too that the authors also proposed changing the NPI Total Return, Income Return, and Capital Return denominator to simply the beginning quarter’s market value.

5 Examples of Partial Sales (PS) include the net sales price of one building from say a multi-building industrial park or the net sales price of an outparcel on the periphery of a shopping center.

6 Capital expenditures are generally reported as positive numbers, but occasionally there will be accounting “reversals” resulting in negative numbers for reported capital expenditures in a particular period. Some reversals may result from journal entries that reclassify or move outlays between periods.

7 Each of these have different risk characteristics per Brown (1998).

8 Passive investment in equity real estate is a fool’s errand. Those who think they can invest passively in real estate by buying shares of REITs soon learn they have just bought stock.

9 The astute observer will immediately recognize a paradox in that efficient frontier graphics constitute a parametric plot that requires a covariance matrix. If Levy-stable distributions have no variance, they can have no covariances. One must remember, however, that Levy-stable distributions lack a variance in the limit. All finite samples have a variance that can be calculated. The demonstration illustrates the shape of the “frontier” using samples that are presumed to be drawn from a Levy-stable population having parameters supplied by the user. The demonstration is located at:

http://demonstrations.wolfram.com/FormingTheEfficientFrontierWhenReturnsAreNonNormal/