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Are There Rational Bubbles in REITs? New Evidence from a Complex Systems Approach

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Abstract

This study applies a complex systems approach to test for the presence of rational bubbles in the Equity REITs market. The applied model is based on theoretical implications of the evolution of prices under rational bubble regimes. The advantage of the approach is twofold. The model is able to detect rational bubbles while they rise and to predict the most likely time of their collapse. We apply the model to daily price data on U.S. Equity REITs from 1989 to 2011. Our findings suggest the existence of a bubble for the period of 2003 to 2007. Tests for sub-markets reveal that the bubble developed in the Residential REITs market, but not in the Office REITs market.

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Notes

  1. For a detailed derivation of the general form of the model we refer the reader to Johansen et al. (2000).

  2. Imitation is at the root of herding behavior and stems from individual factors. Herding results from an intent of investors to copy others. Intuitively, an investor is herding if she would have made an investment without knowing other individuals’ decisions, but does not make the investment if she knows that the others do not make it either (Bikhchandani and Sharma 2000).

  3. The parameter ω reflects the market structure because it is directly connected to the preferred scaling factor λ, with \( \lambda =\exp \left( {{{{2\pi }} \left/ {\omega } \right.}} \right) \) The preferred scaling factor λ reflects the symmetry properties of the assumed hierarchical market structure. It links one hierarchical level to another by a magnifying factor and thus gives a measure for the differing degree of market power of the individual participants.

  4. Drożdża et al. (2003) propose that the log-periodic self-similarity reflected by ω is the outcome of a financial law. This law implies a constant value of the discrete scaling factor λ, which the authors suggest is approximately equal to 2. Given the identity \( \lambda =\exp \left( {{{{2\pi }} \left/ {\omega } \right.}} \right) \) this corresponds to a value of ω ≈ 9.06. By contrast, Johansen and Sornette (2010) isolate an average value of ω ≈ 6.36 from their examination of over 30 crashes in major financial markets. Our own findings, based on a meta analysis of 47 published studies on crash predictions with the LPPL model in stock markets, indicate an average mean value of ω ≈ 8.34. By requiring ω to lie within certain bounds we follow the empirical findings in the literature, which suggest that ω < 5 leads to noise fitting in financial time series (Lin et al. 2009). The upper bound of ω is set to avoid pure trend fitting; however, we rarely encounter estimates of ω beyond its upper bound. For an overview of empirical tests of detecting log-periodicity in both artificial and real financial time series we refer the reader to Sornette and Johansen (2001).

  5. Our method follows for the most part the recommendations of Lin et al. (2009). Compared to estimates with other algorithms we achieve the best estimates with the NM-algorithm with regard to both reliability and efficiency.

  6. Following Payne and Waters (2007) and Jirasakuldech et al. (2006) we also apply the model to monthly data collected from the National Association of Real Estate Investment Trusts (NAREIT). We generate estimates that indicate a bubble from 2000 onwards, but the results are not reliable because the bubble period is too short for reliable estimates. Sornette et al. (2011) recommend a minimum of 100 data points for reliable estimates.

  7. We conduct additional rolling window estimates with varying window sizes. Each time, we find valid fits only for the period between the end of 2003 and the beginning of 2007, as displayed in Table 2 (Panels D and E). No other time periods with valid fits can be identified. The choice of the window size remains to some degree arbitrary because we do not know the duration of a bubble or the exact starting period of a bubble, even with hindsight.

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Authors and Affiliations

  1. Real Estate Management Institute, EBS Universität für Wirtschaft und Recht, Gustav-Stresemann-Ring 3, 65189, Wiesbaden, Germany

    Maximilian Brauers & Matthias Thomas

  2. Department of Economics and Finance, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Joachim Zietz

  3. EBS Business School, EBS Universität für Wirtschaft und Recht, Gustav-Stresemann-Ring 3, 65189, Wiesbaden, Germany

    Joachim Zietz

Authors
  1. Maximilian Brauers
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  2. Matthias Thomas
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  3. Joachim Zietz
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Correspondence to Maximilian Brauers or Joachim Zietz.

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Brauers, M., Thomas, M. & Zietz, J. Are There Rational Bubbles in REITs? New Evidence from a Complex Systems Approach. J Real Estate Finan Econ 49, 165–184 (2014). https://doi.org/10.1007/s11146-013-9420-5

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