1. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 1 Detecting periodically collapsing bubbles in securitized real estate European Real Estate Society Meeting Stockholm, June 2009 Keith Anderson Department of Economics, University of York, York, UK Chris Brooks ICMA Centre, Business School, University of Reading, Reading, UK Sotiris Tsolacos Property & Portfolio Research, London, UK (contact author: sotiris.tsolacos@pprglobal.com)

2. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 2 Structure 1.Periodically collapsing bubbles; research implications for securitised real estate 2.Objectives of paper 3.Methodology 4.Data 5.Results 6.Assessment of findings and the next stage

3. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 3 Research on the collapse of speculative bubbles 1.Observed episodes of price rallies and crashes may constitute the presence of positive or negative speculative bubbles 2.Research implications: 1.Are these bubbles the result of irrational behaviour? 2.Are they predictable? Can we probabilistically time their collapse? 3.How can investors formulate strategy? 4.Develop trading rules based on conditional probabilities of a crash and a rally 5.Estimate risk adjusted returns from exercising these trading rules

4. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 4 Selected work on REIT bubbles  Jirasakuldech, Campbell and Knight (2006) Examine presence of speculative bubbles with four techniques two of which are unit root tests (applied to the residuals of a regression of security prices on fundamental variables) and cointegration (between security prices and fundamental variables; the fundamental variables are CPI, industrial production, risk premium and interest rates The study found no evidence of rational bubbles in equity REITs  Waters and Payne (2007) Further to unit root tests and cointegration these authors attempt to detect bubbles within an MTAR framework; this technique examines for cointegration between prices and dividends but it brings in asymmetric adjustments in particular when the adjustment exhibits more momentum in one direction than the other. MTAR method indicates the absence of collapsing bubbles for all, equity and hybrid REITs; however for mortgage REITs the results are indicative of negative collapsing bubbles  Brooks, Katsaris, McGough and Tsolacos (2001) Variance bounds tests applied to actual and fundamentals series and cointegration analysis is deployed to test for bubbles in the UK securitised market Evidence of transitory bubbles is found

5. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 5 The present work  At this stage it focuses on testing for bubbles in US REIT series  Several direct tests have been developed for the behaviour of bubbles  The study uses a different methodology from the current literature - Deploys the van Norden-Schaller model (1999, 1997) - It reflects recent developments in bubble behaviour in that it brings in stochastic bubble processes in financial data.  We examine whether bubbles are established in different aggregate US series

6. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 6 Intuition behind the van Norden-Schaller model (i) It is an extension of the fads model (ii) Probability of a bubble collapsing depends on the size of the bubble (iii) If (ii) holds switches in regime will be predictable using some measure of the size of the bubble from the previous period (iv) Model is about stochastic bubbles (bubbles which may survive or collapse in each period) (v) REIT returns come from two regimes: one which corresponds to surviving bubbles and the other to collapsing bubbles. (vi) Rational investors take (v) into account when deciding whether or not to hold an asset - In the surviving regime returns should be sufficiently high to compensate investor for the possibility that the bubble may collapse - Larger overvaluations are more likely to collapse

7. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 7 The van Norden-Schaller model Where: r s is the return during the next period in the surviving regimes r C is the return in the collapsing regime B t is the size of the bubble at time t β’s are coefficients to be estimated the u’s are error terms the final equation determines the probability that the series will be in the surviving regime in the next period. The omega denotes that the cumulative normal distribution is used for the probability, so it is bounded between zero and one. The model is estimated using maximum likelihood.

8. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 8 Model restrictions  S,0 > 0 so that the return in the surviving regime is positive, even if the size of the bubble is zero  C,0 <  S,0 so that, even when the bubble is zero, the return in the collapsing regime is lower  S,b > 0 so that the return in the surviving regime varies positively with the size of the bubble  C,b <  S,b so that the return is a lower function of the size of the bubble in the collapsing regime than in the surviving regime. A stricter condition than this is that  C,b < 0 so that the return in the collapsing regime is a negative function of the bubble size (i.e. the bigger the bubble, the more prices will fall in the collapsing regime).  q,0 > 0 so that the probability of being in the surviving regime next period is positive when the bubble size is zero.  q,b < 0 so that the probability of being in the surviving regime next period is smaller the largest is the bubble (i.e. a bigger bubble means it is more likely to collapse).  C >  S so volatility of returns should be higher during a collapsing regime than the surviving one.

9. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 9 Data  Three US REIT series are used  Mortgage  Equity  All REIT  Fundamental values are based on the dividend multiple measure

10. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 10 Mortgage REITs: Actual and Fundamental values

11. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 11 Equity REITs: Actual and Fundamental values

12. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 12 All REITs: Actual and Fundamental values

13. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 13 Results – mortgage REITs betat-ratiop-value β S,0 1.006390.5 Return of (1.006 – 1) x 100=0.6% per month in the surviving regime when bubble is 0 (plausible) β S,b 0.0672.70.00 For every 1% rise in the bubble size as a proportion of the actual price, the return in the surviving regime rises by 0.07% per month β C,0 0.98888.2 Return of (0.988 – 1) x 100=-1.2% per month in the collapsing regime when bubble is 0 (plausible) β C,b -0.028-0.40.33 For every 1% rise in the bubble size as a proportion of the actual price, the return in the collapsing regime falls by 0.03% per month β q,0 0.9594.40.00 β q,b -3.484-2.70.00 For every 1% increase in the bubble size, the probability of being in the surviving regime falls by 3.5% (3.484%). σSσS 0.03612.7 σCσC 0.09910.8

14. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 14 Results for all REIT series considered MortgageEquityAll REITs β S, 0 1.006*1.010* β S, b 0.067*0.014 NS 0.015 NS β C, 0 0.988*0.976*0.971* β C, b -0.028 NS 0.050 NS 0.086 NS β q,0 0.959*1.535*1.639* β q,b -3.484*-5.171*-6.657* σSσS 0.04*0.03* σCσC 0.10*0.09*0.10* * Statistically significant at the 1% level NS not statistically significant

15. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 15 Model Restrictions LR tests Restriction LR test statistic (p-value) MortgageEquityAll REITs β S,0  β C,0 2.68 (0.10) 5.53 (0.02) 7.05 (0.01) β C,b < 0 0.21 (0.65) 0.23 (0.63) 1.00 (0.32) β S,b > β C,b 1.67 (0.20) 0.11 (0.75) 0.57 (0.45) β q,b < 0 6.86 (0.09) 8.24 (0.00) 17.01 (0.00)

16. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 16 Assessment of findings and the next stage  Results partially support the presence of bubbles; not all estimates strongly indicate or strongly reject periodically collapsing bubbles for any one series.  There is relatively stronger evidence for periodically collapsing bubbles in mortgage REITs; perhaps this owes to the negative bubble at the start of our sample period  Results consistent with the work on US REITs reviewed earlier although sample periods differ  As of February 2009 All and Equity REITs seemed to be undervalued by around 25% unlike mortgage REITs which appeared to be fairly valued.  Next step: implementation of trading rules (see Brooks and Katsaris, 2005).  Investors will act on probabilities of a collapse that are estimated to be larger than a certain threshold, in which case the likelihood of a collapse is too great and the investor should sell.

17. PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 17 References Brooks, C. and Katsaris, A. (2005) Trading rules from forecasting the collapse of speculative bubbles for the S&P 500 composite index, Journal of Business 78(5), 2003-2036. Brooks, C., Katsaris, A, McGough, T. and Tsolacos, S. (2001) Testing for bubbles in indirect property price cycles, Journal of Property Research, 18(4), 341-356. Jirasakuldech, B., Campbell, R. and Knight, J. (2006) Aare there rational speculative bubbles are REITs?, Journal of Real Estate Finance and Economics 32, 105-107 Van Norden, S. and Schaller, H. (1999) Speculative behaviour, regime switching and stock market crashes. In Non-linear time series analysis of economic and financial data, ed. Philip Rothman, 321-56, Boston: Kluwer. Van Norden, S. and Schaller, H. (1997) Fad or bubbles? Bank of Canada working paper no.97(2). Waters, G and Payne, J. (2006) REIT markets and rational speculative bubbles: an empirical investigation, Applied Financial Economics 17, 747-753.