PERIODICALLY COLLAPSING BUBBLES Anderson, Brooks & Tsolacos ERES 2009 page 1 Detecting periodically...

PERIODICALLY COLLAPSING BUBBLES

Anderson, Brooks & Tsolacos

ERES 2009

Detecting periodically collapsing bubbles in securitized real estate

European Real Estate Society Meeting Stockholm, June 2009

Keith AndersonDepartment of Economics, University of York, York, UK

Chris Brooks ICMA Centre, Business School, University of Reading, Reading, UKSotiris TsolacosProperty & Portfolio Research, London, UK(contact author: [email protected])



ERES 2009

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



ERES 2009

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



ERES 2009

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



ERES 2009

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



ERES 2009

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



ERES 2009

The van Norden-Schaller model

)()()( ,0,1

1,,0,1

1,,0,1

tbqqtt

tCtbCCC

t

tStbSSS

t

BBqSWP

uBr

uBr

Where:

rs is the return during the next period in the surviving regimes

rC is the return in the collapsing regime

Bt 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.



ERES 2009

Model restrictions

)()()( ,0,1

1,,0,1

1,,0,1

tbqqtt

tCtbCCC

t

tStbSSS

t

BBqSWP

uBr

uBr

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.



ERES 2009

Data

Three US REIT series are used Mortgage Equity All REIT

Fundamental values are based on the dividend multiple measure



ERES 2009

Mortgage REITs: Actual and Fundamental values

0

20

40

60

80

100

120

140

160

De

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1D

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72

De

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c-7

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80

De

c-8

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De

c-8

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84

De

c-8

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08

Actual Fundamental



ERES 2009

Equity REITs: Actual and Fundamental values

0

100

200

300

400

500

600

700

De

c-7

1D

ec-

72

De

c-7

3D

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74

De

c-7

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76

De

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78

De

c-7

9D

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80

De

c-8

1D

ec-

82

De

c-8

3D

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84

De

c-8

5D

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86

De

c-8

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88

De

c-8

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90

De

c-9

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92

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c-9

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06

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08

Actual Fundamental



ERES 2009

All REITs: Actual and Fundamental values

0

50

100

150

200

250

De

c-7

1D

ec-

72

De

c-7

3D

ec-

74

De

c-7

5D

ec-

76

De

c-7

7D

ec-

78

De

c-7

9D

ec-

80

De

c-8

1D

ec-

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De

c-8

3D

ec-

84

De

c-8

5D

ec-

86

De

c-8

7D

ec-

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De

c-8

9D

ec-

90

De

c-9

1D

ec-

92

De

c-9

3D

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94

De

c-9

5D

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96

De

c-9

7D

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98

De

c-9

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De

c-0

1D

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02

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c-0

3D

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04

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c-0

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Actual Fundamental



ERES 2009

Results – mortgage REITs

beta t-ratio p-value

βS,0 1.006 390.5 Return of (1.006 – 1)x100=0.6% per month in the surviving regime when bubble is 0 (plausible)

βS,b 0.067 2.7 0.00 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

βC,0 0.988 88.2 Return of (0.988 – 1)x100=-1.2% per month in the collapsing regime when bubble is 0 (plausible)

βC,b -0.028 -0.4 0.33 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

βq,0 0.959 4.4 0.00

βq,b -3.484 -2.7 0.00 For every 1% increase in the bubble size, the probability of being in the surviving regime falls by 3.5% (3.484%).

σS 0.036 12.7

σC 0.099 10.8



ERES 2009

Results for all REIT series considered

Mortgage Equity All REITs

βS,01.006* 1.010* 1.010*

βS,b0.067* 0.014NS 0.015NS

βC,00.988* 0.976* 0.971*

βC,b-0.028NS 0.050NS 0.086NS

βq,00.959* 1.535* 1.639*

βq,b-3.484* -5.171* -6.657*

σS0.04* 0.03* 0.03*

σC0.10* 0.09* 0.10*

* Statistically significant at the 1% level

NS not statistically significant



ERES 2009

Model Restrictions LR tests

Restriction LR test statistic(p-value)

Mortgage Equity All REITs

βS,0 βC,0

2.68

(0.10)

5.53

(0.02)

7.05

(0.01)

βC,b < 00.21

(0.65)

0.23

(0.63)

1.00

(0.32)

βS,b > βC,b1.67

(0.20)

0.11

(0.75)

0.57

(0.45)

βq,b < 06.86

(0.09)

8.24

(0.00)

17.01

(0.00)



ERES 2009

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.



ERES 2009

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.

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