1. Tail Dependence in REITs Returns Kridsda Nimmanunta Kanak Patel Email: kp10005@cam.ac.ukkp10005@cam.ac.uk ERES Conference 2009, Stockholm, Sweden 24 – 27 th June 2009 University of Cambridge

2. Overview Nimmanunta & Patel 2  Research Questions  Existing Literature  The Generic Models and Data Descriptions  Results and Discussions  Marginal Distributions of REITs  Conditional Copulas  Tail Dependence of REITs with t Copula  Conclusions

3. Research Questions Nimmanunta & Patel 3  Non-normality of asset return distribution (Mills (1927))  Non-normality of asset returns Joint distribution  See e.g. Longin and Solnik (2001), Ang and Chen (2002)  A fall in values of assets beyond some thresholds can trigger a fall in values of other assets that are initially weakly correlated with the former  Evidence of tail dependence and asymmetric dependence structure can be found in almost every market  International equity markets (Longin and Solnik (2001))  Equity and bond markets in G-5 countries (Hartmann et al. (2004))  Currency exchange markets (Patton (2006))  Asian developed future markets (Xu and Li (2009))  The US and European CDS markets (Coudert and Gex (2008))

4. Research Questions Nimmanunta & Patel 4  In Real Estate market,  Knight et al. (2005) – the potential benefits of diversification between real estate and equity markets during downturns disappears.  Real Estate Boom-Burst  During the past ten years, real estate assets have tended to move closely together  Tail Dependence between different sectors of real estate  Tail dependence  Asymmetry

5. Existing Literature Nimmanunta & Patel 5  Time-varying Conditional Copula (Patton (2002)), extending Copula (Sklar (1959))  The dependence structure of assets dynamically over time by conditional on the past information  Patton (2006) finds the dependence between Deutsche Mark-USD and Yen-USD  highly asymmetric in one direction before the introduction of euro currency  marginally asymmetric in the other direction thereafter  Jondeau and Rockinger (2006) investigate the dependence among major stock markets  Dependency between European markets increases over the sample period  Goorah (2007) examines the dependence structure between US and UK listed real estate companies and REITs  Symmeterised Joe-Clayton (SJC) copula - best fit to the daily data from 1990Q1 to 2007Q1  Lower tail dependence is generally stronger than the upper one  In our paper, we examine the tail dependence within US REITs

6. The Generic Model Nimmanunta & Patel 6  Copula-based VAR, GJR-t-GARCH Model  The model consists of two components: Marginals and Copula  VAR cannot be reduced to univariate ARs.  The Granger causality test reveals that REITs sub-index returns are driven by both their own lags and the lags of the other REITs sectors,  Glosten-Jagannathan-Runkle(GJR)-t-GARCH can capture three features  Volatility clustering  Excess kurtosis of the return distribution  Leverage effect  Conditional Copula to deal with (asymmetric) tail dependence  Gaussian, Student t, Gumbel, Frank, Clayton, SJC

7. The Generic Model Nimmanunta & Patel 7  Specification of the Marginal Distributions

8. The Generic Model Nimmanunta & Patel 8  Specification of the Conditional Copula

9. The Generic Model Nimmanunta & Patel 9  The Estimation of Parameters : Two-step ML  Using the extension of Sklar theorem (Patton (2006))  Hence, the log-likelihood function can be expressed as

10. Data Descriptions Nimmanunta & Patel 10  Daily returns of the U.S. equity REITs from Jan 2000 to Mar 2009:  Apartments, Industrial, Office, and Shopping Centre  Total Return Indices of REITs (Base date 1 st Jan 2000)

11. Marginal Distributions of REITs Nimmanunta & Patel 11  VAR( 1 ) is sufficient for all the four series  GARCH( 1,2 ) for Apartment REITs  GARCH( 1,1 ) for Industrial and Office REITs  GARCH( 2,1 ) for Shopping Centre REITs  1 st order GJR is sufficient for all the four series  Leverage effect is found for the four series  Shopping Centre has the highest leverage effect  Significant Student t degree of freedom  Implying the excess kurtosis of the series

12. Marginal Distributions of REITs Nimmanunta & Patel 12  Conditional Volatility for each error term of REITs returns

13. Conditional Copulas – APT & OFF Nimmanunta & Patel 13

14. Conditional Copulas – APT & IND Nimmanunta & Patel 14

15. Conditional Copulas – APT & SHPC Nimmanunta & Patel 15

16. Conditional Copulas - Summary Nimmanunta & Patel 16  TV-Student t copula, which has symmetric tail dependence, provides the highest log-likelihood value, AIC, BIC in all cases.  Hence, the pair-wise contemporaneous dependence structures of REITs  Not significantly asymmetric  Unlike other studies in various asset markets that find the asymmetric dependence structure  The sample includes both the boom and burst in which REITs moved together closely.  As REITs are highly correlated  The general shape of the dependence structure becomes more important

17. Conditional Copulas Nimmanunta & Patel 17  The shape of the dependence structure of REITs is closer to that of Student t and Guassian copulas.  Scatter Plots of the Actual Probability Integral Value and the Simulated Value from Six Copulas: Apartment vs Office

18. Student t Copula Parameter Estimations Nimmanunta & Patel 18

19. Tail Dependence of REITs Nimmanunta & Patel 19

20. Linear Correlation of REITs Nimmanunta & Patel 20

21. Tail dependence vs Linear Correlation Nimmanunta & Patel 21

22. Tail dependence vs Linear Correlation Nimmanunta & Patel 22

23. Conclusions Nimmanunta & Patel 23  Using daily data of four U.S. equity REITs (Jan 2000 - Mar 2009)  leverage effects  Tail dependence within U.S. REITs is not significantly asymmetric  Lower linear correlation does not necessarily imply lower dependency in extreme events

24. Q & A Nimmanunta & Patel 24  Contact: Dr Kanak Patel  Email: kp10005@cam.ac.ukkp10005@cam.ac.uk  Or Kridsda Nimmanunta  Email: k.nimmanunta@cambridgejbs.netk.nimmanunta@cambridgejbs.net