Tail Dependence in REITs Returns Kridsda Nimmanunta Kanak Patel ERES Conference 2009, Stockholm, Sweden 24 27 th June 2009 University of Cambridge 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 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)) 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 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 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 The Generic Model Nimmanunta & Patel 7 Specification of the Marginal Distributions The Generic Model Nimmanunta & Patel 8 Specification of the Conditional Copula 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 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) 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 Marginal Distributions of REITs Nimmanunta & Patel 12 Conditional Volatility for each error term of REITs returns Conditional Copulas APT & OFF Nimmanunta & Patel 13 Conditional Copulas APT & IND Nimmanunta & Patel 14 Conditional Copulas APT & SHPC Nimmanunta & Patel 15 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 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 Student t Copula Parameter Estimations Nimmanunta & Patel 18 Tail Dependence of REITs Nimmanunta & Patel 19 Linear Correlation of REITs Nimmanunta & Patel 20 Tail dependence vs Linear Correlation Nimmanunta & Patel 21 Tail dependence vs Linear Correlation Nimmanunta & Patel 22 Conclusions Nimmanunta & Patel 23 Using daily data of four U.S. equity REITs (Jan 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 Q & A Nimmanunta & Patel 24 Contact: Dr Kanak Patel Or Kridsda Nimmanunta