Modelling the Dependence Structure between Australian Equity and Real Estate Markets – a Copula Approach

Abstract

In the last decade, the Australian market for Real Estate Investment Trusts (REITS) has shown substantial growth rates. Australian Real Estate Investment Trusts (AREITS) are a unitized portfolio of property assets which allows investors to purchase a share in a diversified and professionally managed portfolio of real estate. We apply conditional copula models in order to investigate the dependence structure between returns of AREITS and Australian equity markets. The dynamic analysis is based on an AR-GARCH approach to model time-varying volatility of the individual series in combination with different copulas to capture the dependence structure between the standardized residuals. The Gaussian, Student t, Clayton and Gumbel copula are fitted and so-called ‘blanket’ goodness-of-fit tests are conducted in order to examine the appropriateness of the different copula functions. We also compare the suggested copula models to a standard variance-covariance approach and a multivariate GARCH-BEKK model. We find significant positive correlation between the series what somehow contradicts earlier studies on the topic finding negative or only weak positive correlations between REITS and equity investments. Therefore, for Australian markets the diversification potential of investments in REITS might be less significant than for overseas markets. We also find significant tail dependence, in particular in the lower left tail that is best modeled by the Clayton copula. Conducting a back testing Value-at-Risk study for a portfolio combining investments in real estate and equity we find that the conditional copula as well as the GARCH BEKK model significantly outperform a static variance covariance approach. Our findings suggest that ignoring the complex and dynamic dependence structure in favor of a simple multivariate normal model leads to a significant underestimation of the actual risk.