A robust assessment of asymmetric dependence is crucial for determining the benefits of diversification associated with including real estate in mixed-asset portfolios, but analysing asymmetric dependence is a complex, multi-dimensional problem. Using Monte Carlo simulations, we identify the most suitable metric of asymmetric dependence out of a range of methodologies commonly employed in real estate finance: the Adjusted J statistic (Alcock and Hatherley, 2010). We employ this statistic to empirically examine the dependence structures in a large sample of U.S. Real Estate Investment Trusts (REITs) and a broad range of benchmark assets over the period 1997-2010. Our results suggest that when we control for linear dependence and focus on the strength, direction and statistical significance of higher-order, asymmetric dependence, the benefits of diversification offered by REITs are stronger than sometimes reported, while the dependence with bonds appears to be more complex than previously assumed.