The Fractal Structure of Real Estate Investment Trust Returns: The Search for Evidence of Market Segmentation and Nonlinear Dependency

This article presents a further test for market segmentation between the real estate market and the capital markets. We use rescaled range analysis developed in the fractal geometry literature to test for nonlinear trends in the returns series for different asset classes. We make three major conclusions: (1) the stock market displays tendencies consistent with a random walk, (2) portfolios of mortgage and equity REIT returns display tendencies consistent with a random walk and, (3) conditional upon the methods used, segmentation does not exist between different real estate markets and between the real estate and stock markets.