Real Estate Portfolio Diversification by Sectors Using a RAL Approach

Abstract

We propose a cointegration-based method for evaluating the long-term independence of sectoral Real Estate Investment Trusts (REITs) within a portfolio. We employ this innovative approach to construct diversified portfolios. Our argument is that sectors contributing less to cointegration provide greater risk reduction benefits to the portfolio. To gauge the level of independence, we use the reciprocal of the aggregate likelihood ratio (RAL) statistics. Based on these statistics, we introduce a novel allocation strategy that assigns a higher weight to a sector with a larger RAL. Using CRSP/Ziman REIT sector data, we demonstrate that this new strategy outperforms traditional methods and the real estate market benchmark. Our paper introduces a fresh framework for REIT portfolio management and provides guidance on sector allocation.

Keywords:

• REITs
• sector
• cointegration
• portfolio diversification
• portfolio performance

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 Our REIT market index exhibits correlations of 0.9875 with the Ziman REIT value-weighted index over the 444-month sample period. Using Ziman market index makes our test results more significant.

2 Previous literature (e.g. Chen, Firth & Rui, 2002) provides consistent evidence index price series are non-stationary.

3 If real estate indices exhibit non-linear dependencies the linear autoregressive Johansen results can be questioned. We transform all data series to the logarithm (linear) to mitigate any non-linearity in the data series (Wilson & Okunev, 1996; Gerlach, Wilson & Zurbruegg, 2006). We also include structural break and linear trend components in our model (Gerlach, Wilson & Zurbruegg, 2006) in response to linear deterministic trends (Johansen, 1994) and structural breaks (Johansen, Mosconi & Nielsen, 2000) identified in the data series. Moreover, there has been no documented evidence of non-linear dependencies among property indices. In essence, no need for non-linear nonparametric rank and cointegration tests such as Bierens (1997a, 1997b) and Breitung (2002) is indicated.

4 Full results based on Equation (5)(5) $${\mathit{\text{RAL}}}_A^{\prime }=\frac{1}{{\displaystyle \sum _{k=1}^r\raisebox{1ex}{$L{R}_k$}\!\left/ \!\raisebox{-1ex}{$C{V}_k$}\right.}}$$(5) are available from authors upon request.

5 Using a 120-month long-range estimation window is consistent with the suggestion of DeMiguel, Garlappi, and Uppal (2009) regarding the length of the testing window.

6 Professor Harry Markowitz developed the MPT framework. A complete mathematical description is found in his book titled “Portfolio Selection: Efficient Diversification of Investments” published in 1959.

7 The MPT method we conduct in this study is based on the average trailing 120-month returns. We acknowledge that this is sometimes unrealistic from a practical perspective because prior short-period average returns are a poor predictor of future returns. In practice, many investors would use a theoretically based estimate procedure such as CAPM equilibrium returns, which are more plausible, see Black and Litterman (1992) and Elton and Gruber (1997). However, we focus on the traditional MPT approach in this paper.

8 Note that the first window in the portfolio test is different from the first window in the cointegration test.

9 The regression mean squared error (MSE) represents the variability attributable to unsystematic risk (Haugen, 2001, pp. 140-141).

10 Jennrich (1970) provides a homogeneity test of correlation matrices. In contrast to classical pairwise correlation tests, the Jennrich test accounts for unequal time series from which the matrices are computed. We test the null hypothesis that the correlation matrix is constant between any two time periods (adjacent or not). Results are not tabulated but are available upon request from authors.