Regime switching in yield structures and real estate investment

Abstract

The present study examines the structure of yields between broad asset classes (real estate, equities and government bonds) and the implications for portfolio allocation decisions and real estate investment. It is based on the premise that asset markets are integrated and that yield differentials trigger switching of funds among assets. Therefore, we investigate the claim that the yield ratios of indirect to direct real estate and of real estate to equities or bonds contain useful information for determining the likely direction of future real estate returns. A Markov switching model is used to identify different states in yield differentials. The Markov model identifies distinct regimes for the yield ratios of indirect to direct real estate, indirect real estate to equities and direct real estate to gilts. Trading rules are developed based on the filtered – real time – probabilities of the regime switching models. It is observed that the regime switching trading rules generate a superior risk‐return profile than simple buy‐and‐hold strategies. When transaction costs are allowed for, the Markov switching is still the superior strategy in two out of three portfolios.

Keywords:

• real estate
• equities
• bond yield ratios
• Markov switching model
• regimes
• trading rules

Acknowledgements

This paper has benefited from the insightful comments made by four anonymous reviewers. We are also grateful to Professor Chris Brooks for his suggestions on earlier versions of this paper. The usual disclaimer applies.

Notes

1. Integration has been examined with a number of methodologies: simple contemporaneous and rolling correlations, (linear and non‐linear) causality tests, co‐integration and fractional co‐integration analysis, and joint tests of market integration and the CAPM; see Ling and Naranjo (1999), Okunev et al. (2002), Wilson and Zurbruegg (2003) and Sirmans and Worzala (2003a; 2003b) for a survey of the evidence. It should be noted that the results are subject to sample periods, methodologies and geographical coverage.

2. For example, Hendershott and McGregor (2003) develop a theoretical equilibrium model within which both stock and bond market variables affect property yields and deploy co‐integration analysis to estimate their model.

3. For a comprehensive survey, see Krolzig (1997).

4. For example, Brooks and Persand (2001); Dewachter (2001); Dueker (1997); Duffie and Singleton (1993); Engel (1994); and Schaller and van Norden (1997) among others.

5. See Franses and van Dijk (2002) and Brooks (2002) for a theoretical two‐state Markov AR(1) model and its applications. Further generalisation of this model is possible with more than two states and more dynamic lag structure.

6. Definitions of the data for the construction of the yield ratios are given in Appendix A. Different periods are used because of data availability; in each case we use the longest common pair‐wise time‐period. Indirect property data are available from 1977, while IPD monthly data are available from 1987.

7. Elliot, Rothenberg and Stock (1996) first showed that the power of the ADF (Augmented Dickey–Fuller, 1979) test could be optimised using a form of de‐trending, which is known as GLS de‐trending. For further discussion on the above unit root tests, see Harris and Sollis (2003).

8. The failure to accept the null by the unit root tests reported above does not imply that the yield ratios do not have a long‐run equilibrium level. It has been observed that standard unit root tests are mis‐specified in case the variable of interest is stationary but displays asymmetric adjustment towards its long‐run equilibrium; consequently, these tests may suffer from a lack of power against such alternatives (see Enders and Granger 1998).

9. In the study of Brooks and Persand (2001) the gilt‐equity ratios were stationary and thus no transformation of the data was needed. De‐trending non‐stationary data before the application of the Markov switching methodology has been the choice of a number of authors in the economics literature (e.g. Knüppel, 2004; Simon, 1996).

10. Our approach is based on practices followed in the business cycle literature. For example, Brandner and Neusser (1992) note that facts about non‐stationary time‐series have to be presented in any case and that the Hodrick–Prescott filter is superior to first differencing. See also, Chen (1996).

11. This filter minimises the variance of (y_t + μ _t ), where y_t is the original series and μ _t is the trend component of y_t , subject to a penalty imposed for variation in the second difference of μ _t , that is: λ[(μ _t+1−μ _t )−(μ _t −μ _t−1)]². The parameter λ controls the smoothness of the trend and it is imposed by the analyst.

12. We apply The BestFit programme (Palisade Corporation Copyright), which fits alternative distributions to frequency distributions and uses three tests to assess the goodness of fit of the theoretical distributions: the Chi‐Square, the Kolmogorov‐Smirnov and the Anderson–Darling test. All tests for normality reject the hypothesis that the normal distribution is an adequate fit of the observed returns; the Beta distribution appears the most plausible using all the tests.

13. For the application of downside risk measures to real estate investment portfolios see Booth et al. (2002).

14. When returns are normally distributed, the Sharpe ratio is equivalent to the Sortino ratio; the later uses instead the semi‐standard deviation as the denominator (Markowitz 1952).

15. It should be noted that not all authors in the real estate literature agree that valuation smoothing biases portfolio allocation decisions (see, for example, Booth and Matysiak 2001).