The Behaviour of Value Indices of Commercial Real Estate
Many popular financial models rest on the fundamental assumption that the distribution of asset rates-of-return are multivariate normal with parameters that are constant over time. Empirical tests of both asset pricing models and the efficient markets hypothesis draw statistical inferences that are also conditional on distributional assumptions. The conclusions of Chapter 3 and papers by Blundell & Ward  and Grauer & Hakansson , for example, on the diversification benefits of including real estate within a diversified portfolio, rely on this assumption. It is thus of interest to consider the extent to which these distributional assumptions are satisfied and, if empirical analysis suggests they are not, whether the conclusions are qualitatively altered.
The majority of studies to date analysing the distribution of real estate return series reject the normality assumption. For example, Miles & McCue [1984a] and Hartzell. Hekman, & Miles , compute estimates of skewness and kurtosis for several indices formed from data obtained on the individual properties contained within a large commingled real estate fund in the USA. They found that returns from real estate did not appear to be normal. Myer & Webb  examine the quarterly NCREIF real estate index and its regional/sector sub-indices, and find non-normality exists in all series. However, the empirical evidence is limited.
Following Chapter 2, it may be argued that returns from real estate investment possess the characteristics of both bonds and equities. During certain periods, returns behave like those from bonds, when it produces a fixed income stream, and an equity during others. Under the modern lease, rental income is normally paid in advance. This timing of receipts differs from, and is superior to, other investments, where payments are made in arrears, usually half-yearly. Rents are fixed for a period of time, although the length of this period varies between types of real estate and their markets, with the rent set subject to variations in the terms and structure of leases.
It is thus natural to expect returns derived from commercial real estate to be bimodal, exhibiting two distinctly separate sets of behaviour. To capture these characteristics, the Markov regime-switching model of Hamilton [1989; 1990] has been applied to value indices of commercial real estate in the US and the UK. The Markov regime-switching model allows the modelling of non-stationary processes; those with a non-constant mean and variance.1 Such a model has been extensively used by Hamilton in a variety of applications e.g. interest rates (Hamilton ) and exchange rates (Engel & Hamilton ). Hamilton  reviews these applications.
This chapter is organised as follows. Section 6.2 outlines the Markov regime-switching model employed. Section 6.3 provides details of the data. Section 6.4 reports on the results and statistical tests. Finally, section 6.5 contains a discussion of the results and concluding remarks.
1For an example of a TAR model applied to indirect real estate, see Lizieri, Satchell, Worzala & Dacco .