# Limitations of Present Study and Avenues for Future Research

# Limitations of Present Study and Avenues for Future Research

Tests of the DRT model were limited to consideration of a portfolio comprised of just four asset classes together with a risk-free asset. Knowledge of the model's behaviour would have been improved had a wider investment universe been considered. It would also have been of interest to expand the empirical dimensions of this study, for example by examining the range of returns across real estate managers, rather than across asset classes. However, a lack of data precludes satisfactory study in this area.

Extensions of the work contained herein, would include:

- the application of the DRT model to a wider investment universe;
- relaxing the normality assumption and borrowing restrictions; and
- incorporating improved forecasts of future asset returns.

This would allow a better understanding of the effect of including real estate on portfolio performance, and improve the description of those investors which may or may not benefit from investment in real estate.

Given a reasonable estimate of *α*, *ez post* estimates of *κ* may be extracted, from the DRT model. Knowledge of *κ*'s stability, both cross sectionally and through time, would increase the understanding of the model's efficacy. The model could also be used as a historic definition of fund risk, which in turn may aid decision making. For example, given an investor's required rate-of-return (which is open to sensitivity analysis), unit trusts may be classified in terms of their *κ*.

Due to the nature of many investor's objectives, the structure of the DRT model lends itself to consideration of a portfolio as consisting of many parts. For example, a pension fund may split its portfolio into two parts. One might be dedicated to achieving a short-term required rate-of-return - e.g. to fund current pension liabilities - the other structured to achieve long-term objectives. It would then be able to impose a different set of constraints upon each i.e. a different *α* and *κ*.

It would also be of interest to identify the participants in the investment market, determine their respective *α* and *κ* functions, and then compare these with the percentage of real estate held in their portfolios. This thesis was limited in some ways because knowledge which would have been gained from such a study was not available. For example, *α* was held to be the risk-free rate. Knowledge of how *α* varies with fund maturity and/or size would improve our understanding of the results contained herein.

The utility function specified, although perhaps a good proxy, is unlikely to be an accurate reflection of investor preferences. Instead of a dichotomous utility function that switches at *α*, there is likely to be a transitionary period during which investor preferences change. This point is of particular relevance the more risk-averse an investor: thus the higher *κ*.

The Markov model - discussed in Chapter 6 - may be generalised to include the probability that *x _{t}* =

*p*is dependent not only on the value of

*x*

_{t_}_{1}, but also on a vector of observed variables; see Diebold, Lee, & Weinbach [1994]. Thus, if the parameter estimates depend upon cyclical factors as suggested, then the required parameter shift dates can be forecast and included in models that require parameters to be estimated without prior knowledge. The implication of these results is that it may be possible to forecast value indices of commercial real estate using regime-switching models. In addition, the existence of regime-switching in value indices of commercial real estate, need to be considered with reference to unsmoothing models that depend upon constant parameter estimates through time.