Constrained Real Estate Investment

As discussed previously - and illustrated by figure 3.11 - including real estate within a multi-asset portfolio improves performance, particularly for more risk-averse investors. However, as table 3.9 shows, in order for an investor to follow such an investment policy, he would have to vary his exposure to real estate over the period from a maximum of 77% to a minimum of 2% of total portfolio value, with allocation often fluctuating by more than 20% p. a. In common with other studies of this nature, it fails to account for the characteristics of real estate investment.

As discussed in sections 2.4.4 and 2.4.8, direct real estate investment is relatively illiquid, making exposure levels and thus funds committed difficult to change quickly. Such behaviour also severely violates the models assumption of no transaction costs; see section 2.4.8. Note should also be made that the model considers a 'semi-passive' investor, one who reassesses and rebalances his portfolio just once a year. This would be exacerbated if quarterly or monthly revisions were considered, a point particularly relevant to active managers and discussed further in section 2.3.1.

The import of this issue increases when considered within the context of an individual's or company's exposure to real estate. Firstly, real estate is often a significant component of corporate assets, a vehicle through which its primary activity may be conducted. Within the context of a company's investment in real estate, the cost of finding suitable premises, the possible loss of customers and employees, downtime, moving/reinstalling existing equipment and transaction costs, all contribute to the rigid nature of its investment in real estate. The extent of this constraint depends in part upon the overall cost of real estate as a proportion of total operating costs. Ordinarily it affects retailers more than manufacturers.

Secondly, in considering an investor having a fixed amount of wealth invested in real estate, mean-variance portfolio theory provides the hypothesis that investors optimise investment policies in order to achieve their objective utility. However, it is suggested that the majority of investors seek to optimise only a proportion of their wealth. often ignoring any investment which is non-tradeable. For example, when managing cash reserves, a manufacturing company may ignore the fact that it owns its industrial premises.

These circumstances therefore suggest that if an investment in real estate is made, the liquidity of that investment is constrained, and led us to consider the effects a constraint on the amount allocated to real estate may have on portfolio performance. The effects of constraining real estate investment, by varying the amount held from 0% to 60%, were analysed by assessing the impact of such a constraint on long-term portfolio composition and performance. The benchmark for the study was an investor who naively invests in the market portfolio. Upon obtaining a comparison between the 'naive' strategy and one that accounts for a static investment in real estate, the strategies and/or the performance of each were then tested to determine whether there was a significant difference in performance.

It was assumed that investors have a fixed exposure to real estate, and that they reassess and consequently rebalance their constrained portfolio at the end of each period. Again it was assumed that returns were normally distributed, and that there were no transaction costs. However, the effect of the latter assumption is now limited, due to the low turnover and uniform transaction costs associated with the unconstrained portion of the portfolio.24

The above conditions were accommodated by extending Grauer & Hakansson's [1986]

model. Equations 3.2 and 3.3 were modified as follows:

subject to

Constraint (3.5) above rules out short sales; constraint (3.4) is the budget constraint.

This model was used to investigate the effect of constrained real estate investment on investors with varying attitudes to risk. Figure 3.12 below illustrates the effects of imposing a constraint on the proportion invested in real estate. The benefits of real estate investment for all investors are still evident. However, for the more risk-averse investors (-50 ... -30), who limited their exposure to real estate within an unconstrained portfolio, placing a constraint on the proportion held increased the volatility of their portfolios. This made the benefits of constrained real estate investment less clear.

Tables 3.10 and 3.11 below show the results of the paired t-statistics and f-statistics when returns with and without a constrained investment in real estate are compared for each risk attitude. It is evident that the more risk-averse an investor, the greater the effect a constraint has on performance. This substantially increases the volatility of a risk-averse investor's portfolio, while reducing the volatility of less risk-averse strategies.

Another feature of the results is that, as the constraint placed on real estate investment increases, the relative amount allocated to equities rises at the expense of government bonds; see figures 3.13 and 3.14 below. In the extreme case of a 60% exposure to real estate the risk-neutral investor would, if unconstrained, borrow to invest in equities. This suggests that the treasury manager of a company with a constrained investment in real estate, facing long-term cash flow decisions, could reduce its overall risk by investing cash balances in equities rather than government bonds. For example, this would apply to a manufacturing company,

with a substantial proportion of its wealth tied up in industrial premises, facing a long-term programme of machinery replacement.

Table 3.12 below summarises the results, with the portfolios ranked by reference to Sharpe's measure of performance (Sharpe [1966]). This measure is discussed in section 4.4.1. The table clearly illustrates that by including real estate within a multi-asset portfolio, risk-adjusted returns are substantially improved.

According to the model, within a national context the optimal allocation to real estate is in excess of 20%. As table 3.13 shows, an unconstrained investor would on average hold from 14% to 46% of his portfolio in real estate. However, including the highly risk-averse strategies - -50 ... -30 - in this calculation may prove misleading. Although institutional investor are risk-averse, they generally do not hold portfolios with in excess of 60% in bonds (CSO [1996]). Thus, omitting these strategies from the calculation suggests that the optimal allocation to real estate is closer to 40%.

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24It should also be noted that, as the proportion of real estate held within the portfolio is assumed to be constant, the effect of changing real estate values has been ignored, as has the effects of transaction costs on the reinvestment of investment income.