# Results

# Results

The results and the discussion of them focus on comparing the performance of the DRT and MPI models. The latter was employed in Chapter 3. Note, however, that both models rely on separate sets of assumptions. Their comparison should therefore be considered in relative, rather than specific, terms. For example, although both models allow an investor to specify his degree of risk-aversion, the objective of this factor is very different in the two models. In the DRT model, the larger *κ*, the greater the weight placed on returns below a specified target rate-of-return. In the MPI model, reducing *γ* places increasing importance on minimising the portfolio's variance.

This is well illustrated in table 7.4, and figures 7.7 and 7.8. As *γ* is reduced in the MPI model, the variance of the portfolio dramatically falls while, by increasing *κ* in the DRT model the variance of the portfolio falls, but not to the same degree. Note, however, that the risk tolerant strategy, DRT(RFR, 1), is superior in all cases to -3 ... 0.5 MPI strategies.

As expected, the variance of the portfolio of a risk-averse investor under the DRT model is much higher than under the MPI model. However, the density of the distribution is negatively skewed, with a lower-quartile higher than any of the portfolios generated by the MPI model. Table 7.5 portrays this point well, which shows the negative excess

returns generated under each model. That is, returns below the risk-free/required rate-of-return.

Table 7.6 shows the results of the paired *t*-statistics and *f*-statistics when their returns are compared between the MPI and DRT models. The results suggest that for the less risk-averse investor the DRT model substantially improves performance. This is statistically significant at the 0.05 level in all cases. The effect of using the DRT model on the highly risk-averse investor's performance is less clear, and is dependent on two factors, namely, his attitude towards risk and, as discussed, his definition of risk. Note that the DRT(RFR,8) portfolio has a superior Sharpe measure to MPI -50 portfolio, respectively 0.89 and 0.61. However, in contrast to the DRT measure, the Sharpe measure, *inter alia*, assumes that there is a linear relationship between risk and return.

Figure 7.9 plots the efficient frontier of both unconstrained models. It suggests that the DRT model substantially outperforms the MPI model for less risk-averse strategies. However, the performance of the DRT model for the more risk-averse

investor is again dependent on his definition of risk. Figure 7.10 plots the total returns indices for both unconstrained models over the period 1977-1994.

### Effect of Unsmoothing Real Estate Returns

Unsmoothing the series as outlined above - by increasing its variance - all investors reduced their exposure to real estate. The more risk-averse the investor, the greater the reduction in allocation. Although the average allocation to real estate was lower under the DRT model - than under the MPI - it was less responsive to unsmoothing. A result due to the reduced role of variance under the DRT model. These results are similar to those contained in section 3.4.4,^{17} which employed the methodology in Barkham & Geltner [1994]. It also had a comparable effect on the covariance and correlation of returns; see tables 7.7 and 7.8, respectively.

SDRT

### Allocation to Real Estate

Table 7.9 presents the results when returns are compared between the MPI and DRT models. These include a variable constraint on the proportion held in real estate. Again, the results suggest that for the less risk-averse investor the DRT model substantially improves performance and is statistically significant at the 0.1 level in all cases. The fall in relative outperformance is due to the effect of the constraint on investment in real estate.

Table 7.10 presents the results when returns are compared between unconstrained and variably constrained DRT models. As with the MPI model, placing a constraint on the proportion of real estate held adversely affected portfolio performance.

The performance of the DRT portfolio's was assessed using Sharpe's performance measure,^{18} with the results detailed in table 7.11. The table illustrates that by

including real estate within a multi-asset portfolio, risk-adjusted returns are substantially improved. These results may be compared with those in table 3.12 on Section 3.4.4, which clearly shows that the DRT model outperformed the MPI model over the period 1977-1994.

Table 7.12 on details the average allocation to each asset class, under both the MPI and DRT model. Two points are of interest. Firstly, the average allocation to real estate within a national context, was less under the DRT than the MPI model. However as discussed, the highly risk-averse strategies under the MPI model disguise the extent of the overall reduction in allocation; see Section 3.4.4. If the very risk-averse strategies are omitted from the calculation, the average unconstrained allocations to real estate rise to 44% and 29% under the MPI and DRT models respectively. Giving consideration to the length of time period covered and discrepancy in model performance, this is a substantial difference.

### Overseas Equities

As in Chapter 3, the above analysis was initially restricted to a national context in order to facilitate comparison between the two models. However, as previously mentioned, the relaxation of UK exchange controls in 1979 is often highlighted as the main reason life and pension funds limit their exposure to real estate.

As table 7.13 illustrates, under the proposed DRT model, allowing investors access to Far East equities dramatically reduces their exposure to real estate. These results are in marked contrast to those under the MPI model, in which access to Far East equities also reduced exposure to real estate, however, substantial investment in it was still proposed. Under the DRT model, average investment in real estate drops from 29% to just 8%, with investment switching into Far East equities. This figure is much more consistent with current life and pension fund levels of investment: 6.8% in cash, 54% in UK equities and almost 24% in overseas equities (CAPS [1996]). Again, the theoretical argument that, if the investment universe was further expanded the proportion held in real estate would be expected to fall, stands.

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^{17}See specifically tables 3.5 and 3.6 on section 3.4.3.

^{18}Detailed in section 4.4.1.