# Mixed-Asset Portfolio

# Real Estate within a Mixed-Asset Portfolio

Theoretically, the effect on an investor's portfolio of omitting an asset has been recognized.^{10} However, from an empirical perspective there is doubt as to the significance of such an omission. Both Fama & Schwert [1977b] and Stambaugh [1982] found no significant impact on performance in the estimation of equity returns by omitting assets; see section 5.3.9. However, their results were due to the analysis being confined to the stock market, and were therefore a product of the high correlation between equity returns. Mayer [1972] and Brito [1977] had previously considered the inclusion of human capital within the market portfolio. In a similar way Bosch [1986] and Grossman & Laroque [1990] analysed the impact of durable goods consumption on the pattern of investment. The general result states that an individual who holds a non-tradeable asset e.g. human capital, as in the models of Mayer and Brito, must adapt his^{11} investment policy. Thus, an investor who does not have access to a part of the market portfolio - or has to hold a fixed quantity, possibly non-zero, of an asset - will hold a sub-optimal portfolio as defined by mean-variance portfolio theory, and employ a different investment strategy on the remaining assets. However, the impact of such a restriction may be negligible if the non-tradeable or fixed asset is strictly orthogonal to a tradeable asset, or if the holding is insignificant with respect to his global portfolio. Neither of these points is true of real estate.

Including real estate within available investments has been shown to improve the risk-adjusted performance of a portfolio. Several authors^{12} have demonstrated that real estate earns substantial risk-adjusted excess returns and provides a reasonable vehicle through which to hedge the risk of long-term inflation; see section 2.4.6. Blundell & Ward [1987], Webb & Rubens [1988] and Grauer & Hakansson [1995] supported this, finding that the inclusion of real estate positively affects the performance of an investor's^{13} optimal portfolio.

Life and pension fund attitudes to risk vary widely, depending on e. g. the fund's maturity ratio. Consideration is therefore given to the full spectrum of risk attitudes through the use of multi-period investment theory.^{14}

This has been shown to approximate mean-variance policies well, yet it also provides in formation on an investor's attitude towards rusk, subject central to this thesis. Levy & Markowitz [1979], Pulley [1981, 1983], and Kroll, Levy & Markowitz [1984] investigated how closely portfolios, chosen on the basis of means and variances, approximate portfolios chosen by maximising expected utility. Pulley [1981; 1983], Kallberg & Ziemba [1983], and Grauer [1986] considered whether portfolios with ‘similar’ risk-aversion characteristics would hold ‘similar’ portfolios. With the exception of Grauer [1986], the consensus drawn from this literature is that portfolios chosen on the basis of mean and variance closely approximate those chosen by maximising expected utility, especially when investors have similar attitudes to risk. In addition, while fundamentally single-period in nature, traditional mean-variance portfolio theory also offers little guidance for investors concerned with long-term performance; see section 5.2 (Grauer & Hakansson [1985, p. 25]).

The basic multi-period investment (“MPI”) model used in this chapter is the same as that employed in Grauer & Hakansson [1986]; the reader is referred to their paper -specifically pp. 288-291 - for details.

This model was initially used to construct and rebalance portfolios composed of UK equities, commercial real estate, long-term government bonds and a risk-free asset over the period 1977-1994. The investment universe was then expanded to include Far East equities. These were chosen to represent an investment in overseas equities for two reasons. A historic series was available from 1967, and the indices possessed the main characteristics associated with overseas equities; negative correlation with UK equities and bonds, and highly volatile.

Table 3.1 below contains a summary of the asset category and fixed-weight portfolio symbols used in this chapter, which proceeds as follows. Section 3.4.1 outlines the discrete-time MPI model used and the hypotheses tested. Section 3.4.2 presents the data and methodology which dealt with real estate performance. Section 3.4.3 reports the results and the statistical tests thereon. Section 3.4.4 then proceeds to consider the effects of constrained real estate investment on portfolio performance, and the proportion allocated to real estate when Far East equities are included within the portfolio. The final section contains a summary and concluding comments.

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^{10}This is further discussed in section 5.2.7.

^{11}Where not used in reference to a particular author, the masculine gender shall include the feminine gender throughout this thesis.

^{12}See footnote 2 on page 3.

^{13}The term investor as used here refers to a class of investors who share the utility function specified, and may apply both to an individual investor or a company managing its investment portfolio.

^{14}See e.g. Mossin [1968], Hakansson [1971; 1974], Leland [1972], Ross [1974], Grauer & Hakansson [1982; 1985; 1986]and Huberman & Ross[1983].