# Equilibrium

# Models of Equilibrium in the Capital Markets

## Introduction

Chapter 3 sought to extend conventional methods of risk/return analysis in an attempt to better explain the current low level of institutional investment in real estate. However, the results contained therein provided little further explanation. As a result, the last chapter sought to review the relationship between risk and return, and ultimately the methods by which performance is evaluated.

Two types of risk adjustment procedures were considered in Chapter 4, those which adjust for the total risk of the portfolio, and those which adjust only for the systemic risk of the portfolio. The second of these procedures is based on the framework of the CAPM. Therefore, to ascertain the legitimacy of applying systemic methods of performance evaluation to real estate decisions, specifically their value in determining the risk premium on real estate, the CAPM - the received theory of risk in equilibrium - is now reviewed.

This chapter therefore seeks to review the theoretical foundation of the CAPRI. and the empirical evidence of particular relevance to its use in the evaluation of real estate's performance. However, the question of whether the CAPM should be applied to real estate at all must first be addressed.

We may point to many writers who believe that the CAPM should be applied to real estate,^{1} but we have also identified some who believe otherwise. Baum [1989], for example, provided five reasons for not applying the CAPM to real estate.

*The paucity of data*- The limited frequency and length of data series available for real estate compared to that available on equity markets. This is a valid criticism when considering the performance of real estate in the short-term. However, the effect of this lack of data may be limited if the estimation and holding periods considered are of a reasonable length. Grauer & Hakansson [1982] suggested a period of eight years. As discussed in section 4.5.2, long time series allow for long estimation periods, which theoretically provide lower sampling errors. However, structural shifts over these long time periods i.e. fundamental shifts in economic structure, may occur (Merton [1987, p. 486]). Merton suggested that when considering financial time series, estimation periods of no more than eight years should be considered.

*Price and valuation*- The majority of real estate returns series are appraisal-based and, as discussed in section 2.4.2, are subject to error. As Baum [1989, p. 5] states,
- 'The result is a serious underestimate of price volatility. The conditions underpinning valuation exclude the very circumstances which lead to volatility; and serial correlation further smoothes away variations in return. '

- While this is certainly true of monthly data, the effect of such bias is greatly reduced when considering annual data. Additionally, in attempting to overcome the problem, several methods of 'unsmoothing' real estate returns series have been developed in the literature;
^{2}see section 3.4.2.

- The majority of real estate returns series are appraisal-based and, as discussed in section 2.4.2, are subject to error. As Baum [1989, p. 5] states,
*Sample and index errors*- Due to real estate's high unit value, indivisibility and illiquidity, real estate indices contain specific risk, and are consequently riskier than the underlying population. This criticism is correct in suggesting that the results drawn from a model employing real estate indices as a proxy of performance will only be applicable to those investors in a position to hold a well diversified real estate portfolio. However, this does not prevent the application of CAPM. The issue of diversification is further discussed in section 2.4.3.

*Illiquidity*- The historic volatility of valuation-based indices fails to account for real estate's illiquidity, and may result in an underestimation of risk, or overestimation of return, at any particular point in time.
- The CAPM does not require an investor to trade. As is shown in section 3.4, such criticism may be accommodated by constraining the model. It may also be argued that this apparent inefficiency in the real estate market is no worse than that observed with some small stocks.
^{3}

*Efficient pricing*- Use of the CAPM requires that the market be efficient, which produces three assumptions. According to Baum [1989, p. 6],
- 'The first is that all assets are perfectly divisible and marketable; but property is not.... The second is that there are no transaction costs and no taxes; but in real estate these costs are high, and reduce the realisable returns. The third is that investors have homogeneous expectations.'

- The first two assumptions may be accommodated by again constraining the model; for example, as in section 3.4. The third, however, is more difficult. To the extent that they net out, this criticism holds. Therefore, some investors will hold sub-optimal portfolios.

- Use of the CAPM requires that the market be efficient, which produces three assumptions. According to Baum [1989, p. 6],

Therefore if the following guidelines are observed

- the estimation and holding periods considered are each of a reasonable length;
- real estate indices are unsmoothed; and
- investment in real estate is constrained,

the CAPM may then be applied to decisions involving real estate. The results, however, may only be applied to investors able to hold a well diversified real estate portfolio.

The derivation of the equilibrium relationship between risk and return is central to capital market theory. It provides the foundation of competitive equilibrium asset pricing, as risk premia are dependent not on the total risk of an asset, but on the portion which cannot be diversified away by holding a perfectly diversified portfolio i.e. the market portfolio. The CAPM was the first model of asset pricing to offer a clear parameterisation of the risk/return relationship, and the potential for testing. The model quickly became acceptable to financial theorists and investment practitioners.

The CAPM has been the subject of much discussion and empirical testing. Although the foundations upon which it was originally built have been considerably weakened, it still underpins much of current practice in finance.

The last 20 years has seen much research documenting persistent cross-sectional patterns in returns that are contrary to CAPM predictions:

- that expected returns are not related to
*β*; and - that there is a significant relationship between average returns and other variables; for example, size or earnings per share.

One explanation is that the above results represent violations of the simple model, and that other variables better describe security returns. Absent, however, is any theory to justify the choice of variable(s) used. As the *Economist*^{4 }perceptively noted, the investment community is left with an awkward choice:

'Believe the evidence, despite a theoretical vacuum, and use size and book- to-market ratios as a guide to returns; or stick with a theory that, despite the data, is built on impeccable logic. '

In defence of the CAPM, it has been argued that:

- measurement error of
*β*may be being picked up by other, more precisely measured, variables; - a distinction cannot be made between the two hypotheses - that the market is efficient and that the model is correct; and
- the model is not testable (Roll [1977]).

Most of the early empirical studies used a proxy for the market portfolio e.g. a value- weighted combination of all equities listed on an exchange, and tested if the cross- sectionally *ex post* excess returns for a sample of companies could be explained by their *β* on the index. Roll [1977] criticised this approach, observing that the only testable implication of the CAPM is that the entire market portfolio, not simply any limited index, is mean-variance efficient. It followed, therefore, that the CAPM is not testable unless the exact composition of the market portfolio is known.

Roll's critique questioned not only the ability to test the CAPM, but also its various applications in finance, such as capital budgeting and performance evaluation. This is further discussed in section 4.5.

Fifteen years on, a controversial paper by Fama & French [1992] demonstrated that the relationship between expected return and *β* is flat, not a positive linear function of their market *β* as would be expected i.e. that there is no relationship between expected return and *β*. They found that equity risks are multidimensional, with the various dimensions of equity risk being proxied by four variables; size, book-to-market equity, earnings-price ratio and gearing. Fama & French inferred that the key determinant of expected returns was total risk and not merely systemic risk as postulated by the CAPM.

In two separate interviews, Fama has been quoted as concluding from the study that:

'Beta as the sole variable explaining returns on equities is dead.'^{5}

and

'... that the relation between average return and beta is completely flat.'^{6}

The interpretation of the issues raised in the principal tests of the CAPM, and their application to real estate investment, is fundamental to this thesis. They provide a base from which to consider the legitimacy of the CAPM in real estate investment decisions, specifically its value in determining the required risk premium on real estate. This leads us to review the theory, empirical results and procedures used in these tests of the CAPM.

This chapter is set out as follows. The next section briefly discusses the origins of the CAPM, and considers its theoretical base. Section 5.3 then reviews the empirical evidence most relevant to real estate investment. While the last section concludes.

____________________________

^{1}See, for example Dee [1975], Hettenhouse & Dee [1976], Wu & Colwell [1986], Ennis & Burik [1991], Fisher, Hudson-Wilson & Wurtzebach [1993] and DeCain [1994].

^{2}See for example, Blundell & Ward [1987], Geltner [1989; 1991] and Ross & Zisler [1991].

^{3}See for example, Kemp & Reed [1971] and Girmes & Benjamin [1986].

^{4}March 7^{th}, 1992.

^{5}According to Eric Berg of The New York Times - February 18th, 1992.

^{6}According to Michael Peltz of the Institutional Investor - June, 1992.