Real estate diversification benefits

Abstract. Diversification benefits are shown to vary inversely with the correlation between asset returns. The present study estimates average correlation coefficients between realestate returns from property-specific data of an internationally diversified real estate fund in the Netherlands. It is found that diversification benefits within the United States are much larger than on the European Continent. The low correlation found between U.S. real estate returns implies that portfolios of small numbers of U.S. properties would require large return premia. Also, the study helps to explain why financial intermediaries exist in the real estate industry and when investors should consider employing them.

Introduction

Diversification is crucial to investors because asset returns do not move in perfect unison. Diversification benefits vary inversely with the correlation between asset returns. With respect to real estate assets, however, little empirical evidence exists due to the lack of property-specific data. The present study estimates average correlation coefficients between real estate returns from detailed data in the annual reports of Rodamco N.V, an internationally diversified real estate fund listed on the Amsterdam Stock Exchange.

It is shown that the average correlation coefficient between returns determines several aspects of diversification benefits, that is, the level of maximum risk reduction, the rate at which risk is reduced, and the trade-off between risk and return when portfolios cannot be perfectly diversified. The latter aspect is important for real estate portfolios because property ownership is often indivisible, so that diversification cannot be taken to the limit.

The present study has major implications for the existence of financial intermediaries, such as Real Estate Investment Trusts (REITs) and Commingled Real Estate Funds (CREFs). If real estate portfolios cannot be perfectly diversified, so that investors forgo some of the potential gains from diversification, financial intermediaries may exist as a method for providing lower levels of risk. The present study estimates the excess risk from imperfect diversification in order to assess the costs that investors should be prepared to incur for sharing risks.

The next section of this work provides a discussion of the literature and methodology regarding the measurement of diversification benefits. This is followed, in the third section, by a detailed look at the data. The fourth section delivers the empirical results, and compares these to some earlier findings. The last section concludes and summarizes the study.

Literature and Methodology

Evans and Archer (1968) and Latane and Young (1969) provided the first empirical estimates of the rate at which risk is reduced with increasing numbers of stocks in a portfolio. They did so by fitting a regression model to the standard deviations of simulated portfolio returns. However, Whitmore (1970) showed that, instead of the standard deviations, the models should have used the variances of the simulated portfolio returns. Evans (1975) found that the reduction of the standard deviation of returns is a function of both the number of stocks in a portfolio and the average correlation coefficient between returns.

The incidence of diversification benefits, or the reduction of risk, is kept to a maximum by the nature of the market in which the assets trade. This maximum may thus differ between, for instance, stock markets and real estate markets. The average correlation coefficient between returns is a comprehensive measure of diversification benefits that reflects the level of maximum risk reduction, and also implies the reduction rate of risk, whether risk is defined as the variance or standard deviation of returns.

Furthermore, as will be shown below, the average correlation coefficient between returns is an important determinant of the required excess return from imperfect diversification. Due to the indivisibility of property ownership, diversification cannot be taken to the limit. Real estate portfolios will therefore often contain relatively large quantities of diversifiable risk, for which the investor should require to be compensated: the average correlation coefficient suggests how much.

Similar to Evans (1975) and Elton and Gruber (1977), it is assumed that the means and (co-)variances of returns are identically distributed. With no information about these return characteristics one could assume that they do not differ across assets. Consequently, it would be optimal to buy equal amounts of each investment (see Samuelson, 1967). If the means and (co-)variances of returns can be forecast, however, buying unequal amounts of each investment may lead to further reduction of risk. Equal investment may thus be seen as an upper limit on the risk the investor faces. An operational measure of this bound is developed below.

Data Description

Data is used from the annual reports of Rodamco N.V, the largest real estate fund listed on the Amsterdam Stock Exchange with a market capitalization of $USS.5 billion at 28 February 1990, the end of its 1989/1990 book year. The major real estate funds in the Netherlands, including Rodamco, have obtained the legal status of open-end mutual funds, which enables the funds' management to purchase or sell shares at their discretion. They thus resemble U.S. open-end commingled real estate funds (CREFs), except that the latter do not publicly trade. From its inception in March 1979 through February 1990, the open-end status of Rodamco facilitated a phenomenal 30% annual growth rate of the fund's number of shares outstanding. As a result, Rodamco became the fourth largest stock listed on the Amsterdam Stock Exchange by 1989.

Sample Characteristics

The annual reports of Rodamco during the period 1979-90 provide detailed data with respect to 183 individual properties. From 1987, data are given only for properties worth at least NLG1O million ($US.00=NLG1.91 at 28 February 1990). In order to avoid inconsistencies in the set of data, returns have been calculated only for those properties with a market value greater than NLG1O million. Hence, 56 small properties are excluded from the set of data. Furthermore, 24 large properties have been in the portfolio for just one year and, therefore, do not provide sufficient data to make their inclusion in the set of data worthwhile. Thus, the data set pertains to 103 individual properties, which represent a market value of more than NLG1O million and have been mentioned in at least two annual reports during the sample period.

Further insight into the sample characteristics is provided by Exhibit 1, which gives the means, medians and standard deviations of property values by geographic region for 1989. Hence, the market value of properties sold before the end of 1989 is approximated by multiplying the last available value by the index returns of the relevant country in subsequent years, thus assuming an average value growth of sold properties. Under these conditions, the mean value of the sample properties is $46.9 million at the end of 1989. However, there are some very large properties in the sample, as evidenced by the substantially lower median value of $19.5 million. These large properties are predominantly located in the U.S., where 29 properties have an average value of $98.9 million. The European Continent (E.C.) and U.K. property size is generally much smaller than the U.S. average. The single largest property, however, is a super-regional mall of over 800,000 sq. ft located in the Netherlands, which was partially owned by Rodamco for some years during the sample period; the 1989 value of the (sold) property was approximated at $365 million.

The total market value of all properties in the sample is $4.8 billion by the end of 1989, while the U.S. properties, which are often partially owned by Rodamco, represent a total market value of $2.9 billion. In comparison, the Russell-NCREIF (RN) Index represented $17.4 billion worth of U.S. real estate at year-end 1989. However, the average value of the Rodamco U.S. sample properties is considerably larger than the 1989 average value of the RN Index properties, which is $13.6 million. Moreover, the sample is more concentrated in the East than the RN Index (43% and 25% of total value, respectively), and less concentrated in the West (14% versus 42%).

Exhibit 2 provides some insight into another important aspect of the sample. A large number of properties are offices (63), which thereby outnumber retail, warehouse and apartment type properties. However, most retail properties are relatively large with a floorspace of over 200,000 sq. ft located in the U.S. In terms of value, the sample is, therefore, fairly balanced between office and retail, while it is relatively underweighted in warehouses and apartments. The near absence of industrial and residential properties in the U.S. sample may be contrasted with their weighting in the RN Index by year-end 1989, namely 35% and 7% of the total number of properties, respectively. The unique characteristics of the sample may affect the results of the ensuing analysis.

Appraisal Values

The present study is based upon independent outside appraisals of Rodamco's properties. However, some authors, including Firstenberg, Ross and Zisler (1988), for instance, have criticized the use of appraisal values to infer the riskiness of real estate investments. Empirical analyses of U.S. data have shown that appraisal-based return series are 'smoothed', i.e., display little variation and strong serial correlation. To explain this phenomenon, some authors have argued that appraisers rely heavily on previous appraised values due to `transaction noise' (Quan and Quigley, 1989, 1991) or `lack of confidence' (Geltner, 1989). Yet these theories of potential sources of appraisal smoothing have not been supported by empirical evidence.

De Wit (1993) finds empirical support for the contention that in-house appraisals are a potential source of smoothing bias. In contrast, using the same data as the present study, he cannot reject the hypothesis that independent outside appraisals are not smoothed. This suggests that appraisal smoothing depends on whether in-house or outside appraisers are employed. Using independent outside appraisals only, the present study thus avoids at least one potential source of smoothing bias.

Temporal aggregation of 'outdated' appraisals, however, might still affect the observed variation of returns. Geltner (1993) provides a detailed analysis of temporal aggregation, which indeed happens to be a source of appraisal smoothing in the present study. First, De Wit (1993) finds that the October, November and December stock returns are significantly positively correlated with the appraisal-based returns derived from the financial reports of the years ending following February, thus 4, 3 and 2 months later, respectively. Conforming with this observation, Rodamco's 1992/1993 annual report discloses that each year, instead of at the end of February, all properties are valued at the end of December. Given the temporal aggregation of appraisals over the last quarter of the calendar year, Geltner's (1993) analysis suggests that one might expect the ratio of the 'true' to observed variance of returns to be 1.09.

Second, Rodamco's 1992/1993 annual report admits that, until then, the properties on the European Continent had been appraised evenly throughout the year. This far more serious source of appraisal smoothing can be expected to generate a 'true' variance of 1.50 times the observed variance (see Geltner, 1993). Consequently, the variance of the observed E.C. index returns was multiplied by 1.50, while the variances of the observed U.S. and U.K. index returns were both multiplied by 1.09. For the All Properties Index, the weighted average of these factors was determined at 1.26.3

Empirical Results

Summary statistics for the return distributions of the Rodamco sample and subsamples are presented in Exhibit 3. The individual property returns were equally weighted, while the portfolios were reallocated at the beginning of each period to maintain equal weights. The mean return of the All Properties Index appears to be 16.9% per annum over the 1979-89 sample period. The mean returns of the subindexes for properties located in the U.S., E.C. and U.K. are 19.4%, 11.7% and 32.0%, respectively. The U.K. subindex, however, only pertains to the period 1987-89 of generally 'booming' real estate prices; this affects the time-series' returns, but not necessarily the cross-sectional variation of property returns, which is the primary focus of the present study.

Measures of the variability of the index returns are also reported in Exhibit 3. As stated before, all returns are measured in local currencies, so that currency risks do not add to the reported risk measures. The sample standard deviations, adjusted for smoothing, appear to vary from 5.6% and 9.1% in the U.S. and E.C., respectively, to 28.5% in the U.K.; the standard deviation of the All Properties Index is 8.8%.

It is interesting to note, for instance, that the U.S. properties exhibit higher returns and less risk than the E.C. properties (that is, in the absence of currency risks). This does not seem to support the case for international diversification. The subsequent analysis, however, is confined to estimating real estate diversification benefits within the U.S., E.C. and U.K. using the cross-sections of property-specific data.

For portfolios with finite numbers of U.S. properties, Exhibit 5 provides further insight into the diversification benefits. Using equation (4), the variances of portfolio returns were calculated at given numbers of properties. Evans' Av confirms that the diversifiable component of the total variance of returns reduces at the rate of lIn; by randomly selecting twenty properties, for instance, 95% of diversifiable risk is eliminated.

Also, note that the total variance reduces asymptotically to the average covariance between the property returns, which amounts to 6.0% of total variance. Exhibit 6 illustrates the rate at which the variance of returns is reduced as portfolio size increases, as well as the level of maximum risk reduction.

A different perspective on the diversification benefits of U.S. real estate is provided by the measure of excess variance from imperfect diversification, TV, which relates the remaining diversifiable risk to total portfolio risk (see Exhibit 5). Although Tv declines as portfolio size increases, it is uniformly high; for instance, the variance of returns of a portfolio of twenty randomly selected U.S. properties is 44% diversifiable. This may also be inferred from Exhibit 6, that is by relating the distance between the `variancereduction curve' and the `average-correlation line' to the distance between the former and the horizontal axis.

The excess standard deviation from imperfect diversification, Ts, is iS somewhat smaller in percentage terms than TV, but displays the same pattern (see Exhibit 5). The required excess return from imperfect diversification is a function of this Ts, portfolio size, and the return in excess of the risk-free rate of interest. The latter is, following Statman (1987), assumed to be 8.2% for a lending investor and 6.2% for a borrowing investor.4 Based on these assumptions, the required excess return from imperfect diversification, ST, is determined for portfolios of increasing numbers of properties. It appears that, for example, a portfolio of twenty U.S. properties would require a 2.8% (2.1%) excess return from imperfect diversification for a lending (borrowing) investor, who would thus require an 11.0% (8.3%) return in excess of the risk-free rate of interest. A further discussion of these findings follows below.

For the E.C. subsample, however, very dissimilar results are obtained. The average correlation coefficient between the E.C. property returns is 0.404 (see Exhibit 4). This indicates that only 59.6% of property-specific return variance can be diversified away. Thus, larger diversification benefits are realized within the U.S. subsample than within the E.C. subsample.

Exhibit 7 provides numerical values of the diversification benefits of portfolios with finite numbers of E.C. properties, while Exhibit 8 illustrates the rate at which risk is reduced, as well as the level of maximum risk reduction. These may be compared with Exhibits 5 and 6, respectively. First, note that the rate at which the variance of returns is reduced, Sv, is similar for the U.S. and E.C. properties, that is 1/n. However, the excess variance (standard deviation) from imperfect diversification, TV (Ts), is much larger for U.S. portfolios than for E.C. portfolios of similar size. For instance, the excess variance of U.S. and E.C. portfolios of eight properties is 66% and 16% of total portfolio variance, respectively. Note also that in Exhibit 8 the distance between the variance-reduction curve and the average-correlation line is only a small fraction of the distance between the former and the horizontal axis. This illustrates that the excess variance from imperfectly diversified portfolios of E.C. properties is relatively small.

Due to the relatively low Ts, the required excess return from imperfect diversification is much smaller for E.C. portfolios than for U.S. portfolios of similar size (see Exhibits 5 and 7). For example, a lending investor would require an excess return of 0.3% on a portfolio of twenty E.C. properties, i.e., 250 basis points less than on a U.S. portfolio of the same number of properties; the difference is 190 basis points for a borrowing investor. These differences arise solely from differences between the average correlation coefficients between U.S. and E.C. returns. The relatively low pq for the U.S. market implies that portfolios of small numbers of U.S. properties would require large return premia.

For an explanation of the relatively low level of diversifiable risk of the E.C. properties, one may recall that the E.C. subsample contains few retail properties. This contrasts with the U.S. subsample, which is dominated by retail properties with so-called percentage rents, meaning that the actual rent paid depends partially on (some percent of) realized turnover. Retail rents on the E.C. are usually fixed for three to five years, adjusted only for the rate of inflation. Thus, the absence of retail properties with percentage rents in the E.C. subsample may help to explain the relatively low level of diversifiable risk found within this subsample.

Finally, the average correlation coefficient between the U.K. property returns is estimated at 0.189 (see Exhibit 4). Thus, 81.1% of property-specific returns variance in the U.K. portfolio can be diversified away. The diversification benefits within the U.K. subsample appear to be smaller than within the U.S. subsample, but considerably larger than within the E.C. subsample. Exhibits detailing the diversification benefits of portfolios with increasing numbers of U.K. properties would fall in between the 'extremes' of the U.S. and E.C. subsamples and are therefore not shown.

Comparison with Previous Findings Little evidence on real estate diversification benefits exists to put our findings into perspective. Firstenberg et al. (1988), and Froland, Gorlow and Sampson (1986), for instance, use aggregate data on property groupings.5 However, due to the indivisibility of property ownership, an investor typically holds an imperfectly diversified portfolio of real estate assets, which contains at least some diversifiable risk. Emperical analyses of real estate diversification benefits should, therefore, use property-specific data. The following studies comply with this criterium.

Dokko, Edelstein, Pomer, and Urdang (1991) compute annual appraisal-based returns for 102 (mostly industrial) properties, which are held in various CREFs, during the period 1976-84. Their Table 2 reports the real mean annual rate of return of all properties in each of the nine years, as well as the standard deviations. By backing in the annual CPI figures, the nominal index returns can be retrieved, from which the variance of the index returns through time (2N) is found to be 4.197. Also, the average variance of the property returns results from summing the average variance with respect to the index and oN, that is 22.562. Then, using equation (6), pi is found to be 0.178.

Grissom, Kuhle and Walther (1987) simulate real estate returns based upon transaction prices, net operating income data and financing terms, for 170 properties in two Texas cities during the period 1975-83. They report that the average variance of a portfolio of ten properties is reduced by 58.3% of the average variance of one property. These proportions may be substituted into equation (6) to yield an estimate of pij, i.e., ((0.417/1.000) (10/9)- 1/9=) 0.352.

Hartzell, Hekman and Miles (1986) use property-specific data from a large open-end CREF. These authors present proportions of non-diversifiable return variation to total return variation for the 220 (mostly industrial) properties that were held continuously in the fund's portfolio from 1978 until 1983. Note that these ratios differ from estimates of pi for a finite number of assets. From the figures presented by the authors' Tables 11 and 12, it can be inferred that the average correlation coefficient between the properties' quarterly returns is 0.087, and that the average correlation coefficient between the annual returns is 0.178. The authors refer to `the appraisal problem' as an explanation of the finding that the annual returns indicate smaller diversification benefits than do the quarterly returns; the latter are based upon the fund's in-house appraisals in three of every four quarters.

Webb, Miles and Guilkey (1992) construct quarterly real estate returns for a sample of 322 unsold properties contained in the Russell-NCREIF Index from the third quarter 1980 through the second quarter 1988. These returns are derived from a valuation model based on transaction prices of a sample of sold properties. Webb et al. present the average standard deviation of the individual property returns, as well as the standard deviation of an equally weighted index thereof (see the authors' Table 5). From these figures, it can be inferred that the average correlation coefficient between the transactions-driven property returns is 0.014. For appraisal-based returns of the same sample of unsold properties, it appears that the average correlation coefficient is 0.055.

The findings from these studies are summarized in Exhibit 9. The relatively small diversification benefits found in Grissom et al. (1987) is possibly explained by the properties being located in only two cities, whereas the other studies pertain to more regionally diversified samples. In the latter instances, the estimates of the average correlation coefficient among returns range from 0.014 to 0.178. It may thus be concluded that our estimate of 0.060 is at the lower end of the range of estimates from earlier studies of U.S. diversification benefits.

Evidence of non-U.S. real estate diversification benefits is scarce, especially concerning E.C. real estate. For the United Kingdom, Brown (1991, pp. 165-205) uses monthly appraisal values and cash flows of 135 properties during the period 1979-82. This author estimates diversification benefits by fitting the empirical model of Evans and Archer (1968) to the properties' returns data, but this model has been shown above to yield incorrect results. The average correlation coefficient between the returns may nevertheless be estimated from Brown's tables 4.4 and 4.5: the outcome appears to be 0.095, as shown in Exhibit 9, which is about half our estimate of U.K. real estate diversification benefits.

Conclusions

Diversification benefits have been shown to depend on the average correlation coefficient among returns. This measure indicates the level of maximum risk reduction, the rate at which risk is reduced, and the required excess return from imperfect diversification. The latter aspect is particularly important for real estate portfolios because property ownership is often indivisible, so that perfectly diversified portfolios are illusory.

The evidence generated using data of the Rodamco portfolio indicates that as much as 94% of the total risk of U.S. properties can be diversified away. For the U.K. properties, the percent diversifiable risk has been estimated at 81%. The diversifiable risk of the E.C. properties appears to be less than 60% of total risk. Estimates from the previous literature are either higher or lower than our findings regarding U.S. real estate and lower with respect of U.K. real estate; the evidence of E.C. real estate diversification benefits presented here, however, is unprecedented.

Due to the relatively low average correlation coefficient between the U.S. returns, the required excess return from imperfect diversification is much higher for U.S. portfolios than for E.C. portfolios of similar size. Under plausible assumptions, a portfolio of twenty U.S. properties would require an excess return of 210 to 280 basis points, whereas a similar E.C. portfolio would require an excess return of only 20 to 30 basis points. The required excess return from imperfectly diversified portfolios of U.K. properties would be between those of U.S. and E.C. portfolios.

These findings have major implications for the behavior of real estate investors and for the existence of financial intermediaries, such as REITs and CREFs. Because real estate portfolios cannot be perfectly diversified, financial intermediaries may exist as a method for providing lower levels of risk. The preceding analysis suggests that U.S. real estate investors with little information about property-specific returns and covariances would be prepared to incur large costs for sharing risks through REITs and/or CREFs. Alternatively, investors who hold direct property ownership should expect that their inhouse real estate expertise adds enough value to offset the estimated opportunity costs. The present study, thus, provides a framework for investors to decide between direct and indirect ownership of real estate investments.

This study is based on part of my doctoral dissertation, which I completed at the Tinbergen Institute/University of Amsterdam in 1993. I wish to thank L. A. Ankum, Graeme Newell, Kerry D. Vandell, and participants at the 1993 Annual Meeting of the American Real Estate Society for helpful comments on earlier drafts. The study was previously entitled `Additional Diversification Benefits from Alternative Real-Estate Portfolio Investment Strategies".

References

Brown, G. R., Property Investment and the Capital Markets, London: E & FN Spon, 1991.

Cole, R., D. Guilkey, M. Miles, and B. Webb, More Scientific Diversification Strategies for Commercial Real Estate, Real Estate Review, 1989, 19:1, 59-66.

De Wit, D. P M., Smoothing Bias in In-House Appraisal-Based Returns of Open-End Real Estate Funds, Journal of Real Estate Research, 1993, 8:2, 157-70.

Dokko, Y, R. H. Edelstein, M. Pomer, and E. S. Urdang, Determinants of the Rate of Return for Nonresidential Real Estate: Inflation Expectations and Market Adjustment Lags, Journal of the American Real Estate and Urban Economics Association, 1991, 19:1, 5269.

Elton, E. J. and M. J. Gruber, Risk Reduction and Portfolio Size: An Analytical Solution, Journal of Business, 1977, 50:4, 415-37.

, Modern Portfolio Theory and Investment Analysis, New York: John Wiley, fourth edition 1991.

Evans, J. L. and S. H. Archer, Diversification and the Reduction of Dispersion: An Empirical Analysis, Journal of Finance, 1968, 23:5, 761-67.

Evans, J. L., An Examination of the Principle of Diversification, Journal of Business Finance and Accounting, 1975, 2:2, 243-55.

Firstenberg, P M., S. A. Ross and R. C. Zisler, Real Estate: The Whole Story, Journal of Portfolio Management, 1988, 14:3, 22-34.

Froland, C., R. Gorlow and R. Sampson, The Market Risk of Real Estate, Journal of Portfolio Management, 1986, 12:3, 12-19.

Geltner, D., Estimating Real Estate's Systematic Risk from Aggregate-Level Appraisal-Based Data, AREUEA Journal, 1989, 17:4, 463-81.

, Temporal Aggregation in Real Estate Return Indices, Journal of the American Real Estate and Urban Economics Association, 1993, 21:2, 141-66.

Grissom, T. V, J. L. Kuhle and C. H. Walther, Diversification Works in Real Estate, Too, Journal of Portfolio Management, 1987, 13:2, 66-71.

Hartzell, D., J. Hekman and M. Miles, Diversification Categories in Investment Real Estate, AREUEA Journal, 1986, 14:2, 230-54.

Hartzell, D. J., D. G. Shulman and C. H. Wurtzebach, Refining the Analysis of Regional Diversification for Income-Producing Real Estate, Journal of Real Estate Research, 1987, 2:2, 85-95.

Latane, H. A. and W H. Young, Test of Portfolio Building Rules, Journal of Finance, 1969, 24:4, 595-612.

Mao, J. C. T., Essentials of Portfolio Diversification Strategy, Journal of Finance, 1970, 25:5, 1109-21.

Mueller, G. R. and B. A. Ziering, Real Estate Portfolio Diversification Using Economic Diversification, Journal of Real Estate Research, 1992, 7:4, 375-86.

Quan, D. C. and J. M. Quigley, Inferring an Investment Return Series for Real Estate from Observations on Sales, AREUEA Journal, 1989, 17:2, 218-30.

, Price Formation and the Appraisal Function in Real Estate Markets, Journal of Real Estate Finance and Economics, 1991, 4:2, 127-46.

Samuelson, P. A., General Proof that Diversification Pays, Journal of Financial and Quantitative Analysis, 1967, 2:1, 1-13.

Statman, M., How Many Stocks Make a Diversified Portfolio? Journal of Financial and Quantitative Analysis, 1987, 22:3, 353-63.

Webb, R. B., M. Miles and D. Guilkey, Transactions-Driven Commercial Real Estate Returns: The Panacea to Asset Allocation Models? Journal of the American Real Estate and Urban Economics Association, 1992, 20:2, 325-57.

Whitmore, G. A., Diversification and the Reduction of Dispersion: A Note, Journal of Financial and Quantitative Analysis, 1970, 5:2, 26364.

*School of Banking and Finance, The University of New South Wales, Sydney 2052 Australia and Stichting De Quintessents, Amsterdam, The Netherlands. Date Revised-May 1996; Accepted-October 1996.

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