Executive Summary. The purpose of this study is to determine whether or not private real estate portfolios can be diversified or rebalanced using public real estate (equity real estate investment trust stocks). An examination of resulting efficient frontiers and their corresponding optimal portfolio weights across various levels of expected return reveals that the ability of public real estate to rebalance private real estate only portfolios, using either long or short positions, is very much in doubt. The results found in a mixed-asset setting are more promising, but not convincing. Hence, if institutional investors wish to continue to hold public real estate, they should do so for reasons other than rebalancing or diversifying their private real estate portfolios.
There are two major ways in which institutional investors can invest in real estate. The first is to purchase unsecuritized real estate directly through property pools, commingled real estate funds (CREFs), syndications or separate accounts that are managed by professional real estate portfolio managers or investment advisors. This form of ownership will henceforth be referred to as "private real estate." The second category of real estate investment involves the purchase of securitized real estate, or equity real estate investment trusts (EREITs). Since most equity REIT shares are publicly held, this type of real estate ownership will be referred to as "public real estate."
The importance of including private real estate in optimally diversified mixed-asset portfolios has long been recognized (Webb and Rubens, 1987; Ennis and Burik, 1991; Giliberto, 1992, 1993; and Hartzell, Wurtzbach and Watkins, 1995). Private real estate helps reduce the risk of a portfolio because it has less than a perfect correlation with stocks, bonds and all other assets. The numerous problems associated with private real estate ownership, especially the liquidity and lumpiness problems, are the impetus for pursuing the possibility that public real estate could be used instead. For example, if a portfolio optimization generates ideal weights for both private and public real estate in one period, then in the next period the optimal percentage to invest in private real estate changes by a small fraction, exact portfolio rebalancing cannot be achieved because of the lumpiness problem associated with private real estate.
EREITs represent only a small fraction of the aggregate institutional real estate available. Hence, EREITs can theoretically be used in conjunction with, rather than in lieu of, private real estate. More specifically, once a mixed-asset portfolio containing private real estate is optimized, EREITs could potentially be used to rebalance the portfolio from one period to the next to reflect changing expectations surrounding future returns. However, for EREIT stocks to be used for rebalancing private real estate portfolios, it must be established that EREITs are reasonable substitutes for private real estate. The greater the degree of substitutability, the greater the likelihood that EREITs could be used for rebalancing/diversifying private real estate portfolios.
Literature Review
Are REITs Real Estate?
Based on the extant literature, it is known that real estate should be included in a mixed-asset portfolio (Fogler, 1984; Irwin and Landa, 1987; Firstenberg, Ross and Zisler, 1988; Webb, Curico and Rubens, 1988; and Kallberg, Liu and Greig, 1996). Due to numerous problems associated with private real estate (appraisal smoothing versus transactions-based pricing, liquidity, short selling constraints, noise and overreaction in pricing, lumpiness and transactions costs), institutional investors would like to use EREITs in conjunction with, or in lieu of, private real estate. The degree of substitutability between private and public real estate is currently unknown. Seck (1996) defines substitutability as "...two assets are deemed substitutable if there exists a mathematical-- unspecified transformation of the process underlying the pricing of one asset that closely approximates-within a tolerance range-or exactly replicates the process underlying the pricing of the other asset."
If private and public real estate are perfectly substitutable, then institutional investors should use EREITs, particularly when it comes to rebalancing real estate and mixed-asset portfolios.
Fundamental Differences
In theory, since private and public are two forms of owning the same underlying real estate assets, they should behave in a similar manner. However, there are many differences between private and public real estate that call into question the substitutability of the two asset types. To repeat, these differences include appraisal smoothing versus transactions-based pricing, liquidity levels, short selling constraints, noise and overreaction in pricing, management and transactions costs. These differences cause the returns on private real estate to behave quite differently, not only from each other, but also when compared to other investment assets. Myer and Webb (1993a,b, 1994) and Seiler, Webb and Myer (1999) show that private and public real estate returns are dissimilar based on a number of criteria, including autocorrelation, normality, risk-adjusted return, and lead-lag relationships. These results are consistent with much older and tentative findings by Miles and McCue (1984) and Hartzell, Heckman and Miles (1986).
Testable Hypotheses
Based on the preceding literature review, it is clear that the returns on real estate assets are different from the returns on other investment assets. Moreover, the returns within the real estate asset class (public versus private) are very different. The differences hold not only cross-sectionally, but intertemporally as well. For this reason, this study tests three hypotheses that examine the potential for the use of EREITs in lieu of private real estate in real estate only and mixed-asset portfolios. They are as follows.
Hl: Private and public real estate are reasonable substitutes in real estate only portfolios.
H2: Private and public real estate are reasonable substitutes in mixed-asset portfolios.
H3: Shorting an EREIT index is a reasonable substitute for directly selling private real estate holdings.
Methodology
Hypotheses One and Two
Once comparable securitized and unsecuritized real estate indexes (by property type) have been created (see Data), the substitutability of the two indexes can be tested. This analysis will be performed by first creating an all private real estate efficient set consisting of four property types: office, retail, apartment and industrial. In the second step, one of the four unsecuritized real estate property types will be replaced with its comparable securitized real estate index (of the same property type). The percentage allocations in each property type and the efficient frontiers will then be compared on a before and after basis. The more dissimilar the pre and post allocations and efficient sets, the lower the degree of substitutability. The above outlined procedure will be pairwise repeated for each of the four different property types in the real estate only portfolios and the mixed-asset portfolios.
Hypothesis Three
One of the primary differences between private and public real estate is the ability of public real estate to be sold short. Hypotheses one and two test for the substitutability of private and public real estate for long positions. Hypothesis three will test for the degree of substitutability in short positions. It is possible that private and public real estate are substitutes for long positions, but not for short positions, or visa-versa.
Initially, an institutional investor is assumed to hold an all private real estate portfolio. When it becomes time to change the percentage holdings for any of the four property types, assuming constant relative wealth in each property type, the investor must sell one type (industrial, for example) and purchase another (retail, for example). Since private real estate cannot be sold short, this rebalancing results in two separate transaction costs. However, because public real estate holdings can be sold short, the investor now has the option to sell short the EREIT property type equivalent (industrial) to decrease the percentage holding and buy (or long) the retail property type to increase percentage holdings. This procedure allows for a further examination of private and public real estate substitutability.
Empirically, this hypothesis will be tested by creating two distinct all-private real estate efficient portfolios. Portfolio one will consist of only three property types. This portfolio will be void of the property type wishing to be altered (i.e. industrial) and will eventually be used as a benchmark for comparison.
Portfolio two will consist of all four private property types. That is, it will continue to hold the industrial property. Additionally, an equal and offsetting short position will be taken in the equivalent securitized industrial index. Since the purpose of this hypothesis is to determine the ability of EREITs to rebalance private real estate portfolios, a reasonable amount to short (a weight) must be chosen. Ten percent is the selected weight used throughout the testing of hypothesis three because it represents a reasonable rebalancing percentage.
If private and public real estate are perfect substitutes in a short selling scenario, the resulting allocation weights will be equivalent to what they are in portfolio one (the three property type case where industrial was not included) because the short position in public industrial real estate should, in theory, exactly off-set the long position in private industrial real estate. The more similar the two sets of allocations and the resulting efficient frontiers, the greater the degree of substitutability in a short selling context. The above outlined procedure will be pairwise repeated for each of the four different property types just as was done in the testing of hypothesis one and two. The greater the substitutability of securitized real estate (EREITs) for unsecuritized real estate, the more likely it is that EREITs will be the preferred choice for institutional investors to diversify/rebalance private real estate portfolios.
Data
The typically used NCREIF and NAREIT indexes do not contain the same percentages of real estate by property type. NCREIF contains higher percentages of office and retail, while NAREIT contains more residential properties. Moreover, the NAREIT equity index contains healthcare, whereas the NCREIF has no healthcare representation. Hence, it should not be surprising that comparisons between these two indexes result in the conclusion that EREITs are not real estate. To the extent that property type is a determinant of return behavior, the standard comparison of private and public real estate returns will be problematic. In order to correct for the differences in the two real estate asset classes, comparable indexes are constructed.
Constructing Indexes
The method of constructing comparable private and public real estate indexes is consistent with that used by NAREIT (which commenced in January, 1994). NAREIT examines the dollar amount invested, in each property type. If an EREIT invests at least 75% of its value in one property type (retail, for example), then that EREIT is classified accordingly. If an EREIT does not have at least 50% invested in any one property type, the EREIT is classified as a diversified EREIT. Investment percentages between 50% and 75% are classified at the discretion of NAREIT. This flexibility is designed to enable an EREIT to be consistently classified as a certain property type even if its relative investment values shift slightly from period to period. NAREIT uses nearly the same categories as NCREIF to facilitate equitable comparisons. The property types considered in the current study are apartment, office, retail, and industrial.
Ex ante Returns
Most studies that construct efficient frontiers do so based on ex post (or historical) data. Sharpe (1990) explains that this will bias results because: "While results vary from asset class to asset class and from time period to time period, experience suggests that for predicting future values, historic data appear to be quite useful with respect to standard deviations, reasonably useful for correlations and virtually useless for expected returns."
For this reason, all efficient frontiers constructed for this study are based on expected returns. This is a more realistic approach because investors must make allocation decisions ex ante.
Because all efficient frontiers are constructed using ex ante expected return data, it is necessary to choose variables known to drive returns on stocks, bonds and real estate assets. The variables chosen are some of the variables that were successful in Fama and Schwert (1977), Chen, Roll and Ross (1986), Fama and French (1988, 1989), Chan, Hendershott and Sanders (1990) and Ferson (1990). Specifically, the variables chosen are default spread, risk spread, term spread, dividend yield and unexpected inflation.
Default spread is defined as the return on longterm corporate bonds minus long-term government bonds. Risk spread is calculated by subtracting the return on Aaa rated corporate bonds from the return on Baa rated corporate bonds. A related variable, term spread, is defined as the return on long-- term government bonds minus the return on treasury bills. The final two explanatory variables are the dividend yield (latest twelve months dividends/price) on the S&P 500 and unexpected inflation [estimated by the Fama and Schwert (1977) method].
These independent variables will be used to forecast the returns on both large and small capitalization stocks, long-term corporate bonds, long-- term government bonds, treasury bills, and private and public real estate in aggregate and by property type. Financial asset returns are from the Ibbotson & Associates, Stocks Bonds, Bills and Inflation Yearbook (SBBI). There are seven return series taken from this source. The index of large capitalization stocks is a measure of the S&P 500. The index of small capitalization stocks includes the returns on all NYSE firms with capitalization levels in the lowest quintile. The five remaining financial measures from Ibbotson & Associates are the returns on long-term corporate and government bonds, the yield on treasury bills, the rate of inflation and the dividend yield on the S&P 500.
Data for the variable risk spread are from the Federal Reserve Bulletin, Table 1.35. Property type classifications for public real estate are determined from investment percentages found in the NAREIT Handbook. Private real estate returns by property type are from the NCREIF Property Index Detailed Quarterly Performance Report. Public real estate returns (EREITs) are from the CRSP tapes. For a detailed discussion of the return properties of the private and public real estate used in this study, see Seiler, Webb and Myer (1999).
These variables will be used in twenty period (quarterly) rolling regressions in an attempt to forecast returns (ex ante). After each regression is performed, the relationships will be used to forecast an expected return, which will be an input (along with the correlation and standard deviation measures over the same twenty periods) used to construct an efficient frontier. This process is repeated using data from the sample period from the first quarter of 1986 through the fourth quarter of 1996.
Results
Hypothesis One
Exhibits 1 through 4 show the results from testing Hypothesis one, which examines whether public real estate is substitutable for long positions in real estate only portfolios. The first type of real estate considered is Apartment real estate. Exhibit 1 lists the percentage allocations and expected return-standard deviation combinations for private real estate only portfolios in Part B and for private real estate only portfolios with public apartment EREITs (RAPT) in place of the private Apartment NCREIF index (NAPT) in Part A. The two factors that indicate the degree of substitutability are (1) the optimal allocation weights at each level of expected return and (2) the positioning of the efficient frontiers.
Concerning the optimal allocation weights in the private only portfolio (Part B), retail private real estate is the dominant property type at lower levels of risk and return (83.5%). Moving along the efficient frontier to higher levels of risk and return, private apartment real estate becomes the more dominant property type (16.5% versus 76.3%). Private industrial real estate enters the portfolio eventually as retail exits, but private office real estate never enters.
For the private/public portfolio (Part A), allocation weights for all property types are very different. Private industrial real estate carries a weight (23.2%) even at the lowest levels of expected return. Office warrants inclusion at almost all levels, although the percentage is very low (up to 2.6%). The retail property type has large and declining weights throughout (63.1% to 21.9%), but the amounts are much higher in the private only portfolio. Finally, the EREIT apartment index carries large weights, just as did the private apartment real estate, but these weights are substantially lower when compared to the private only real estate portfolio (13.6% through 60.8% compared to 16.5% through 76.3%).
Thus far in the discussion of the results, statistical significance testing has not been attempted. The reason is that the efficient frontiers are deterministic. Therefore, the employment of significance testing is inappropriate. Instead, the positioning of the resulting efficient frontiers are compared. If the efficient frontier of one portfolio dominates the efficient frontier of the other at all points, the investor is deemed to be better off with the first portfolio. If the efficient frontiers intersect, then one portfolio will be preferred at expected return levels above 'X' percent, while the second portfolio will dominate at levels below X. Of course, there is no reason why the efficient sets have to cover the same risk levels. In the event that the efficient frontiers do not cover the same risk levels, there is no way to compare the two portfolios since they have no overlapping expected return-standard deviation combinations.
In Exhibit 1, the attainable level of expected returns increases dramatically in Part A from 3.5% to 6%, quarterly. But this higher level is reached only by engaging in much greater levels of risk-- taking. At an expected return of 1.0 per quarter, the private only real estate portfolio has a standard deviation of 1.35%, whereas the private/ public portfolio has a risk measure of 1.58%. At this point, the efficient sets are relatively close. As return levels increase, however, the private only portfolio continues to possess low levels of risk. The risk of the portfolio containing apartment EREITs increases dramatically causing the efficient frontiers to spread further and further apart. The efficient frontiers are presented in Part C.
Since the efficient frontiers never intersect, it is clear that the public/private real estate portfolio is less desirable than the private only real estate portfolio. The public/private portfolio allows for much greater expected return levels, but does so at much greater levels of risk. Thus, for apartment real estate, there appears not to be an ability to rebalance the private real estate portfolio.
The same procedure is performed for the remaining three property types in Exhibits 2 through 4. Exhibit 2 shows the results for the testing of industrial real estate. As was the case with apartments, industrial real estate efficient frontiers are very different in both positioning and allocation weights at each point along the curve. For example, retail real estate has weights from 0% to 41.7% in the public/private portfolio and 0.3% to 83.5% in the real estate only portfolio. Also, industrial private real estate allocations range from 0% to 27.6%, while its private real estate counterpart has allocations from 7.3% to 65.7%. The private only real estate portfolio dominates the public/private real estate portfolio over the comparable range. Hence, for industrial real estate, there appears to be no ability to rebalance using EREITs.
Exhibit 3 contains the results for office real estate. Although the allocation percentages are again different for each property type between the two portfolios, the most dramatic difference occurs in the weight of office real estate. In the private only real estate portfolio, the office property type does not enter into the efficient set at any point along the curve. In the public/private real estate portfolio, however, it builds to a weight of one-third of the portfolio at the 6% return level. Part C shows that the private only real estate portfolio strictly dominates the public/private real estate portfolio. Moreover, because the allocation units are so dissimilar across portfolios, it appears that once again, (office) EREITs cannot be used to rebalance public real estate portfolios.
Retail real estate is the final property type to be tested for Hypothesis one. Exhibit 4 contains the results. Not surprisingly, the conclusion that EREITs cannot be used to rebalance public real estate portfolios is reached again.
What is interesting is the allocation weights. The industrial weights (0% through 35.5% compared to 0% through 27.6%) and office weights (0% at all points throughout both) are approximately the same between the private only real estate portfolio and the private/public real estate portfolio, but the weights for both apartment and retail are roughly reversed. That is, in the private real estate only portfolio, apartment weights range from 16.5% at an expected return level of 1.0% per quarter, to 76.3% at an expected return of 3.5%. However, in the public/private real estate portfolio, the allocations are reversed. At an expected return of 1.0%, the weight is 92.1%, whereas at the highest level of expected return the optimal allocation weight is 20.9%. The same reversing is observed for retail real estate. Retail real estate switched from 83.5% to 0.3% in the private only real estate portfolio to 7.9% through 44.0% in the public/private real estate portfolio. Because only public retail real estate is substituted for private retail real estate, this clearly indicates a dissimilarity between public and private retail real estate.
Hypothesis Two
Institutional investors may hold real estate not only in isolation, but in mixed-asset portfolios as well. Moreover, just because public real estate cannot be used to rebalance private real estate only portfolios, does not necessarily imply that it will be useless in mixed-asset portfolios. For this reason, the substitutability for long positions is tested within a mixed asset portfolio in Exhibits 5 through 8.
Exhibit 5 shows asset allocation percentages and expected return-risk combinations for apartments. The difference from Exhibit 1 is that five additional assets are now included. These assets include S&P 500 stocks (large capitalization), small capitalization stocks, long-term corporate bonds, long-term government bonds and treasury bills. Part B of the table contains these five assets and the four types of private real estate (apartment, industrial, office and retail). Part A consists of the five non-real estate financial assets, three types of private real estate and one type of public real estate.
As expected, Part B of the table indicates that at lower levels of return, treasury bills dominate the optimal allocations (83.5%), then dissipate to zero as returns increase. Also, at lower levels of return, the two stock indexes (S&P 500 and small cap) carry low weights (0.6% and 1.5%, respectively) because of their high levels of risk. As expected returns increase, so too do the optimal weights assigned to both stock indexes. Long-term corporate and government bonds increase in optimal weights at lower levels of expected return, then decline at higher levels.
The behavior of private real estate is mixed when compared to their weights in real estate only portfolios. In both cases, private office real estate is absent from the efficient set at all points along the curve. The weights of private apartment, industrial and retail real estate are all substantially reduced in the mixed-asset portfolio. In fact, private retail real estate is reduced all the way to zero.
Within the mixed-asset portfolios shown in Exhibit 5, the weights are relatively consistent for securities between Parts A and B with the exception that public and private apartment real estate are dissimilar. This finding of dissimilarity in optimal allocation is not surprising, given the results from Exhibit 1. What is surprising is that the difference in apartment real estate from public to private does not substantially change the efficient frontiers that result from their inclusion. As seen in Part C, the efficient frontiers intersect. In fact, they intersect at more than one point. At these intersection points, the two portfolios are effectively the same. This is not to say that apartment private and public real estate are substitutes for one another, but only that the two portfolios offer the same risk and return at the points of intersection.
Exhibit 6 demonstrates that industrial real estate causes a reaction similar to apartment real estate in that the allocation weights are different across assets, but the efficient sets are similar. In Exhibit 6, the two efficient frontiers intersect at only one level of expected return. Therefore, at levels below the intersection the mixed-asset portfolio lacking public real estate representation is dominated by the public real estate portfolio, whereas the reverse is true at levels above the point of intersection.
The one-point intersection case is demonstrated by the office real estate property type, as well as shown in Exhibit 7. The difference is that the intersection is located at a much higher level of expected return (between 5.0% and 6.0%). It is also interesting to note that the weights in public office real estate are higher at all levels when compared to private office real estate (by a margin of 0.2% to 9.9%). This is not the case for apartments and industrial real estate, which are quite similar between the two portfolios.
The final property type to consider is retail real estate. The results from testing this real estate type are displayed in Exhibit 8. Again, allocation weights are similar between portfolios for all assets except the public and private real estate. The difference is that these private only and public/ private real estate portfolios are the only two mixed-asset efficient frontiers that do not ever intersect.
In sum, the mixed-asset results are quite revealing when compared to the real estate only portfolios. In the real estate only portfolios, the allocations of all four real estate property types are very different, and so too are the resulting efficient frontiers. In the mixed-asset portfolios, the optimal allocation weights for the substituted real estate are again very different, but the remaining financial asset weights are similar. Moreover, the efficient frontiers are relatively the same. In fact, they intersected at least once in three of the four cases.
Hypothesis Three
Exhibits 9 through 12 examine the ability of public real estate to rebalance private real estate portfolios by utilizing the short sale possibility of public real estate. As described in the Methodology section, the portfolios in Part A of each exhibit contain only three private real estate property types. Part B of each exhibit contains the same three types. The difference is that in Part B, an equal and offsetting short and long position are taken in the fourth property type. For example, in Exhibit 9, apartment REITs are shorted and an equal amount of private apartment real estate is added (long) to the portfolio. If the optimal allocation weights and the efficient frontiers are exactly the same for the two portfolios, then private and public apartment real estate are substitutes and apartment REITs can be used to rebalance/diversify a private real estate portfolio on the short side.
Exhibit 9 shows the results from shorting apartment real estate. The exhibit reveals that optimal allocation weights between the two portfolios are relatively similar. The industrial property type allocations at corresponding points along the efficient frontier are only different by up to 15%. For the retail property type, the weights are again similar throughout, but vary by somewhat more. Office real estate never enters into the efficient frontier. Even though the allocation weights are similar for each property type, the conclusion that private and public apartment real estate are substitutes for each other cannot be reached because the risk at each level of expected return is substantially higher for the second portfolio. That is, the private/public portfolio has a substantially greater risk than the private only portfolio. This is due to the dramatic difference in return behavior between public and private real estate. Therefore, since the private only portfolio provides the same level of return at a lower level of risk, no investor would want to substitute private real estate with public real estate in a short selling sense.
The differences in the portfolios where industrial real estate has been shorted are not nearly as dramatic. As shown in Exhibit 10, the maximum allocation difference is 8.7% (86.6%-77.9%) for the apartment property type. Retail real estate allocations are very similar as are office weights. However, the standard deviations are still much higher for the private/public portfolio than for the private only portfolio. Since the private only portfolio strictly dominates the private/public portfolio, investors would not wish to rebalance in this way.
The remaining two exhibits, Exhibits 11 (office) and 12 (retail), are consistent with the results from the first two property types (apartment and industrial). Moreover, they are even more pronounced. Not only are the allocation percentages more decidedly different, but so too are the standard deviations. In sum, even at a low rebalancing level of just 10%, the ability of public real estate to rebalance private real estate portfolios by short selling is indeed suspect.
Conclusion
This study examined the ability of public real estate (EREITs) to rebalance/diversify private real estate portfolios. The results indicate that the substitution of public real estate (EREITs) for private real estate in a private real estate only portfolio for the purpose of rebalancing appears not to be fruitful. Allocation weights and efficient frontiers on a before and after basis are quite different. When the analysis takes place in a mixed-asset setting, the results change somewhat. While the optimal weight of the substituted real estate property type remains dissimilar, the efficient frontiers are surprisingly close. In fact, for three of the four property types, the efficient frontiers intersect. This indicates that rebalancing is not completely without its benefits.
Lastly, tests were performed in order to determine if public real estate can be used to rebalance private real estate portfolios by exercising the ability of EREITs to be sold short. The results reveal that this added ability is not helpful when attempting to rebalance.
In sum, the ability of public real estate to rebalance private real estate only portfolios, using either long or short positions, is very much in doubt. However, in a mixed-asset setting, while private and public real estate are not substitutes, the efficient frontiers do remain relatively similar when public real estate is used to rebalance private real estate holdings.
What implications do these findings offer for private institutional real estate investors? Currently, many institutional investors holding primarily private real estate portfolios also hold some public real estate. Generally their hope is likely that they can rebalance their portfolios with more liquidity and lower transaction costs offered by public real estate. However, the results from this study cast doubt on this ability. Instead, if institutional investors wish to continue to hold public real estate, they should do so for reasons other than rebalancing their private real estate portfolios.
In an optimal portfolio context, public real estate should be viewed as just another type of financial asset similar to the way in which stocks, government securities and corporate bonds are viewed. Instead of being substitutes for private real estate, public real estate should be analyzed based solely on the expected return, risk and correlation with other assets in the portfolio.
This is not to say that public real estate has no place in an optimal mixed-asset portfolio. On the contrary, the results in this study reveal that public real estate does warrant inclusion in mixed-- asset portfolios. The conclusion that should be reached is that public real estate has very limited use in terms of rebalancing private real estate portfolios.
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