Substitutability between Equity REITs and Mortgage REITs

Abstract

This study extends Seck's (1996) approach to investigate the degree of substitutability between equity real estate investment trusts (EREITs) and mortgage real estate investment trusts (MREITs). The variance ratio test and the variance decomposition of forecast errors yield results indicating the existence of informational commonality between EREITs and MREITs. The findings indicate that the two types of REITs are substitutable. A direct implication is that investors who believe they have superior forecasting ability will be indifferent to invest in either type of REIT. Another implication is that REITs can be treated as a single asset class in constructing a diversified multi-asset portfolio.

Introduction

The National Association of Real Estate Investment Trusts (NAREIT) classifies real estate investment trusts (REITs) into equity REITs (EREITs), mortgage REITs (MREITs) and hybrid REITs (HREITs) with the REIT type being based on the asset type of 75% of their invested assets [Glascock, Lu and So (2000); hereafter GES].1 Given this classification, the study asks a simple question: Is the differentiation between EREITs and MREITs essential to a multi-asset portfolio manager who has superior information on a subset of common factors and will use the knowledge to construct a portfolio? The findings of the current study indicate the answer is no.

REITs are pooled real estate funds that provide investors with an opportunity to invest in securitized real properties and mortgages. The market capitalization of the REIT universe has experienced significant growth, from $5.6 billion in 1990 to over 130 billion in 1997 (GES, 2000). While EREITs are the largest subset of securitized real estate investments, investors often perceive them as substitutes to unsecuritized real estate because they believe that the same set of common factors drive both EREITs and unsecuritized real estate investments (Giliberto, 199O).2 The author also concludes that the low contemporaneous return correlation between EREITs and unsecuritized real estate casts doubt on the presumption.3

Many studies examine the substitutability between EREITs and unsecuritized real estate investment, but the results are mixed. Giliberto (1990) documents that EREIT return residuals are significantly correlated with unsecuritized real estate return residuals after adjusting for the influences from stock markets and bond markets. GLS (2000) show that EREITs are cointegrated with unsecuritized real estate.4 Gyourko and Keim (1992) and Myer and Webb (1993) show that EREIT returns Granger-cause unsecuritized real estate returns. These findings suggest that EREIT returns tend to track corresponding returns on their underlying real estate portfolios, and that they are substitutes to each other. In contrast, by examining the various compositions of return variance, seek (1996) finds that the two types of real estate investments respond differently to common factors (i.e., they are not substitutable).

The controversy on substitutability extends to EREITs and MREITs. KuIe, Walther and Wurtzebach (1986) show that EREITs outperform common stocks under the null hypothesis of the CAPM, while MREITs fail to do so.5 When a five-factor version of Fama and French (1993) is used, Peterson and Hsieh (1997) find that EREITs have a similar performance with respect to common stocks, but MREITs significantly underperform common stocks by an average of 6.8%. These results imply that EREITs and MREITs are not substitutable. In contrast, GLS (2000) demonstrate that EREIT returns and MREIT returns cointegrate with each other and they are driven by the same common factors during the 1972-1992 period. However, the substitutability disappears after 1992. GLS (2000) further suggest that EREITs act more like stocks and MREITs act more like bonds after 1992, while both act like fixed-income securities before 1992.

The answer to the substitutability between EREITs and MREITs has an important economic value for investors who believe they have superior forecasting ability for a certain set of economic factors. If EREITs and MREITs are not substitutable, they should invest in the type of REITs driven by the economic factors that they are able to better forecast. In addition, the substitutability has implications in constructing a diversified multi-asset portfolio that includes REITs.6 Given the importance of the issue, the study uses the variance decomposition of a vector autoregression (VAR) to examine how economic and financial variables affect the two types of REITs. In this way, the study extends seck's (1996) approach to MREITs and provides new evidence supporting the existence of the substitutability between EREITs and MREITs.

The next section briefly describes seck's notion of substitutability and selects the information set. This is followed by a description of the data, the methodology and a discussion of the empirical results. The final section is the conclusion.

Substitutability, Pricing Process and Information Set

Giliberto (1990) argues that investors perceive two assets to be substitutable if a set of common factors drives both assets. Consistent with the concept, seek (1996) defines substitutability as the existence of a mathematical transformation of the process underlying the pricing of one asset that closely approximates or exactly replicates the process underlying the pricing of the other asset.

According to Seck (1996), substitutability requires the pricing processes of substitutable assets belong to the same class of stochastic process. The reason for this requirement is that the identification of the stochastic process plays a key role in forecasting the future variance of the process and its forecast error. In addition to this necessary condition, informational commonality exists only if the information set on which the future pricing of a given asset is expected is identical to the information set on which the future pricing of a substitutable asset is expected.

Following seek (1996), a variance ratio test is used to investigate the underlying pricing processes of EREITs and MREITs. Specifically, the test examines whether the pricing processes for both types of REITs follow a random walk. Variance decomposition of a VAR is then proposed to examine informational commonality. The merit of the VAR approach is that it does not rely on the validity of a particular asset-pricing model, such as the CAPM or the five-factor model of Fama and French.

The essential gradient for the analysis is a subset of the complete information set to generate unbiased forecast. Chan, Hendershott and Sanders (CHS, 1990) identify several economic variables for explaining EREIT returns: change in term structure, change in default risk premium, change in expected inflation, unexpected inflation and change in industrial production. Fama and French (1988, cited in Chordia and Shivakumar, 2000) show that term premium is closely related to short-term business cycle and default risk premium tracks long-term business cycle conditions. Chen, Roll and Ross (CRR, 1986) suggest that changes in expected inflation influence both nominal expected cash flows and nominal interest rate. Unexpected inflation also has an effect because pricing is determined in real terms. CRR (1986) suggest that changes in the level of industrial production affect the current real value of cash flows. Seek (1996) uses S&P 500 returns and mortgage rates for forecasting EREIT returns. It has been suggested that S&P 500 returns have an influence on EREIT returns (Ling, Naranjo and Ryngaert, 2000, LNR hereafter). Also, as one can expect, mortgage rates should relate to real estate market activity. Following LNR (2000) who use construction starts to proxy for real estate market activity, this study includes new private housing starts.

In sum, this study first inspects the stochastic pricing processes of EREITs and MREITs with a variance ratio test. The study then uses a total of seven informational variables suggested by previous studies to examine the informational commonality between the returns on the EREIT index (EREITR) and the returns on the MREIT index (MREITR) via variance decomposition. These variables are industrial production (INDPRO), term spread (TS), default risk premium (DEF), inflation (INFL), S&P 500 returns (SP500R), mortgage rates (MTGE) and new private housing starts (HSTARTS).

Data and Methodology

Data was collected from three sources: (1) the United States Department of Commerce, Survey of Current Business; (2) the Webstract database; and (3) the NAREIT website. Next, tests of unit roots and cointegration we conducted. Finally, variance ratio tests, variance decomposition analyses and bootstrap tests were conducted to examine the substitutability between EREITs and MREITs.

The Data

The following monthly series are used in the study:

1. Equity REIT Index of NAREIT

2. Mortgage REIT Index of NAREIT

3. Returns on the Equity REIT Index of NAREIT

4. Returns on the Mortgage REIT Index of NAREIT

5. Total industrial production index

6. Yield on U.S. Treasury bonds with maturity more than ten years

7. 3-month T-bill rates

8. U.S. city average CPI

9. S&P 500 Composite Index

10. Moody's seasoned AAA bond rates

11. Moody's seasoned BAA bond rates

12. 30-year conventional mortgage rates

13. Number of private new housing starts

The data sources for series 1,2,3 and 4 were retrieved from the NAREIT website. The NAREIT computes the returns on the REIT indexes as the percentage changes in the REIT indexes. The data sources are the U.S. Department of Commerce, Survey of Current Business for series 5, 6, 7 and 8, and the Webstract database for series 9, 10, 11, 12 and 13. all series are from January 1972 to December 1999.

Among the above series, the first two series, the Equity REIT Index (EREITI) and the Mortgage REIT Index (MREITI) are used to examine whether their pricing processes belong to the same class of stochastic process. The other series are used to examine informational commonality in forecasting EREITR and MREITR.

The study defines default risk premium, term spread and inflation as follows. The default risk premium (DEF) is the difference between the seasoned average yield of BAA bonds and the seasoned average yield of AAA bonds. The term spread (TS) is the difference between the average yield of U.S. Treasury bonds with more than ten years to maturity and the average yield of T-bills that mature in three months. Inflation (INFL) is the percentage change in the CPI. S&P 500 returns (SP500R) are the percentage change in the S&P 500 Price Index. Exhibit 1 presents the abbreviations of all the variables used in the study and their data sources. Exhibit 2 reports their summary statistics.7

The point-optimal test (PT) and the modified Dickey-Fuller t-test (DFGLS) (Elliot, Rothenberg and Stock, 1996) was applied to the two REIT index return series and to the seven forecasting variables.8 Exhibit 3 reports the results of the unit root tests. Consistent with Seck (1996), EREITI and MREITI are not stationary and EREITR, MREITR are stationary. The exhibit also shows that EREITR, TS, INFL, DEF, SP500R and HSTARTS are stationary and that INDPRO and MTGE are not stationary.

The cointegration testing results are reported in Exhibits 4 and 5. The [lambda]^sub trace^ and [lambda]^sub max^ statistics suggest that the two sets of eight series (EREITR or MREITR with the other seven variables) are not cointegrated. Therefore, the change in industrial production (INDPROD) is computed as the percentage change of INDPRO and change in mortgage rates (MTGED) as the first difference of MTGE to obtain stationarity. These stationary series are then used in the empirical VAR.

Methodology

This subsection consists of two parts. The first part explains the variance ratio test. The test is used to inspect the stochastic pricing processes of EREITs and MREITs. The second part describes the variance decomposition method and the bootstrap test. These methods are used to examine the informational commonality between EREITs and MREITs.

Next, the Choleski decomposition decomposes the forecast error variances into the primitive shock variances. The decomposition forces (B^sup e^)^sup -1^ and (B^sup m^)^sup -1^ to lower triangular matrices. As a result, the primitive shock to the first variable in the system has a direct effect on all variables; the primitive shock to the second variables has a direct effect on all variables except the first variable, and so on. By doing so, the decomposition forces a potentially important asymmetry into the system. Thus, the ordering of the variables may affect the outcomes of the decomposition. To consider the ordering effect, method of Enders (1995) is followed to obtain the decomposition: first using a particular ordering and then reversing the ordering. Both outcomes together are compared to directly determine whether substitutability exists between EREITs and MREITs. Specifically, if the patterns of variance decomposition for EREITs are similar to those for MREITs, they are deemed substitutable.

A bootstrap test is used in the study to test the similarity in the patterns of variance decomposition between EREITs and MREITs. Let [Omega]^sub EREITR^ = ([omega]^sub INDPROD^,...,[omega]^sub EREITR^) and [Omega]^sub MREITR^ = ([omega]^sub INDPROD^,...,[omega]^sub MREITR^) be the cumulative distributions of the variance decomposition percentages for EREITR and MREITR, respectively. Suppose that the difference vector [Omega] = [Omega]^sub EREITR^ - [Omega]^sub MREITR^ is randomly drawn from an unknown probability distribution. The purpose of the bootstrap method is to estimate the sampling distribution of the random variable of interest D^sub K-S^, which is defined as the element of [Omega] that has the largest absolute value.10 Under the null hypothesis of no distributional difference between [Omega]^sub EREITR^ and [Omega]^sub MREITR^, D^sub K-S^ has the value of zero.

Following Efron (1979), the sampling distribution of the D^sub K-S^ is estimated by the bootstrap distribution of D^sub K-S*^. Each D^sub K-S*^ is obtained by bootstrapping the data. In light of time dependence in the data, block bootstrapping is used. The block length used in the study is four, which is the optimal asymptotic block length specified in Hall, Horowitz and Jing (1995). Monte Carlo realizations of bootstrapped data are generated 1,000 times to obtain 1,000 D^sub K-S*^ in the study.

Let H be the empirical bootstrap distribution of D^sub K-S*^. The r% critical values are the r/2 and (1 - r)/2 percentiles of H. That is, at the 5% level of significance, the critical values are the 25th and 975th observations of the ranked D^sub K-S*^. Once the critical values are obtained, statistical inferences can be made in the usual way. If the hypothesized value of zero for D^sub K-S*^is not covered by the 95% confidence interval of H, the null hypothesis of no distributional difference can be rejected at the 5% level.

Empirical Results

This section is composed of two parts. The first part presents the empirical results of the variance ratio tests. The second part describes the results of variance decomposition and bootstrap tests.

Results of Va r lance Ratio Tests

Variance ratio tests were conducted for EREITI and MREITI for a number of lags ranging from one to sixteen months. Exhibit 6 presents test results. For EREITI, none of the test statistics are statistically significant. In other words, consistent with seck's (1996) finding, the EREIT Index of NAREIT follows a random walk. In addition, all the test statistics for the MREIT Index are statistically insignificant as well. MREITI also follows a random walk. The results show that the pricing processes of EREITs and MREITs belong to the same class of stochastic process. Thus, it is quite plausible that the two types of REITs are substitutable.

Results of Variance Decomposition and Bootstrap Tests

The final VAR of Equations (1) and (2) has a lag length of one month and three seasonal dummies. In variance decomposition, several considerations shape the ordering of the variables. Stock returns are responding to macro-economic forces (CRR, 1986). REIT returns are responding to the stock market, the real estate market and macro-economic forces." Likewise, activities in the real estate market are responding to macro-economic fundamentals. Housing starts are responding to change in mortgage rates. In the spirit of Real Business Cycle theory, total industrial production is the initiating and perpetuating force behind business cycle variables and then inflation. Therefore, INDPROD is always the first variable, and EREITR or MREITR is always the last variable. METGD, HSTARTS and SP500R always follow DEF, TS and INFL. INFL follows DEF and TS.

Exhibit 7 displays the results of the variance decomposition.12 Each panel represents the percentage of the variance of forecast errors for the REITs. Thus, the numbers on the same row add up to 100%. Each pair of panels has the same ordering of the variables. The order is from left to right. That is, INDPROD affects all other variables contemporaneously. On the other hand, EREITR or MREJTR cannot contemporaneously affect any other variables. Comparison of the variance pattern within each pair reveals whether EREITs and MREITs are substitutable given a particular specification of contemporaneous structure of the variables.

The decomposition results are reported in Panels Al and A2 of Exhibit 7 for the ordering (INDPROD, DEF, TS, INFL, SP500R, MTGED, HSTARTS, EREITR or MREITR). Both panels show that the largest percentage, 60% to 69%, of forecast error variance for each step is explained by innovations (primitive shocks) in REITs themselves. The stock market explains the second largest percentage, 20% to 30%, of forecast error variance. Term structure has the next largest influence, but only around 2% to 4% of forecast error variance of EREITR or MREITR.

Next, the ordering of the variables is reversed. The decomposition results are reported in Panels Bl and B2 of Exhibit 7 for the ordering (INDPROD, TS, DEF, INFE, MTGED, HSTARTS, RETURNE, RETURNE or RETURNM). The results show that only the one-month-ahead forecast error variance is best explained by the innovations in REITs themselves, around 62% to 68%. Innovations in the stock market returns have the largest contribution to future variations, over 80%, for two-month-ahead forecast and afterwards. As expected, the ordering of the variables has an impact on the outcomes, particularly on the determination of the economic importance of the returns on the S&P 500 Index.13 Nevertheless, the point here is whether the results obtained by reversing the ordering produce the same implications (Enders, 1995). Thus, more importantly, the focus of the study is whether Panel A and Panel B both suggest the existence of substitutability between EREITs and MREITs in terms of similarity in decomposition patterns.

As shown in Panel A and Panel B of Exhibit 7, the two orderings produce very similar variance decomposition patterns for all steps. There is little difference across EREITs and MREITs in the decomposition pattern. The bootstrap test confirms this observation. The testing results are reported in Exhibit 8. Panel A shows that when the ordering of the variables is specified (INDPROD, DEF, TS, INFE, RETURNSP, MTGED, HSTARTS, RETURNE or RETURNM), the maximum deviation of test statistic ^sub K-s*^ has an average value ranging from 4.93% to 6.08%. Because the standard deviation of D^sub K-s*^, is above 6%, the null hypotheses of no distributional difference between the variance decomposition patterns for RETURNE and RETURNM are not rejected for any step. The bootstrap p-values range from .378 to .534. Similarly, the testing results are not statistically significant for the alternative ordering of the variables (i.e., INDPROD, TS, DEF, INFE, MTGED, HSTARTS, SP50OR, EREITR or MREITR). The bootstrap p-values range from .350 to .518. Overall, the evidence suggests that there is no significant difference in the pattern regarding the relative degree and the speed of the impact of the information set on EREITR and MREITR. Thus, EREITs and MREITs are substitutable.

Conclusion

Previous studies using the CAPM or the Fama-French five-factor model find that EREITs and MREITs are not substitutable. The validity of these studies is dependent on the validity of the underlying asset pricing models, while any asset pricing model is to some degree contaminated by the bad-model problem. Studies using cointegration analysis find that EREITs share common forces with MREITs before 1992 and thus imply their substitutability up to 1992 but un-substitutability after 1992. Nevertheless, as pointed out by seek (1996), these studies do not investigate the speed of responsiveness of REIT pricing to the common forces.

This study extends seck's approach to investigate the substitutability between EREITs and MREITs. The empirical evidence shows that the two types of real estate investment trusts are highly substitutable. They respond to the economic and financial forces at a similar magnitude and speed. Particularly the stock market appears to have a great impact on their pricing. This is consistent with seck's (1996) finding that the stock market contributes considerably in the error variance for predicting future returns of REITs.

Overall, this study provides new evidence to the substitutability among securitized real estate (REITs) and adds evidence in the literature that securitized real estate is closely related with stock markets.14 An important implication of this study is that investors who believe they have superior forecasting ability for a set of economic factors will be indifferent to invest in either EREITs or MREITs. Another implication is that REITs can be treated as a single asset class in constructing a diversified multi-asset portfolio.

End notes

1 Equity REITs hold at least 75% of their invested assets in the ownership of equity real estate interests. Mortgage REITs holds at least 75% of their invested assets in mortgages secured by real estate. Otherwise they are hybrid REITs.

2 Implicitly, this view of substitutability assumes equilibrium asset pricing models such as CAPM or APT does not hold across stock market and unsecuritized real estate market. Otherwise, EREITs and unsecuritized real estate should already be priced appropriately commensurate with their risk. Thus, they are already substitutable (in the same indifference curve in terms of return and risk).

3 High contemporaneous correlation does not necessarily lead to substitutability, as Giliberto (1990) claims. Mike McCracken gives us the following excellent example. Asset 1 has return Rl and asset 2 has return (Rl + 1). In this case, asset 1 and asset 2 have a prefect contemporaneous correlation. But investors always prefer asset 2. So the two assets are not substitutable. One can say correlation is not a sufficient condition for substitutability. In addition, correlation only considers linear dependence between returns of two assets. Therefore, correlation is not even a necessary condition for substitutability.

4 GLS (2000) also show that MREITs are cointegrated with unsecuritized real estate.

5 As seek (1996) points out, this interpretation assumes that the pricing model is valid.

6 Simple correlation analysis looks only at linear relationships. This is sufficient in mean-variance world. However, beyond mean-variance measures, one may simply want to diversify his or her exposure to economic fundamentals. In this case, examining the common forces behind assets would be beneficial.

7 Iensen performance indexes were also calculated for EREITs and MREITs. There were significant and positive indexes for both EREITs and MREITs. Nevertheless, the Jensen's index for EREITs is significantly larger than that for MREITs. The results imply that EREITs and MREITs are not substitutable. However, the inference depends on the validity of the CAPM.

8 Elliot, Rothenberg and Stock (1996) show that the point-optimal test and the modified Dickey-Fuller test are more powerful than the usual augmented Dickey-Fuller test and the Phillips-Perron test at the limit.

9 BIC was selected because VAR tends to be overparameterized with AIC. For this study, BIC shows that the optimal lag is one month. The result is consistent with previous studies [e.g., LNR (2000) and Chordia and Shivakumar (2000)].

10 The subscript of the test statistic is specified as K-S because the test statistic is similar to that of the Kolmogorov-Smirnov test. The Kolmogorov-Smirnov test is one of the most popular tests to comate two distributions.

11 This consideration is consistent with CHS (1990), Giliberto (1990), Peterson and Hsieh (1997) and Liu and Mei (1998).

12 The same analyses were also performed for the two sub-periods from 1972 to 1991 and from 1992 to 1999. The results are not reported here because they are similar to the benchmark results with the use of full sample.

13 The ordering of variables also affects the standard errors of forecast errors because the ordering affects the impulse response functions that in turn affect the forecast errors and their standard errors (Enders, 1995).

14 GLS (2000) list a number of such studies.

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Ming-Long Lee, National Yulin University of Science and Technology, Touliu, Yulin, Taiwan 640 or leeming@yuntech.edu.tw.

Kevin C. H. Chiang, University of Alaska Fairbanks, Fairbanks, AK 99775 or jfkcc@uaf.edu.

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