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1、 On the Time-Series Properties of Real Estate Investment Trust BetasKevin C.H. Chiang*College of Business AdministrationNorthern Arizona UniversityFlagstaff, AZ 86011-5066Ming-Long LeeDepartment of FinanceNational Yulin University of Science and TechnologyTouliu, Yulin Taiwan 640Craig H. WisenSchool
2、 of ManagementUniversity of Alaska FairbanksFairbanks, AK 99775USAReal Estate Economics, Summer 2005, 33 (2)On the Time-Series Properties of Real Estate Investment Trust BetasAbstractThe relation between real estate investment trust (REIT) returns and stock market returns is of significant importanc
3、e to investors, practitioners, and academics. The temporal properties of this relationship have a critical impact on the usefulness of REIT risk estimates and portfolio allocations to this asset class. Recent studies have suggested a decline in the market betas of equity real estate investment trust
4、s (EREITs). This study applies a rigorous statistical test of the hypothesis that the market betas of EREITs have remained unchanged during the 1972 through 2002 time period. There is weak evidence of a downward trend in EREIT betas using a single-factor model; however, the hypothesis is not rejecte
5、d when using a three-factor model.On the Time-Series Properties of Equity Real Estate Investment Trust BetasThe stability of a risky securitys market beta is important to those who use the estimated coefficient for performance evaluation, event studies, valuation, and asset allocation. A number of r
6、ecent studies have observed an apparent decline in the market betas of equity real estate investment trusts (EREITs). If the decline is of statistical and economic significance, then the implication is that estimates of EREIT betas that rely upon historical returns are biased upwards. Although sever
7、al explanations have been proposed for the apparent decline in EREIT betas, no formal tests for a significant time trend have been conducted. This paper rigorously tests the time-series properties of EREIT betas.Related LiteratureMcIntosh, Liang, and Tompkins (1991) were the first to detect a declin
8、e in EREIT betas during the 1974 through 1983 time period. Khoo, Hartzell, and Hoesli (1993) expanded the McIntosh et al. sample period to 1970 to 1989, and provided additional evidence of a temporal decline in EREIT betas. Khoo et al. applied a two-sample test for a regime shift under the assumptio
9、n of time independence. As will be shown below, however, beta innovations are serially correlated. Khoo et al. also found that EREIT betas during the 1982 through 1989 period were significantly lower than the 1970 through 1981 period. Although the current analysis does not contradict or support the
10、findings of Khoo et al., it does offer evidence that previous assertions of a temporal decline in REIT betas could be erroneous. This study is not the first to question the validity of previous evidence of a temporal decline in EREIT betas. Liang, McIntosh, and Webb (1995) extended the focus of Khoo
11、 et al. by examining intermediate-term variations in beta estimates, and found significant shifts in return-generating regimes in the vicinity of 1983. Nevertheless, their results (Figure 10) did not imply a declining trend in EREIT betas since bias in the studys data may have contributed to the abs
12、ence of a declining trend. Liang et al.s (1995) dataset include small, illiquid EREITs and their EREIT returns are retrieved from the CRSP database. The delisting bias in the CRSP database of Shumway (1997) may be amplified by higher chance of failures among small, illiquid EREITs.This study employs
13、 the Fama-French (1993) three-factor model and the Vogelsang (1998) method to test the null hypothesis that EREIT betas have remained constant over time. The Fama-French three-factor model is selected because Peterson and Hsieh (1997) found that the Fama-French factors helped to explain EREIT pricin
14、g and performance. Peterson and Hsieh (1997) demonstrate that REIT performance, in terms of the statistical significance of the intercept term from an asset pricing regression, is sensitive to model specification. Because of this sensitivity, one would expect that the time-series of market beta esti
15、mates could exhibit different time trends under different model specifications. The Vogelsang (1998) test is applied primarily because of the methods generality. This method is useful when EREIT beta innovations are serially correlated, and when the nature of the innovations is unknown. These featur
16、es are desirable when testing for deterministic time trends in EREIT betas because serial correlation is induced by the use of rolling regressions to obtain time-series estimates of betas. The generality is also beneficial since unit root tests often have very low power. This study finds weak eviden
17、ce for a decline in EREIT betas based upon a single-factor model. However, when the three-factor model is used, the declining trend in EREIT betas disappears. This study also uses the tests of Liang et al. to investigate whether EREIT betas have shifted and, if so, when the changes occurred. Our res
18、ults demonstrate that detecting regime shifts in market betas is sensitive to both the nature of the data and the asset pricing model that is used. Statistical MethodsWe employ rolling 60 month windows to obtain a series of EREIT beta estimates. The asset pricing models include the one-factor model
19、of Sharpe (1964) and the three-factor model of Fama and French (1993). The one-factor regression is specified as:Rp,t = a + b Rm,t + ep,t(1) where Rp is the monthly EREIT excess return and Rm is the monthly market excess return. Excess return is expressed as the difference between the monthly return
20、 on the market portfolio and the monthly return of the 30-Day U.S. Treasury Bill. The three-factor regression is as follows:Rp,t = a + b Rm,t + s SMBt + h HMLt + ep,t(2) where SMBt is the difference between the returns on portfolios composed of small and big stocks, and HMLt is the difference betwee
21、n the returns on portfolios composed of stocks with high and low BE/ME (book-to-market) ratios. Next, we apply Vogelsangs (1998) t-PST1 test to check for a deterministic trend. The t-PST1 test is valid for errors that are integrated of order zero (I(0), and for errors integrated of order one (I(1).
22、Therefore, a priori knowledge about beta innovations, and testing whether the innovations are I(0) or I(1), is not required. The t-PST1 test is based on the following specification: = a + b t + mt(3)where a is the initial level of , b is the average slope of time trend in , and mt is a serially corr
23、elated random process. Testing for a time-trend in beta estimates is essentially a test of whether the parameter b is different from zero. The t-PST1 test statistic is specified as:t-PST1 = T -1/2 tz exp(-c JT)(4)where T is the sample size, tz is the set of t-statistics for testing the null hypothes
24、is that the individual parameters in the partial-sums regression of equation (3) are zero, c is a constant, and JT is a unit root statistic proposed by Park and Choi (1988) and Park (1990). When the innovations in betas are known to be I(0), the specification of c = 0 is appropriate and most powerfu
25、l. In contrast, when it is unclear whether the innovations are I(0) or I(1), c can be chosen such that the critical values of the PST1 test statistics are same, whether mt is I(0) or I(1). Therefore, different values for c are used for different levels of statistical significance. Because the asympt
26、otic distribution of the t-PST1 statistic is nonnormal, statistical inferences are based upon on the critical values tabulated in Vogelsang.To investigate intermediate-term variations in EREIT betas, this study uses the cusum of squares test applied by Brown, Durbin, and Evans (1975) and by Liang et
27、 al. (1995). The method defines recursive residuals as: wr = , r = k + 1, , T(5)where xr is the column vector of observations on k regressors, Br = (Xr Xr)-1Xr Xr, and Xr = (x1, , xr). Under the assumption that recursive residuals are stationary, Dicky-Fuller (1979) t-test shows that recursive resid
28、uals of EREITs are stationary. the test statistic of cusum of squares is defined as: Sr = (6)The lines of statistical significance are plotted and defined as d2 + (r - k)/(T - k). If Sr travels outside the lines of significance, the null hypothesis of a constant regression relationship is rejected.
29、According to Durbin (1969), d2 is 0.15483 and 0.12823 for the 1% and 5% level, respectively. Brown et al. (1975) also derive a first-moment test statistic, called the cusum test. Nevertheless, Liang et al. (1995) show that the cusum of squares test is more powerful when statistical inferences are ba
30、sed on the cusum of squares test. The current study focuses on the cusum of squares test in order to directly compare the results with Liang et al. In addition to the cusum of squares test, a standard likelihood ratio, Lr, can be used to detect the point of change:Lr = r log(s12) + (T - r) log(s22)
31、- T log(s2)(7)where s12, s22, and s2 are the ratios of the residual sums of squares to the number of observations, when the regression is run on the first r observations, the remaining (T - r) observations, and the T observations, respectively. The point of change occurs when Lr reaches its minimum
32、value.DataThe monthly return from the Center for Research in Security Prices (CRSP) value-weighted index is used as the proxy for the return on the market portfolio. Monthly U.S. Treasury Bill returns are retrieved from the CRSP database. Monthly SMB and HML factor returns are provided by Kenneth Fr
33、ench. Because SMB and HML are constructed from equity returns, they are most appropriate for explaining the returns on equity securities. As a result, the study focuses on the intertemporal changes in the riskiness of EREITs. The study uses monthly returns on the EREIT index of the National Associat
34、ion of Real Estate Investment Trusts (NAREIT). The sample period is from January 1972 through December 2002. There were 170 REITs in the index as of September 30, 2003. The NAREIT index allows for greater comparability with prior REIT studies, albeit at the cost of a higher level of survivorship bia
35、s. The study also uses monthly returns on the Wilshire REIT index. The minimum market capitalization within the NAREIT index was less than $5 million, whereas the minimum market capitalization within the Wilshire REIT index was greater than $100 million. Thus, one might expect a lower level of survi
36、vorship bias relative to the NAREIT index. As of June 30, 2003, there were 88 REITs in the capitalization-weighted Wilshire REIT index. The liquidity of the Wilshire REIT indexs constituent REITs is commensurate with that of other institutionally held equity real estate securities. As of June 2003,
37、the Wilshire REIT index listings are largely equity properties with the following sector weights: office (20.96%), apartment (19.41%), regional retail (14.44%), local retail (12.69%), diversified (12.23%), industrial (7.50%), hotels (4.44%), storage (3.96%), manufactured homes (1.60%), factory outle
38、ts (1.38%), and cash (1.39%). The inception date of the Wilshire REIT index is September 1991. Since the Wilshire REIT index was introduced in September 1991, returns prior to this date were backfilled to January 1978. The monthly returns on the Wilshire REIT index are retrieved from the Datastream
39、database. The sample period is from January 1978 through December 2002.Empirical ResultsTimes Series Estimates of Market BetasThe time-series regression results for the one-factor and three-factor models are reported in Table 1. Panel A presents the one-factor regression results with the use of NARE
40、IT returns. Over the sample period beginning January 1972 and ending December 2002, the beta of EREITs is 0.4734. The adjusted R-squared is 32%, suggesting that the one-factor model provides a limited explanation of EREIT returns. To shed light on the evolution of EREIT betas, the study splits the f
41、ull sample period into three subsamples: January 1972 to February 1983, March 1983 to December 1991, and January 1992 to December 2002. The study also experiments with other cutoff points in the vicinities of 1976, 1981, 1986, and 1988. The results in Table 1 are not sensitive to the use of cutoff p
42、oints. March 1983 is used as the first cutoff to reflect the Tax Reform Act of 1981 (Liang et al. (1995). The second cutoff, January 1992, reflects the potential impact of the Tax Reform Act of 1993 (Glascock, Lu, and So (2000). Panel A of Table 1 reports the regression results for the three subsamp
43、les. The betas for the three subsamples are 0.6531, 0.4903, and 0.2316. In addition, the regression results indicate that the low R-squared value for the full sample is largely driven by the most recent subsample, in which the adjusted R-squared is 8%.Panel B of Table 1 reports the three-factor regr
44、ession results using NAREIT index returns. The beta and the adjusted R-squared are 0.5485 and 49%, respectively. The betas for the three subsamples vary less when a three-factor model is used rather than a one-factor model. Specifically, the market betas for the three subsamples are 0.5966, 0.5579,
45、and 0.3980. The decrease in the market beta for the last subsample is largely driven by 2002 returns. While not reported, the beta for the period beginning January 1992 and ending December 2001 is 0.5530 nearly identical to the market beta estimated for the period beginning March 1983 and ending Dec
46、ember 1991. The SMB factor is more useful than the HML factor in describing EREIT returns in the first two subsamples; however, the coefficient of the HML factor increases in the last two subsamples. For the most recent subsample, the loading of 0.5228 on the HML factor is even higher than that of 0
47、.3980 on the market beta. The results are consistent with the findings of Chiang and Lee (2002) and of Chiang, Lee, and Wisen (2004), who document a value return component in EREIT returns. This result is useful in resolving the asymmetric REIT-beta puzzle of Goldstein and Nelling (1999) and Sagalyn
48、 (1990). The usefulness of the HML factor in describing REIT returns in the latest subsample may be due to the wider participation of institutional investors who perceive REITs more like value stocks because real estate rents frequently have upper limits in their annual increase (Chiang and Lee (2002). Moreover, the use of the three-factor model improves the R-squared for the t
