On the time‐series properties of real estate investment trust betas

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 rej

29、ected. 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

30、 are based 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 = ½ r log(s12) +

31、89; (t - r) log(s22) - ½ 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

32、when lr reaches its minimum 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 return

33、s are provided by kenneth french. 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 in

34、dex of the national association 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 high

35、er level of survivorship bias. 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 e

36、xpect a lower level of survivorship 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 s

37、ecurities. as of june 2003, 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

38、homes (1.60%), factory outlets (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 re

39、trieved from the datastream 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

40、results with the use of nareit 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 b

41、etas, the study splits the full 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 sens

42、itive to the use of cutoff points. 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 r

43、esults for the three subsamples. 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 r

44、eports the three-factor regression 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 sub

45、samples are 0.5966, 0.5579, 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 ¾ nearly identical to the market beta estimated for the period

46、beginning march 1983 and ending december 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 f

47、actor is even higher than that of 0.3980 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 golds

48、tein and nelling (1999) and sagalyn (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 a

49、nnual increase (chiang and lee (2002). moreover, the use of the three-factor model improves the r-squared for the three subsamples, particularly for the most recent subsample. panels c and d of table 1 report the one-factor and three-factor regression results using the wilshire reit index. in genera

50、l, the results are similar to those using the nareit index. the notable difference is that during the earliest subsample, the use of wilshire reit index produces high market beta estimates of 0.9718 and 0.9405 under the null of the one-factor and the three-factor models, respectively. this is not su

51、rprising since the wilshire reit returns are backfilled prior to september 1991. it is generally accepted that backfilled data may contain a higher degree of data bias.long-term trend of market betasfigure 1 depicts the evolution of ereit betas over time using the nareit return index. betas of ereit

52、s under the null of the one-factor model appear to exhibit a downward trend over the sample period. furthermore, the slope of the time series of betas is particularly steep after 1995. the location of the switching point in 1983 (documented by liang et al. (1995) is identified by arrow 3. in contras

53、t to the single-factor model, use of the three-factor model suggests that ereit betas were stable over the past three decades, except in 2002. before 2002, the maximum market beta of ereits is approximately 0.7, and the minimum market beta is approximately 0.5. figure 2 plots the estimates of ereit

54、betas under the one-factor and three-factor models using the wilshire reit index. rolling beta estimates in figures 1 and 2 have the same pattern. that is, the beta estimates under the three-factor model are more stable over time than those under the one-factor model. figure 2 is also consistent wit

55、h the notion that wilshire reit returns yield particularly high market beta estimates during the period when the index values were backfilled.before applying vogelsangs (1998) method to test for a deterministic time trend, one should emphasize the difficulties in detecting such a trend. the main dif

56、ficulty is that the power of the test largely hinges on whether the innovations in market betas are i(0) or i(1). if the process is stochastic, a trend that is visually obvious can be stochastic in nature and yield no statistical significance when one attempts to test for a deterministic trend. ther

57、efore, a priori knowledge about the nature of the innovations in market betas is useful to the extent that it can improve the power of the t-pst1 test. in general, one would expect the innovations in market betas to be i(0) because, as time goes to infinity, market betas are unlikely to go to infini

58、ty. by definition, market beta is a ratio where the numerator is the covariance in returns between ereits and the market portfolio, and the denominator is the variance of the market portfolio. since the variance of any risky asset is positive, and the minimum possible return for any risky asset is -100%, the only scenario in which market beta could approach infinity is when the maximum possible