Another Look at the Asymmetric REIT-Beta Puzzle

Transcription

1 Another Look at the Asymmetric REIT-Beta Puzzle Authors Kevin C.H. Chiang, Ming-Long Lee and Craig H. Wisen Abstract The diversification benefit provided by real estate investment trusts (REITs) is of great importance to investors, practitioners and academics. This benefit critically relies on the correlation properties between REIT returns and the factors used to explain REIT returns. Recent studies have documented an asymmetry of the market-beta of equity REITs based on high and low GDP growth states as well as in positive and negative monthly market excess returns. The asymmetry has been labeled a puzzle because attempts to explain the asymmetry have failed and because it persists after controlling for a number of known effects. This study helps to resolve this puzzle by including the Fama-French (1993) book-to-market factor into a model that controls for size and market returns. Introduction The relationship between real estate returns and the returns of other asset classes has been the focus of many academic studies. Several studies have recently documented a curious aspect in the relationship between real estate returns and capitalization weighted equity returns. Goldstein and Nelling (1999) find that the returns on equity real estate investment trusts (REITs) have different risk and return properties in advancing and declining equity markets. The finding relies on multivariate analysis showing that REIT returns more closely track the returns of the S&P 500 Index when the general stock market is declining than when it is advancing. Similar findings are also documented by Sagalyn (1990). The author finds a higher (lower) beta during periods of low (high) economic growth. Chatrath, Liang and McIntosh (2000) characterize these seemingly peculiar findings as the asymmetric REIT-beta puzzle. The purpose of the current study is to reexamine the relationship between the performance of equity REITs and that of the general economy and stock market. Special attention is devoted to the fragility of the asymmetry finding based on its absence after controlling for a common risk-factor. Many studies have investigated the return association between equity REITs and the general stock market. Gyourko and Linneman (1988), Giliberto (1993), Myer JRER Vol. 26 No

2 26 Chiang, Lee and Wisen and Webb (1993), Han and Liang (1995), Liang, Chatrath and McIntosh (1996), and Oppenheimer and Grissom (1998), among others, show that REITs are exposed to beta risk. Several studies further show that REITs have greater exposure to small stock returns (Han and Liang, 1995; and Nelling and Gyourko, 1998) because of the typically small market capitalization of REIT issues. Chiang and Lee (2002) furthermore demonstrate that equity REITs behave more like small-cap value stocks because real estate rents frequently have upper limits in their annual increases. However, it is worth noting that Sagalyn (1990) and Goldstein and Nelling (1999) produce an interesting twist to the documented relationship between REIT returns and general stock market returns. The analysis of Sagalyn and Goldstein and Nelling shows that REIT risk and return is dependent on business cycles and the direction of the market return. The asymmetric relationship has important implications for portfolio managers in terms of the diversification potential for REITs and the asymmetry complicates the investor s asset allocation decision with regard to REITs. Sagalyn (1990) and Goldstein and Nelling (1999) find that REITs have higher betas in low-growth economic states and in declining markets than in high-growth economic states and advancing markets, respectively. Chatrath, Liang and McIntosh (2000) motivate and test three hypotheses that explore why the differential response occurs. First, stock returns in the 1990s are unusually high and the return association between the general stock market and REITs appears to be declining over time. As a result, the low beta in advancing markets may simply be the result of the decay in the REITs-stock market relationship. Second, the single-factor model may not adequately explain time series prices of disparate assets (Fama and French, 1993; among many others). Banz (1981) and Reinganum (1981) show that size helps to explain stock returns. Therefore, asymmetric betas can be due to the fact that REITs possess small market capitalizations. Third, REITs pay stable dividends and are well known to be less sensitive to the state of the general economy and to the capitalization weighted market return than the average stock. An improvement (deterioration) in the economy and stock market is likely to be associated with an increase (decrease) in the yield spread between stocks and REITs. Given the previously documented relationship between stock returns and dividend yields, the asymmetry in market betas may well be a byproduct of the asymmetry in yield spreads. Chatrath, Liang and McIntosh (2000) conclude that the small stock explanation is more useful in explaining the asymmetric betas in REITs than the two remaining hypotheses; however, the asymmetric phenomenon persists. The current study is a natural extension of Chatrath, Liang and McIntosh (2000). Their results show that the use of an incorrect asset pricing model could create a asymmetry in the market beta of REITs. This highlights the need to examine the robustness of the asymmetric betas under a variety of asset pricing specifications. The three-factor model from Fama and French (1993) is selected as the null for the current study because the model has been shown to possess empirical power relative to CAPM-based models in terms of its ability to explain individual equity

3 Another Look at the Asymmetric REIT-Beta Puzzle 27 and mutual fund returns. It is also important to note that the three-factor model, by construction, is able to describe the value return component in REITs. According to Chiang and Lee (2002), the style of REITs more closely resembles the style of small-cap value stocks. The current study produces two main results. The first is that the asymmetry in market betas in the context of high and low growth economic states does not exist in our more recent subsample spanning almost two decades. The second result is that the asymmetry in market betas in advancing and declining markets virtually disappears under the null of the Fama-French three-factor model. This conclusion is robust to alternative regression specifications. Data This study uses the monthly returns of the National Association of Real Estate Investment Trusts (NAREIT) Equity REIT Index. The Center for Research in Security Prices (CRSP) Value-Weighted Index and the S&P 500 Index are used as the proxies for the market portfolio. Monthly CRSP value-weighted returns, monthly S&P 500 returns and the risk-free rates are retrieved from the CRSP U.S Indices Database. Factor returns that are used to control for size and book-tomarket are provided by Kenneth French. Fama and French (1993) construct size and book-to-market factor returns using six capitalization-weighted portfolios formed on market capitalization and bookto-market ratio. The portfolios are reformed annually on June 30. The breakpoints for value and growth portfolios are the 30th and 70th NYSE percentiles based on the book-to-market ratio. The size breakpoint is the median NYSE market capitalization at the end of June. The size factor (SMB) is based on the monthly returns of a zero-cost portfolio that places long positions in stocks with small capitalizations and short positions in stocks with large capitalizations. The bookto-market factor (HML) is based on the monthly returns of a zero-cost portfolio that places long positions in stocks with high book-to-market values (i.e., value stocks) and places short positions in stocks with low book-to-market values (i.e., growth stocks). HML can be interpreted as the difference in returns between value and growth investment styles. The sample period is from 01/1972 to 12/2001. Empirical Results The one-factor model of Sharpe (1964) is first used to examine the unconditional association between REIT returns and the U.S. stock returns. That is, monthly REIT returns (R p ) are regressed on either CRSP value-weighted returns or S&P 500 returns (R m ): R br. (1) p,t m,t p,t JRER Vol. 26 No

4 28 Chiang, Lee and Wisen The regression results are reported in Exhibit 1. Consistent with the literature, when the CRSP value-weighted returns are used the market beta for REITs is only during the sample period of 01/ /2001. To examine the robustness of this estimate, the full sample period is divided into two sub-periods. The first sub-period is from 01/1972 to 12/1985 and the second is from 01/1986 to 12/2001. To mitigate data mining concerns, the delineation of the sub-periods is Exhibit 1 Unconditional REIT Betas Panel A: CRSP Value-Weighted Returns Intercept b R 2 (%) F Full Sample (3.18)** (13.33)** 01/ / (2.66)** (11.60)** 6.60** 01/ / (2.03)* (7.60)** 01/ / (2.63)** (14.51)** 9.47** 01/ / (2.05)* (3.00)** Panel B: S&P 500 Returns Full Sample (3.10)** (12.10)** 01/ / (2.61)** (10.35)** 6.63** 01/ / (1.95) (6.98)** 01/ / (2.58)** (12.90)** 7.85** 01/ / (2.01)* (2.72)** Notes: This table reports the regression results from the following specification: R br, p,t m,t p,t where R p is the monthly REIT return and R m is proxied by the monthly CRSP value-weighted return or the monthly S&P 500 return. The sample period is 01/ /2001. t-statistics appear in parentheses. The reported F-Statistics are Chow test statistics with critical value of 4.61 at the 1% level. *Significant at the 5% level. **Significant at the 1% level.

5 Another Look at the Asymmetric REIT-Beta Puzzle 29 taken from Chatrath, Liang and McIntosh (2000) who use the 1985 year-end as the terminal year for the first sub-period perhaps to consider the effects of the Tax Reform Act of In light of the fundamental impacts of the Revenue Reconciliation Act of 1993 on REITs, the study also divides the full sample period into 01/ /1992 and 01/ /2001. The regression results for these sub-periods suggest that the association between REIT returns and the U.S. stock returns is decreasing over time. The beta declines from and during the first sub-sample to and during the second sub-sample, respectively. The Chow test statistics of 6.60 and 9.47, which are both statistically significant at the 1% level, suggest that the beta estimates during the latter subsamples are lower than those during the earlier sub-samples. Overall, the single factor model is not able to explain REIT returns very well based on R 2. The R 2 values for these regressions range from 7.99% to 45.93%, indicating that the usefulness of the one-factor model in explaining REIT returns is limited. Together, the results suggest that the asset pricing of REITs demands a richer set of risk factors. To examine the robustness of the regression results, the study repeats the analysis with the use of the S&P 500 Index as the proxy for the market portfolio. The results are reported in the Panel B of Exhibit 1. In general, the results are similar. Because the fitness of the regressions with the use the CRSP value-weighted returns is better than that of the regressions with the use of the S&P 500 returns, the study uses the CRSP value-weighted returns in the following analysis. To reproduce the beta asymmetry documented in the literature by Chatrath, Liang and McIntosh (2000), the following regression is applied to the data: Rp,t br u m,tdrm,t br d m,tdrm,t p,t, (2) where d Rm,t (d Rm,t) takes on the value of one (zero) if market excess returns are positive (zero or negative) or if the economy is in a high (low) growth period. The study adopts Sagalyn s (1990) definition of high and low growth economic states. Sagalyn identifies two periods of low growth (1973:Q3 1975:Q1 and 1979: Q1 1982:Q4) and two periods of high growth (1975:Q2 1978:4 and 1983:Q1 1987:Q4) from 1973 to The current study identifies two additional periods of low growth (1990:Q3 1993:Q1 and 2000:Q3 2001:Q3) and three additional periods of high growth (1988:Q1 1990:Q2, 1993:Q2 2000:Q2 and 2001:Q4) from 1988 to The regression results are reported in Exhibit 2. Consistent with the literature, Panel A clearly shows that the betas for REITs are much higher in declining markets than in advancing markets. For the full sample, the advancing-market and declining-market betas are and , respectively. The null hypothesis of equal advancing-market and declining-market betas is rejected at the 1% level based on the F-Statistic of Note that the statistical JRER Vol. 26 No

6 30 Chiang, Lee and Wisen Exhibit 2 Conditional REIT Betas Panel A: REIT Betas in Up and Down Markets Intercept b u b d R 2 (%) F(b u b d ) Full Sample ** (4.32)** (5.36)** (9.51)** 01/ / ** (4.22)** (4.99)** (8.48)** 01/ / * (2.84)** (2.29)* (5.93)** 01/ / ** (4.16)** (6.40)** (10.41)** 01/ / (2.40)* (0.25) (2.83)** Panel B: REIT Betas in High and Low GDP Growth Periods Full Sample ** (3.51)** (8.30)** (11.08)** 01/ / * (2.88)** (5.53)** (10.67)** 01/ / (2.01)* (6.45)** (3.96)** 01/ / ** (2.87)** (8.47)** (12.88)** 01/ / (1.64) (3.24)** (0.51) Notes: This table reports the regression results from the following specification: Rp,t br u m,tdrm,t br d m,tdrm,t p,t, where R p is the monthly REIT return, R m is the monthly CRSP value-weighted return. For Panel A, d Rm,t (d Rm,t) takes on the value of one if market excess returns are (not) positive and zero otherwise. For Panel B, d Rm,t (d Rm,t) takes on the value of one if GDP growth rate is high (low) and zero otherwise. The sample period is 01/ /2001. t-statistics appear in parentheses. *Significant at the 5% level. **Significant at the 1% level.

7 Another Look at the Asymmetric REIT-Beta Puzzle 31 rejection is largely driven by the earlier sub-samples in which the F-Statistic of during 01/ /1985 and the F-Statistic of during 01/ / 1992 are both statistically significant at the 1% level, while the more recent subsamples yields F-Statistics of 4.00 and Panel B of Exhibit 2 shows that REITs have a lower market beta in high growth periods than in low growth periods over the full sample period. The market betas for high and low growth periods are and , respectively. The F-Statistic of 8.31 leads to a statistical rejection of equal betas at the 1% level. However, the asymmetry in beta over the business cycle that is documented by Sagalyn (1990) is primarily driven by the two low growth periods during 1973: Q3 1975:Q1 and 1979:Q1 1982:Q4. For the more recent sub-sample of 01/ /2001, the market betas for high and low growth periods are approximately equal; the estimates are and , respectively. The F- Statistic of 0.01 is not statistically significant at any level. During the sub-sample of 01/ /2001, the market beta of for low growth periods is even lower than that of for high growth periods. Comparing the F-tests for the period 01/ /2001 in Panel A and Panel B of Exhibit 2 to those estimated for prior period, one concludes that the previously documented asymmetry in beta over business cycles could be sample specific and may not be robust over time. Note that the inability of the F-test to reject the hypothesis of equal coefficients for up and down markets, and for high and low GDP growth periods, is associated with the relatively low R 2 values for the period 01/ /2001 in comparison to the values for earlier time intervals. Given that the asymmetry in betas over business cycles is sample specific, the robustness of the asymmetry in betas in advancing and declining markets may also be suspect. In order to apply the Fama-French (1993) three-factor model, it is necessary to motivate the inclusion of the two risk factors, SMB and HML, to explain REIT returns. The selection of the three-factor model study relies on the claim that REIT returns contain small stock return and value stock return components. Sharpe s (1992) return-based style analysis of REIT returns supports this claim. The returnbased style analysis assumes that a n-asset class factor model generates the return on asset p: R [b F bf... bf ] e, (3) p,t 1 1,t 2 2,t n n,t p,t where F j,t is the return on factor (investment style or asset class) j, j 1, 2,..., n, and the sensitivity terms (b i,j values) sum to 1. The return of b 1 F 1,t b 2 F 2,t b n F n,t is the part of return that can be ex post duplicated by combining a set of n asset classes. Sharpe calls the distribution of these sensitivities style. The model in Equation (3) is solved using a quadratic programming algorithm. This JRER Vol. 26 No

8 32 Chiang, Lee and Wisen optimization problem minimizes the variance of e p,t, subjected to the following two sets of constraints: (1) the sensitivity terms sum to 1, and (2) a typical set of institutional constraints: no short positions in any asset class. The study first follows Chiang and Lee (2002) and selects a set of eight asset classes: (1) S&P 500/Barra Growth Index; (2) S&P/Barra Value Index; (3) Independence International Associates Small-Cap Growth Index; (4) Independence International Associates Small-Cap Value Index; (5) U.S. 30-day T-bills from the SBBI Yearbook published by Ibbotson Associates Inc.; (6) U.S. government bonds from the SBBI Yearbook; (7) U.S. corporate bonds from the SBBI Yearbook; and (8) MSCI EAFE Index from the MSCI website. The sample period for the above series is from 01/1975 to 06/1997. This slightly shorter sample period in Chiang and Lee (2002) is dictated by the availability of Independence International Associates Index values for small-cap value and growth returns. The results are reported in Exhibit 3. It is clear that the style and return association of REITs primarily resembles that of small value stocks, with a loading of 53.11%. Because small value stocks are an intersection of small stocks and value stocks, the evidence suggests that REIT returns contain small and value stock return components. To check whether REITs have recently exhibited different return behavior, the study extends the above analysis to 07/2001 by merging Independence International Associates Small-Cap Growth and Value Indices and the Russell 2000 Growth and Value Indices at 06/1997. The analysis ends at Exhibit 3 REIT Style 01/ / / /2001 S&P 500/Barra Growth S&P 500/Barra Value IIA Small-Cap Growth IIA Small-Cap Value U.S. T-bills U.S. Government Bonds U.S. Corporate Bonds MSCI EAFE R 2 (%) Notes: This table reports the return-based styles of REITs. The explanatory asset classes include the (1) S&P 500/Barra Growth Index, (2) S&P/Barra Value Index, (3) Independence International Associates Small-Cap Growth Index before 06/1997 and Russell 2000 Growth Index after 07/ 1997, (4) Independence International Associates Small-Cap Value Index before 06/1997 and Russell 2000 Value Index after 07/1997, (5) U.S. 30-day T-bills from the SBBI Yearbook, (6) U.S. government bonds from SBBI Yearbook, (7) U.S. corporate bonds from the SBBI Yearbook and (8) MSCI EAFE Index. The sample period is 01/ /2001.

9 Another Look at the Asymmetric REIT-Beta Puzzle 33 07/2001 because of the data availability of the MSCI EAFE Index. The results are quite similar, indicating that merging Independence International Associates Small-Cap Growth and Value Indices and the Russell 2000 Growth and Value Indices is appropriate and, indeed, REIT returns contain small and value stock return components. While the small stock return component in REITs has long been known to the literature, the recognition of the value stock return component is more recent. To further motivate the use of the HML factor, a moving window of thirty-six months is used to estimate style sensitivities. Exhibit 4 plots the time series of value style exposures to REITs, which is the aggregation of small value and big value Exhibit 4 REIT Style over Time This figure plots the return-based styles of REITs over time using a moving window of 36 months. The explanatory asset classes include (1) S&P 500/Barra Growth Index, (2) S&P/Barra Value Index, (3) Independence International Associates Small-Cap Growth Index before 06/1997 and Russell 2000 Growth Index after 07/1997, (4) Independence International Associates Small-Cap Value Index before 06/1997 and Russell 2000 Value Index after 07/1997, (5) U.S. 30-day T-bills from the SBBI Yearbook, (6) U.S. government bonds from SBBI Yearbook, (7) U.S. corporate bonds from the SBBI Yearbook, and (8) MSCI EAFE Index. The sample period is 01/ /2001. JRER Vol. 26 No

10 34 Chiang, Lee and Wisen exposures. The growth style exposures of REITs are the aggregation of small growth and big growth exposures. The exhibit demonstrates that the value stock exposure consistently represents a large component of equity exposures for REITs over the sample. This implies that the use of the HML factor is necessary for uncovering the true risk exposures of REITs. Note that while the style of fixed income is also substantial for REITs, the inclusion of the U.S. government bond returns has little effect on the findings. As a result, the study does not report regression results that are augmented by a fixed income factor. Augmenting the standard regression in Equation (2) to the Fama-French threefactor regression yields the following specification: Rp,t br u m,tdm,t br d m,tdm,t ssmbt hhmlt p,t, (4) where SMB t is the difference between the returns on portfolios of small and big stocks and HML t is the difference between the returns on portfolios of high- and low-be/me (book-to-market ratio) stocks. The regression results are reported in Exhibit 5. In Panel A, over the full sample, the advancing and declining market betas, b u and b d, are and , respectively. The beta difference of is much smaller than the beta difference of in Exhibit 2. As a result, the F-Statistic drops considerably to 2.99 and is no longer statistically significant at conventional levels. However, the earlier sub-sample s (01/ /1985) F- Statistic of 6.58 is statistically significant at the 5% level. Perhaps the most important finding in this panel is that the advancing-market and declining-market betas for the more recent sub-sample of 01/ /2001 are elevated to and , respectively. Testing their difference yields an F-Statistic of 0.11, indicating that their population parameters are virtually identical. By separating the full sample into 01/ /1992 and 01/ /2001, the study finds that neither of the two sub-samples yields an F-Statistic that is statistically significant at any conventional level. The values of the F-Statistic for the two sub-samples are 3.24 and 0.84, respectively. Overall, comparing the results to those in Exhibit 2, it is evident that the advancing-market beta is considerably underestimated under the one-factor model. The asymmetry in REITs advancing and declining market betas is no longer a puzzle after controlling for capitalization and bookto-price return components. The test results in the Panel B of Exhibit 5 are similar to those in the Panel B of Exhibit 2. That is, the statistical rejection of equal betas over the full sample is driven by the rejection during the early sub-sample. Indeed, there is no asymmetry in betas over business cycles in the more recent sub-samples of 01/ /2001 and 01/ /2001 as indicated by their F-Statistics of 0.69 and 0.02, respectively. Furthermore, under the three-factor model, the market betas in the more recent sub-sample are substantially elevated as well. Are the results of the current study robust? While empirical results often require the test of time, several observations suggest that the answer is yes. For example,

11 JRER Vol. 26 No Panel A: REIT Exposures in Up and Down Markets Exhibit 5 REIT Betas under the Three-Factor Model Intercept b u b d s h R 2 (%) F(b u b d ) Full Sample (1.95) (9.04)** (10.82)** (7.79)** (9.95)** 01/ / * (2.78)** (5.92)** (7.94)** (4.84)** (4.11)** 01/ / (0.55) (6.31)** (7.66)** (6.37)** (8.61)** 01/ / (2.50)* (7.97)** (9.41)** (7.02)** (4.28)** 01/ / (0.71) (3.65)** (5.47)** (5.37)** (7.83)** Panel B: REIT Exposures in High and Low GDP Growth Periods Full Sample ** (1.31) (11.72)** (14.17)** (8.07)** (10.33)** 01/ / ** (1.50) (5.71)** (10.74)** (5.27)** (4.45)** 01/ / (0.56) (10.50)** (7.33)** (6.67)** (8.85)** 01/ / ** (1.85) (9.37)** (12.79)** (7.18)** (4.75)** 01/ / (0.09) (7.13)** (4.27)** (5.55)** (7.76)** Another Look at the Asymmetric REIT-Beta Puzzle 35

12 Exhibit 5 (continued) REIT Betas under the Three-Factor Model Notes: This table reports the regression results from the following specification: Rp,t br u m,tdrm,t br d m,tdrm,t ssmbt hhmlt p,t, 36 Chiang, Lee and Wisen where R p is the monthly REIT return, R m is the monthly CRSP value-weighted return, SMB t is the difference between the returns on portfolios of small and big stocks, and HML t is the difference between the returns on portfolios of high- and low-be/me (book-to-market ratio) stocks. For Panel A, d Rm,t (d Rm,t) takes on the value of one if market excess returns are (not) positive and zero otherwise. For Panel B, d Rm,t (d Rm,t) takes on the value of one if GDP growth rate is high (low) and zero otherwise. The sample period is 01 / /2001. t-statistics appear in parentheses. *Significant at the 5% level. **Significant at the 1% level.

13 Another Look at the Asymmetric REIT-Beta Puzzle 37 the puzzlingly low unconditional market betas of and during the more recent sub-samples of 01/ /2001 and 01/ /2001 are much improved under the three-factor model. Moreover, the seemingly outstanding performance of REITs under the one-factor model is considerably accounted for under the three-factor model. For example, the intercept estimate of with a t-statistic of 4.32 in Panel A of Exhibit 2 becomes with a t-statistic of 1.95 in Panel A of Exhibit 5. These improvements suggest that the results are unlikely to be spurious. There are, nevertheless, a few concerns that still need to be addressed. First, although the regression specifications in Equations (2) and (4) are straightforward, they do not allow for two separate intercept terms one for advancing market (or high growth) and the other for declining market (or low growth). Second, the two dummy variables are perfectly negatively correlated. The use of both dummy variables could introduce problems related to multicollinearity. Finally, one may argue that when the three-factor model is used it is possible that the asymmetry in the market beta is transferred to one of the remaining risk factors. If so, the results do not fully resolve the REIT-beta puzzle and they may create a separate one. To deal with these concerns simultaneously, the following two textbookstandard regressions (Greene, 1997: ) were run: Rp,t ( )dm,t br d m,t (bu b d)rm,tdm,t p,t. Rp,t ( )dm,t br d m,t (bu b d)rm,tdm,t ssmb (s s )SMB d hhml d t u d t m,t d t (hu h d)hmltdm,t p,t. (6) (5) The statistical significance of (b u b d ), (s u s d ) and (h u h d ) is used to infer the asymmetry in risk exposures. The regression results are reported in Exhibit 6. As before, the analysis is applied to the full sample and sub-samples. For a more concise presentation, this robustness analysis focuses on the two sub-samples of 01/ /1985 and 01/ /2001 and presents the results for the two sub-samples. While the results for the two sub-samples of 01/ /1992 and 01/ /2001 are not reported, the results are similar. In general, the regression results are similar to the baseline results. The three-factor model is useful in mitigating the beta asymmetry during the early sub-sample and resolving the asymmetry during the more recent sub-sample. The documented asymmetry over business cycles is sample specific regardless whether the three-factor model is used. Furthermore, only one out the twelve estimates for (s u s d ) and (h u h d ) is statistically JRER Vol. 26 No

14 Exhibit 6 Robustness Checks Full Sample 01/ / / /2001 Panel A: REIT Exposures in Up and Down Markets (4.47)** (2.78)** (4.53)** (3.44)** (1.17) ( ) (1.88) (2.01)* (1.98)* (2.34)* (0.40) (1.11) b d (9.33)** (9.88)** (8.53)** (8.40)** (5.37)** (6.31)** (b u b d ) (2.69)** (1.35) (3.07)** (2.71)** (1.90) (0.13) s d (4.58)** (2.19)* (4.62)** (s u s d ) (0.15) (1.70) (0.76) h d (6.09)** (2.34)** (5.78)** (h u h d ) (0.21) (0.05) (0.24) R 2 (%) Chiang, Lee and Wisen

15 JRER Vol. 26 No Exhibit 6 (continued) Robustness Checks Full Sample 01/ / / /2001 Panel B: REIT Exposures in High and Low GDP Growth Periods (3.11)** (1.00) (1.06) (0.24) (3.43)** (1.89) ( ) (1.30) (0.27) (1.07) (1.53) (2.77)** (1.72) b d (10.96)** (10.71)** (10.76)** (8.79)** (3.99)** (4.78)** b u b d ) (2.62)** (1.45) (2.44)* (2.02)* (0.21) (0.97) s d (6.01)** (4.69)** (4.21)** (s u s d ) (1.73) (1.37) (0.89) h d (5.39)** (2.51)* (3.79)** (h u h d ) (1.55) (0.56) (2.07)* R 2 (%) Another Look at the Asymmetric REIT-Beta Puzzle 39

16 Exhibit 6 (continued) Robustness Checks Notes: This table reports the regression results from the following two specifications: Rp,t ( )dm,t br d m,t (bu b d)rm,tdm,t p,t, and 40 Chiang, Lee and Wisen Rp,t ( )dm,t br d m,t (bu b d)rm,tdm,t sdsmbt (su s d)smbtdm,t hdhmlt (hu h d)hmltdm,t p,t, where R p is the monthly REIT return, R m is the monthly CRSP value-weighted return, SMB t is the difference between the returns on portfolios of small and big stocks, and HML t is the difference between the returns on portfolios of high- and low-be/me (book-to-market ratio) stocks. For Panel A, d Rm,t (d Rm,t) takes on the value of one if market excess returns are (not) positive and zero otherwise. For Panel B, d Rm,t (d Rm,t) takes on the value of one if GDP growth rate is high (low) and zero otherwise. The sample period is 01 / /2001. t-statistics appear in parentheses. *Significant at the 5% level. **Significant at the 1% level.

17 Another Look at the Asymmetric REIT-Beta Puzzle 41 significant at the 5% level, which is quite close to the allowance for Type I error. As a result, the risk exposures of REITs are symmetric at least in market beta and size. In addition, the risk exposures of REITs with respect to HML is symmetric for most of the periods evaluated with the exception limited to the period 1986 to 2001 for state variables based on high and low GDP growth (Exhibit 6, Panel B). This result may be the product of chance given the conventional 5% significance threshold and the number of coefficients estimated. The result may also be caused by the relatively few periods of low GDP growth that were experienced during the 1986 to 2001 time span. Only sixteen of the sixty-four quarters comprising the period 1986 to 2001 were assigned to the low GDP growth state. Of course, the relatively few periods of low GDP growth in the more recent sub-sample also suggest that one cannot rule out that some asymmetry in risk exposures may remain. Conclusion The relationship between the returns of REITs and that of the capitalizationweighted market return is dependent on model selection, factor selection and factor construction. This study evaluates the conclusions of prior studies that investigate the asymmetry of REIT risk exposures based on market beta and it finds that the omission of factors that control for capitalization and book-to-price variables explain a substantial portion of the asymmetric REIT-beta puzzle. The REIT-beta appears to be symmetrical when performance is estimated using the Fama-French three-factor model and the fulcrum point is defined by the sign of the market s excess return. The asymmetric-beta puzzle based on the observation that returns of REITs were more sensitive to declining markets and low growth economy than advancing markets and high growth economy could mislead investors to the extent that the observation is not robust and does not persist over time. The observation could also mislead investors if they use a CAPM-based asset pricing model to estimate REITs risk in different market and economic conditions. The conclusion that factor sensitivities appear to be largely symmetric in the case of the Fama-French three-factor model therefore may increasingly lead investors to view REITs as an alternative to small-cap value stocks in declining and advancing markets. References Banz, R.W., The Relationship between Return and Market Value of Common Stocks, Journal of Financial Economics, 1981, 9, Chatrath A., Y. Liang and W. McIntosh, The Asymmetric REIT-Beta Puzzle, Journal of Real Estate Portfolio Management, 2000, 6, Chiang, K. and M. Lee, REITs in the Decentralized Investment Industry, Journal of Property Investment & Finance, 2002, 20, Fama, E. F. and K. R. French, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics, 1993, 33, JRER Vol. 26 No

18 42 Chiang, Lee and Wisen Giliberto, S. M., Measuring Real Estate Returns: The Hedged REIT Index, Journal of Portfolio Management, 1993, Spring, Goldstein, A. and E. F. Nelling, REIT Return Behavior in Advancing and Declining Stock Markets, Real Estate Finance, 1999, 15, Greene, W. H., Econometric Analysis, Third edition, White Cliffs, NJ: Prentice-Hall, Gyourko, J. and P. Linneman, Owner-Occupied Homes, Income-Producing Properties, and REITs as Inflation Hedges: Empirical Findings, Journal of Real Estate Finance and Economics, 1988, 1, Han, J. and Y. Liang, The Historical Performance of Real Estate Investment Trusts, Journal of Real Estate Research, 1995, 10, Liang, Y., A. Chatrath and W. McIntosh, Apartment REITs and Apartment Real Estate, Journal of Real Estate Research, 1996, 11, Myer, F. C. N. and J. R. Webb, Return Properties of Equity REITs, Common Stocks and Commercial Real Estate: A Comparison, Journal of Real Estate Research, 1993, 8, Nelling, E. and J. Gyourko, The Predictability of Equity REIT Returns, Journal of Real Estate Research, 1998, 16, Oppenheimer, P. and T. V. Grissom, Frequency Space Correlation between REITs and Capital Market Indices, Journal of Real Estate Research, 1998, 16, Reinganum, M. R., Misspecification of Capital Asset Pricing: Empirical Anomalies Based on Earnings Yields and Market Values, Journal of Financial Economics, 1981, 9, Sagalyn, L., Real Estate Risk and the Business Cycle: Evidence from Security Markets, Journal of Real Estate Research, 1990, 5, Sharpe, W., Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, Journal of Finance, 1964, 19, , Asset Allocation: Management Style and Performance Measurement, Journal of Portfolio Management, 1992, 18, The authors would like to thank Kenneth French for providing data used in this study and Ivo Jansen, Ko Wang (the editor) and four anonymous referees for helpful comments and suggestions. Kevin C.H. Chiang, University of Alaska Fairbanks, Fairbanks, AK or ffkcc@uaf.edu. Ming-Long Lee, National Yulin University of Science and Technology, Touliu, Taiwan 640 leeming@yuntech.edu.tw. Craig H. Wisen, University of Alaska Fairbanks, Fairbanks, AK or ffchw@uaf.edu.