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To determine the incremental role of these arbitrage costs in the existence of value effect, we carry out the multiple regression tests as below:

1

where Re3 is the buy-and-hold return over 36 month beginning in July of year t.

Ivolatility is square root of residual variance derived from the regression of monthly returns on a value-weighted market index over 36 months ending on June of year t.

Price is the closing price of a REIT stock at end of June of year t. DAnalysts is a dummy variable which takes the value of 1 if a REIT is covered by I/B/E/S, and value of 0 if not. ME is the market value of equity in millions of dollars at the end of June of year t.

Following the Fama and MacBeth (1973)’s procedure, Equation [3] is estimated every year from 1991 to 2000, and means of the annual estimates are reported. The coefficients on the interaction terms in Equation [3] capture how the B/M effect varies cross-sectionally with the arbitrage cost measures. According to Ali, Hwang, and Trombley (2003), all the arbitrage costs measures are also included by themselves to keep the unbiased coefficient of the interaction terms. The model also incorporates beta of individual REIT to control the effect of systematic risk. To keep consistent signs of the coefficients on all the interaction terms, Ivolatility is included into the equation in its reverse. Firm size (ME) is included in the model

with log transformation because of the distributional properties of these variables (Brennan et al., 1993).

Table 7.1 presents the descriptive statistics of the variables. Over the sample period, there are substantial cross-sectional variations of these variables, which are shown by their high standard deviations relative to their means. The mean of DAnalysts is 0.441, which suggests that over half of the REITs in our sample are not covered by analysts. In addition, the mean for Ivolatility, Price, and beta is 0.072, 20.6, and 0.280, respectively. The mean for B/M, ME, and Re3 is 0.910, 485, and 58.7%, respectively.

Table 7.1 Descriptive Statistics of Variables (1991-2000)

DAnalysts is a dummy variable which takes the value of 1 if a REIT is covered by I/B/E/S, and value of 0 if not. Ivolatility is square root of residual variance derived from the regression of monthly returns on a value-weighted market index over 36 months ending on June of year t. ME is the market value of equity in millions of dollars at the end of June of year t. Price is the closing price of a REIT stock at end of June of year t. For each year, we calculate the mean, median and standard deviation of the variables, and the numbers are then averaged across the sample period.

DAnalysts Ivolatility B/M ME Price Beta Re3

Mean 0.441 0.072 0.910 485 20.6 0.280 0.587

Median 0.400 0.061 0.731 266 17.4 0.256 0.521

Stdev. 0.463 0.043 0.904 629 22.8 0.460 0.908

Source: Author’s Calculation

Table 7.2 reports the correlation matrix of these arbitrage cost measures. Overall, the correlations between the arbitrage cost measures are reasonably low. In particular, Ln(ME) is only moderately correlated with the other three measures (0.371 with DAnalysts, -0.324 with Ivolatility, and 0.296 with Price) . The correlations between the Ivolatility, Price, and Analyst are all less than 0.3. Thus, it indicates that the four variables are capturing different aspects of arbitrage cost.

Table 7.2 Correlations among Arbitrage Cost Measures

DAnalysts is a dummy variable which takes the value of 1 if a REIT is covered by I/B/E/S, and value of 0 if not. Ivolatility is square root of residual variance derived from the regression of monthly returns on a value-weighted market index over 36 months ending on June of year t. ME is the market value of equity in millions of dollars at the end of June of year t. Price is the closing price of a REIT stock at end of June of year t. Pairwise correlation coefficients are calculated each year from 1991 to 2000, and mean of the annual correlation coefficients are reported.

Variable DAnalysts Ivolatility Ln (ME) Price

DAnalysts 1.000

Ivolatility -0.259 1.000

Ln (ME) 0.371 -0.324 1.000

Price 0.094 -0.066 0.296 1.000

Source: Author’s Calculation

Table 7.3 reports the regressions estimates based on the above equation. Column 1 and 2 also presents two reduced version of Equation [1]. The first column shows results from using Beta and B/M as explanatory variables. The mean slope coefficient on Beta is positive but insignificantly different from zero. This is consistent with findings of studies on REIT market (e.g., Chan, et al., 1990; Mei, 1999), that beta has little direct impact on individual REIT returns. The mean value of coefficient for

B/M (0.340) is positive and significant at 1% level, consistent with findings from previous portfolio results that value effect significantly exists in REIT market.

The second column reports results of a model with beta, B/M, Ivolatility and its interaction term with B/M. Coefficients on beta and B/M remain their sign and significance. Coefficient on B/M*Ivolatility^-1 is significant negative (-0.435), similar with Ali, Hwang, and Trombley (2003), this result suggests that the B/M based value effect increases with the idiosyncratic risk. The third column further presents the results using all variables in Equation [1]. The coefficient on B/M*Ivolatility^-1 is still significantly negative (-0.330). In addition, other measures of arbitrage cost do not have significant explanatory power for value effect in the presence of idiosyncratic risk. Therefore, the idiosyncratic risk plays the most important role in the existence of value anomaly in REIT returns.

Table 7.3 Regression Tests of Arbitrage Costs in Existence of Value Anomaly

The dependent variable is Re3, three-year buy-and-hold return, beginning in July of year t. Beta is systematic risk estimated using 36 monthly returns end in June of year t. B/M is book value per share year t-1 divided by market value of equity at end of June of year t. DAnalysts is a dummy variable which takes the value 1 if a REIT is covered by I/B/E/S, and value 0 if not. Ivolatility is square root of residual variance derived from the regression of monthly returns on a value-weighted market index over 36 months ending on June of year t. ME is the market value of equity in millions of dollars at the end of June of year t. Price is the closing price of a REIT stock at end of June of year t. Regression models are estimated for each year from 1991 to 2000, and means of annual estimates are reported. The t-statistics is computed as mean divided by standard error of the annual estimates. The sample period is from 1991-2000. To correct for serial correlation in returns induced by overlapping holding periods, we use the Newey and West (1987) procedures to estimate standard errors. ***, **, and * indicate significance at 1%, 5%, and 10%

levels, respectively.

(1) (2) (3)

Intercept 0.212 ** 0.065 0.348

(1.945) (0.157) (0.981)