An Empirical Investigation of Herding Behavior in the U.S. REIT Market

Although our test of herding is similar to that of CCK, our measure of CSAD _t differs from their. Their measure was derived from the conditional version of the CAPM, whereas ours follows the method used by (Christie and Huang 1995) and Gleason et al. (2004), which does not require the estimation of beta. This avoids the possible specification error associated with the asset pricing model.

During the period of 1980–2010, a total of 107 mortgage REITs have ever existed. However, the number of cross sections for mortgage REITs is small: it ranges from 4 to 43. This means that at some days, only 4 mortgage REITs exist. Further, we find for half of our sample period, the number of cross sections does not exceed 20 for mortgage REITs. The situation is even worse for hybrid REITs, for which a total of only 40 have ever existed. As can be imagined, for some extended periods of time the number of cross sections had been zero.

There have been a total of 383 equity REITs ever existing over our sample period. Given this, the number of cross sections remains sufficiently large: it ranges from 46 to 202.

It has been shown in the financial literature (e.g. Goyal and Santa-Clara 2003) that cross-sectional dispersion and time series volatility are significantly positively correlated, and they tend to move together. Such a point can be verified in this study. To do so, we first need to estimate the time series of market volatility. There are two alternative measures suitable for our study (e.g. Cotter and Stevenson 2008 and Zhou 2011): one is the power transformations of the market returns (e.g. absolute returns or squared returns), and the other is the conditional volatility obtained from GARCH-type models. Following the first alternative, the most apparent proxy for market volatility in our study is the absolute aggregate REIT return, i.e. |R _m,t | . Using it, we find that the correlation coefficient between market volatility and CSAD are highly positive and significant: 0.70 for daily, 0.75 for weekly, and 0.79 for monthly. Similar results are found when the second alternative is followed (i.e. using volatility generated from a GARCH(1,1) model of R _m,t ).

As noted by an anonymous reviewer, the reported results could be explained by an alternative hypothesis. That is, market sensitivities are unstable and they could become smaller during times of market stress. To test for the changes in market sensitivities, we first estimated the time-varying β for each equity REIT based on the capital asset pricing model (CAPM) through the application of the commonly used rolling window method. Then we run a fixed-effect panel regression: \( {\beta_{i,t}} = {a_1} + {a_2}{D_{i,t}} \), where i represents the ith REITs, t is the time index, and D is a dummy variable indicating whether market is under stress. To define D, we follow Christie and Huang (1995): D _i,t  = 1 if the aggregate REIT market return (R _m ) at time t lies in the extreme tails, which is usually identified by using small percentages (e.g. 1% or 5% of the return distribution). Given the above setting and using the 5% measure for the tails (the results are similar using the 1% as tails), we run the panel regression based on the daily data and find a ₁ = 0.684 (0.000) and a ₂ = 0.048 (0.000), where p-values are in parenthesis. As can be seen, a ₂ is positive and significant. This suggests that during stressful times, market sensitivities turn out to be larger than under usual times. So the alternative hypothesis is not supported. It is worth noting that a window of 252 days (one-trading year) is used to obtain the time varying β in the above regression. However, further experiments show that our results are robust to different sizes of the window ranging from one trading quarter to 5 years and even alternative methods of beta estimation. Further, when weekly and monthly data are used, we find the results are qualitatively unchanged.

To define small cap stocks, we follow the common practice to use deciles. Specifically, we use deciles 8–10 to define small cap stocks. This practice is consistent with those of some empirical studies (e.g. Sa-Aadu et al. 2010), and also with the size based indices kept at Professor French’s data page (http://​mba.​tuck.​dartmouth.​edu/​pages/​faculty/​ken.​french/​data_​library.​html) where indices are classified as low 30 (the smallest 30% of stocks, i.e. small cap), med 40 (the intermediate 40% of stocks, i.e. mid cap), and high 30 (the largest 30% of stocks, i.e. large cap). For the above defined small cap stocks (REITs excluded), their daily and monthly price data are obtained directly from the Center for Research in Security Prices (CRSP) over the period of January 1980 through December 2010. The weekly data are constructed by us in the same way as we did for REITs.

The OLS-CUSUM procedure tests for structural breaks based on the cumulated sum (CUSUM) of the OLS residuals within a time series regression framework. The rationale is that CUSUM tends to drift off following a structural break. So if CUSUM is found to become too large (i.e. crossing some predefined critical lines), structural breaks could be said to occur. Thanks to Zeileis et al. (2007), this procedure can now be easily implemented in R using the ‘Strucchange’ package.

As a robustness check, we experiment with different break dates which are either several months before or after July 1, 2008. The estimation results are similar to those reported here. To save space, they are not presented but are available upon request.

We thank an anonymous reviewer for bringing up this suggestion.

According to its annual reports, Kimco held its IPO in November 1991.