This section illustrates the method we use to compute the weighted-average dividend and dividend yield series for the value-weighted REIT portfolio. CRSP has two return figures: RET and RET X.
RET is total holding period return, and RET X is holding period return excluding distributions.
While both of these contain factors to adjust for stock splits, conceptually, we have:
RETt = Pt+ Dt
Pt−1 − 1 (12)
RET Xt = Pt
Pt−1 − 1 (13)
Thus, the dividend yield yt= Dt/Pt for our weighted portfolio is constructed as
yt = (rett− retxt) × (retxt+ 1)−1 (14)
This is because
(rett− retxt) × (retxt+ 1)−1 =
Pt+ Dt
Pt−1 − 1 − Pt
Pt−1 + 1
×Pt−1 Pt
(15)
= Dt
Pt−1 ×Pt−1
Pt
= Dt/Pt
Here rett and retxt are the total returns and price returns respectively, to our value-weighted portfolio of REITs over quarter t. Ptis the price at the end of quarter t, and Dtthe total dividend paid out over quarter t, to someone holding one share of the value-weighted index.
Subsequently, the dividend for quarter t (Dt) is computed as the dividend yield above, multiplied by the level of our REIT price index. This figure is once again only correct up to an arbitrary multiplier that is consistent over time. However, since we use log-differences of this dividend series for our study, this is irrelevant.
Adjusted R−squares for 49 Industries (F−F 3−Fac)
Adjusted R−square
Frequency
0.0 0.2 0.4 0.6 0.8
024681012
Figure 1: This figure shows the distribution of adjusted R2 obtained by regressing each of the Fama-French 49 industries on a Fama-French three-factor model.
Note: Mean: .565. Median: .602.
R2 for REITs: .537.
Table 1: Stock Returns.
The dependent variable is the real return on a value-weighted portfolio of NYSE, AMEX, and NASDAQ stocks on CRSP.
Reported estimates correspond to the regression of real returns on innovations in predictive variables. Innovations are residuals from a VAR system that includes all predictive variables, time trend, and quarterly dummies. Predictive variables are the logarithm of real dividends on the value-weighted stock index, long-term and short-term interest rates, the logarithm of volatility, the logarithm of industrial production, and the logarithm of the real money supply. Panel A includes real dividends over the most recent quarter. Panel B includes annual dividends–the average real dividends over the most recent four quarters. (t-statistics in parentheses.)
Real Interest Rates Industrial Real
Lags Dividends Long Short Volatility Production Money R2 Panel A: Quarterly Dividend
1 0.215 −0.836 −0.908 −0.063 0.287 0.162 0.222
(2.383)∗∗ (−0.466) (−0.987) (−4.963)∗∗∗ (0.438) (0.318)
2 0.336 −1.111 −0.856 −0.057 0.607 −0.020 0.216
(3.078)∗∗∗ (−0.608) (−0.857) (−4.271)∗∗∗ (0.816) (−0.036)
1 0.294 −0.809 −1.038 0.414 0.191 0.060
(3.014)∗∗∗ (−0.418) (−1.048) (0.575) (0.341)
2 0.441 −1.009 −0.914 0.707 0.010 0.099
(3.867)∗∗∗ (−0.526) (−0.878) (0.912) (0.016)
1 −1.530 −0.519 −0.068 0.217 0.094 0.190
(−0.871) (−0.573) (−5.322)∗∗∗ (0.325) (0.182)
2 −1.667 −0.510 −0.065 0.401 0.006 0.157
(−0.919) (−0.521) (−4.830)∗∗∗ (0.524) (0.010) Panel B: Annual Dividend
1 0.837 −1.392 −0.114 −0.055 −0.233 0.258 0.231
(2.878)∗∗∗ (−0.769) (−0.119) (−4.242)∗∗∗ (−0.344) (0.493)
2 1.002 −1.348 −0.348 −0.053 −0.138 −0.027 0.214
(3.085)∗∗∗ (−0.730) (−0.342) (−3.760)∗∗∗ (−0.178) (−0.047)
1 1.163 −1.354 −0.127 −0.289 0.249 0.105
(3.861)∗∗∗ (−0.707) (−0.126) (−0.398) (0.443)
2 1.384 −1.098 −0.422 −0.376 −0.038 0.122
(4.243)∗∗∗ (−0.573) (−0.406) (−0.469) (−0.065)
Table 2: REIT Returns
The dependent variable is the real return on a portfolio of Real Estate Investment Trusts (REITs). Reported estimates correspond to the regression of real returns on innovations in predictive variables. Innovations are residuals from a VAR system that includes all predictive variables, time trend, and quarterly dummies. Predictive variables are the logarithm of real dividends (both for directly owned properties and for REITs), long-term and short-term interest rates, the logarithm of volatility, the logarithm of industrial production, and the logarithm of the real money supply. Panel A includes both stock market volatility and REIT volatility as measures of risk. Panel B includes REIT volatility as risk measure and in Panel C risk is measured by stock market volatility. (t-statistics in parentheses.). All VAR specifications use two lags.
Dividends Interest Rates Volatility Industrial Real
Property REIT Long Short Stock REIT Production Money R2
Panel A
0.204 0.437 −0.926 −0.037 −0.030 −0.947 −1.054 0.147
(0.656) (0.232) (−0.963) (−1.826)∗ (−1.498) (−1.316) (−1.884)∗
0.147 0.319 −1.423 −0.030 −0.034 −0.803 −1.028 0.187
(2.580)∗∗∗ (0.173) (−1.493) (−1.500) (−1.774)∗ (−1.136) (−1.890)∗
0.213 0.138 0.352 −1.412 −0.029 −0.036 −0.828 −1.040 0.238
(0.663) (2.240)∗∗∗ (0.190) (−1.477) (−1.420) (−1.848)∗ (−1.157) (−1.898)∗
Panel B
0.277 −0.034 −0.860 −0.058 −0.981 −1.108 0.135
(0.890) (−0.018) (−0.918) (−4.363)∗∗∗ (−1.369) (−1.977)∗∗
0.161 −0.159 −1.344 −0.056 −0.845 −1.084 0.183
(2.864)∗∗∗ (−0.089) (−1.457) (−4.452)∗∗∗ (−1.208) (−1.999)∗∗
0.260 0.151 −0.098 −1.328 −0.057 −0.883 −1.092 0.180
(0.815) (2.468)∗∗∗ (−0.054) (−1.437) (−4.431)∗∗∗ (−1.250) (−2.001)∗∗
Panel C
0.108 0.858 −1.122 −0.059 −0.730 −0.847 0.132
(0.351) (0.457) (−1.165) (−4.310)∗∗∗ (−1.024) (−1.542)
0.127 0.834 −1.600 −0.056 −0.561 −0.829 0.166
(2.238)∗∗ (0.453) (−1.669)∗ (−4.221)∗∗∗ (−0.803) (−1.542)
0.107 0.128 0.863 −1.592 −0.056 −0.602 −0.822 0.160
Table 3: Direct Property Returns
The dependent variable is the real return on a portfolio of directly held real estate properties. Reported estimates correspond to the regression of real returns on innovations in predictive variables. Innovations are residuals from a VAR system that includes all predictive variables, time trend, and quarterly dummies. Predictive variables are the logarithm of real dividends (both for directly owned properties and for REITs), long-term and short-term interest rates, the logarithm of volatility, the logarithm of industrial production, and the logarithm of the real money supply. Dividends are average real dividends over the most recent four quarters. Panel A includes both stock market volatility and REIT volatility as measures of risk. Panel B includes REIT volatility as risk measure and in Panel C volatility is measured by stock market volatility. (t-statistics in parentheses.) All VAR specifications use two lags.
Dividends Interest Rates Volatility Industrial Real
Property REIT Long Short Stock REIT Production Money R2
Panel A
0.487 0.128 −0.153 −0.004 0.002 0.307 −0.190 0.082
(2.787)∗∗∗ (0.318) (−0.746) (−0.964) (0.472) (1.979)∗∗ (−1.565)
0.111 −0.061 −0.187 −0.004 0.002 0.328 −0.141 0.052
(2.104)∗∗ (−0.152) (−0.889) (−0.879) (0.496) (2.078)∗∗ (−1.127)
0.397 0.097 0.172 −0.220 −0.004 0.002 0.242 −0.197 0.078
(2.196)∗∗ (1.826)∗ (0.419) (−1.058) (−0.862) (0.511) (1.495) (−1.578) Panel B
0.511 −0.070 −0.009 0.000 0.234 −0.212 0.083
(2.929)∗∗∗ (−0.179) (−0.046) (0.000) (1.534) (−1.754)∗
0.113 −0.260 −0.043 0.000 0.254 −0.165 0.050
(2.153)∗∗∗ (−0.661) (−0.214) (0.000) (1.638)∗ (−1.328)
0.406 0.101 0.012 −0.098 0.000 0.161 −0.225 0.080
(2.249)∗∗ (1.908)∗ (0.029) (−0.487) (0.000) (1.016) (−1.811)∗ Panel C
0.496 0.103 −0.118 −0.003 0.270 −0.226 0.092
(2.857)∗∗∗ (0.261) (−0.582) (−1.081) (1.774)∗ (−1.926)∗
0.110 −0.070 −0.163 −0.002 0.280 −0.181 0.060
(2.109)∗∗ (−0.177) (−0.782) (−0.873) (1.837)∗ (−1.510)
0.402 0.095 0.155 −0.190 −0.002 0.200 −0.238 0.089
(2.235)∗∗ (1.804)∗ (0.386) (−0.923) (−0.866) (1.264) (−1.970)∗∗
∗: p < 10%;∗∗: p < 5%;∗∗∗: p < 1%.
Table 4: Summary Statistics for REIT and Property Portfolios.
This table presents summary statistics for the REIT– and Direct Property data, as of the end of each year in our sample. The statistics presented are the total market capitalization of the REIT industry (in millions of Dollars), the fraction of market capitalization that we matched against NCREIF’s property types (Apartment, Hotel, Industrial, Office Retail), the fraction of the matched portfolio market capitalization that is made up by each property sector, and the total appraised value of all properties in NCREIF’s property universe (also in millions of Dollars).
Year Total Industry Fraction Matched Apartment Hotel Industrial Office Retail Total NCREIF
Capitalization Portfolio Value
1980 3, 365 0.361 0.305 0 0.069 0.048 0.579 1, 770
1981 3, 115 0.307 0.384 0 0.091 0.049 0.477 3, 351
1982 4, 451 0.301 0.456 0 0.121 0.033 0.39 4, 603
1983 5, 554 0.411 0.395 0.095 0.054 0.025 0.43 8, 427
1984 5, 901 0.436 0.408 0.107 0.048 0.041 0.396 10, 828
1985 7, 673 0.362 0.305 0.128 0.095 0.049 0.422 14, 575
1986 10, 438 0.325 0.326 0.091 0.102 0.037 0.444 17, 214
1987 9, 890 0.334 0.264 0.093 0.118 0.046 0.48 21, 025
1988 11, 140 0.343 0.235 0.063 0.107 0.106 0.488 26, 472
1989 11, 889 0.372 0.196 0.034 0.082 0.106 0.581 30, 801
1990 9, 302 0.343 0.187 0.018 0.065 0.108 0.622 37, 066
1991 13, 289 0.336 0.219 0.008 0.043 0.104 0.626 37, 423
1992 16, 903 0.394 0.229 0.004 0.027 0.069 0.671 39, 289
1993 33, 336 0.532 0.3 0.006 0.048 0.081 0.565 39, 872
1994 44, 429 0.665 0.313 0.024 0.105 0.089 0.469 38, 919
1995 59, 305 0.661 0.281 0.073 0.1 0.118 0.429 45, 896
1996 82, 171 0.68 0.275 0.096 0.123 0.163 0.342 51, 817
1997 137, 833 0.769 0.213 0.132 0.127 0.276 0.252 61, 744
1998 146, 105 0.78 0.198 0.167 0.132 0.247 0.257 63, 344
1999 126, 649 0.779 0.227 0.118 0.141 0.242 0.271 77, 024
2000 137, 756 0.819 0.234 0.124 0.149 0.265 0.227 89, 383
2001 162, 026 0.758 0.231 0.106 0.145 0.248 0.27 105, 175
2002 170, 319 0.741 0.219 0.104 0.141 0.231 0.305 110, 797
2003 229, 935 0.727 0.211 0.101 0.133 0.215 0.34 119, 999
2004 321, 050 0.691 0.198 0.12 0.158 0.2 0.323 127, 365
2005 363, 112 0.708 0.194 0.132 0.136 0.206 0.332 155, 700
2006 494, 965 0.701 0.195 0.163 0.117 0.23 0.296 195, 663
42
Table 5: OLS Regression of NOI Yield on the Risk-Free Rate.
This table shows results from an OLS regression which models changes in NOI yield on changes in the risk-free rate. The dependent variable is the first difference in the natural logarithm of the NOI Yield (defined as the ratio of the weighted average quarterly total Net Operating Income (NOI) per square foot to the NCREIF property portfolio, over the weighted average share price of the REIT portfolio). The independent variable is the quarterly change in the natural logarithm of the long-term interest rate. (T-statistics in parentheses).
∆noi.yield (Intercept) 0.0015
(0.1510)
∆lt.rate 0.2393 (1.7307)∗
R2 0.02698
F 2.995∗
N 110
∗: p < 10%;∗∗: p < 5%;∗∗∗: p < 1%.
Table 6: Matrix of Results from First-Order Vector Autoregression
This table presents coefficient estimates from a first-order Vector Autoregression (VAR). The system consist of the natural logarithm of the dividend yield to the value-weighted REIT portfolio (div.yield), the quarterly dividend growth rate to this portfolio (∆dividend), the NOI Yield, defined as the ratio of the quarterly Net Operating Income (NOI) to the direct property portfolio over the weighted average price of the REIT portfolio, the quarterly NOI growth rate for the direct property portfolio (∆noi), and the long-term interest rate (lt.rate). All variables are computed as the natural logarithm of their respective raw series, and all change variables are computed as the first difference of the natural logarithms. A time trend variable is included in the VAR system. All variables are de-meaned. The F-statistic included is the joint significance test that all variables are different from zero, for each equation of the system. (T-statistics in parentheses).
div.yieldt−1 ∆dividendt−1 noi.yieldt−1 ∆noit−1 lt.ratet−1 trend R2 F div.yieldt 0.210029 −0.21323 0.197454 0.019985 0.660167 −0.000197 0.5867 26.31∗∗∗
(1.5252) (−1.9961)∗∗ (1.9099)∗ (0.0701) (4.5899)∗∗∗ (−0.54)
∆dividendt −0.726002 −0.258301 0.216349 −0.097534 0.628109 −0.000228 0.4679 16.68∗∗∗
(−5.7235)∗∗∗ (−2.6251)∗∗∗ (2.2719)∗∗ (−0.3714) (4.7408)∗∗∗ (−0.6779)
noi.yieldt −0.072603 −0.02268 0.926821 −0.146556 0.035216 4 × 10−6 0.8339 90.50∗∗∗
(−1.1039) (−0.4445) (18.7703)∗∗∗ (−1.0762) (0.5126) (0.0229)
∆noit −0.007475 −0.0683 −0.05502 −0.263807 0.006015 1.6 × 10−5 0.1450 4.02∗∗∗
(−0.1654) (−1.9477)∗ (−1.6212) (−2.8186)∗∗∗ (0.1274) (0.1351)
lt.ratet 0.088218 −0.042538 −0.073408 0.119099 0.857163 −0.000208 0.9524 358.13∗∗∗
(1.973)∗ (−1.2264) (−2.1868)∗∗ (1.2865) (18.3539)∗∗∗ (−1.7571)∗
Number of observations: 108
∗: p < 10%;∗∗: p < 5%;∗∗∗: p < 1%.
44
Table 7: Results from Rolling Vector Autoregressions.
This table presents statistics comparing the predicted dividend yield for quarter t + 1 (generated by a VAR using 40 quarters’
worth of data, ending at t), pred.div.yieldt,t+1, with the ex-post realized dividend yield at quarter t+1, div.yieldt+1. Specifically, the table presents, for each VAR specification, the ratio of the standard deviations between the predicted and the realized series, as well as their correlation coefficient. In parentheses there is the value of a t-statistic testing the hypothesis that the actual correlation between the two series is 0. The set of candidate variables for the VAR consists of div.yieldt, the dividend yield to the value-weighted REIT portfolio, ∆dividendt, the quarterly growth in the weighted-average REIT dividend, noi.yieldt
the ratio of the quarterly weighted-average net operating income (NOI) per square foot to the property portfolio, over the weighted-average end-of-quarter price to the REIT portfolio, ∆noit the quarterly NOI growth, and lt.ratet, the long-term interest rate. All variables are computed as the natural logarithm of their respective raw series, and all change variables are computed as the first difference of the natural logarithms. All variables are de-meaned.
VAR System 1: [div.yieldt, ∆dividendt, lt.ratet]′
Lags: 1 2
σ(pred.div.yieldt,t+1)/σ(div.yieldt+1) 0.6941 0.7108 cor(pred.div.yieldt,t+1, div.yieldt+1) 0.4593 0.4528 (4.201)∗∗∗ (4.126)∗∗∗
VAR System 2: [div.yieldt, ∆dividendt, noi.yieldt, lt.ratet]′
Lags: 1 2
σ(pred.div.yieldt,t+1)/σ(div.yieldt+1) 0.9298 0.9563 cor(pred.div.yieldt,t+1, div.yieldt+1) 0.6086 0.6847 (6.232)∗∗∗ (7.631)∗∗∗
VAR System 3: [div.yieldt, ∆dividendt, noi.yieldt, ∆noit, lt.ratet]′
Lags: 1 2
σ(pred.div.yieldt,t+1)/σ(div.yieldt+1) 0.9765 0.9813 cor(pred.div.yieldt,t+1, div.yieldt+1) 0.6503 0.7323 (6.955)∗∗∗ (8.736)∗∗∗
VAR System 4: [div.yieldt, noi.yieldt, ∆noit, lt.ratet]′
Lags: 1 2
σ(pred.div.yieldt,t+1)/σ(div.yieldt+1) 0.9464 0.9291 cor(pred.div.yieldt,t+1, div.yieldt+1) 0.5949 0.7313 (6.012)∗∗∗ (8.712)∗∗∗
VARs are computed on a rolling 40-quarter window. Statistics are computed on the remaining 68 observa-tions.
∗: p < 10%;∗∗: p < 5%;∗∗∗: p < 1%.
Plot of Actual and Predicted Dividend Yields
Date
log(div.yield), de−meaned
1995 2000 2005
−0.8−0.6−0.4−0.20.00.20.4
Figure 2: This figure shows a plot of the log of realized dividend yields (the black continuous line) and predicted dividend yields from VAR System 4 (Table 7) for the same quarter (the red dashed line).
Table 8: Regression Results of Residual Dividend Yield on Realized Quarterly REIT Volatility.
This table presents results from an OLS regression of the difference between ex-post realized dividend yield on the REIT portfolio (div.yieldt+1) minus the predicted dividend yields, generated through a 40-quarter rolling window VAR in quarter t, and concerning quarter t + 1. Each of the variables pred.div.yieldt,t+1,icorresponds to the predicted dividend yields generated by VAR system i in Table 7. The independent variable is the logarithm of the volatility of daily returns on the value-weighted REIT portfolio for quarter t + 1, minus its mean. (T-statistics in parentheses).
div.yieldt+1 div.yieldt+1− div.yieldt+1− div.yieldt+1− div.yieldt+1− pred.div.yieldt,t+1,1 pred.div.yieldt,t+1,2 pred.div.yieldt,t+1,3 pred.div.yieldt,t+1,4
(Intercept) 0.00056 0.0043 0.0405 0.0523 0.0295
(0.0173) (0.1421) (1.6213) (2.2286)∗∗ (1.2912)
reit.volt+1 0.00702 0.0207 0.0509 0.0399 0.0441
(0.1800) (0.6111) (1.8298)∗ (1.5273) (1.7311)∗
R2 0.0003 0.0056 0.0482 0.0341 0.0434
F 0.0324 0.3734 3.348∗ 2.333 2.997
N = 68
∗: p < 10%;∗∗: p < 5%;∗∗∗: p < 1%.
47