Correlation and Volatility Dynamics in REIT Returns: Performance and

IRES2010-002

IRES Working Paper Series

Correlation and Volatility Dynamics in REIT Returns: Performance and Portfolio Considerations Peng FEI [email protected] Lusk Center for Real Estate University of Southern California

Letian DING [email protected] Department of Physics and Astronomy University of Southern California Yongheng DENG [email protected] Institute of Real Estate Studies National University of Singapore

Correlation and Volatility Dynamics in REIT Returns: Performance and Portfolio Considerations     Peng Fei*  Lusk Center for Real Estate University of Southern California Phone: (310)256-6883 Fax: (213)740-6170 Email: [email protected] *Corresponding Author Address: 2801 Orchard Ave APT#9 Los Angeles, CA 90007-2364

Letian Ding  Department of Physics and Astronomy University of Southern California Phone: (213)-281-1546 Fax: (213)-470-6170 Email: [email protected]

Yongheng Deng  Lusk Center for Real Estate School of Policy, Planning and Development Marshall School of Business University of Southern California Phone: (213)821-1030 Fax: (213)740-6170 Email: [email protected]

Sep 2008

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Correlation and Volatility Dynamics in REIT Returns:  Performance and Portfolio Considerations    Abstract    We  examine  the  dynamics  in  correlations  and  volatility  of  REITs,  stock  and  direct  real  estate  returns  using  the  monthly  data  from  Jan  1987  to  May  2008.  To  explore  asymmetries  in  conditional  correlation,  the  multivariate  asymmetric  dynamic  diagonal  conditional  correlation  (AD‐DCC)  GARCH  specification  is  utilized  in  this  paper.  We  document  that  the  time‐varying  conditional  correlations  can  be  explained  by  macroeconomic  variables  such  as  the  term  and  credit  spreads,  inflation  and  the  unemployment  rate.  We  also  find  strong  relationship  between  correlations  and  REITs  returns,  while  those  patterns  are  distinguishable  for  different  types  of  REITs.  Interestingly,  when  the  correlation  between  REITs  and  S&P  are  the  lowest,  the  future  performance  of  REITs  is  the  best.  For  equity  REITs,  there  exists  a  robust  relationship  between  correlations  and  future  returns:  the  higher  (lower)  correlation  between  equity  REIT and direct real estate is, the higher (lower) the future returns of equity REIT.  Our  results  also  have  significant  economic  implications  regarding  the  time‐dependent  diversification  benefits  of  REITs  in  a  mixed‐assets  portfolio  and  the  unique  risk  and  return characteristics of REITs.  

        Keyword    Dynamic Conditional Correlation, REIT returns, Multivariate GARCH, Stock,  Real Estate, Diversification    JEL Code    G11 G15   

     

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This paper examines the dynamics in correlations and volatility of REITs, stock and direct real estate returns using the monthly data from Jan 1987 to May 2008. While there are extensive studies on the dynamics of stock markets conditional correlations and portfolio diversification, far less attention has been devoted to such studies in the real estate literature. This is mainly due to the lack of longer and high frequency time series for real estate returns. Consequently, many real estate studies focus on the unconditional real estate and REITs correlation with the broader market. Moreover, with considering the possible asymmetry in the conditional correlations, this paper investigate the time-varying conditional correlations and volatilities in REITs, real estate and stock return series by deploying a new generalized autoregressive conditionally heteroskedastic (GARCH) process, the asymmetric dynamic conditional correlation (AG-DCC) GARCH technique. Then we test whether the estimated conditional correlations are a good indicator to estimate the future returns of REITs and whether the dynamics in correlations can be explained by the macroeconomic factors such as the term and credit spreads, inflation and the short rate of interest. This paper attempts to draw together two strands of real estate studies on the correlation between REITs and other asset classes, which determines diversification benefits of REITs in a mixed-asset portfolio. The first strand involves examination of the behavior of security-backed property vehicles in particular real estate investment trust shares in relation to the underlying direct real estate investment market (See, e.g. Liang, McIntosh and Webb, [1995]; Ghosh, et al., [1996]; Liang and McIntosh, [1998]; Seiler et al., [2001]). The second stand seeks to analyze the nature and behavior of the correlations between REITs and other financial assets. An extensive body of literature show that macroeconomic variables that have been found to explain stock and bond returns and risks have significant power in explaining REIT return and risks (Ling and Naranjo, [1997]; Peterson and Hseih, [1997], Karolyi and Sanfers, [1998]; Calyton and Mackinnon, [2003]). However, the empirical results about the direction and extent of the relationship between REITs and stock have been also mixed and sometimes contradictory depending on the time periods or the methodology used in the studies (Chen and Peiser, [1999]; Hartzell, et al., [1999]; Clayton and MacKinnon, [2001]; and others). Our results show that over the 1987-2008 time period, the correlations among REIT, direct real estate and stock returns are time-dependent and volatile which can be

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explained by macroeconomic variables such as the term and credit spreads, inflation and the unemployment rate. However, different to the previous evidences of existing significant asymmetry in correlations among financial assets (see e.g. Cappiello, et al. 2006), this study only find little asymmetry in the conditional correlations of REITs, stock and direct real estate returns. We also find strong relationship between correlations and REITs returns, while those patterns are distinguishable for different types of REITs. Interestingly, when the correlation between REITs and S&P are the lowest, the future performance of REITs is the best. For equity REITs, there exists a rubust relationship between correlations and future returns: the higher (lower) correlation between equity REIT and direct real estate is, the higher (lower) the future returns of equity REIT. This study makes two main contributions to the literature. First, it explicitly examines correlation dynamics among REIT, direct real estate and stock asset classes and investigate the presence of asymmetric responses in conditional variances and correlations to negative returns. The findings in this paper actually resolve the long debate by academics and industry practitioners on the role of REITs in mixed asset portfolios, questioning whether REITs actually provide exposure to the private real estate asset class or simply represent additional exposure to common stocks (see e.g. Clayton and Mackinnon, [2003]). Second, in addition to estimating the time-varying correlations among these asset classes, we examine the economic determinants of correlations and volatilities as well as the implications on future REIT returns. This allows us to quantify the time-varying diversification ability of REITs in a mixed assets portfolios and to better understand the risk and return characteristics of REITs.

Methods Multivariate generalized autoregressive conditionally heteroskedastic (MGARCH) models are deployed to explore the stochastic behavior of financial time series and, in particular, to explain the behaviors of the return volatility and covariance over time (Bollerslev, et al., [1992]). Most of early MGARCH models parameterize timevarying covariance in the sprit of Bollerslev [1990] where correlation coefficients are assumed to be constant over the sample period. Although setting all conditional correlations to be constant greatly simplifies estimation, the assumption is neither theoretically justified nor robust to the empirical evidence. Tse and Tsui [2002] and -4-

Engle [2002] propose a new class of models that both preserve the ease of estimation of the Bollerslev’s constant correlation model but make the conditional correlation matrix time-dependent. However, econometric specifications that explicitly model asymmetry in conditional covariances and, specifically, conditional correlations are far less common1. Very recently, Cappiello, et al. [2006] advance dynamic conditional correlation (DCC) models further by considering the asymmetry effect in the correlations discussed above. This paper uses the asymmetric generalized dynamic conditional correlation (AGDCC) model of Cappiello et al. [2006] to model the dynamic conditional correlations in stock, bond and foreign exchange markets. The AG-DCC process extends previous specifications along two dimensions: it allows for series-specific news impact and smoothing parameters and permits conditional asymmetries in correlation dynamics. The AG-DCC specification is well suited to examine correlation dynamics among different asset classes and investigate the presence of asymmetric responses in conditional variables and correlations to negative returns. The AG-DCC model can be written as follows: rt t 1 ~ (0, H t ),

t  1,..., T

H t  Dt t Dt ,

(1) (2)

where rt be a n 1 vector of asset returns, which is assumed to be conditionally normal with mean zero and covariance matrix H t ; and t 1 is the time t  1 information set, and Dt is the n  n diagonal matrix of time-varying standard deviations from univariate GARCH models with

hit on the i th diagonal, and t is

the time-varying correlation matrix. The AG-DCC model is designed to allow for three-stage estimation of the conditional covariance matrix, H t . In the first stage, univariate volatility models are fit for each of the assets and estimates of hit are obtained. As Engle and Sheppard [2001] indicate, any univariate GARCH process that is covariance stationary and assumes normally distributed errors can be used to model the variances. However, 1

There exist studies that account for asymmetry in conditional covariances, see, for instance, Koutmos and Booth [1995], Booth, et al. [1997], Scruggs [1998], and Christiansen [2000], however in their model specifications, the correlation coefficients are assumed to be constant over the sample period.

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since the conditional variance is an asymmetric function of past innovations, which increases proportionately more after a negative than after a positive shock of the same magnitude, the so-called asymmetric effects thus becomes another important issue in the applications of the univariate GARCH models. Asymmetric GARCH models include Nelson’s [1991] exponential GARCH model, Glosten et al. [1993]’s GJRGARCH model and Zakorian’s [1994] threshold-GARCH model. While in this paper we tried and compared with all these asymmetric models and the GJR-GARCH model specification is selected according to the Bayesian information criterion (BIC). The conditional variances follow a univariate GJR-GARCH (1, 1) specification: hit   i ,0   i ,1 i2,t 1   i I [ i ,t 1  0] i2,t 1   i hi ,t 1 , i  1,2,..., n

(3)

where  i ,1 measures the ARCH effect. The persistence of volatility (i.e. GARCH effect) is measured by  i . The unconditional variance is finite if  i  1 ;  i is the coefficient that measures the asymmetric (leverage) effect; I [ i ,t 1  0]  1 if the

innovation in last period is negative,  i ,t 1  0 and otherwise I [ i ,t 1  0]  0 . In the second stage, after the GJR-GARCH model are estimated, the standardized residuals, it  rit / hit , are calculated to estimate the parameters of the dynamic conditional correlations. The details about the dynamic equation for the conditional correlations can be found in Cappiello et al. [2006]. Finally, the third stage conditions on the correlation intercept parameters constraint to estimate the coefficients governing the dynamics of correlation. The parameters are estimated by the Maximum Likelihood method assuming that the assets returns are conditional Gaussian. Because the AG-DCC generalization comes at the cost of added parameters and complexity, which actually require n 2 parameters in each correlation term, two simplified modifications of AG-DCC models are used in this paper: 1) the scalar version known as the asymmetric DCC model (A-DCC), where has only 3 parameters, 2) the diagonal matrix version known as the asymmetric diagonal DCC model (ADDCC), where has 3n parameters.

Data and Empirical Results The Data

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The empirical tests conducted in this paper utilize the monthly return data on REITs, common stocks and unsecuritized (private) real estate in the U.S market. The sample ranges from Jan 1987 to May 2008, with 257 observations for each return time series. The National Association of Real Estate Investment Trusts (NAREIT) indices including the composite REIT index, the equity REIT index, the mortgage REIT index and the hybrid REIT index are used in this study, allowing an analysis of not only the overall REIT market but also the Equity, Mortgage, and Hybrid sub-markets. As the most widely known stock index, the S&P 500 composite index is used as a proxy for the stock market. We use the S&P/Case-Shiller® Home Price Indexes to represent the private (or direct) real estate. The key reason is that the estimation methods employed here are for high frequency data, hence S&P/Case-Shiller home price index works because it is available monthly2. There are other two major housing indexes commonly used in the literature to track the performance of the U.S. housing market: the National Association of Realtors (NAR) Indexes and the Office of Federal Housing Oversight (OFHEO) Indexes. However, the NAR Indexes quote median values without recourse to a repeat sales methodology, which creates a significant potential for bias, while the OFHEO indexes are quarterly data and confined to the Fannie Mae and the Freddie Mac conforming mortgages, which are skewed to the lower end of the housing market. This is a significant issue because, for instance, only approximately one-sixth of housing in California is sold with a conforming mortgage. In addition, the OFHEO indexes also utilize appraisal data to supplement their samples, which creates the possibility of bias that have an appraisal smoothing effect on persistence of housing returns. Thus using monthly Case-Shiller Indexes should exorcise the criticism for

2

We do not use commercial Property Price Index in this study for three reasons: 1) housing and

commercial property valuation dynamics usually share common drivers (Gyourko [2009]). 2) Only the monthly data since 2000 for commercial Property Price Index such as the Moody’s commercial Property Price Index is available to us. 3) The average correlation among REIT indexes and S&P/CaseShiller® Home Price Index in this same period are found to be much larger than the average correlation among REIT indexes and Moody’s commercial Property Price Index, which suggests the home price in U.S housing market has more direct impact on REITs returns. However, we noted that the dynamic patterns for the correlation among Moody’s commercial Property Price Index and REITs Indexes and their relations with the macroeconomic variables actually are similar to what we shown in this paper. Those results can be obtained by contacting the authors directly.

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that appraisal smoothing effect. In this study, all the price index data, Pi ,t , at time t is transformed into the continuously compounded monthly returns as follows:

Ri ,t  log( Pi ,t / Pi ,t 1 ) ,

(4)

where Pi ,t and Pi ,t 1 are the closing prices of asset i at time t and t  1 , respectively. To capture the economic determinants of conditional correlations among the assets, this paper uses those macroeconomic variables widely used in finance literature which include the unemployment rate, the term spread (the difference between the yields on 10-year and 1-year Treasuries), the credit spread (the difference between the yields on BAA-and AAA-rated corporate bond), Consumer Price Index (CPI) inflation rate and 3 month Treasure bill rate (e.g. Campbell and Shiller, [1988]; Fama and French, [1989]; Torous, Valkanov and Yan, [2005]). All these data, except the 3-month Treasury bill rate, are taken from the FRED database. The 3-month Treasury bill rate is obtained from Ibboston Associates. The panel A in Table 1 contains descriptive statistics for the data which exhibit the expected properties of financial returns and real estate returns. All markets exhibit an average positive monthly return with left skewness and fat-tails. As expected, the private real estate has the highest Sharp ratio due to the least volatility/standard deviation of returns. Without considering other factors such as transaction cost, direct real estate asset do have a definite role in the formation of efficient portfolio. That’s why Webb, et al. [1988] suggest that two-thirds of investment wealth should be allocated to real estate and only one-third to financial assets. During the sample period, all REITs, except the hybrid REIT sub-sector, are less volatile than the S&P 500 stock index; while the ex post composite and equity REITs returns are higher than stocks. This reflects some kind of superior risk and return characteristics of equity returns since the high-tech bubble bursts. The panel B in table 1 summarizes the unconditional correlations for REITs, stock and real estate returns. It is found that although both are positive, the unconditional correlations between REITs and stock are much higher than the correlations between REITs and direct real estate returns during the sample period. This suggests that the REITs and unsecuritized real estate returns have significantly different statistical properties and that the degree of substitutability of REITs for private real estate in static mixed-asset portfolios is quite limited. This is consistent with the previous studies that little connection was found

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between REIT investment performance and unsecuritized income-property (see, e.g. Corgel, et al., [1995]; Seck, [1996] and Seiler, et al. [2001]). Among the three subsectors of REIT markets, the correlation between the equity REIT and the S&P 500 returns is the highest, nearly to 0.45. Surprisingly, the hybrid REIT return has the higher correlation coefficient to the unsecuritized real estate than the other two REIT sectors. Finally, we can find that the unconditional correlation between housing and the S&P 500 is slightly negative. The similar result is also found by Goetzmann [1993]. The negative correlation indicates again that housing returns has strong diversification benefits to the stock asset portfolio.

Empirical Results

Estimated Dynamic Correlations As described above, two different parameterizations are estimated for the dynamics of the correlations among different asset classes. The first and simplest model is a asymmetric scalar DCC (see Equation (6)). Second, the full diagonal version of AGDCC model (see Equation (8), with diagonal matrices A , B and G ). According to the Akaike’s information criterion (AIC), the diagonal asymmetric DCC specification outperforms the competing model. The table 2 reports the results relative these two DCC specifications. Most parameters are significantly different to zero, with exceptions noted in the table. Log-likelihood values also suggest that the diagonal version significantly outperform the scalar specification. Interestingly, most asymmetric terms gi are not statistically significant in the model at 95% confidence level. This suggests that the correlations among the assets classes tested in our model may not therefore be higher after a negative innovation than after a positive innovation of the same magnitude, although for an individual asset return series; there still exist the significant asymmetric volatility phenomenon in fitting univariate GJRGARCH model in the first step. Our finding that the absence of significant asymmetry in the conditional correlations among REIT, direct real estate and stock returns is quite different to the previous evidences found in the capital market, where both equities and bonds exhibit significant asymmetries in conditional correlations (see e.g. Cappiello, et al. [2006]; Christiansen, [2000]). The possible reason for this difference maybe attribute to the segmentation between real estate market and stock market and

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the unique “hybrid” characteristics of return and risk in REITs. Actually in addition to possible explanations for asymmetries in return volatility, little theoretical framework is available to justify the empirical evidence of asymmetric correlations. Figure 2 contains the dynamic conditional volatility series for REITs, direct real estate and stock returns. Except for the direct real estate returns, the conditional volatility linkages among other assets were most evident during some certain tumultuous periods such as black Tuesday in October 1987, the Iraqi invasion of Kuwait, and the Gulf war in 1990/1991. Interestingly, most recently the volatility of the mortgage REIT and the hybrid REIT sectors exhibit a spike as the same as what happened in the conditional volatility in private real estate returns. This seems the volatility linkages in these three groups are strengthening increasingly. Figure 3a plots the estimated correlations between REITs and private direct real estate returns. The correlation is not high and fluctuates in a narrow range from -0.12 to 0.25. However, recently since 2007, the correlation is increasing. The pattern is generally consistent with the previous findings that the correlation between REIT and direct real estate is limited and recently the REIT can reflect more fundamentals in the direct real estate market. The time-varying correlations between REITs and stock returns are exhibited in Figure 3b. The correlations of the assets under consideration show considerable variation. Our findings actually resolve the mixed empirical evidences about the correlations between REITs and stock returns. For instance, Ghosh, et al., [1996] found that the correlations between REIT returns and S&P 500 declined over time from1985 to 1996; Mueller, et al.[1994], REIT returns are shown to exhibit strong positive correlations with the S&P 500 from 1976 to 1993; Mull and Soenen [1997]find that REITs is a good diversification vehicle in the 1990–1994 period, they were not as attractive in the period 1985–1990. All of these empirical results are consistent with the dynamic correlations plotted in the Figure 3b. In addition, Figure 3 also shows the obvious cyclical nature of the REIT returns sensitivities to financial assets and unsecuritized real estate, which also reaffirms the findings by Calyton and Mackinnon [2001].

Economic Determinants of Dynamic Correlations

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To whether the dynamic conditional correlations are determined by the economic fluctuations, we test the following regression models for each return series separately: Corri ,t   i Corri ,t 1   0,i X t  1,i X t 1  dt   i ,t

(5)

where Corri ,t denotes the conditional correlation between REIT i and other asset at time t , the parameter  i is the auto-regression parameter which reflect how Corri ,t 1 at time t -1 affect the current correlation value Corri ,t ; the parameters  0,i and 1,i are vector parameters which measure the sensitivities of the conditional correlations to the current and lagged macroeconomic variable vector X t . We also include a time dummy variable to constraint the seasonal effect. Since the macroeconomic variables always tend to correlate each other, we select the best set of macroeconomic determinants into the regression by utilizing the Sequential Elimination of Regressors approach to decide on possible constraints. This strategy sequentially deletes those regressors which lead to the largest reduction of the selected criterion until no further reduction is possible (see, e.g. Bruggemann and Lutkepohel [2001] for more details). Table 3 reports the results of estimation. Firstly, we find that the conditional correlations between REITs and both unsecuritized real estate and stock returns are quite persistent over the sample time period. The coefficient on lagged conditional correlation keeps significance at a 1% level. Secondly, the results indicate the correlations are significantly affected by the macroeconomic variables, although the best set of economic regressors is a little different across different REIT sub-sectors. For example, the correlation between equity REITs and direct real estate returns is mainly determined by the lagged CPI inflation rate with the corresponding coefficient is statistically significant at the 1% level. While as for the correlation between equity REITs and S&P 500 index, the credit spread, the term spread and the unemployment rate enter the regression after the SER subset selection. Those coefficients are also statistically significant at the 5% level or better. Thirdly, we also find the distinct effects of economic variables on the dynamics in the correlations. The effects of the term spread on the correlation are always negative, while the credit spread, CPI inflation rate and the unemployment rate always have positive effects on the correlations. In addition, the magnitudes of those coefficients are also different.

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Finally, the adjust R2 coefficients of determination are around 0.9 for all those regressions and indicates our models fit the data quite well.

Expected Returns and the Dynamic Correlations Most financial decisions involve a trade-off between future risks and asset returns. The volatilities and correlations of assets returns are often the major components of risk (Cappiello, et al., 2006). Since the correlations between REITs and both private real estate and stocks evolve over time as the economy changes, the time-varying conditional second moments may demand to be compensated by returns. To understand the role of conditional correlations of REITs on its future returns, we examine the historical impacts of the conditional correlations on REIT sector performances via a non-parametric test. For each REIT sub-sector, the estimated conditional correlations (between REIT and direct real estate returns, and between REIT and stock returns, separately) are grouped into four regimes which are determined by equally dividing the range of correlations during the sample time period, while the regime ranking is also recorded for each month. Then using the resampled monthly correlations data in every regime, we calculate the conditional probability of the loss and gain, as well as the expected gain or loss for the next month. Table 4 contains the results about the relationship between the equity REIT and the conditional correlations. As for the correlation between equity REIT and direct real estate represented by the Case & Shiller HPI, we find there is strong impact of the correlation on the equity REIT returns. For example, as shown in the first part of Table 4, when the correlation is negative (the first regime -0.104 to -0.03) the odds are high (about 53% monthly) that investors will only gains of 0.8% monthly which is much lower than the average return of equity REIT (1%, see Table 1). However, as the correlations increase from the first regime to the fourth regime, the expected return of equity REIT also increase from 0.8% to 1.78% accordingly. These findings suggest that when the correlations between equity REITs and unsecuritized real estate is positively higher, the performance of equity REIT is better. The second part in Table 4 indicates that the correlation between equity REIT and S&P 500 has different impact on the equity REIT returns. Contrary to the relationship between equity and direct real estate, here we find that when the correlation to stock is low, the expected gain of REIT is high, except in the fourth regime. However, Figure 3B shows that the

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fourth regime (high correlation with stocks) actually took place only during 1988 1989. In this way, we find that the higher (lower) the relationship between equity REITs and unsecuritized real estate (stock), the better the performance of REITs exhibits. To test whether or not equity REITs is a superior diversifier to the stock market given the correlations between equity REITs and the S&P 500 is time-varying, we calculate the S&P 500 return at the four different regimes of the correlation between equity REIT and S&P 500. The results are presented in Table 5. We find that both the return and sharp ratio of the equity REITs are much better (the 1st and 3rd regimes) or comparable (the 2nd regime) to S&P 500. Considering the fourth regime is really an exception, which is mainly due to the stock market crash of 1987, our findings suggests that although the correlations between equity and S&P 500 returns are time-varying, the equity REIT is still persistently a superior diversifier to the S&P 500 portfolio. However, the relationships between the correlations and the future returns in mortgage REITs and hybrid REITs are mixed. Table 6 reports the results of correlations impact on the mortgage REIT. When the correlations between mortgage REIT and private real estate are in two extreme regimes: the first regime and the fourth regime, the expected gains are much higher than the average mortgage REITs. Table 7 present the results of correlations impact on the hybrid REIT. However, one interesting finding is that when the correlation between REIT and S&P 500 is in the first regime (lowest correlation), whatever equity REIT, mortgage REITs or hybrid REIT, the return in next month are always highest in all four regimes. This implies that the lowest conditional correlations between REIT and stock markets are a good predicator for the best future returns in REIT. At last, it needs to be mentioned that we found that all the above observations are still robust when one moves to quarterly data. Conclusion

This paper utilizes the AG-DCC GARCH model to explore correlation dynamics between REITs and other two important assets: unsecuritized real estate and stock returns. While a growing body of literature has shown both equities and bonds exhibit asymmetry in conditional correlation, however, this study finds little asymmetry in the dynamic conditional correlations among REIT, direct real estate and stock returns. Using the monthly data of REITs, direct real estate and stock returns, this paper finds the time-varying conditional correlations in REITs can be explained by the -13-

macroeconomic variables. Since the correlations are the main component of risk, this paper also investigates whether the future REIT return is affected by the correlations between REITs and stock returns/underlying direct returns. Although the patterns are distinguishable for different type of REITs, generally there is strong relationship between conditional correlations and future returns. Interestingly, we find that when the correlation between REITs and S&P are lowest, the future performance of REITs is best. For equity REITs, there exist strong relationships between correlations and future returns: the higher (lower) correlation between equity REIT and direct real estate is, the higher (lower) the future returns of equity REIT. Our results have important economic motivations and implications. First, this paper offers the direct evidence about the time-varying diversification power of REIT stocks in a mixed-assets portfolio. Moreover, it concerns the potential integration of REIT, direct real estate, and stock markets and the possibility of including information about conditional correlations to design more optimal portfolio using REITs assets. Second, our findings also build upon the literature dealing with REITs the “hybrid” risk characteristics and return predictability using conditional correlations with underlying real estate and stocks return. Moreover, our findings give the first analysis of the macroeconomic impacts on the dynamics in the conditional correlations and volatilities in REITs. Finally, we find that although the correlations between equity and S&P 500 returns are time-varying, the equity REIT is still persistently a superior diversifier to the S&P 500 portfolio since 1990.

Reference

Bollerslev T. “Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH approach.” Review of Economic and Statistics, 72(1990), 498-505. Bollerslev T., Chou, R. Y. & Kroner, K. F. “ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence.” Journal of Econometrics, 52 (1992), pp. 5-59. Booth, G. G., T. Martikainen, and Y. Tse. ‘‘Price and Volatilities Spillovers in Scandinavian Stock Markets.’’ Journal of International Money and Finance, 21(1997), pp. 811–823.

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Bruggemann, R. and Lutkepohl, H. Lag selection in subset VAR models with an application to a U.S. monetary system, in R. Friedmann, L. Kn¨uppel and H. L¨utkepohl (eds), Econometric Studies: A Festschrift in Honour of Joachim Frohn, LIT Verlag, M¨unster, (2001). pp. 107–128. Campbell, J.Y. and R.J. Shiller. “Stock prices, earnings, and expected dividends.”Journal of Finance, 43(1988):pp.661-676. Cappiello L., Engle, R.F. and K. Sheppard. “Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns.” Journal of Financial Econometrics, vol. 4(4) (2006), pp.537-572. Chen, J. and R. Peiser, “The Risk and Return Characteristics of REITs—1993–1997.” Real Estate Finance, (Spring, 1999), pp. 61–8. Christiansen, C. ‘‘Macroeconomic Announcement Effects on the Covariance Structure of Government Bond Returns.’’ Journal of Empirical Finance, 7 (2000), pp.479–507. Clayton, J. and G. MacKinnon, “The Time-Varying Nature of the Link between REIT, Real Estate and Financial Asset Returns.” Journal of Real Estate Portfolio Management, 7:1 (2001), pp.43–54. Clayton, J., and G. Mackinnon. “The Relative Importance of Stock, Bond and Real Estate Factors in Explaining REIT Returns.” Journal of Real Estate Finance and Economics, 27:1(1999), pp.39-60. Corgel, J., W. McIntosh and S. Ott, “Real Estate Investment Trusts: A Review of the Financial Economics Literature.” Journal of Real Estate Literature, 3 (1995), pp.13– 43. Engle R. F. “Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models.” Journal of Business and Economic Statistics, 20(2002), pp.339– 350 Engle R. F. and K. Sheppard. “Theoretical and Empirical Properties of Dynamic Conditional Correlation MVGARCH.” Working Paper No. 2001–15, (2001) University of California, San Diego. Fama, E.F. and K.R. French, “Business conditions and expected returns on stocks and bonds.” Journal of Financial Economics, 25(1989): pp.23-49. Ghosh, C., M. Miles and C. F. Sirmans, “Are REITs Stocks?” Real Estate Finance, (fall, 1996) pp. 46–53. Glosten, L. R., R. Jagannathan, and D. E. Runkle. “On the Relationship Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48 (1993), 1779–1801.

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Goetzmann, W. N., “The Single Family Home in the Investment Portfolio.” Journal of Real Estate Finance and Economics, (1993), 6, pp.201–22. Gyourko, J. “Understanding Commercial Real Estate: Just How Different from Housing Is It?” NBER Working Paper No. 14708 (2009). Hartzell, D. J., H. M. Stivers, M. K. Ludgin and T. J. Pire, “An Updated Look at Constructing a Public and Private Real Estate Portfolio.” Real Estate Finance, (1999, Summer), pp.49–57. Karolyi, G.A., and A. Sanders. “The Variation of Economic Risk Premiums in Real Estate Returns.” Journal of Real Estate Finance and Economics, 17(1998), pp. 245262. Liang, Y. and W. McIntosh, “REIT Style and Performance.” Journalof Real Estate Portfolio Management, (1998), 4:1, pp.69–78. Liang, Y., W. McIntosh and J. R. Webb, “Intertemporal Changes in the Riskiness of REITs.” Journal of Real Estate Research, (1995), 10:4, pp.427–43. Ling, D., and A. Naranjo. “Economic Risk Factors and Commercial Real Estate Returns.” Journal of Real Estate Finance and Economics, 14(1997), pp. 283-307. Mueller, G. R., K. R. Pauley and W. K. Morill, “Should REITs Be Included in a Mixed-Asset Portfolio?” Real Estate Finance,(1994, Spring), pp. 23–8. Mull, S. R. and L. A. Soenen, “U.S. REITs as an Asset Class in International Investment Portfolios.” Financial Analysts Journal, (1997), pp.55–61. Nelson, D. B. “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica, 59(1991), pp.347–370. Peterson, J., and C. Hsieh. “Do Common Risk Factors in the Returns on Stocks and Bonds Explain Returns on REITs?” Real Estate Economics, 25(1997), pp.321-345. Scruggs, J. T. “Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach.” Journal of Finance, 53(1998), pp.575–603. Seck, D. “The Substitutability of Real Estate Assets,” Real Estate Economics, 24(1996), pp.75-95. Seiler, M., J. R. Webb and F. C. N. Myer, “Diversification Issues in Real Estate Investment.” Journal of Real Estate Literature, (1999), 7, pp. 163–79. Seiler, M. J., J. R. Webb and F. C. N. Myer, “Can Private Real Estate Portfolios Be Rebalanced Diversified Using Equity REIT Shares?.” Journal of Real Estate Portfolio Management, (2001), 7:1, pp. 25–41.

-16-

Torous, W., R. Valkanov and S. Yan. “On predicting stock returns with nearly integrated explanatory variables.” Journal of Business, 77(2005): pp. 380-403. Tse, Y.K., and Tsui, A.K. “Multivariate Generalized Autoregressive Conditional Heteroskedasticity Model with Time-varying Correlations.” Journal of Business and Economic Statistics, 20(3), (2002), pp. 351-362. Webb, J. R., R. J. Curcio and J. H. Rubens, “Diversification Gains from including Real Estate in Mixed-Asset Portfolios.” Decision Sciences, (1988), 19:3, 434–52.

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Figure 1 The Performance of REITs, Real Estate and Stocks Returns FTSE NAREIT Equity REITs 12000

4000

10000

Total Return

Total Return

FTSE NAREIT All REITs 5000

3000 2000 1000 0

8000 6000 4000 2000 0

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

Year

FTSE NAREIT Mortgage REITs

FTSE NAREIT Hybrid REITs 2500

Total Return

Total Return

1500

1000

500

0

1500 1000 500 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

Year

Case&Shiller HPI

S&P 500 2000

Total Return

Total Return

2000

0

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

250 200 150 100 50

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

1500 1000 500 0

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

-18-

Figure 2: Conditional Volatility of REITs, Direct Real Estate and S&P 500

-3

7

x 10

FTSE NAREIT All REITs

-3

6

5 4 3

Year

FTSE NAREIT Mortgage REITs

FTSE NAREIT Hybrid REITs Volatility

Volatility

0.02

0.005

x 10

0.01 0.005

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

Year

Case&Shiller HPI

S&P 500 0.01 0.008

Volatility

0.8

Volatility

0.015

0

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

-3

0.6 0.4 0.2 0

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

0.01

1

3

1

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

0.015

0

4

2

2 1

FTSE NAREIT Equity REITs

5

Volatility

Volatility

6

x 10

0.006 0.004 0.002 0

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Year

-19-

Figure 3A: Dynamic Correlation for the REITs to Direct Real Estate

0.5 FTSE NAREIT All REITs-Case&Shiller HPI FTSE NAREIT Equity REITs-Case&Shiller HPI FTSE NAREIT Mortgage REITs-Case&Shiller HPI FTSE NAREIT Hybrid REITs-Case&Shiller HPI

Correlation

0.25

0

-0.25

88

89

90

91

92

93

94

95

96

97

98

99

00

01

02

03

04

05

06

07

08

Year

Figure 3B: Dynamic Correlation for the REITs to S&P 500

0.75

Correlation

0.5

0.25

FTSE NAREIT All REITs-S&P 500 FTSE NAREIT Equity REITs-S&P 500 FTSE NAREIT Mortgage REITs-S&P 500 FTSE NAREIT Hybrid REITs-S&P 500 0

88

89

90

91

92

93

94

95

96

97

98

99

Year

-20-

00

01

02

03

04

05

06

07

08

Table 1 Descriptive Statistics of the Respective Series 1987-2008

Composite REITs Panel A: Descriptive Statistics Mean 0.0078 Median 0.0097 Standard Deviation 0.0381 Minimum -0.1656 Maximum 0.095 Skewness -0.8019 Kurtosis 5.349 Sharpe Ratio 0.2047 Panel B: Correlation Matrix Composite REITs 1 Equity REITs Mortgage REITs Hybrid REITs S&P 500 Case&Shiller HPI

Equity REITs

Period Jan 1987 to May 2008 Mortgage Hybrid S&P 500 REITs REITs

Case&Shiller HPI

0.0092 0.0108 0.0391 -0.1653 0.1038 -0.7432 5.2506 0.2352

0.0027 0.0098 0.061 -0.2758 0.1325 -1.475 7.4193 0.0443

0.0032 0.0084 0.0523 -0.2249 0.1928 -0.9303 6.9362 0.0612

0.0068 0.0111 0.0428 -0.2454 0.1238 -1.1532 7.7786 0.1589

0.0041 0.0047 0.008 -0.0285 0.0227 -0.6923 4.6088 0.5125

0.9849 1

0.6035 0.5120 1

0.6873 0.6312 0.6519 1

0.4423 0.4500 0.3246 0.3497 1

0.0617 0.0619 0.0604 0.1355 -0.0154 1

Panel A in this table reports summary statistics for the 6 indexes returns used in this paper. The standardized skewness and kurtosis are the skewness and kurtosis of the returns standardized by their estimated standard deviation. Panel B reports the unconditional correlations of indexes returns.

Table 2 DCC GARCH models

NAREIT Composite REIT NAREIT Equity REIT NAREIT Mortgage REIT NAREIT Hybrid REIT Case & Shiller HPI S&P 500 Scalar model

ai

bi

gi

0.2114 0.2116 0.2298 0.2245 0.1270 0.1383 0.2068

0.9705 0.9686 0.9709 0.9704 0.8886 0.9762 0.9719

0.0210* 0.0013* 0.0486 0.0299 0.0517* 0.0071* 0.0000

This table reports parameter estimates for asymmetric DCC GARCH models (diagonal and scalar models). *Insignificance at the 5% level

-21-

Table 3 Economic Determinants of Dynamic Correlations Correlations Correlation CreditSpread

INFt

TermSpread

TreasureBillR

Unemployrate

2 adjust

R

Lag 1

EREIT and HPI

EREIT and Stock

MREIT and HPI

MREIT and Stock

HREIT and HPI

HREIT and Stock

0.938***

0.918***

0.969***

0.931***

0.955***

0.957***

Lag 0

---

0.039***

---

---

0.028**

---

Lag 1

---

---

---

---

---

---

Lag 0

---

---

---

---

0.010*

---

Lag 1

0.010***

---

---

---

---

---

Lag 0

---

-0.011**

---

-0.009**

---

---

Lag 1

---

---

---

---

---

---

Lag 0

---

---

---

---

-0.021*

---

Lag 1

---

---

---

---

0.020*

---

Lag 0

---

---

---

---

---

---

Lag 1

---

0.013**

---

0.008***

---

0.003**

0.8906

0.9384

0.9269

0.8989

0.9556

0.9318

Notes: 1. EREIT, MREIT and HREIT represent the equity REIT, mortgage REIT and hybrid REIT, respectively; HPI denotes the Case & Shiller housing price index; Stock denotes the S&P 500 stock index. 2. Significance at the 10%, 5% and 1% level is denoted with one, two and three asterisks, respectively. And --- denote zero restriction is posed in this coefficient. The R2adj goodness of fit measure is also displayed.

-22-

Table 4 Relationship between Equity REIT Returns and Conditional Correlations (Monthly Data: Jan, 1987- May, 2008) Correlation between Equity REIT and Private Real Estate (Case & Shiller HPI) Correlation % Chance % Chance If Up Regime Range Up Month Down Month Avg Gain 1st -0.104 - -0.030 47.37% 52.63% 4.35% nd 2 -0.030 - 0.043 61.39% 38.61% 3.11% rd 3 0.043 - 0.116 64.71% 35.29% 3.21% 4th

0.116 - 0.190

62.50%

37.50%

Correlation between Equity REIT and Stock (S&P 500) Correlation % Chance % Chance Regime Range Up Month Down Month 1st 0.244 - 0.365 67.57% 32.43% nd 2 0.365 - 0.486 61.36% 38.64% 3rd 0.486 - 0.607 54.17% 45.83% th 4 0.607-0.728 55.26% 44.74%

If Down Avg Loss -2.39% -2.51% -2.68%

Expected Gain/Loss 0.80% 0.94% 1.13%

Volatility Next Month 4.33% 3.59% 3.56%

Sharpe Ratio Next Month 0.1072 0.1730 0.2274

6.50%

-6.08%

1.78%

7.53%

0.1592

If Up Avg Gain 3.30% 3.58% 3.42% 2.71%

If Down Avg Loss -2.46% -3.05% -2.52% -1.60%

Expected Gain/Loss 1.43% 1.02% 0.70% 0.78%

Volatility Next Month 3.51% 4.11% 4.08% 3.09%

Sharpe Ratio Next Month 0.3186 0.1657 0.0876 0.1598

* Risk free rate is assumed to be 3%(annual)

-23-

Table 5 Relationship between S&P 500 Returns and Conditional Correlations Correlation between Equity REIT and Stock (S&P500) Correlation % Chance % Chance Quartile Range Up Month Down Month

If Up

If Down

Expected

Volatility

Sharpe Ratio

Avg Gain

Avg Loss

Gain/Loss

Next Month

Next Month

1

0.244 - 0.365

48.65%

51.35%

2.81%

-4.71%

-1.05%

4.59%

-0.3039

2

0.365 - 0.486

66.67%

33.33%

3.05%

-2.78%

1.11%

3.56%

0.2209

3

0.486 - 0.607

64.58%

35.42%

3.05%

-4.21%

0.47%

4.95%

0.0186

4

0.607 - 0.728

63.16%

36.84%

3.87%

-2.68%

1.46%

4.03%

0.2792

* Risk free rate is assumed to be 3%(annual)

-24-

Table 6 Relationship between Mortgage REIT Returns and Conditional Correlations (Monthly Data: Jan, 1987- May, 2008)

Correlation between Mortgage REIT and Private Real Estate (Case & Shiller HPI) Correlation % Chance % Chance If Up Regime Range Up Month Down Month Avg Gain 1st 2

If Down Avg Loss

Expected Gain/Loss

Volatility Next Month

Sharpe Ratio Next Month

-0.110 - -0.024

67.57%

32.43%

4.53%

4.44%

1.62%

5.22%

0.2315

nd

-0.024 - 0.062

53.42%

46.58%

3.54%

3.99%

0.03%

5.23%

-0.0662

rd

0.062 - 0.150

63.27%

36.73%

4.78%

6.98%

0.46%

7.36%

-0.0102

th

0.150 - 0.230

65.22%

34.78%

4.88%

5.37%

1.31%

6.85%

0.1094

If Up Avg Gain 5.87%

If Down Avg Loss 3.92%

Expected Gain/Loss 2.37%

Volatility Next Month 5.47%

Sharpe Ratio Next Month 0.3629

3

4

Correlation between Mortgage REIT and Stock (S&P 500) Correlation % Chance % Chance Regime Range Up Month Down Month 0.148 - 0.273 64.29% 35.71% 1st 2nd

0.273 - 0.398

60.44%

39.56%

4.05%

4.60%

0.63%

5.87%

0.0319

rd

0.398 - 0.523

61.11%

38.89%

3.73%

5.43%

0.16%

6.00%

-0.0434

th

0.523 - 0.648

45.24%

54.76%

4.69%

3.48%

0.22%

5.62%

-0.0332

3

4

* Risk free rate is assumed to be 3%(annual)

-25-

Table 7 Relationship between Hybrid REIT Returns and Conditional Correlations (Monthly Data: Jan, 1987- May, 2008) Correlation between Hybrid REIT and Private Real Estate (Case & Shiller HPI) Correlation % Chance % Chance If Up Regime Range Up Month Down Month Avg Gain 1st -0.120 - -0.032 55.77% 44.23% 4.02%

If Down Avg Loss 5.35%

Expected Gain/Loss -0.12%

Volatility Next Month 6.13%

Sharpe Ratio Next Month -0.0901

2nd

-0.032 - 0.054

61.67%

38.33%

2.76%

2.74%

0.65%

3.91%

0.0830

rd

0.054 - 0.141

56.36%

43.64%

3.83%

4.11%

0.37%

5.08%

-0.0027

th

0.141 - 0.228

60.71%

39.29%

4.80%

5.24%

0.86%

7.39%

0.044

If Up Avg Gain 4.80%

If Down Avg Loss 2.26%

Expected Gain/Loss 2.69%

Volatility Next Month 4.52%

Sharpe Ratio Next Month 0.5306

3

4

Correlation between Hybrid REIT and Stock (S&P 500) Correlation % Chance % Chance Regime Range Up Month Down Month 0.096 - 0.243 70.00% 30.00% 1st 2nd

0.243 - 0.390

60.27%

39.73%

3.62%

5.71%

-0.09%

5.99%

-0.0846

3rd

0.390 - 0.538

57.98%

42.02%

2.89%

3.74%

0.10%

4.86%

-0.0530

4th

0.538 - 0.685

43.48%

56.52%

2.83%

1.98%

0.11%

3.51%

-0.0563

* Risk free rate is assumed to be 3%(annual)

-26-