We apply a multivariate asymmetric generalized dynamic conditional correlation GARCH model to daily index returns of S&P500, US corporate bonds, and their real estate counterparts (REITs and CMBS) from 1999 to 2008. We document, for the first time, evidence for asymmetric volatilities and correlations in CMBS and REITs. Due to their high levels of leverage, REIT returns exhibit stronger asymmetric volatilities. Also, both REIT and stock returns show strong evidence of asymmetries in their conditional correlation, suggesting reduced hedging potential of REITs against the stock market downturn during the sample period. There is also evidence that corporate bonds and CMBS may provide diversification benefits for stocks and REITs. Furthermore, we demonstrate that default spread and stock market volatility play a significant role in driving dynamics of these conditional correlations and that there is a significant structural break in the correlations caused by the recent financial crisis.
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Following a large body of the literature as reviewed below, we investigate dynamic interactions between these asset classes at the aggregate level in this study. Such an investigation is interesting in itself, as investors with passive portfolio management style are most interested in price dynamics of asset classes at the aggregate level. Certainly, within each of these asset classes, there are different subgroups of securities with certain common characteristics that may respond to economic shocks in substantially different manners. Allowing for such heterogeneity within each asset class is obviously an interesting extension of our study. Nevertheless, due to serious limitations of GARCH models when applied to a high-dimensional system (as discussed below), such a task is practically infeasible, particularly given the sample size of this study.
A number of specific criteria apply to construction of the Barclays Capital (formerly Lehman Brothers) CMBS investment grade index: (1) all CMBS securities are rated investment grade by Moody’s (BBB or higher) and offered publicly; (2) all transactions must be private label. No agency transactions will be included; (3) the collateral for each transaction must be new origination; (4) each original aggregate transaction size must be at least $500 million and aggregate outstanding transaction sizes must be at least $300 million; (5) all certificates must be either fixed rate, weighted average coupon (WAC) or capped WAC securities. No floating rate certificates will be included; (6) all certificates must have an expected maturity of at least 1 year.
We choose VAR (1) because it is the optimal lag for all returns based on Schwarz Criterion (SC). The optimal lags based on Akaike Information Criterion (AIC) are typically somewhat longer. We also use these alternative lags to run regressions and find that results are similar.
Furthermore, a potential structural break point (July 31, 2007) can be incorporated in the DCC and AG-DCC models. However, this addition has not significantly improved the goodness of fit, perhaps because the structural break might have been captured by the modeling of time variations in conditional correlations and their asymmetries.
Although there might be alternative dates which can be identified as potential structural break points and there are also techniques to search for unknown break points, the feedback from the industry suggests that the crisis began to have a substantial impact on various securities markets since July 31, 2007.
According to Chan et al. (2003), during the period from 1990 to 2000, the total debt to total capital ratio is 48% for equity REITs and 65% for mortgage REITs and the total debt to market cap ratio is 42% for equity REITs and 52% for mortgage REITs.
A variety of diagnostic tests are conducted on the standardized residuals from the VAR-AG-DCC-GJR-GARCH model. Although the skewness and kurtosis are still significantly different from zero, the values of kurtosis are much smaller than those of asset returns. Ljung-Box Q tests show that autocorrelations of the standardized residuals are insignificant at the 1% level and that autocorrelations of the squared standardized residuals are either insignificant or at least much weaker than those of asset returns. LM tests suggest no remaining ARCH effects in the standardized residuals for general financial markets but not for securitized real estate markets. Overall, the results (available on request) suggest that the estimation of the VAR-AG-DCC-GJR-GARCH model leads to a better fit of the data but still leaves room for further improvement.
Noteworthy, there are far fewer mortgage REITs forming the index than equity REITs. Furthermore, components of the mortgage REIT index are very heterogeneous: Some are mortgage lenders; some are MBS/CMBS investors. Such data limitations could lead to less robustness of our finding regarding the mortgage REIT index.
The linear time-trend coefficients for the three significant cases are 4.9 × 10−6 at the maximum. By multiplying the sample size (2320), the increase of these correlations over time is no more than 0.01 over the study period, which is small. It suggests that the trending behavior is not a major driving force of conditional correlation movement, particularly compared to macroeconomic variables under consideration.
One might also consider using the system estimation methods such as SUR and GMM. Although SUR in general is more efficient, its efficiency would be the same as separate estimation of individual OLS regressions in the case that all regressions in the system have identical independent variables. Furthermore, as our OLS regressions are also conducted following Newey and West’s (1987), the results probably would remain qualitatively unchanged compared with applying GMM to a system of linear regressions. Finally, we also conduct unit root tests on the residuals from these regressions. While the variables used in the regressions are persistent, the augmented Dickey-Fuller tests reject the null hypothesis of a unit root for all regression residuals, which suggests the stationarity of these regression residuals and thus nonexistence of the spurious regression problem.
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We gratefully acknowledge helpful comments from Warren Bailey, Amitabh Godha, Qiao Liu, Christopher Schwarz, Ko Wang, session/seminar participants at Sun Yat-Sen University, Hunan University, 2010 Midwest Finance Association annual meeting, 2010 China International Conference in Finance, 2010 Global Chinese Real Estate Congress annual meeting, and 2010 Asian Real Estate Society annual conference. An earlier version of this paper was awarded the 2010 Global Chinese Real Estate Congress Best Paper Award. Extensive comments from an anonymous referee have greatly improved the paper. Zhou acknowledges the financial support of a direct grant from the Research Grants Council of the Hong Kong Special Administration Region, China (Project No. Chinese U 2070446).
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Yang, J., Zhou, Y. & Leung, W.K. Asymmetric Correlation and Volatility Dynamics among Stock, Bond, and Securitized Real Estate Markets. J Real Estate Finan Econ 45, 491–521 (2012). https://doi.org/10.1007/s11146-010-9265-0
- Dynamic conditional correlation
- Macroeconomic variables