1
Study the Time Varying Risk Exposures
of US REIT
By
Zhang Ying (10429719)
Supervisor: Erasmo Giambona
September 2013
University of Amsterdam
Amsterdam Business School
Master in International Finance
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Abstract
This study examines the shifting risk exposures of REIT from 1994 to 2012. The linear regression model is employed to identify the linkages in the specific time range, and the dynamic conditional correlation model is used to prove the found connections. The main finding is that in the short term, the private real estate market factor has little explanation power for the volatility of REIT, but in the long run it shows a similar return to REIT. The volatility of REIT is caused by the Fama-French risk premiums. The “modern REIT” effect does not sustain after 2000, as the correlation to the stock market or the large cap stock start to rise again. In the 2008 financial crisis period the conditional correlation remains high, which may partially ascertain the observation of the beta puzzle or the asymmetric correlation.
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Table of Content
1. Introduction ………...………. 4 2. Literature Review………...…….. 8 3. Data………... 13 4. Methodology ………….……….………..165. Empirical results and discussion ………..………..……….18
6. Further study—Dynamic conditional correlation model……….….. 23
7. DCC graph and discussion ………..…. 25
8.The DCC Model further discussion with literature review...…..……….. 28
9. Conclusion ……….……. 31
10. Appendix ……….…..32
11. References……….33
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Introduction
National Association of Real Estate Investment Trust (NAREIT) reports that total market capitalization of REIT reaches 700 billion in 2013, representing 1 trillion corresponding real estate assets holdings. REIT has provided the channel for all income level investors to get the real estate exposure. As the REIT market continues to grow, institutional investors are becoming more comfortable in this form of real estate investment (Willoughby, 1997). This increase in institutional investment in the REIT market is facilitated by the tax reform act in 1993. Before the modification, an investment plan from the pension firm is treated as investment from an individual, even if the pension plan has many participants. However, to be qualified as REIT, more than 50% of the shares cannot be owned by five or fewer individuals. Because of this 5/50 rule, pension investment in REIT is restricted. The new tax act entitles REITs to be an entity of many participants. Thus, the tax reform permits more institutional investment without jeopardizing the trust's tax-favored status (Glascock, Lu and W.SO, 2010). The consequence agreed by the academic world is the so called “modern REIT era” that the correlation to other financial assets changed after the tax reform. Generally it can be a decreasing relation to the stock market and the increasing association to the private real estate. However, since the conclusion is mostly found in the literature in 1990s, it is necessary to assess the relation in the new environment after 2000. In addition to the improvement in the regulation environment, the macro-economic evolvement and some important historical events such as financial crisis can influence the linkages
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among asset classes. Therefore this thesis divides the time horizon 1994-2012 into 3 sub-period, 1994-2000, 2001-2007, and 2008-2012. The division of time considers the traditional “modern era” 1994-2000, and the financial crisis time 2008.
Since the REIT is invented in the 1960s, statistical and econometric models have been used to analyze return and risk characteristics. The CAMP model argues that in the very long run idiosyncratic risk is not priced, as in the long run equilibrium only the systematic risk determines the corresponding required return in a perfectly diversified portfolio. The beta in the model tells the sensitivity to the change of total market and the risk at the same time. However, the CAMP model is not perfect as it make strong assumptions that investors make the same rational decisions with the same amount of information. Therefore multifactor models specifying the potential imperfections of the market or describing the short term effect are more popular. The additional risk premiums mainly refer to the literature of Clayton and Mackinnon (2003), which are the small cap value index returns and the private real estate returns. They emphasize that this may not be an equation to explain the relationship in the very long run with economic meanings, but a statistically significant model to describe the short term dynamic relations.
In this thesis, the NCREIF Transaction Based Index is used to represent the private real estate. Earlier researches have various unsmoothing models to get the NCREIF returns, and this thesis may first implement the NCREIF TBI published by NCREIF in 2011. The linear regression test shows the private factor is statistically insignificant in the total sample to explain the REIT returns. It might have a higher effect on the return in the
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booming times than in a crisis period. Nevertheless, from the basic statistics, it demonstrates similar returns to REIT, low volatility and low correlation, making it an inevitable allocation in the real estate portfolio.
The small cap value factor is found significant in the overall sample period. The small cap value return shows a quite high correlation to the REIT return during the financial crisis, which may partially prove the phenomenon “beta puzzle” or the asymmetric correlation. The beta puzzle means the REIT index returns have a higher correlation to the stock market when the stock market drops into a crisis, but a lower correlation when the stock market is in a booming period.
In order to give a more clear view of the above time varying relation, the bivariate DCC-GARCH (1, 1) model is implemented to confirm the findings. The dynamic conditional correlation model is raised by Engle in 2002, and it has important implications to analyze the shifting correlations among asset classes. It denies constant correlation assumption and gives a continuous picture of the correlation pattern. While many literatures have used the DCC model to find the changing correlations between financial markets such as bonds and stocks, the application to the real estate sector is far less. The DCC graph further ascertains the finding that, the private real estate index NCREIF TBI has rather limited the ability to influence the volatility of REIT in the short run, but converges with REIT returns in the long run. The small cap value factor affects the volatility of REIT more significantly, leading to the asymmetric volatility of REIT returns.
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The contribution of the thesis can be that the regression models and conditional correlation models are used to cross prove the empirical findings. The regression models have the advantage to estimate the betas, and to give an estimation of the significance of the risk factors. But the regression model only gives an average value of the risk factor, but not the whole trend of it. The DCC model complements the regression model that shows the graph of the dynamic correlation patterns scientifically. The findings in the regression can be further explained by the DCC model. The DCC model has its important implications for the portfolio management and the risk management. In the portfolio, the private real estate shows an obvious advantage especially after 2000. The REIT shows weak protection of the stock portfolios, especially in a financial crisis. It may have an even lower proportion in the portfolio where small cap stocks have already been allocated.
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Literature review
The securitization revolution in the US has led to the development of the real estate derivatives, which are the REIT on the equity side and the CMBS markets on the debt side. They build a link between the private market (Main Street) and the wider capital market (Wall Street). REIT mainly engages in the management of the commercial properties, so rent is the main part of income. In the micro economic view, REITs can be regarded as operative firms, and the economic profits are created from the entrepreneur business activities, but in the macro level, real estate as a basic asset class has unique characteristics compared to other asset classes such as equity and bonds (Geltner et al, 2008). The complex in nature make REIT exposed to both the real estate fundamental factors and the macro capital market factors. In a portfolio management view, the REIT truly provides an investment vehicle for getting exposure to the real estate, but the diversification effect has been debated in the last several decades. Generally the effect may depend on the time horizon of the investment. In the long run the performance may align with fundamental values, but in the short run the performance seem to involve some equity characteristics. Previous studies before 2000 have examined the REIT return primarily in two ways. The first one uses the risk factors models, and the second one attempts to build a link by the direct data analysis, such as Pagliari (2005). In the recent study until 2012, time series models like co-integration tests and multivariate GRACH models are more often applied.
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In the risk factor based analysis, the studies often adopt the multi-factor models. The first important point is that risk factor exposures of REIT shift in the last several decades. Before 1990, the research (Peterson and Hseih, 1997) shows that the REITs are only influenced by the stocks and bonds returns, and real estate market has little or no role in explaining the return. In the later periods, more findings start to support that the private and public market are closely related. The unsmoothed NCREIF index is used as the private factor and it is found to be significantly positively correlated with the NCREIT index (Clayton and Mackinnon, 2000). The explanation is that as the market is becoming more efficient in nature, the information about the REIT is more much available to the investors in broad market. The institutional investors in 1993 start to invest in the REIT market, and they might believe the REIT behaves more like real estate in nature, but the individual investors tend to trade REIT shares using the stock market information (Yang, Case Yildrim, 2010). It is also addressed as a maturation process of REIT after 1993, which signifies a potential transition for REIT to reflect more real estate fundamental factors. Another feature described in the maturation process is the correlation with the stocks such as S&P 500 is decreasing after the 1990’s. The bond and the stock market factors to explain the REIT return declined in the later periods.
If all of the transitions including the increasing correlation to private market and decreasing correlation to the stock market are continuous, the correlation feature will make REIT an inevitable investment vehicle to diversify the risk. Nevertheless, it is still uncertain in the future the pattern will remain the same. The market can be cyclical in nature, and in a financial crisis or the market downturn a different correlation may occur.
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Goldstein and Nelling (1999) find that the REIT has higher betas in low-growth economic states and lower beta in the advancing market. Chatrath, Liang and McIntosh (2000) raise three hypotheses to explain this. Firstly, the stock returns in the 1990’s are unusually high, but in the same time periods the REIT correlation to stock is declining. So the low beta is the result of the decay in the REIT-stock relationship. Secondly, the REIT to some extent resemble the payment of bonds, which pays stable cash flows and are less sensitive to some economic factors. The economic boom will create the return spread between the REIT and the stocks. Thirdly, the small capitalization stock factors account for the beta puzzle, as REIT performance resembles the small cap stocks. Their conclusion is that the small cap stock factor is more useful in explaining this issue. The reason of asymmetry of REIT risk exposure is debated by Chiang, Lee and Wisen (2000). They find that if the Fama-French three factor model is used, the “beta puzzle” is not so obvious. The robust test by Clayton also shows that the three factor model supports the using of the small cap value index factor. Therefore in this thesis we will include the small cap value factor as suggested by Clayton.
The performance of REIT in a financial crisis is evaluated by Basse et al (2009) who use the linear co-integration model. They argue the REIT resembles utility stocks before the financial crisis, but in the crisis the relation suddenly breaks. They propose that a structural change happened in that period and a changing correlation may explain the dramatic move. Another paper by Simon and Lon Ng (2009) examines the tail behavior and dependence of REIT and stock returns. They use mixed copulas approach in the models and argue that in the extreme market situations, the co-movement should be
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discovered, rather than just be measured by the beta. The empirical result shows that in the financial crisis period, especially in the days when the market drops most, the investment in the REIT can protect the stock market portfolios. In the data selection they use the daily basis data, and their ideas may not be proved in this thesis as the quarterly data is used, but at least they give an important observation. The unstable risk factors fact is also found by Okunev, Wilson (1997). The Engle Granger co-integration test indicates no evidence of linear integration, but a fractional non-linear co-integrative relationship statistically significant. That shows that a potential long term relationship exists, but in a nonlinear way. Okunev, Wilson and Zurbruegg (2000) test the causal relationship between the REIT market and stock market, using the linear causality tests and the non-linear tests. The linear test shows a structural break after the 1989 period. In the 1972-1989 period, the result shows the equity REIT market causes the changes in the S&P 500. However, during the 1989-1998 period a noticeable change in the relationship occurs, where at 15 percent significance, return in stock market cause changes in real estate returns, plus no significant influence from real estate to stock market. The non-linear test shows no structural breaks, and a clear causal relationship shows shocks flow from stock market to the real estate market, with a lag period of about 6 months. Given the non-linear observation and changing relationship in the linear function, the way stock market influences the real estate market remains to be discussed. Allen, Madura and Springer (2000) use a two factor model to identify how REIT is influenced by the stock market return and interest rate, and then examine what are the internal characteristics influenced by these two environment factors. The study
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shows, although the interest factor is significant, its relation to the internal characters like financial leverage, specialization and management is not clear. The stock market factor is statistically insignificant in the time period 1993-1997.
The method to investigating the REIT and the private real estate returns directly is sufficiently discussed by Pagliari et al (2005). The research compares the return characteristics of private index NCREIF and public index NCREIT after three necessary adjustments. The first adjustment is the property mix of the index, as different properties have various return and risk characteristics. The core property categories are retained in the comparison, reducing the volatility for NCREIT but increasing its return. Then the NCREIT is de-leveraged, leading to a 2.4% decrease in return, but 5.5% in lower volatility. At last the NCREIF index is adjusted in category and unsmoothed. The finding is that the difference in return and volatility of both indexes are not statistically significant. The finding however cannot deny that there can be temporal gaps between the two returns. This can be reasons of the market trading noise or the systematic behavior reasons in the short run. In the long term, the passage reflects that the difference in 1993-2001 has substantially narrowed compared to the 1980s, and the two platforms may only differ in the transaction cost, agency cost and management capabilities. This research avenue confirms the necessity to put the private real estate market in the REIT risk factor exposures.
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Data
It is commonly known that the private real estate index NCREIF has the temporal lag bias. In fact most real estate indexes suffer from two errors: the random error and the temporal lag bias. The random error can be eliminated by large size of sample. If we assume all the observations have a normal distribution, in that situation all the random errors will cancel each other to get the mean. The second error is the temporal lag bias, and this error is the result of using the old data, a compromise if not enough current transactions are available. The data itself is auto-correlated in nature and thus has to be processed to use. The two type of errors have a trade-off when the data is collected. In the micro level appraisal, when the transaction is not enough, the sellers may need to reach back relatively far in time to find the similar real estate transactions, creating the time lag bias. Normally this decision is still better than use the current data, which is not sufficient. It can also be the behavioral reason that the appraiser tend to be conservative in adjusting the changes, but the conservative is necessary to reach a reasonable price prediction (Geltner, 2008). In the macro level appraisal or the aggregate level, such as the index level, the random error is hugely decreased as the large sample scale, without increasing the temporal lags, however, the temporal bias can still exist as the pure behavioral reason just discussed.
NCREIF index is an example of this temporal lag error series, and the moving average in nature does not just comes from the micro appraisal levels, but also from the stale appraisal effect. The stale appraisal effect is that not all properties in the index are
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valued at the same time. Some valued property prices in the index maybe be used in the next several periods. This determines the moving average series in nature explicitly.
The return series formulas shows that the return is a moving average time process, which signifies the beta is lower for the index, as the coefficient for current return at time is less than zero. Therefore we can explain the volatility is consistent lower than REIT in the last 3 decades.
Geltner proposes a way to de-auto-correlate this series, and it applies the reverse-engineering model. L is the number of years of lag on the average level for all the years. This can be estimated by the historical evidence or by studying the normal appraiser behavior. It may not change so dramatically so the average is believed and used. From
Fisher and Geltner (2000), the L is usually 1.5, so the parameter is 0.4. However, it is an ad hoc process that can only be used to the annual data basis, when the random error is quite small to neglect. In this thesis that is not applicable as we try to use the quarterly data.
In an effort to get the monthly data, Anderson et al. (2006) used another approach to get the NCREIF data. They use the Green Street---REIT Net Asset Value data combined
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with REIT price series to find the average price premium first, and then they apply the premium to calculate the market wide REIT Net Asset Value data series. The percentage change in this market wide NAV series is used as the return of un-securitized real estate. The potential concern in this data is that the NAV are estimated values, and that is not a directly observable from the market.
In 2011 the NCREIF starts to publish the NCREIF Transaction based index, which is used in this thesis. This index is previously published by MIT that uses the NCREIF data as the basis statistic and does a hedonic regression to unsmooth the data. Now the academic product is slightly modified to publish the NCREIF TBI, which is more comparable to the stock and bond indexes (Geltner, 2011). The small cap value index refers to the Wilshire small cap value stock index, and it provides the monthly returns of this time series.
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Methodology
The methodology in this part mainly refers the method adopt by Clayton and Mackinnon (2003), in which they confirm the necessity of the small cap value index. As discussed in the previous session, the REIT can be viewed as a hybrid of stocks and real estate, and the risk factors exposure might shift in the last three decades. This thesis will use a three factor model, in which the return of REIT is specified as a linear function of the stock return and private real estate factors as follows:
r
REIT=
+
r
SP+
r
RE+
r
SM+
TThe rsp is the return of the stock market (e.g S&P 500 or the CRSP total market index), rRE
is the return of the private real estate market index, which is the NCREIF TBI in this case. rSM is the return of small cap value stocks, and we use the Wilshire small cap value index.
The s measures the sensitivity of REIT returns to other index returns and the includes
factors not explained by the three factors, and it also includes the idiosyncratic risk in this model.
The model tries to find the risk factors that REIT returns are exposed to but not the factors that REIT returns is driven by. The dependent and independent factors in this model are all the index returns, which are aggregate statistics, and a specific causal relationship cannot be found in this model. Many similar researches use the risk factor models to identify which are the most important factors should be included in the model (Clayton and Mackinnon, 2003).
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Considering the problem of multi-co-linearity, which means the independent factors can be highly correlated, we solve it by only inserting the “pure effect” in the regression. In this part we mainly utilize the method from Clayton and Mackinnon, and they orthogonalize the right-hand side variables.
•
r
Small=
+
r
SP+
r
RE+
Small(a)
•
r
REIT=
+
r
SP+
Small+
r
RE+
(b)
Because the small cap value factor has a high correlation with S&P 500, in the first equation (a), we do a regression to small cap factor
r
Small on other two variablesr
SP andr
RE. The correlated ingredients can be eliminated and the “pure effects” of small capfactor will be conserved in the
small. Then the pure effect is used in the equation (b). In the empirical results section, the first part will look at the whole time periods from 1980 to 2012. The relative contributions for stocks and real estate are identified. Then the sub-periods are also analyzed in order to find the shifting relationships discussed earlier.18
Empirical results and discussion
Basic Statistics
Full Sample Sub Periods
1994-2012 1994-2000 2001-2007 2008-2012
Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. NCREIF TBI 2.70% 5.60% 3.43% 5.40% 3.47% 4.47% 0.61% 6.92%
REIT 3.13% 10.39% 2.53% 6.06% 3.90% 7.91% 2.90% 16.84% S&P 500 1.85% 8.59% 4.03% 7.22% 0.69% 7.86% 0.44% 10.87%
Small Cap Value 3.09% 10.02% 3.48% 7.85% 3.20% 8.79% 2.37% 14.07%
CRSP 2.41% 9.14% 4.17% 8.04% 1.59% 8.34% 1.09% 11.46%
(Notes: This table shows the means and standard deviations of the index returns. The data is quarterly based data. “NCREIF TBI” is the NCREIF transaction based index return. “REIT” is the Ziman REIT capitalization weighted index return. “S&P 500” is the standard & poor 500 index return. “Small Cap Value” is the Wilshire small capitalization value stock index return. “CRSP” is the CRSP total market index return. The total sample period 1994-2012 is first calculated and the sub period’s statistic is also calculated for comparison. The Ziman REIT index and CRSP data is obtained from the WRDS database. The S&P 500 is downloaded from the FED bank St. Louis official website. The Wilshire small cap value index and NCREIF TBI are from the organization official website. The numbers are given in percent. )
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Correlations to REIT
Full Sample Sub Periods
1994-2012 1994-2000 2001-2007 2008-2012 NCREIF TBI 7.22% 21.61% 20.45% -3.83% Small cap value 80.94% 61.95% 72.98% 92.26% S&P 500 61.21% 18.52% 53.75% 87.12%
(Notes: This table shows REIT return to other index returns. Therefore the correlations are all computed to the REIT return. The total and sub sample periods statistic is calculated for discussion and the numbers are given in percent. The data is quarterly based data. “NCREIF TBI” is the NCREIF transaction based index return. “REIT” is the Ziman REIT capitalization weighted index return. “S&P 500” is the standard & poor 500 index return. “Small Cap Value” is the Wilshire small capitalization value stock index return. )
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Regression Result
Full Sample Sub-Periods
1994-2012 1994-2000 2001-2007 2008-2012 Intercept 0.018 0.014 0.026 0.023 (0.027) (0.190) (0.057) (0.165) S&P 500 0.740 0.106 0.525 1.353 (0.000) (0.414) (0.000) (0.000) NCREIF TBI 0.004 0.195 0.270 0.077 (0.973) (0.267) (0.260) (0.742)
Small cap value 1.089 0.695 0.967 1.352
(0.000) (0.000) (0.000) (0.005)
R-squared 0.678 0.505 0.585 0.857
Adjusted R^2 0.664 0.443 0.533 0.830
sample number 76 28 28 20
(Notes: This table summarizes the outcome of the regression rREIT = + rSP + Small+rRE+ .
The numbers in the first part are coefficients “”to the risk factors. The number in the bracket is the P-value of the coefficient. The regression uses the outcome of Eviews 7.0. In the regression equation, is the intercept, is the S&P 500 risk factor coefficient. is for small cap value and is for NCREIF TBI. The R square and adjusted R square are calculated at last. The regression is run on the total sample period and also on the sub sample period. The data is quarterly based data. )
Analyzing the basic statistics, we can see that the NCREIF TBI has the lowest volatility, and that may imply that the data is still subjected to some smoothing effect in the appraisal process. It still gives higher return than the S&P 500, so that the Sharpe ratio of NCREIF TBI is larger. The REIT gives the highest return from 1994, but the variance in
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the return is also the highest. The REIT returns and NCREIF TBI index returns do not differ substantially, which confirms the idea of Pagliari (2005) that in the long run the two indexes show similar result. In the cross correlation table (unconditional correlation), the NCREIF TBI index has a consistent much lower correlation with S&P 500, compared to REIT with S&P 500. This suggests that the REITs and un-securitized real estate returns have significantly different statistical properties in building a portfolio and that the degree of substitutability of REITs for private real estate is quite limited (Fei, Ding, and Deng, 2010).
The correlation table and the regression results clearly shows the time varying nature in S&P 500 risk factor. In the previous studies, a structural change found after the 1993, the so-called REIT market maturation process, that the S&P risk factor is not significant in explaining the REIT returns. This test first demonstrates that the large capital factors are surprisingly disappearing in the 1994-2000 time period, with a P-value 0.4141, after controlling the effect of multicollinearity. Furthermore, the correlation can also prove this finding. The correlation between the S&P 500 and the REIT index is only 18.52% in this time period, the lowest correlation in the three time period. The studies doing the similar researches like Clayton and Mackinnon often choose the time from 1992 to 1998, which does not include the dot.com bubble. In the internet bubble time the returns of REIT index only falls below zero one quarter, but the S&P enters the bear market in the second quarter in 2000 and start to pick up at late 2001. So the different response to this crisis can be an important reason. A similar reason is the Asia financial crisis, when the REIT endures a continuous 5 quarter return below zero, but the S&P is not so
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severely affected. Nevertheless, the lower correlation with S&P seems not a structural change for the REIT risk factors. The relationship to the broad market increases after 2000, and the beta to the large capital firms comes to the 0.5 level.
The NCREIF TBI index is used to represent the exposures to the underlying private real estate market. The index is this test cannot prove to be significant (p-value 0.1) to explain the REIT returns, in the total time period and in every sub time period. In the studies of Clayton and MacKinnon, the real estate factors have been proved to be significant in the time 1992-1998 time range, and this is explained as a signal to build a rational market as the market is more closed to the real estate fundamentals. In this study, the coefficient is insignificant, (with a P-value around 0.25 in 1994-2000). Similar patterns also happened in the time period in 2000-2007, in a similar P-value and a slightly higher coefficient 0.26. The correlation table also proves that the correlation to the REIT index is around 0.2 in both the two time period. This study cannot prove that the NCREIF is statistically significant to explain the REIT returns, but at least it shows that the in the next seven years after 1992-1998, the correlation value is similar. Therefore the 2001-2007 time-span may be summarized as a time with stable real estate factors influence, but increasing large capital market exposure.
The small cap value index is significant in all the three time periods, and the correlation is also the highest in these three periods. That seems to prove the conclusion of Clayton and MacKinnon that most of the volatilities of REIT can be explained by the small factor. The small stock effect is used to explain the “REIT beta puzzle”, which means the small cap factors are more sensitive to the market when the market is going down, and that
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will drive down the REIT returns, but REIT will detach this small cap factors when the market is growing. In our study, the correlation in the 2007 crisis reaches 0.8, partially proving this point.
In considering the effect of the whole model, the R square and adjusted R square statistic increased in the last two decades. The model has the lowest adjusted R-square 0.44 in 1994-2000. It may prove that in this time period the systematic risk including the risk to the small cap factors is quite low, but at the same time the idiosyncratic risk is a large part for the REIT returns. In the recent financial crisis period, this model has a strong R-square of around 85%. The convergence of the indexes in the crisis time may explain a strong correlation between the REIT and broad market. However, this financial crisis shows a different pattern than the last two times, the Asian financial crisis and the dot.com bubble, when in the crisis the indexes did not strongly converge.
As suggested by Case, Yang and Yildirim (2010), the S&P 500 has included the REIT sectors after 2001 and the correlation between the S&P 500 and REIT index can have a sudden increase. Feng et al (2006) proves this by the evidence that after the inclusion of REIT in S&P 500, the beta of REIT to S&P increases from 0.24 to 0.35, on the daily basis data. Ambrose et al. also illustrate this by the sub periods comparison and fond the beta in the sub period increased substantially and the shock is persistent. Therefore it is suggested that the CRSP total market index should be used to eliminate the effect of the sudden increase and to check the de-correlation between REIT and macro market. However, in the regression using the CRSP total market index to substitute the S&P 500, we cannot find the significant difference between the two models in the statistic result,
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as the beta difference is smaller than 0.01 when the macro market is used as the basis. It will be shown in the Appendix 1.
Further Study: Dynamic Correlation Model
In order to illustrate the correlation relationship clear and give a more accurate observation, a dynamic conditional correlation model is employed to demonstrate the linkages among the indexes in the following discussion. The mean-variance optimization models and the traditional market factor models such as CAMP make many assumptions about the return and volatility. They are regarded as constant in doing the portfolio allocations. The problem is that investors have to check the historical data to find the expected values as their only parameters in investment. The expected values may change in the future and are unobservable in nature. Furthermore, to infer the expected value, especially the key variable—correlation is very difficult, as correlations often change as the investment environment change. The second problem is that, as discussed by Case, Yang and Yildirim (2010), even if the unconditional expected values can be found, investors might make superior returns by using a conditional model, as the conditional model will make more accurate prediction than the unconditional ones in the short run. The FLS approaches in the Clayton papers show fluctuating betas to the market, and this gives an idea to find a model to empirically capturing the trend, and in this thesis we use DCC-MVGARCH model.
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In a financial econometric view, the return series may be more difficult to model than the volatility series. The return series are modelled and stimulated using the Browning motion and it is a mean reverting process. The conclusion can be that the price of the index follows a random walk, and sometimes a drift or a momentum is found in the time series, but the momentum is still not so predictable to make abnormal returns, given the irrational behaviors of investors or market sentiment. Therefore we may use the variance models to find more interactions between the real estate market and the broad market.
The literature working on volatilities in REIT and stocks normally applies the GARCH model. It addresses the problem of heteroskedasticity and volatility clustering, which are frequently found in the return time series. Volatility clustering and persistence is a key finding and that builds the basis to empirically model the financial series. It means the large fluctuations yesterday can lead to a large fluctuation tomorrow with high possibilities. The model combines the auto-correlation and moving average process effect in time series to build the general model. So the conditional variance depends on the squared residues (deviation from expected returns) and a moving average of past conditional variances (Engle, 2002). Compared to the rolling basis correlation, the conditional model is more accurate in estimation and prediction, as the correlation rolling assigning equal weight to the historical data, and that does not relate to the clustering nature (Case, Yang and Yildirim, 2010). The other issue is that the window to include in the observation cannot be empirically defined. The chosen period will be
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given equal weight but the unchosen series receives no weight, which can result in a “ghost effect” that a sudden change can happen in the expected volatility.
To extend the GARCH models to the portfolios, the covariance series also follow a GARCH process. The covariance today of two assets will be affected by the return fluctuations of both assets. The models examples are the BEKK and VECH model, and the DCC-MVGARCH model is considered relatively more powerful in explaining the correlated series, by depicting the correlation series in a GARCH process. In this thesis the bivariate DCC-GARCH (1, 1) model is used to find the correlations among the indexes. The DCC model uses the maximum likelihood method to build the models. The models in implementation can be done in two steps; first we will apply the GARCH models to each return series. Then we will use the residues series generated by the univariate GARCH model to the DCC model to find the dynamic correlation and show the graph.
ij=
ij,t/
sqrt(
ii,t)
sqrt(
jj,t)
ii,t= c
i+ a
i
2i,t-k+ b
i
ii,t-k(2)
ij,t= (1-
-
ij+
i,t-1
j,t-1+
ij,t-1(3)
it=
it/
sqrt(
ij,t)
ij,t represents the standardized covariance matrix elements.
it represents the standardized residue elements.
ij is the element in the correlation matrix. In the27
equation (2), the
a,b,c
represents the parameters of the univariate GARCH process.
are the parameters in the covariance GARCH process.DCC graph and discussion
Conditional Correlation between REIT and S&P 500 returns
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Conditional Correlation between REIT and Small Cap Value returns
(Notes: the graphs are made from the Eviews 7.0. They display the dynamic conditional correlations between REIT return and other index returns. The first correlation graph is REIT to S&P 500, the second one is REIT to NCREIF TBI and the third one is REIT to small cap value.The data is quarterly based data. “NCREIF TBI” is the NCREIF transaction based index return. “REIT” is the Ziman REIT capitalization weighted index return. “S&P 500” is the standard & poor 500 index return. “Small Cap Value” is the Wilshire small capitalization value stock index return. )
The graph of conditional correlations demonstrates the changing expected correlations during the sample period 1994-2012. In the correlation graph S&P 500 with REIT, it shows a declining correlation trend until 2000, which gives the same conclusion with the ‘modern period REIT’ betas, but after 2000 it starts to quickly pick up and go back to a level like in 1994, around 0.4. In the recent financial crisis, the correlation has a large jump and reaches the highest level in the sample period, around 0.65. From this map it is difficult to find a structural and permanent change. The big shock of recent financial crisis persists in the pattern, showing no signs of decay. The REIT correlation with CRSP
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has a rather similar pattern. After 2000 a jump happened like the S&P 500, and therefore the sudden increase of the beta (REIT to S&P 500) cannot just be explained by the inclusion of REIT to S&P 500, but also affected by some macro-economic factors.
In the correlation graph REIT with NCREIF TBI, it is found that the correlation fluctuate at a range 0.1 to -0.1 before 2007. In the 2008 crisis the correlation shows a large negative value at -0.4, and then follows a “big V” come back to the highest level at 0.2. For the institutional investors, the lower correlation might provide a hedge by including the private real estate in the property portfolio. The recent increase in the correlation might signify the trend of increasing correlation between public and private real estate, but it cannot be proved in a financial crisis, when all the correlations increase.
The small factor correlation graph resembles the pattern of S&P 500, but the correlation level is always higher. The highest correlation happened at the 2008 financial crisis period, when the conditional correlation reaches 0.8. The graph does not show a clear pattern of the beta puzzle, as the correlation in 2001-2007 is not low, but the total market is increasing at this time.
In a summary, the DCC-GARCH (1, 1) model gives a clearer and more accurate view of the time varying correlations of REIT to other index returns. The REIT “modern area” with the features of increasing correlations to the fundamental factors and declining correlations to the stock market is not obvious after 2000. The REIT correlation to the private index fluctuate in the range from 0.1 to -0.1, with a 0.2 change after the 2008, which means in the short run the private market has a very limited influence on the
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public market return volatility. The correlation to the small cap value stocks is high in the total sample period. The correlation is on average 0.7, and reaches the highest 0.8 in the financial crisis. It suggests that the volatility of REIT in the short term is mainly linked to the stock market factors, especially the small cap value stocks.
The DCC Model further discussion with literature review
The DCC model is more frequently used in the recent researches, and many scholars give comments. Yang, Zhou and Leung (2010) find the asymmetric patterns in the dynamic correlation time series between REIT and the stock market. The asymmetric volatility is tested by the GJR-GARCH model in the correlation series. It is hypothesized that a negative shock can generate a larger influence in the next time period than a positive shock. The return fluctuations, especially the large drops, are mostly attributed to the REIT risk premium factors, which are the Fama-French risk premium. That is in line with the finding that the small-cap factor has the largest explanation power in the volatility. In addition, they find the correlation between the REIT and stock market is high when the default spread is high. Default spread is a macro-economic indicator, and this indirectly proves the high sensitivity to stock market when the market is going down. They also identify and interpret the upward trend after 2000. Besides the reason of inclusion of REIT to the S&P 500, as the REIT Modernization Act (RMA) is published, taxable REIT subsidiaries were created in 2001 to expand the business activities of REITs.
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Changes in the regulations have forced REITs to become more like operating companies. The operating view gives the REIT a value above the NAV, and they will take the business risk too for the growth opportunities (Geltner, 2008).
However, Fei, Ding and Deng (2010) do not find significant asymmetric correlation pattern between REIT and stock. They argue that it can be the reason of market segmentation or hybrid nature in the return and risk of REIT. Little theoretical framework is available to justify the empirical evidence of asymmetric correlations. However, in a further test the link between correlation (REIT, stock) and macro-economic factors, the credit spread, term spread and unemployment rate are found significant at the 5% level or better. The term spread has a negative coefficient and the other two has positive coefficient. Finally, a lower correlation this quarter, can signify a higher return in next quarter for REIT, by showing the conditional expected return.
A study by Zhou and Anderson (2011) exploring the herding behavior in REIT market gives other evidence for the asymmetric correlation from the behavior finance side. Firstly, they find that the herding behavior occurs more often at the declining market than the rising market. Then they illustrate that in the financial crisis the herd start to occur when the market is becoming extremely turbulent. Another important finding is that investors are more likely to herd in the modern era than the pre-modern era, signifying the REIT is switching to the mental category of operative company to some extent.
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Conclusion
This thesis examines the REIT dynamic risk exposures. Combining the finding of the two models, the period after 2000 demonstrates a new trend in the correlation, different from the modern REIT prediction in 1990s. The correlation between the REIT and stock market increases again, and in the financial crisis the two indexes co-move noticeably. The private real estate market has little influence on the short term volatility of REIT, but shows close return in the total sample period. The Fama-French risk premiums (size and book/market ratio) found in 1990s still works to explain the return asymmetric volatilities.
This thesis has limitations. Firstly, due to the issue of data availability, we choose the quarterly data in the research. A quarterly database may reveal lower volatility and correlation compared to the monthly or daily data. Secondly, the thesis cannot relate the findings to the macro-level signals or the micro level firm’s economic rational motivations. Only the fact at the index level is investigated. Finally, without economic theories support, the models have limited capacity to predict the correlation in the long run, but only at very short run.
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Appendix 1 CRSP is used to substitute S&P 500
Full Sample Sub-Periods
1994-2012 1994-2000 2001-2007 2008-2012
C 0.014 0.014 0.022 0.014
(0.069) (0.182) (0.000) (0.363)
CRSP 0.698 0.102 0.518 1.273
(0.000) (0.375) (0.000) (0.000)
Small Cap Value 1.133 0.716 0.987 1.440
(0.000) (0.000) (0.000) (0.002) NCREIF TBI 0.008 0.194 0.249 0.104 (0.951) (0.263) (0.301) (0.654) R-squared 0.683 0.513 0.583 0.860 Adjusted R-squared 0.670 0.452 0.530 0.834 sample number 76 28 28 20
(Notes: This table summarizes the outcome of the regression rREIT = + CRSP + Small+rRE+ .
The numbers in the first part are coefficients “”to the risk factors. The number in the bracket is the P-value of the coefficient. The regression uses the outcome of Eviews 7.0. In the regression equation, is the intercept, is the CRSP risk factor coefficient. is for small cap value and is for NCREIF TBI. The R square and adjusted R square are calculated at last. The regression is run on the total sample period and also on the sub sample period. The data is quarterly based data. )
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Conditional Correlation between REIT and CRSP returns
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