July 2014
European REIT beta stability,
structural breaks and the influence of interest
uncertainty during the 2007-2009 financial crisis
A Master Thesis by: Bsc J.A.M.A. Postma For the title of: Msc in Business Economics
Specialization: double degree: Real Estate Finance and Finance Supervised by: Dr. P.J.P.M. Versijp (Finance)
2
Acknowledgement
I would like to thank my parents, for encouraging me through my complete study period, and Dr. Versijp, who is my thesis supervisor, for all the input and feedback and the pleasant cooperation. I also thank Melline, for her unconditional support in times of stress, and Main Capital Partners and all employees for the useful discussions on the matter of my topic during lunch breaks.
3
Abstract
This paper is written as a combined Master Thesis to graduate at the University of Amsterdam in the fields of Real Estate Finance and Finance.
The topic of Real Estate Investment Trust (REIT) market betas in Europe and the possibility of structural breaks during the 2007-2009 financial crisis is researched in this paper.
Mixed results with different models are found, but the ultimate structural break-test could not confirm a possible structural break in market betas at the beginning of the 2007-2009 financial crisis. The extended study on interest rate uncertainty and the relationship with REIT market betas confirm the formed hypothesis that this relationship is significant and positive during economic recessions. A structural break confirms that this relationship was present at the start of the 2007-2009 financial crisis. However there is a presumption that the relationship fades away over time.
4 Table of Contents Acknowledgement ... 2 Abstract ... 3 Table of Contents ... 4 1. Introduction ... 5 2. Literature ... 6
2.1 REITs, distinctive characteristics ... 6
2.2 REITs in the CAPM ... 8
2.3 REIT betas in a multi-factor model ... 10
2.4 REITs and the relationship towards interest rates ... 11
2.5 (REIT) betas during a financial crisis ... 13
2.6 Summary ... 14
3. Hypothesis and methodology ... 15
3.1 Hypothesis ... 15
3.2 Methodology ... 16
3.2.1 Model ... 16
3.2.2 Regression methodology ... 17
3.2.3 Structural break testing ... 18
3.2.4 Uncertainty in interest rates and REIT market betas ... 20
3.2.5 Summary ... 21
4. Data description and results ... 23
4.1 Data ... 23 4.2 SMB & HML factors ... 23 4.3 Results ... 26 4.3.1 Descriptive statistics ... 26 4.3.2 Regressions ... 28 4.3.3 Rolling regression ... 28 4.3.4 (G)ARCH regression ... 31 4.4 Structual breaks ... 35
4.5 Interest rates vs. market beta ... 39
4.6 Discussion ... 42
5. Conclusion ... 43
6. Literature List ... 44
5
1. Introduction
Stability testing of CAPM betas is an intriguing subject, especially important for portfolio managers and other (institutional) investors. If betas of different investment assets perform a complete random walk, the ability to predict future betas is almost impossible. However if betas are stationary over time, they could be well used for portfolio risk analysis or asset allocation.
Besides this practical use of REIT betas, there is even a broader perspective. Real estate and REITs are considered to have low risk profiles in literature and in the general investment environment. Transferring this general opinion towards the CAPM, a low beta for REITs is expected. Within literature this low beta is found, however quite some reports questions the stability of the (REIT) betas over time and therefore the perceptual low risk profiles that comes with them.
It is possible that there are structural shifts in beta during different economic life cycles or economic/financial crisis (2001,2007 and 2011). Therefore the overall beta could be non-stationary, but the beta during these different economic time spans could be. Then the magnitude and direction of this shift in beta is important.
In literature there are multiple articles known on the subject of beta stability. In the specific field of REIT beta stability a lot of research has been done. However most of the articles were done for the US market or are very much out-dated. Therefore the focus is on the European market and the influence of the 2007-2009 financial crisis on the stability of beta will be researched. As this is divergent from previous research it is considered as added-value to the academic world.
Therefore the research question would be:
Whether the European REIT betas of a three factor CAPM regression against a General European market Index were stable during the financial crisis or could structural breakpoints be
observed at the start of the financial crisis?
Besides the research on beta stability and structural breaks during the 2007-2009 financial crisis, special attention has been paid to the relationship between interest rates and beta. Especially the influence of interest rate uncertainty on REIT market betas was researched in literature and empirically.
This paper contains a literature overview. It will form a hypothesis, explain the data used for empirical testing, describe the different methodologies, present results and recap all findings in a general conclusion.
6
2. Literature
It can be said that the research on modeling relationships within the capital markets all started with the papers of Sharpe (1964) and Lintner (1965). Both authors independently introduced a model that investigated the relationship between expected excess return and systematic market risk: the CAPM. Since then lots of research has been done on different or extended market models (multifactor models), other time periods, geographical areas, business cycles and so on.
In this chapter a theoretical framework for the research question is provided. It is not only required to examine different studies specifically about time varying betas of REITs, but also for the general research on beta stability, the general REIT environment and REITs distinctive characteristics and academic literature that deals with the (economic) crisis (in 2007).
2.1 REITs, distinctive characteristics
To start this paper it is of importance to know the REIT market, some of the definitions and to get a general feeling of the REIT market in a brief historical overview. In general, REITs are about real estate. In real estate there are different ways to invest: public, private, direct and indirect.
Public and private are two contrary strategies just like direct and indirect. Public means that the investment strategy is traded in public, for instance on a stock exchange, and private contains the non-public traded companies. Direct and indirect has to do with the strategy of investing in real estate assets directly. Buying a house for instance is a direct investment. Investments by means of an investment vehicle like a REIT are considered as indirect. REITs are mostly seen as publicly traded indirect investment vehicles.
The first thing to notice about the activities of Real Estate Investment Trusts, or short REITs, is that they develop, own and/or operate real estate. More specific a REIT is often a publicly traded company that gives individual investors the opportunity to earn a share of the income generated through real estate, without actually owning the property. REITs can be focused on office buildings, residential or commercial properties and logistic areas, but also golf courses, hotels and storage facilities and even mortgages. The main difference between REITs and other real estate companies is that REITs have to own some of the developed properties for rental income collection purposes. Not all developed or acquired properties can be divested.
7 The qualification requirements for REITs presented by the US SEC1 stated that 90% of the taxable income of REITs should be distributed as dividends. Other noteworthy requirements presented by the US SEC are:
All shares should be fully transferable
A minimum of 100 shareholders after the first year as a REIT
A maximum of 50 percent of the shares should be held by five or fewer individuals
A minimum of 75 percent of its total assets should be invested in real estate assets and cash
At least 75 percent of its gross income should be derived from real estate related sources
In return to all these requirements the REIT will be given a favorable tax status, to expel the double taxation on company and shareholder level. This tax status provides the individual investor with a return on the REIT shares that closely mimic the return of hypothetically owning the property by himself.
As described above the requirements for REITs in the US are now known. However the requirements for Europe are different. Eichholz and Kok (2007) did research on the different REIT regimes in the EU27 area. Only 13 countries have a REIT or similar entity recognized by law. One of the conclusions was that the different regimes keep the market fragmented. The different taxation rules also provide an additional disadvantage in European real estate diversification. The overview of the EU27 countries with some REIT structures recognized and their differences provided by Eicholtz and Kok (2007) is added in Appendix 1.
REITs were first introduced in the 1960’s in the US by signing the REIT Act. Since then, the developments of REITs in both an organizational way and in terms of research have gone in a nutshell. One of the most important distinctions within the REIT literature is the difference between EREIT and MREIT. Shulkin (1971) described both variations as long term investment REITs, with the difference that EREITs focus on the equity side of investment (i.e. purchase assets and renting them out). MREITs focus on provision of mortgages and collect accompanying mortgages payments as a form of real estate income. In this paper, with REITs, the EREIT type is meant.
This overview should give a quick insight in the basic understanding of the activities of REITs. In the literature review in this paper more information on the relationship of REITs is provided with the different asset pricing models and the REIT behavior.
8
2.2 REITs in the CAPM
Groenewold and Fraser (1999), Khoo, Hartzell and Hoesli (1993) and Chiang, Lee and Wisen (2005) are all articles that examine the time varying beta of REITs in the CAPM model.
Groenewold and Fraser (1999) investigate the Australian market (23 different share price sector indexes from the Australian Stock Exchange) from 1979 to 1994. In this article the Durbin-Watson statistic and the RESET test showed that 5 out of 23 sectors had a misspecification in their constant parameter model. The Chow test caught again just 5 out of the 23 sectors to have a structural break in parameter stability in Oct. 1987. Furthermore Groenewold and Fraser (1999) used 3 different methods of estimating the time-varying betas: recursive regressions, rolling regressions and the Kalman Filter. The authors give the impression that they were somewhat biased in their opinion about beta stability in the CAPM, as they opened their paper with: “It is well known that the CAPM beta is not stable over time” (Groenewold and Fraser (1999)). The result for the recursive regression confirmed this statement as all betas, including the Property Trusts, follow a random walk. Nevertheless both the rolling beta regression and the Kalman Filter, including a dummy for Oct ’87, for Property Trusts show significant stationary patterns through time.
Khoo, Hartzell and Hoesli (1993) had a more specified paper about changing EREIT betas. They found that the betas of EREITs in the US significantly declined during 1976-1989 as a result of lower variability of returns. They used 14 individual EREITs and 69 EREITs combined in a Value-Weighted and an Equally-Value-Weighted index to research the beta development in a CAPM. The CRSP value-weighted NYSE index is used as a market return in those CAPM regressions. The periods which the authors compare for beta parameter comparison are: period I 1976-1982 to period II 1982-1989). The break in ‘82 is because of the tremendous increase in listings of EREITs on the American exchanges in 1982. Furthermore they didn’t research the beta stability in those different periods.
This result is the same as Sagalyn (1990) and Gyourko and Keim (1992) found in comparable studies. However Sagalyn’s conclusion was that REIT betas correspond to different business cycles in a way that betas will fall in bullish markets because of the higher returns and lower risk. Gyourko and Keim found that in the 1975-1982 period the betas for REITs didn’t significantly differ from 1, and betas do differ in from 1 in the 1983-1990 period. They give some explanations but didn’t test any of them empirically, those explanations were: the increase in number of REITs for better diversification purposes, better understanding of REITs and their characteristics would led to better understanding of investment opportunities and lower correlation with the market. Also they mention a carryover effect of the MREITs to the EREITs because of the declining interest rates.
Khoo, Hartzell and Hoesli (1993) nevertheless explain more detailed and prove empirically that the lower standard deviation of return was explained by an increasing level of information availability about EREITs. This result comes from a regression of the monthly standard deviation of
9 EREITs on proxy variables for information availability. These variables are: the number of EREITs traded on the national market, the number of analysts that follow EREITs and the volume of trades in EREITs within the author’s sample. However their research focused on the reasons of beta change and did not look for any stationary beta coefficient.
Chiang, Lee and Wisen (2005) started their research with the knowledge that a lot of literature already showed that EREIT market betas declined over time. They said that if this is the case then all beta estimates based on historical performance are biased upwards. A rigorous statistical test of the hypothesis that the market betas of REITs did not change between 1972 and 2002 is the opposite of all previous research and the contribution of their paper. This is done by the deterministic trend test (Vogelsang, 1998) on the rolling regression estimated betas in a single- and three-factor CAPM. The Vogelsang test is useful when beta innovations are serially correlated and because of the generality of this test it has more power than unit root tests. The CRSP value-weighted index is used as a proxy for the market return and both the returns on the NAREIT and the Wilshire index are used in the CAPM. Chiang, Lee and Wisen (2005) compared 3 different time periods: from 1972-1983 because of the Tax Reform act in 1981, 1983-1991 because of the Tax Reform act in 1992 and 1992-2002. They found weak evidence for a downward trend in their estimated betas for a single-factor model. In the three-factor model this hypothesis was fully rejected. However the market betas in the last sub-sample of the three-factor model are sharply declined. This was almost entirely due to the decline of betas in 2002.
These articles show some differences and similarities in their results and methods. Firstly Chiang, Lee and Wisen (2005) found contradicting results compared to Sagalyn (1990), Gyourko and Keim (1992) and Khoo, Hartzell and Hoesli (1993) on beta stability in almost the same time period. This could be explained by Khoo, Hartzell and Hoesli’s (1993) self-constructed EREIT indexes or Chiang, Lee and Wisen’s (2005) applied Vogelsang test to allow for time-varying adjustments. A closer look shows that both articles found (weak) evidence for a downward trend in market betas in a single-factor model. The three factor model fully rejects this downward trend (Chiang, Lee and Wisen (2005)).
Groenewold and Fraser (1999) focus completely on the Australian market instead of the US and found that just 5 out of 23 sectors have a structural break in 1987. Which sectors show this break is not noticed. More interesting is the evidence that 2 out of 3 methods have stationary beta capacities for Property Trusts over the full sample when a dummy for the October 1987 financial crisis appeared. Just like Chiang, Lee and Wisen (2005) the allowance for time-varying betas exclude the existence of a downwards trend and assumes stationary betas.
10
2.3 REIT betas in a multi-factor model
Instead of solely looking for a CAPM with the stock market as market portfolio, Clayton and MacKinnon (2001) came up with a new model: a regression of the REIT return to the Bond, Large Cap, Small Cap and Direct Real Estate market; i.e. the multi-factor model. This model is partly chosen to research the relationship between Direct and Indirect real estate, as institutional investors experiment with REITs as a more liquid way of including real estate asset classes in their portfolio in the ‘90s. Clayton and MacKinnon’s (2001) study was conducted over the 1978-1998 period on the US market with a Flexible Least Squared method (FLS). The NAREIT index (excluding Healtcare REITs) is used as proxy for REITs, Direct real estate is represented by an unsmoothed NCREIF index. They conclude that the sensitivity of REIT returns to financial asset returns varies over time, possibly due to both structural and cyclical influences. Evidence of a declining trend in REIT betas on Large Cap stock and an increasing beta with Direct real estate over time is found.
Niskanen and Falckenbach (2010) based their methods on the research of Clayton and MacKinnon, but apply their method to the European Market. The FTSE EPRA/NAREIT Developed Europe REITs Index is used as benchmark for the REIT return and the analysis is done over 2006-2009. Niskanen and Falckenbach (2010) were looking whether the European REIT stock market was integrated with a general European or Global stock market. A rolling regression is performed as the current economic environment signals that constant parameters over time may be questionable. Their results on the specific relationship between REITs return and equity indexes returns, as represented by the beta, show an upward sloping beta through time for over their sample. A more important conclusion is the positive relationship between volatility of equity market returns and the REIT market beta.
A different approach in risk perception of REITs is the research by Case, Yang and Yildirim (2009). They studied over 3 different time periods the market correlation, instead of the market beta, of all REITs in a multi-factor model. The first period was the era of the first REIT IPO’s towards the start of modern REITs 1972-1991, the second period was from 1991 to 2001, the last period was from 2001- 2008. The second period is seen as the start of the modern REIT era in which institutional investors shifted their perception of REITs in such a way that their stock performance should behave in a similar way as their underlying assets, instead of a return based on general market information. The last period is unique in the way that as of then REITs were included more often in broader market indexes, which could explain the increasing correlation. They performed a dynamic correlation regression on a multi-factor model with the FTSE NAREIT All-REIT as proxy for REIT return and the CRSP value-weighted Cap-based Portfolio market index, which excludes all REITs, as general market proxy. Ultimately they found that the correlation between REIT and stock returns over the 3 different time periods shifted from steady 59%, steady 30% and steadily increasing to 59%. They also
11 conclude that the decline in correlation between REIT and stock returns during the ‘90s started in August 1991. This is 2 years before some REIT ruling relaxation in the US, but at the time of some big IPO’s in 1991.
In general the findings of these multi-factor financial asset classes’ analyses are quite similar. The decreasing relationship between REITs and Large Cap equity as is proven by Clayton and MacKinnon (2001) is described by Case, Yang and Yildirim (2009) as a result of the changed perception of REITs by institutional investors. Also the later stage (‘00s) increase discovered by Niskanen and Falckenbach (2010) is earlier described by Case, Yang and Yildirim (2009). However it is interesting that although these authors described different markets, the ultimate relationship between REITs and Large Caps was almost the same for Europe and the US in comparable time periods.
2.4 REITs and the relationship towards interest rates
In previous paragraphs the different literature on changing or stable betas is presented. Some time periods are more turbulent in terms of beta volatility than others. The reason for the (structural) changes or increased volatility is another interesting topic covered in the literature. One of the main drivers for these indicators of changing risk perspectives is the interest rate. The relationship between REIT betas and the interest rate is therefore more extensive researched in this paper.
In their most cited paper, Rosenberg and Guy (1976ab) discussed all the influences on beta from an economic perspective. One thing they described is all the different factors that influence the beta, such as: interest rates, expected inflation, growth rate of GDP, institutional regulation and so on. The influence of these factors on a beta plays a role through the systematic risk of a certain company. Otherwise stated: the beta is created by the stock and market return, but both variables are independently affected by economic events. When companies are more affected by a specific factor (such as interest rates) than the market and the uncertainty of this factor rise, the return of this particular stock will be more uncertain than the average market return. The company will experience a more agile reaction in return on the outcome of this uncertainty than the market. This higher level of risk in return of the stock compared to the market will be shown in the relationship between stock and market, the beta. The beta of this particular stock compared to the general market will rise (companies which are not affected by this factor will show decreasing betas, ceteris paribus).
This is an important understanding, because within the crisis years the interest rates become highly unstable and declined over time. As learned from the paper of Rosenberg and Guy (1976ab), all stocks that are more than average sensitive to interest rates will face this uncertainty with higher
12 betas as a result. This development in interest rates is clearly shown in figure 1, in which the height and the monthly relative change in the risk-free rate are displayed, given by Kenneth R. French. The free rate in this case is a good proxy for the interest rate, as Kenneth R. French based this risk-free rate on the one-month Treasury bill rate presented by Ibbotson Associates2. In figure 1 the monthly relative change in interest rates showed a tremendous increase in at the end of 2008. This has a great overlap with the start of the global financial mortgage crisis in 2007.
Figure 1. Overview of the Risk-free rate (right axis) and the monthly changes (%; left axis) over the period of 1990-2010, based on the interest rate presented by Kenneth R. French.
The relationship between REITs and interest rates is researched by He, Webb and Myer (2003), Allen, Madura and Springer (2000) and Swanson, Theis and Casey (2002). He, Webb and Myer (2003) researched seven different proxies of interest rates mentioned in academic literature and their relationship with both mortgage and equity REITs return in the time period 1972-1998 for the US. They performed both Ordinary Least Squares (OLS) and Flexible Least Squares (FLS) regressions and found that equity REITs (EREIT) return was only affected during their whole sample by changes in bond yields, long-term US government bonds and high-grade corporate bonds. The high-grade corporate bond yield was the only measure that had a constant negative relation with REIT returns over different subsamples. All other proxies showed different positive and negative coefficients in the regression, He, Webb and Myer (2003) conclude that the specific influence of those interest rate proxies on REIT return is time dependent.
2
Ibbotson Associates was incorporated by Roger G. Ibbotson a Yale professor and expert in the field of finance and capital markets especially. The company was an independent investment advisor that provides research and information on capital markets and was acquired by Morningstar in 2006.
-1 -0,5 0 0,5 1 1,5 2 2,5 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 ju l-9 0 ap r-9 1 ja n -92 o kt -9 2 ju l-9 3 ap r-9 4 ja n -95 o kt -9 5 ju l-9 6 ap r-9 7 ja n -98 o kt -9 8 ju l-9 9 ap r-0 0 ja n -01 o kt -0 1 ju l-0 2 ap r-0 3 ja n -04 o kt -0 4 ju l-0 5 ap r-0 6 ja n -07 o kt -0 7 ju l-0 8 ap r-0 9
Risk-free rate (RF) and the monthly change (%), presented by Kenneth
R. French
13 Allen, Madura and Springer (2000) again found evidence for the US EREIT market (1992-1999). They estimated a two-factor model on REIT return with interest rates and the market return. As proxies for interest rates the one-year and ten-year constant maturity Treasury securities were used to cover the short and long term models. EREIT return is found to be significantly and negatively affected by both short- and long-term interest rates. They also found an insignificant relation between market returns and the EREIT returns. This implicated an evolved EREIT market where fundamental changes cause a declining beta over time, which was explained earlier in the research of Khoo, Hartzell and Hoesli (1993).
Allen, Madura and Springer (2000) investigated whether the financial leverage, asset structure, degree of specialization or internal management had any influence on a REITs market or interest rate beta. Leverage and self-management are both significant and have respectively positive and negative influence on market beta.
Similar to previous literature, Swanson, Theis and Casey (2002) found that EREITs are more sensitive to the maturity rate spread between long- and short term treasuries than other interest indicators, such as the credit rate spread between commercial bonds and treasuries. The difference in their method compared to the 2 studies above was that their focus was on excess return instead of total return; however their results were the same.
Concluding, from the last 3 articles, higher interest rates will have a negative effect on EREIT returns. An explanation could be that REITs will use financial leverage to finance their real estate portfolio. Rosenberg and Guy (1976ab) showed that uncertainty in economic factors can cause a rise in beta. None of the research provided any suggestions about the relationship between the market beta and REITs or the direction of shift in market beta when interest rates will rise. This last statement is therefore an important topic to be researched in this paper. Later on, in the methodology section, the method of research on this relationship will be explained.
2.5 (REIT) betas during a financial crisis
Whilst the behavior of betas of REITs in different market models is covered and the special relationship between REIT betas and interest rates is known, one topic is left: “How did (REIT) betas behave during known crises”?
From existing literature, hypothesis can already be formed on REIT beta behavior during the 2007-2009 financial crisis, however it is important to see which results on beta behavior during crisis are already presented in the literature. Currently only 2 articles are noted in the academic literature focusing specifically on the changes in market betas during a financial crisis.
14 Choudhry (2005) has done research on the influence of the Asian financial crisis in 1997-1998 on time varying betas of 20 firms, equally distributed over Taiwan and Malaysia. Choudhry stated that the change in general business or macro-economic conditions could influence the relevant future economic expectations of a firm and therefore may have an influence on the time-varying beta. To estimate his betas, Choudhry use a bivariate BEKK GARCH model. The 20 firms are distributed over different sectors and have all their individual regression. The outcome of Choudhry’s research is that the crisis had influence on the time-varying beta, however there was no consistency in the direction or magnitude of this influence. Some firms show a rise in beta while other firms show a declining beta.
Basse, Friedriech and Vazquez Bea (2009) did research specifically for REITs and their betas during the financial crisis in 2007 for the United States compared to the betas of Utility stocks. They found evidence that there was a structural break during the 2007 financial crisis for REIT betas and that the relative risk has risen compared to the Utility stocks.
2.6 Summary
REITs are a special investment class with its own distinctive characteristics. Therefore the research that is done over the years on beta stability of REITs is a special class on its own in the field of market beta studies. Both the traditional CAPM and more extended models like the multi-factor model are used to investigate the behavior of REITs compared to the general stock market and other asset classes. Both models also find comparable and contradicting results on beta stability. Most of the breaks or trends in beta development could be explained and the general opinion is that beta stability does not occur in the long run. However stationary betas do appear in different time periods, both with and without a certain trend line that is included.
In a historic perspective there are some specific time periods in which a structural break in REIT beta is found. For instance during the crisis of 1997 in Taiwan and Malaysia, researched by Choudhry (2005), or the break of REIT betas compared to Utility stocks in the US at the start of the 2007 financial crisis (Basse, Friedriech and Vazquez Bea (2009)).
Besides the beta stability this literature overview also provides an insight in the relationship between REITs and interest rates. The general conclusion is that REITs are negatively related towards interest rates, possibly explained by the relative high usage of financial leverage in REITs. Uncertainty in interest rates can also cause rising betas. This relationship is important for the development of a model to test the influence of interest rate uncertainty on REIT market betas.
15
3. Hypothesis and methodology
In this chapter the hypotheses based on the literature are presented and the methodology of research is explained. All different regression models and break tests will be discussed. The hypotheses are split in a general research question and the specific hypothesis on the interest rate uncertainty and the market beta.
3.1 Hypothesis
For the definition of the hypothesis in this paper it is assumed that the results from literature are globally applicable. A rising REIT beta is expected after the start of the crisis, because of the comparable findings of Basse, Friedriech and Vazquez Bea (2009) on REIT betas. An explanation could be the increased uncertainty in interest rates during the crisis. However the magnitude of such a rise in REIT beta is still unknown. The exact research question is: “Are REIT betas increased after the structural breaks caused by the crisis”?
Defined in a hypothesis, the H0 would be rejected:
H0: REIT betas do not show a structural break during crisis years compared to pre-crisis years
As a sub question this paper also investigates the relationship between uncertainty in interest rates and the market beta of REITs. The model to be used will be explained in the methodology part. The research question for this sub question will be: “The relationship between the uncertainty of interest rates and the market beta of REITs is expected to be positive and significant during the crisis years”.
The positive expectation of this research question is based on the paper of Rosenberg and Guy (1976ab). The significance attitude of this relationship expected especially during crisis years is because of the sudden increase in uncertainty of interest rates. This relationship is expected to have had a major impact specifically during the 2007-2009 financial crisis. Outside this time period other more fundamental factors probably have a bigger impact. Of course the relationship between interest rates and REIT return is still expected, however the impact on REIT market beta is solely focused on.
The ultimate hypothesis for this sub question is almost the same as the main hypothesis and researches a structural break in the relationship between the uncertainty of interest rates and the market beta of REITs.
16 H0: The relationship between the uncertainty of interest rates and the market beta of REITs do not
show a structural break during crisis years compared to pre-crisis years
3.2 Methodology
The research on the CAPM all started with Sharpe (1964) and Lintner (1965). Later the model expanded through time in multiple directions. As explained in the literature section, there are 2 general directions in this development: a multi-factor model and what might be called an equity market-factor model (which is actually also a multi-factor model but solely with equity market factors such as: Large- and Small-Cap). The regression methods on these models have changed over time. In the field of beta stationary or stability testing the regression came from constant parameter regression, like OLS, towards highly sophisticated time-varying beta models, such as FLS.
In this part the methodology aspects that are used for the research on REIT beta stability during the 2007-2009 financial crisis will be described. It will start with the description of the model that is used. The different types of regression and the different structural break-tests are also explained. After that, the relationship between interest rate uncertainty and the beta of REITs will be modeled.
3.2.1 Model
This paper focuses on the market-factor model. Therefore the 3-factor model constructed by Fama and French (1993) is used. The market-factor model is chosen because of the determined focus on the REIT market beta relationship in this paper. The 3-factor model is used, because it is described by Peterson and Hsieh (1997) as the best model for REIT beta estimating, and is shown below:
( 1 )
is the monthly excess return of the REIT index and the is the monthly excess return of the
general European stock portfolio. The variable is the difference between the returns on portfolios composed of small and big stocks, and is the difference between the returns on portfolios composed of stocks with high and low BE/ME (book-to-market) ratios. All variables on the left-hand side of the equation are gathered from the Kenneth R. French database, which also provides the risk-free rate to calculate excess return. The REIT index is gathered through Datastream and the earlier described risk-free rate is used for excess return calculations. The last variable, , is the error term for this equation.
17 3.2.2 Regression methodology
Literature describes that the assumption of constant parameter estimation for (REIT) market betas is not applicable. Time-varying models are more useful as they display the evolution in the relationship of (REIT) market. No static regression such as OLS will therefore be used. Instead a rolling regression, as Groenewold and Fraser (1999) did, will be used as a representation of a time-varying regression and is shown below.
Choosing the right time frame for a rolling regression is of special importance. When done rightly only the long term trends will be covered into a beta. In practice, a rule of thumb exisits, the betas are assumed to be constant over 4-5 years. This constant timeframe is considered the best forecast for current return (Groenewold and Fraser (2000)). Therefore the rolling estimation will be performed on 55 months. This 55 month rolling period is taken into account by selecting the starting point in time of the data. To have good estimates of a rolling beta before the 2007-2009 financial crisis, the first data point is gathered 7 years before the crisis starts. Hereby 4.5 years are used to calculate the first beta estimation and 2.5 years of REIT market beta development can be analyzed before the crisis starts. Therefore the data gathering time frame for this paper will be 2000-2014.
The normal fixed window time-frame rolling regression is used in this paper, because of the eventual fading effect of historical influence and the overlap with existing literature. To perform rolling beta estimations on both normal OLS as on an ARCH, the different models are explained further on. Both methods are used to compare the results of different modeling techniques in the time varying beta estimations.
Besides the rolling regression method, literature also quotes different forms of (G)ARCH modeling in time series analysis for the creation of more stable regressions. Choudhry (2005) for instance used a BEKK GARCH model. However this is quite a complex model to use and therefore an intermediate step with a multivariate (G)ARCH model would be more appropriate as extension on the rolling regression in this paper. The (G)ARCH model is in essence the same as the 3-factor model presented earlier (equation 1), however the error term is calculated differently. More precisely equation 1 will be used as estimator for the mean and a separate model for the conditional variance is used. The conditional variance model for the ARCH regression is presented in equation (2) the conditional variance for the GARCH model is different compared to the ARCH conditional variance and is the final conditional variance estimator is presented also below in equation (4):
18 This is an ARCH(q)-model, with the squared standard deviation dependent on “q” lagged variables of the error term estimated in the mean equation model (equation 1). stands for a constant estimator and to are coefficients for the different error terms. There is one requirement in this model: all coefficients should be equal or exceed zero, otherwise the variance could be negative. A normal ARCH(1) model as is used in this paper would look like this:
( 3 )
The GARCH estimation of the conditional variance is an extended version of the ARCH conditional variance estimator. The difference is that the variance of a model not only depends on the lagged error terms of the model, but also on the lagged variance. A normal GARCH(1,1) with only 1 lagged error term and 1 lagged variance term will look like this:
( 4 )
Again the is the estimated variance of the standard model (equation 1), dependent on the lagged squared error term ( ) and the lagged conditional variance ( ). In this model the only
requirement is that all terms are equal or exceed zero.
In contrast to structural break tests, all GARCH models do not focus on the stability of the parameters in different subsamples, but are used for conditional heteroscedasticity research. Conditional heteroscedasticity is the dependency during time series analyses of the variance of the error term in a regression on previous error terms and previous variances of error terms. When this is observed a model or coefficient is considered to be non-stationary. In other words, when a model or coefficient shows conditional heteroscedasticity it means that the variance of a time series is correlated with past error terms and or variances. This implies that changing parameters could be misinterpreted as they only change because of the biased variance of the mean equation model. When this conditional heteroscedasticity appears, GARCH models can provide a solution by adjusting the error term in the time series regression. With this method a stationary regression is created and the different parameters could be interpreted in the right way.
3.2.3 Structural break testing
To test when in the time-series there could be a structural break; the Quandt Likelihood Ratio test could give this insight as it is a modified Chow test, according to Stock and Watson (2007). This test
19 appoints (as the QLR statistic) critical points in maximum value of the F-statistic. This F-statistic can be used to research the change in certain parameters in a time series analysis. The equation of the Quandt Likelihood Ratio test is:
( 5 )
In this equation the τ stands for the different dates, with τ0 is the first date in range and τ1 is the last
date in range. The F-statistics are calculated on all the dates between the firs and the last date. However the F-statistic doesn’t use the first and last date of the sample, but these are based on a trimmed sample. The outer 15% of the dates are removed so the breaks are computed for the dates in the central 70% of the sample. This trimming is a normal procedure, because of the large-sample approximation of this test (Stock and Watson (2007)) and τ0 is therefore the equivalent of 0.15T. The
model used to calculate the F-statistics is based on historical terms of the variable researched and is presented below.
( 6 )
is the generated market beta from the rolling regression and the is the lagged term of
the generated market beta from the same rolling regression. Four lagged terms are used to research the break of the current market beta with the historical data. With this method the ultimate critical value of the Quandt-Likelihood ratio test is 3.66, based on 5 lagged terms and a significance level of 5%.
This paper also considers a more explicit structural break test. There are 2 ways known for structural break testing. The first, and most basic, method is the inclusion of a dummy variable in a regression such that the regression is split up. The second method in structural break tests is the Chow-Breakpoint test. Both methods ultimately give the same answers, this is inter alia shown by Gujarati (1970), if all variables are tested: dummy variable group test versus the Chow-Breakpoint test. The differentiating factor of the dummy variable method is that individual variables in different subsamples could be tested; on the other hand the Chow-Breakpoint test is much quicker when all variables are compared. In further research the dummy variable test could give an outcome when you specifically look at the different factors explaining REIT betas. However for now the Chow-Breakpoint test is the only structural break test considered and presented below:
20 ⁄
⁄ ( 7 )
The Chow-Breakpoint test follows a F-distribution (k;T-2k)3, with as the H0 hypothesis that all
coefficients in the different subsamples are equal to their counter coefficients in all the other subsamples. This test therefore could be used for specific time period testing, for instance between financial crisis.
The RSSR is the Restricted Sum of Squared Residuals, for the whole sample, and the SSR1 and
the SSR2 are the Sum of Squared Residuals of the observing and the verifying subsamples. This
version of the Chow-Breakpoint test now only includes 2 sample periods. This could easily be extended towards a test including multiple subsamples.
With the Chow-Breakpoint test this paper will investigate the existence of a structural break in parameters for a pre-, in- and after- financial crisis sub-sample for both the ARCH- and the GARCH-model (as suggested by: Cosimano and Jansen (1988) and Van der Weide (2002)). To determine the start and duration of the financial crisis the European GDP quarterly growth statistics (EU 15) presented by EUROSTAT are used. This dataset shows that the financial crisis started in Q4 2007 and ended Q2 2009, see figure 3.
3.2.4 Uncertainty in interest rates and REIT market betas
Besides the research on market beta stability during the crisis this paper shows additional research on the relationship between interest rate uncertainty and market beta. Market betas are always estimated on the basis of different input measures and not on a variable that is observable in the market. Time-varying regression can generate best fitting market beta estimates over a certain time period. This capacity makes it possible to do further research on the direct relationship of different factors on estimated betas through time. To research the direct relationship between interest rate uncertainty and the market beta of REITs the generated output of the rolling regression methodology on the market beta is used. This market beta will be regressed upon a constant and a proxy for interest rate uncertainty. The equation is presented below:
( 8 )
21 In this equation represents the generated market beta from the rolling regression, the is
the interest rate uncertainty and is an error term. The proxy for interest rate uncertainty is the normalized latest 3-month standard deviation of the risk-free rate presented by Kenneth R. French and is calculated as presented in equation 9.
( 9 )
The 3-months standard deviation ( ) is calculated as the standard deviation of the
interest rate over all interest rates in the last 3 months up to t, which is the normal way to calculate standard deviations over any variable. The standard deviation is normalized to give a relative insight in the change of the standard deviation change. To normalize this standard deviation; is divided by the current interest rate ( ). As the interest rates decline over time towards 0 (see figure 1) the fluctuations of this interest rate will be relative high as the minimum registered change in interest rate is 0.01%. To rightfully interpret these relatively high standard deviations, these are normalized as described above.
OLS regression over the total sample period and over sub-sample periods is done to analyze the different sign of γ and its significance. The (adjusted) R^2 measure over different sub-samples is especially interesting for the comparison of the in crisis sample (2007-2009) with the pre- and after-crisis samples. For easy interpretation purposes the logarithm of both the market beta and the interest rate uncertainty will be used in the above regression.
3.2.5 Summary
A rolling regression and an ARCH/GARCH regression is performed on the three factor model to interpret the development of the beta during the sample period. Over the estimated beta of the OLS method a Quandt-likelihood ratio test is done to get a first impression of the allocation of possible structural breaks. Besides that a Chow-Breakpoint test is run to investigate the structural breaks matching with the start of the financial crisis exactly.
These different regressions and two (structural) break tests to the answer on the research question:
Are the European REIT betas of a three factor CAPM regression against a General European market Index were stable during the financial crisis or could structural breakpoints be observed at the
22 Profound research into the relationship between interest rate uncertainty and REIT market betas is executed. This is done by a simple OLS regression of a normalized latest 3-month standard deviation of the risk-free rate on obtained betas from the rolling regression. This OLS regression is performed on different sub samples, matching the start of the 2007-2009 financial crisis, to compare significance and signs of the relationship between interest rate uncertainty and REIT market beta.
23
4. Data description and results
Previous chapters provide a theoretical framework on the market beta stability of REITs and the relationship between interest rates and the REIT performance. The methodology for continued research on this subject in this paper is also described.
This chapter focuses, firstly on an in depth analysis of the data used and secondly on the outcome of the regression performed and the corresponding structural break tests. Then the results of the research on the relationship between interest rates and REITs market betas will be presented and finally a discussion is provided.
4.1 Data
All data necessary can be subtracted from the available databases at the UvA (Datastream) or received online. The data needed is the monthly return from the European REIT index: the FTSE EPRA/NAREIT Eurozone Total return Index (this index is also used by Niskanen & Falkenbach, 2010). For the monthly return from a general European Market Index the goal is to have an index as broad as possible, this is because the index has to represent the total European market.
Niskanen & Falkenbach (2010) used the total return index from the MSCI Europe. This index only captures large and midcap companies within 15 developed markets (consisting of 432 constituents). There are broader indexes, more countries and or constituents, available for the European market (the Stoxx Europe 600 for instance), however there is a hurdle when choosing an extensive database.
When a standalone database is chosen as the right benchmark, all the SMB & HML variables have to be recalculated. The development of these variables is time consuming and not necessarily contributing for an academic paper, especially because Kenneth R. French is gathering these variables and has published them all online. Below the explicit calculation and determination of the SMB & HML variables by Kenneth R. French is explained.
4.2 SMB & HML factors
Kenneth R. French published the SMB & HML factors and a market return for the European market on the website of Darthmouth4. The most important aspect of the calculation method for these variables is that a region’s return is calculated with a value-weighted index minus the US one month Treasury bill rate. A region in the previous sentence should be interpreted like the United States, European area or other large scale regions.
24 To use the US T-bill rate as in a European benchmark is quite contradictory at first, however the use of this rate can be explained. Most European institutional investors and nowadays also the smaller investors can access the US capital market due to all new technology. The explicit use of a European risk free rate is therefore unnecessary. Another aspect that excludes the availability of currency investment is the interest rate parity. Interest rate parity is the economic equilibrium in which investors are indifferent between investing their cash on deposit bank accounts in different countries, taking into account the different deposit rates and currency rates. For the EU and the US the existence of disruptive interest rate parity is unknown.
Besides these arguments the absolute difference between the short term interest rates of the US and the EU do not differ that much, as can be seen in figure 2. Both the 1-month risk-free interest rates follow a similar pattern and the absolute difference is less than 0.01%. Most of the time thus can be said that the use of the Kenneth R. French risk-free rate is legitimized.
Figure 2. Overview of the 1-months Risk-free interest rate return for both the EU and the US market from 2004 to 2014. EU data is based on the EU area from Eurostat, US data is the US 1-month Treasury bill from the Kenneth R. French
database.
The data collected from the Kenneth R. French database consist of 16 European countries (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and the United Kingdom), without knowing which stocks are exactly included.
As explained earlier, the data for a general European benchmark should be as broad as possible. This could be one of the reasons to choose an independent market index, like the Stoxx -0,003 -0,002 -0,001 0 0,001 0,002 0,003 0,004 0 0,001 0,002 0,003 0,004 0,005 ja n -04 ju n -04 n o v-04 ap r-0 5 se p -0 5 fe b -06 ju l-0 6 d ec -06 m ei-07 o kt -0 7 m rt-0 8 au g-0 8 ja n -09 ju n -09 n o v-09 ap r-1 0 se p -1 0 fe b -11 ju l-1 1 d ec -11 m ei-12 o kt -1 2 m rt-1 3 au g-1 3
1-months Risk-free interest rate return
25 Europe 600 benchmark, and calculate the SMB & HML variables stand-alone. However the weight of this research is not on whether the available databases are good enough. Therefore the use of the Kenneth R. French data is legitimized.
One final note on this subject is the inclusion of REITs in the Kenneth R. French data. When REITs are included in a market portfolio, the correlation will increase and the market beta of researched REITs will be biased upwards. As the exact composition of the market portfolio in the French data is unknown, it remains a blind spot whether these betas are biased or not.
Finally the European GDP quarterly growth statistics of EUROSTAT are used to give insights in the exact moment when the European crisis did start. EUROSTAT presents 3 different geographic areas over which they calculate economic growth: EU 28, EU 27 and EU 15. The EU 15 is chosen as it represents a GDP measure for 15 European countries. This number is the closest match with the Kenneth R. French database that consists of 16 countries. Besides that, the EU 15 does not differ that much from the other 2 geographic allocations (see figure 3 and table 1). The commonly accepted definition of a recession is two or more consecutive quarters (a period of three months) of contraction in national GDP5. In this paper it is assumed that the end of the recession is the opposite of this definition: 2 consecutive quarters of growth in national GDP. Both start (red dot = Q4 2007) and end (green dot = Q2 2009) of the financial crisis, according to the EU 15 GDP data, are presented in figure 3. Data used will be consistent with the other data gathered and range from 2000 to 2014.
Figure 3. Overview of the quarterly GDP growth of the EU 15 and EU 28, presented by EUROSTAT. The start and the end of the financial crisis are marked with a red and green dot respectively.
5 http://www.cbs.nl/nl-NL/menu/methoden/begrippen/default.htm?ConceptID=586 -2 -1,5 -1 -0,5 0 0,5 1 1,5
EU 28 and EU 15 GDP index growth figures
26
Table 1, Descriptive statistics (number of observations, mean, standard deviation, minimum and maximum value of the European GDP quarterly growth statistic composed of the EUROSTAT data for the EU 15, EU 27 and EU 28 region.
4.3 Results
This chapter presents and discusses the results of this paper, but most of all it connects the found results with the hypothesis and research question. At first descriptive statistics are shown, later on the regressions and the structural break tests are analyzed. Finally the interest rate uncertainty and REIT market beta relationship is explained by means of the OLS regression.
4.3.1 Descriptive statistics
Over the complete dataset from January 2000 till December 2013 descriptive statistics are shown in the table below. The descriptive statistics are presented for the different subsamples, such as: the Pre-crisis period (2000-2007Q4), the In-crisis period (2007Q4-2009Q3) and the After-crisis period (2009Q3-2014).
In table 2 the Excess REIT return, the Excess Market return, the SMB and the HML factor are presented. The Excess REIT is the excess monthly return of the FTSE EPRA/Nareit index, the Excess Market is the excess monthly return of the market portfolio provided by Kenneth R. French. SMB and HML are respectively the Small minus Big and High minus Low factors, also provided by Kenneth R. French. A combined skewness/kurtosis test for normality is run in Stata, based on the methods described in D’Agostino, Belanger and D’Agostino Jr. (1990).
Obs. Mean std.dev min max
EU 15 56 0,366 0,496 -1,3 1,1
EU 27 56 0,393 0,573 -1,9 1,4
27
Table 2. Descriptive statistics (number of observations, mean, standard deviation, minimum value, maximum value, skewness, kurtosis, probability of skewness, probability of kurtosis and probability of normality) over the whole and all of the sub-samples. Excess REIT and Excess Market represents the FTSE EPRA/Nareit index and the Market index by Kenneth R. French minus the Kenneth R. French interest rate. SMB and HML stands for Small-Minus-Big and High-Minus-Low portfolio coefficients
The standard deviation of the excess REIT return shows a clear path with a low value (3.795) pre-crisis a very high value (7.905) in-pre-crisis and a lower value again (5.094) after-pre-crisis. This indicates that the excess REIT return during the financial crisis was more volatile than before and after the crisis. The excess market return shows a similar path, which is all normal and expected. The negative sign for the mean excess return for both the REIT and the market during the crisis is also as anticipated.
In the case of a normal distribution the skewness and the kurtosis parameters should be respectively 0 and 3. The skewness is the measure for asymmetric distribution in a positive or negative sentence. A high (>3) kurtosis indicates that a few data points have tremendous influence on the variance of the distribution. Over the total sample the kurtosis of the excess REIT return is quite high (5.400), this is more in balance in all the subsamples with the in- and after-crisis samples with almost perfect kurtosis. However the normality test shows that on a 1% significance level there is no reason to assume the excess REIT return over the whole sample is non-normal distributed. Therefore no outliers, which heavily affect the variation, are taken into account. The excess market return, the SMB and the HML variables are normal distributed on a 1% significance level either in the whole sample period. Contradicting to the normal distribution over a longer time period, almost all variables in the different sub-samples show a non-normal distribution. This is as expected because the different subsamples are composed of bull or bear markets (pre-, in- and after-crisis) and therefore show a certain positive or negative trend. In these cases the returns are not distributed around zero, but should demonstrate certain skewness that match the type of market.
Summary for variables FTSEminsRF, MRKTminusRF, SmallminusBigMarketCap and HighminusLowBEMEratio by categories of Period
Period N mean sd min max skewness kurtosis Pr (skew) Pr (kurt) Prob>chi2 Aftercrisis Excess REIT 54 1,216 5,094 -12,320 12,860 -0,077 3,145 0,798 0,520 0,783 Excess Market 54 1,261 5,885 -12,310 11,850 -0,417 2,839 0,178 0,906 0,384 SMB 54 0,099 1,857 -4,490 4,740 -0,075 2,984 0,802 0,703 0,901 HML 54 -0,072 2,836 -4,470 7,450 0,502 2,439 0,109 0,419 0,183 Incrisis Excess REIT 21 -2,785 7,904 -21,030 12,570 -0,440 3,221 0,323 0,397 0,390 Excess Market 21 -2,287 8,947 -22,140 13,780 -0,147 2,741 0,737 0,800 0,915 SMB 21 -0,209 2,575 -4,650 4,850 0,122 2,454 0,781 0,841 0,943 HML 21 -0,406 2,337 -4,600 5,600 0,416 3,550 0,350 0,241 0,283 Precrisis Excess REIT 93 1,179 3,795 -11,850 10,400 -0,718 4,205 0,006 0,036 0,006 Excess Market 93 0,548 4,518 -13,150 13,170 -0,460 3,804 0,063 0,101 0,053 SMB 93 0,265 2,416 -6,940 9,310 -0,281 5,425 0,245 0,002 0,009 HML 93 1,342 2,658 -9,570 10,960 0,019 7,405 0,935 0,000 0,001 Total Excess REIT 168 0,695 5,039 -21,030 12,860 -0,855 5,400 0,000 0,000 0,000 Excess Market 168 0,423 5,743 -22,140 13,780 -0,586 4,103 0,003 0,018 0,002 SMB 168 0,153 2,264 -6,940 9,310 -0,176 4,730 0,337 0,002 0,009 HML 168 0,669 2,770 -9,570 10,960 0,206 4,675 0,261 0,002 0,009
28 4.3.2 Regressions
As the literature presented that both the rolling regressions and the GARCH models are of special interest in the research on beta stability, different regressions are performed in this paper. Besides these models the normal ARCH model will also be researched.
The ARCH and GARCH model use a maximum likelihood estimation method to compute the regression most closely related to the truth. As these regressions are sensitive to multicollinearity and are highly correlated to underlying independent variables, it is useful to check these mutual correlations to start with. The dataset did not have any missing data nor was it treated abnormally, therefore non-surprising correlations were expected. The different correlations are displayed below in table 3.
Table 3. Overview of the different correlations between Excess REIT return, Excess Market return, Small-minus-Big and High-minus-Low portfolio coefficient in the whole and the different subsamples.
As can be seen in table 3 the correlation coefficients of the regression are unsurprisingly normal. The correlation between the excess REIT return and the excess market return over the total sample is quite low with 0.667. Both the SMB and HML factors show a negative correlation with the excess market return over the whole sample. The subsamples of in-crisis and after-crisis show a higher correlation between the excess REIT return and the excess market return: 0.808 and 0.765 respectively. Despite these higher correlations in the subsamples no direct signs of multicollinearity are given nor is multicollinearity expected. All these observations do not give any reason to estimate that there should be a problem in the GARCH regression.
4.3.3 Rolling regression
The rolling regression method is a way of estimating a coefficient within a defined regression model based on historical estimations of this coefficient. The models that can be used differ from normal
Excess REIT Excess Market SMB HML Excess REIT Excess Market SMB HML
Excess REIT 1 Excess REIT 1
Excess Market 0,667 1 Excess Market 0,406 1
SMB 0,063 -0,079 1 SMB 0,102 -0,143 1
HML 0,343 0,204 -0,147 1 HML -0,002 -0,296 -0,189 1
Excess REIT Excess Market SMB HML Excess REIT Excess Market SMB HML
Excess REIT 1 Excess REIT 1
Excess Market 0,808 1 Excess Market 0,764 1
SMB 0,274 0,168 1 SMB -0,216 -0,216 1
HML 0,679 0,560 -0,203 1 HML 0,605 0,677 -0,126 1
Full Sample (obs=168) Pre-crisis (obs=93)
After-crisis (obs=54) In-crisis (obs=21)
29 OLS to GARCH. In this paper the rolling regression is performed both on the OLS and ARCH model. The timeframe of historical coefficients taken into account with the calculation of the ultimate rolling coefficients is 55 months, or slightly more than 4.5 years. The data used to calculate the output below therefore started 55 months earlier (January 1994) than the first rolling estimation presented (July 1998).
Below in figure 4 the output of the rolling regression is displayed. The output of this rolling regression consists of an estimate of the beta between the Excess REIT return and the Excess Market return, depending on which model and regression is chosen.
Figure 4. Output of the rolling regression estimate, based on both the OLS and the ARCH regressions.
As can be seen the OLS and the ARCH based REIT market beta estimates are almost the same. Roughly judged, the period March 2003 – November 2005 and December 2012 till December 2013, the ARCH model presents somewhat lower beta estimates than the OLS model. However both regressions are so a-like that this could barely be of any importance.
At first sight, both rolling estimations show a quite constant REIT market beta over the beginning of the sample of 0.4 and it is (for now) assumed to be the historical average. A clear decline in REIT market beta at the beginning of 2007 (to 0.1) and a sharp rise towards previous constant levels started in June 2008 is also visible. After the beta had risen towards its historical average at the beginning of 2009 it continued to rise towards approximately 0.65 in November 2013. After this date a drop in market beta is shown. Because of the data used, almost till now, it is too
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 ju l-9 8 fe b -99 se p -9 9 ap r-0 0 n o v-00 ju n -01 ja n -02 au g-0 2 m rt-0 3 o kt -0 3 m ei-04 d ec -04 ju l-0 5 fe b -06 se p -0 6 ap r-0 7 n o v-07 ju n -08 ja n -09 au g-0 9 m rt-1 0 o kt -1 0 m ei-11 d ec -11 ju l-1 2 fe b -13 se p -1 3
REIT market beta, the rolling regression estimate
30 early to tell whether this drop will continue towards the historical average (0.4) or that this drop is just part of a correction towards a new average that will lie between 0.5 and 0.6.
It is interesting to notice that this sharp drop and rise of the rolling regression REIT market beta estimates occur around the start and the end of the 2007-2009 financial crisis. It is especially interesting when the estimation procedure of 55 historical months that contribute to the estimation output is taken into account. A significant drop in the rolling regression output (the beta) should therefore be seen as an even more significant drop in the beta at the moment of the falling rolling regression output. As a consequence of that, the start of the viewed drop in market beta might have occurred before the graphical shown start (January 2007).
All these findings are reported on interpretations of the graphical view of the market beta of the rolling regressions. The graph clearly shows a change in market beta, but the drop (January 2007) and rise (June 2008) do not match the earlier estimated starting (October 2007) and end point (April 2009) of the financial crisis. This could be explained by the fact that a change in REIT market betas is an overture to GDP changes, however this cause-effect relationship cannot be measured with this graphical explanation. Further statistics on both rolling regression estimates for comparison of the differences and analysis are presented in table 4 to gain more insights in periodic changes.
Table 4. Descriptive statistics (number of observations, mean, standard deviation, minimum value and maximum value) on the output of the rolling regression estimates for the whole and the different subsamples, based on both the OLS and
the ARCH regression.
The first thing that stands out is the lower number of observations in the ARCH model compared to the OLS model. The REIT market beta rolling regression estimate based on the OLS methods shows exactly the same number of observations as there are data points available (168). The 3 missing data
Period N mean sd min max
Precrisis 93 0,418 0,048 0,225 0,502
Incrisis 21 0,300 0,127 0,128 0,457
Aftercrisis 54 0,562 0,050 0,434 0,650
Total 168 0,449 0,107 0,128 0,650
Period N mean sd min max
Precrisis 90 0,407 0,057 0,207 0,510
Incrisis 21 0,285 0,135 0,105 0,450
Aftercrisis 54 0,552 0,053 0,427 0,666
Total 165 0,439 0,113 0,105 0,666
Summary for REIT market beta in OLS by categories of Period
Summary for REIT market beta in ARCH by categories of Period
31 points in the ARCH estimation are: 2001m8, 2002m1 and 2002m3. The original data source was checked and no blanks or outliers were noticed. The reason for elimination during the rolling regression estimation process by Stata is therefore unknown6.
Besides the 3 missing data points there are no real differences between the 2 methods. Over all the samples (including the whole) the ARCH method has slightly lower means, but higher standard deviations. So corrected for possible existence of heteroscedasticity the variables differ somewhat from the standard OLS output. However, as the difference between the OLS and the ARCH model is very small, it can be neglected. No direct explanation for the higher standard deviations is at hand.
As this paper focuses on the beta stability the comparison of the different samples is necessary. Both OLS and ARCH rolling regression estimators of the REIT market beta show a clear path over time. When comparing the mean of the beta over different subsamples the Pre- and After-crisis samples are in both regressions higher than the In-crisis sample. Also the After-crisis sample is slightly higher than the Pre-crisis sample. Both regressions also assert a higher standard deviation for the In-crisis sample compared to the other two.
Those findings, including the visual interpretations of the graphical view, clearly indicate that a break in beta (for REITs compared to the general market) occurred during or around the financial crisis of 2007-2009. Not only the mean of the beta during the crisis evidently fell but also the volatility of the relationship of REITs with the market obviously changed. Later on in this paper structural break test should clarify if these findings are significant or not.
4.3.4 (G)ARCH regression
An ARCH and a GARCH regression are performed besides the rolling regression estimator. In this paragraph the results of both regressions will be demonstrated and analyzed. As is explained earlier no abnormalities in the output of the ARCH and GARCH models is expected as signs of multicollinearity did not appear. Below the results of the ARCH regression are presented at first, followed by the GARCH regression. Both regressions are performed on the whole and on all the subsamples.
As explained earlier the Excess REIT and the Excess Market in the models correspond with the total return index of the FTSE EPRA/NAREIT minus the Kenneth R. French risk-free rate and the Market index return also presented by Kenneth R. French minus that same Risk-free rate respectively. In
6 The reason no GARCH estimation of the rolling regression is done is in line with this. Stata dropped out more than 100 data point, without explanation or missing original data, so no representative output was created.
