University of Amsterdam
MSc Business Economics, Finance track
Master Thesis
The diversifying power of REITs to the multi-asset market portfolio at times of changing
economic conditions
Marita Mitrovic
July 2014
Thesis supervisor: Mr. Giambona
--- abstract---
This study is an attempt to create more insights into the diversifying potential of US and UK REITs. Sharpe-optimized portfolios are constructed on a monthly basis, consisting of domestic and international bonds, stocks and REITs. By using ex-post data, the amount that should have been allocated to real estate stocks is determined on a monthly basis. By regressing the US and UK REIT optima on the return performances of the other asset classes, a selection of macroeconomic variables and a crisis-dummy, the time-varying fundamentals of REITs’ diversifying power are analyzed. Using this model, no direct relationships are measured. Any significance represents an asymmetric effect of the independent variable on one of the assets in the portfolio, causing the necessity to reallocate the portfolio in order to remain Sharpe-optimized. It turns out that the international bond market is highly significant for both the US and UK. No clear time-patterns are detected between REIT optima and the independent variables. The House Price growth rate and Interest Rate turn out to be significant for the UK sample, while GDP is more important for the US sample. Financial distress does not have an additional effect on determining the diversifying power of REITs as the crisis-dummy turned out to be insignificant in all models.
Index
I. Introduction p. 1
II. Related literature 4
A. Lack of understanding REITs
a. Fundamentals b. Time component
B. Constructing the model
a. Selecting macroeconomic variables b. Crisis
III. Methodology 11
A. Constructing the dependent variable; optimal portfolios
B. Data frequency
C. Sharpe ratios
D. Subperiods
E. REITs’ dependence on stocks and bonds
F. REITs’ dependence on macroeconomic variables
G. Orthogonal regressions
H. Crisis-‐dummy
IV. Results 21
A. Optimal portfolios
B. REIT optima and other assets
a. Regressing UK REITs on stocks and bonds b. Regressing US REITs on stocks and bonds
C.
REIT optima and the macroeconomic environment
a.
Regressing UK REIT optima on macroeconomic variables
b.Regressing US REIT optima on macroeconomic variables
D.Interaction terms with crisis-‐dummy
V. Analysis 35
A. Introduction
B. Reliance on other assets
a. Analyzing UK coefficients and difference estimators b. Analyzing US coefficients and difference estimators
C. Reliance on macroeconomic variables
a. Introduction
b. Analyzing UK coefficients
c. Analyzing US coefficients
D. Crisis-‐variable
VI. Conclusion 44
References 47
1 I. Introduction
REITs were introduced to the market in the United States when president Dweight Eisenhower signed the REIT Act in 1960, making it possible for investors to purchase liquid securities of large-‐ scale, diversified, income-‐generating real estate portfolios. REITs popularity stems from the fact that their taxable income needs to be distributed for at least 90% to the investors. This condition should be met in order to benefit from the tax benefits that make REITs attractive to invest in. Because the majority of the income generated by REITs is distributed directly, investments are scarcely financed with earned income. Debt is taken on in order to invest in the real estate portfolio and therefore REITs are directly affected by a change in the interest rate. Additionally, REITs are affected by changes in the value of the underlying real estate portfolio. For this reason, economic growth has an ambiguous effect on REITs; it increases the total value of real estate portfolio, but is also often
accompanied by increased interest rates that suppress yields. This contradicting mechanism makes it, among others, complicated to unravel the fundamentals driving REIT performance and therefore makes it difficult to assess its potential of portfolio enhancement.
This study focuses on the diversifying potential of REITs over time, to a mixed-‐asset portfolio consisting of international and domestic stocks and bonds. Portfolio diversification is about the risk reduction potential of an asset to a portfolio. The diversifying power of real estate is statistically determined by the level of co-‐integration with the other financial assets included in the portfolio. As explained before, determining the diversifying power of real estate is a complicated issue. The literature clearly discloses the complexity of this topic, since evidence can be found supporting contradictory theories. Differences in findings can be explained by the fact that different categories of real estate are included and different statistical procedures have been used (Wilson and
Zurbruegg, 2003). Furthermore, differences in findings can be explained by the selection of countries that are taken into account (Chang et al., 2012) and the study duration that has been chosen (Liow et al., 2009; Yang et al, 2010; Zhou, 2014; Chang et al., 2012; Clayton and MacKinnon, 2001). The last mentioned studies show that results change when the period analyzed is adjusted, therefore suggesting a time-‐varying component in the diversifying power of real estate.
In this study, the domestic REIT markets of the US and UK are taken into account, covering the period of 1995 to 2013. In order to gain more insight in the investment enhancement of REITs, this topic is approached from a different angle. This study includes variables derived from the literature which predictive powers on REIT performances remain unclear. Instead of regressing them on REIT returns and volatilities, which is a common statistical methodology, the variables will be regressed on the percentage of REITs that should have been allocated to the mixed-‐asset portfolio. This optimal
2 amount takes into account the return aspect of REITs, as well as the variance, relative to the risk and return performances of other financial assets at that time. By doing so, all aspects concerning the investment question are addressed directly.
First, the optimal allocation amounts of REITs to the mixed-‐asset portfolio should be collected of the full length of the study on a monthly basis for both countries. Note that portfolios are constructed in retrospect, based on historical information. By using ex-‐post data, the influence of future economic expectations on the portfolio allocation decision are excluded from this study. By doing so, this study focuses on the true interactions between REITs and its fundamentals and is not contaminated by other aspects, for instance expectations. If it turns out that, in retrospect, nothing should have been invested in real estate stocks at a given time, then real estate stocks did not add any risk-‐return enhancement to the portfolio and therefore did not posses any diversifying power.
Second, a selection of variables is derived from the literature that might contain predictive power of the performances of REITs. Roughly said, the variables could be categorized by other assets and
underlying macroeconomic fundamentals. As mentioned before, the diversifying power, and
therefore the investment attractiveness of REITs, depends on the interactions of the different asset classes included in the portfolio. Therefore, a selection of bonds and stocks are included and are used as a benchmark for the national and international stocks and bonds performances. Additionally, a selection of macroeconomic variables is included, as it is expected that the macroeconomic
environment influences the correlation structure among assets and affects asset performances directly.
Third, a multiple regression model will be constructed using the before mentioned variables derived from the literature. Since it is widely recognized that correlation structures among different asset classes evolve over time as macroeconomic conditions change (Yang et al., 2012, Brenner,
Pasquariello, and Subrahmanyam, 2009; Yang, Zhou, and Wang, 2010), the effects of these variables will be measured at different economic stages in order to capture a plausible time-‐effect. The factor loadings will be estimated for the full study duration and for several subperiods covering different market conditions. By extending the model with time-‐indicating dummy-‐variables, a potential change in the predictive power of the independent variables will be captured.
Although the set of macroeconomic variables jointly represent the macroeconomic environment at a given timeframe, it is not possible to capture all latent variables. For this reason, the previous model will be extended by adding another dummy-‐variable. This dummy-‐variable will take on value 1 if the concerning month is considered a crisis period and will take on value 0 otherwise. This variable will capture a potential additional effect caused by economic distress, not covered by the
3 macroeconomic variables. By applying OLS to the new extended model it will be tested whether the crisis-‐dummy helps to reduce the omitted variable bias by reducing the unexplained variance of the previous model. Exhibit 1 represents the structure of this study and the steps that are undertaken in order to disclose the time varying diversifying power of REITs.
Exhibit 1, The time-‐varying diversifying power of REITs
The aim of this study is not simply to advise on whether one should buy or sell REIT stocks at a certain point in time. This study aims to generate more insight in what is driving REIT’s diversifying power over time by closely analyzing its fundamentals and the composition of its fundamentals over time. The results will help investors to pay attention to the right variables at the right time in order to make the right investment decisions concerning REITs.
Furthermore, this study attributes to the growing literature on real estate investments since it does not simply focus on REIT returns solely, but on the total investment performance of REITs in general. REIT optima are taken as the dependent variable in the regression, therefore comparing the total REITs performances relatively to other financial assets. Although the behavior of REITs has been studied carefully, using investment optima as the dependent variable has not been done before. By addressing the behavioral topic of REITs from a different perspective, one could yield new predictive factors or confirm previous findings concerning the fundamentals that had been unclear up to this point.
What is affecting
the diversifying
power of REITs?
Other asset
classes
Does the interaction (corrrelations) change
over time?
OLS-regression before-after analysis
Macroeconomy
Does the dependence on macroeconomic variables change over
time?
(Orthogonalized) OLS-regression before-after
analysis
Crisis
What are the additional effects of the presence of a crisis?
Dummy-variable indicating crisis
4 II. Literature review
What are the fundamentals that drive indirect real estate performance and therefore affect the investment potential of REITs? Furthermore, to what extent are these fundamentals affected by changing economic conditions?
Lack of understanding REITs Fundamentals
The diversity of literature on REITs can be explained by the fact that little consensus exists as to whether REITs should be viewed merely as a sector of the broader equity market or as a distinct asset class for asset allocation purposes (Lee and Stevenson, 2007). This debate stems from a lack of understanding the fundamentals behind real estate stocks. Understanding the driving forces behind REIT returns is crucial when one wants to know whether the asset possesses diversification benefits. When the underlying fundamentals overlap the fundamentals of the assets already in the portfolio, it is less likely that the new asset will create portfolio enhancement, in terms of mean-‐variance (Seiler et al., 1999). Up to this point, much research has been conducted in which real estate stocks are treated differently. As summarized by Chang et al. (2012), Gyourko and Keim (1992) treat REITs as a proxy of the assessment of the real estate market value, Liu and Mei (1992) argue that REITs are like small stocks, while other studies argue that REITs behave like common stocks. According to Hudson-‐ Wilson (2001), REIT performance is always inferior to stock and bond portfolios, while
Chandrashekaran (1999) supports the risk diversification argument and indicates that REIT returns are related to their historical returns. Clayton and MacKinnon (2003) reported that while through 1970s and 1980s the US NAREIT returns were driven largely by the same economic factors that drive large cap stocks, they are more closely related to both small cap stock and real estate-‐related factors in the 1990s.
Time component
Despite the lack of understanding REITs’ fundamentals, scientists continued their research in an attempt to capture the diversification benefits. Worzala and Sirmans (2003) compared fourteen studies that aim to capture the benefits of including international real estate stocks into the mixed-‐ asset portfolio. The results concerning the diversifying power of real estate stocks are mixed,
although the majority detects diversifying benefits to some extent. Diversification gains are possible, but benefits are reduced when currency risk is included in the analysis. However, it should be mentioned that all fourteen studies mainly cover the bull periods of REITs and therefore probably show biased results. The timespan of the fourteen studies cover on average eleven years, of which the only bear period taken into account is December 1997 to November 1999, which lasted only 23 months. Except for the study of Mull and Soenen (1997) and Gordon and Canter (1999), no attention
5 is paid to a possible time aspect, therefore neglecting the possibility of a time-‐varying component in the diversification power of REIT stocks. This is unfortunate, because results can differ significantly when time periods change. Hoesli et al. (2004), for example, covers the bull period of the 1980s partly and fully covers the bear period of the 1990s. According to this study, investing in real estate stocks does not generate portfolio enhancement at all. Investing in real estate securities in the US and UK generates higher returns than bonds and lower than stocks. The variance of the REITs, however, is higher than the variance of stocks, therefore making them unappealing to invest in. Mull and Soenen (1997) consider both periods of economic growth and economic downturn. They find marginal portfolio enhancement when US REITs are added to the portfolio for the whole period of their study, but find REIT stocks playing a different role when their data is separated by subsets. In the period of 1985 to 1990 US REITs were never part of an optimized Sharpe portfolio, but this changes dramatically for the subsequent period of 1990 to 1994. Adding US REITs in this period generates a substantial and statistically significant increase in the mean return and the Sharpe Index. Comparable results can be found in the study of Gorden and Canter (1999).
The different outcomes of before mentioned studies are not surprising when one examines the correlation structure among assets at times of an economic downturn. Although REITs were not always included, other studies clearly disclose a time-‐varying correlation structure among assets. Assessing the interdependence of asset markets is a complicated task as all measures are
accompanied with certain limitations. The simplest model, the Pearson correlation, is limited as it only represents the average deviation from the mean. The correlation coefficient does not make any distinction between large and small returns or between negative and positive returns (Poon et al., 2004) and is therefore inadequate in explaining asymmetric correlation between bull and bear periods (Garci and Tsafack, 2011). Using other models can be useful in overcoming these limitations, such as the multivariate GARCH model or the multivariate extreme value theory and copula functions. These models generate more insights in the interdependence topic, as the multivariate GARCH model allows observations to be nonnormal, while the last two approaches allow to deal with the extreme dependence structure of lags (Garcia and Tsafack, 2011). Nevertheless, using these traditional dependence measures could generate inaccurate portfolio risk assessment (Poon et al., 2004). Longin and Solnik (2001) warn for this as well, as they point out that many researchers have dropped wrong conclusions due to the existence of spurious relationships between correlations and volatility. However, by using extreme value theory, they derive the distribution of extreme
correlation for a wide class of return distributions and also find that correlations increase in bear markets and do not increase in bull markets. This conclusion is underlined by Mashal and Zeevi (2002), Hu (2006) and Ning (2010), whom all have found asymmetric extreme dependence among equity returns during bearish markets. Garcia and Tsafack (2011) make a distinction between
6 domestic and international stock and bond markets. They measure comovements among assets by constructing their own model which captures asymmetric effects in more detail. Their results show that dependence between international assets of the same type is strong and sometimes represents extreme comovement, while dependence between the equity and bond markets is weak, even within the same domestic markets.
Constructing the model
The before mentioned literature points out two concerning aspects to take into account. There is a lack of understanding REITs driving forces and the unknown driving factors change over time. This study will focus on both aspects, by testing a selection of possible fundamentals and their effects in general and their interaction with REITs over time. Based on the literature, a selection of variables, which plausibly explain REIT performances, will be tested. Instead on focusing on their effects on REIT returns or REIT variances solely, as previous studies have done, the effects on the REIT Sharpe optima will be measured. This optima takes into account both returns and variances of REITs, relative to the performances of other asset classes. By allowing more information to be analyzed (so both return and variances of REITs and other asset classes), more of the dynamics between the
independent variables and/or other assets are captured. A crucial aspect as mature financial markets are highly integrated and a change of one variable could be affecting all markets. Therefore,
addressing the investment strategy topic directly by taking REIT optima as the dependent variable, a valuable contribution to the literature is constructed.
Selecting macroeconomic variables
When the literature is consulted regarding the question “what variables influence the performance of REITS”, two variables arise on which authors agree. These variables directly affect the underlying real estate investments; the present value of the lease rental income (which is directly influenced by the interest rate) and the residual value of the property at the end of the lease period (which is influenced by the general economic conditions) (Chandrashekaran, 1998). Therefore, the variable interest rate should be included in the model, next to a selection of variables that jointly represent the macroeconomic conditions well.
Interest rate
The interest variable has been proven to contain predictive power of the performance of REITs (Chndrashekaran, 1998; Estrella and Mishkin, 1998) and will therefore be included. But a note of caution should be made. The reason why interest matters is because the current interest rate influences the yield curve (Estralla and Mishkin, 1998). The slope of the yield curve is often interpreted as an expectation of future economic activities, which in turn influence REIT portfolio allocation. This study, however, does not take into account future expectations, but focuses on
7 ex-‐post data solely. For this reason, it is not clear whether the interest rate will affect REIT optima in this study as well. Since one would say intuitively that the interest rate affects REITs performance directly, because it affects the discount rate of its underlying income stream, the interest variable will be included in the model. The interest rate in this model will be presented by the policy rate of the Federal Reserve and the Bank of England.
Next to the interest rate variable, a selection of variables should be added which represent the macroeconomic environment well. The literature is consulted in order to find what variables capture economic changes most accurately.
Stock market
Estrella and Mishkin (1998) examine which financial variables are the right indicators in predicting future macroeconomic outcomes for both the short term and long term. Their main conclusion is that stock prices are the best indicator of predicting recessions for time horizons of one to three quarters. Moreover, the stock market turns out to be an important predictor of the correlation structures among assets (Yang et al.,2012). In the study of Yang et al. (2012) several macroeconomic variables are used as instruments to predict daily conditional correlations among financial markets, including REITs. They find that the default spread and stock market volatility are the strongest predictors driving the correlation. Since the stock market turns out to be a predictor of both the macro economy and assets correlation structures, this variable should be added to the model. The second significant variable found in the study of Yang et al. (2012), the default spread, is in this study used as an indicator of general market conditions and turns out to be significant as it is interpreted as an estimation of future economic activity. Since this study ignores the effects of future
expectations, a different benchmark for general market conditions will be used.
Further proof of the importance of the stock market is derived from the study of Chang et al. (2012). In this study, the relationship between REIT returns and the stock market index, the interest rate and an additional general economic growth variable are examined. The expected interest rate in this model is defined by the slope of the interest yield curve and the variable credit spread is used as a proxy for the general economic activity. These variables are of no use for this study due to reasons mentioned before. The variable of interest is the stock market, which is captured by the Dow Jones index for the US sample. In contrast to the expectations, only the stock market takes on a significant value during the whole study period. After dividing the study period into a pre-‐ and post crisis period with the recent credit crunch as turning point, the interaction between the variables is measured both in bullish and bearish markets. Although the interaction between REIT returns and the stock market is significant in both periods, a stronger correlation occurs during the crisis, meaning REITs diversifying power is reduced when the economy is down.
8 GDP and unemployment
Reinhart and Rogoff (2009) conduct an opposite study of Estrealla and Mishkin (2014). Instead of focusing on variables that could indicate recessions, they focus on the effects of the aftermath of a crisis. They conduct an in-‐depth study to the depth and duration of the aftermath of financial crisis, based on all historical financial crisis that occurred in the post-‐World War II period. Their findings show that the consequences of a crisis become most apparent in the housing and equity market and are associated with a major decline in output and employment in the subsequent period. Based on a peak-‐to-‐through basis, real housing prices decline on average 35 percent in the following six years after the eruption of the crisis. Equity price collapses on average with 55 percent stretched over a period of three and a half years. The unemployment rate rises on average 7 percent points in the four years following the crisis, while output falls an average over 9 percent. The decline in output lasts shorter then the rise of unemployment, but is accompanied with a large drop of Real GDP. Real GDP drops on average 9.3 percent stretched over a period of almost two years. A remarkable
exception being the United States, which suffers from an almost 30 percent decrease in Real GDP in a period covering 4 years. These outcomes are based on countries of the so called “big five” crisis which consist of Spain, Norway, Sweden, Finland and Japan. The selection of countries is extended by emerging countries which were infected by the Asian crisis of 1997 – 1998 and the United States. According to this study, these benchmarks can be used to assess the trajectory of a financial crisis. For this reason, all before mentioned variables will be included as they jointly reflect the
macroeconomic environment. That is, the monthly unemployment rate measured by the national bureau of statistics of both countries and the quarterly nominal GDP values. In order to accurately compare today’s values with the historical values, which date back more than 25 years, inflation is ignored. For this reason nominal GDP is preferred over real GDP.
House prices
Housing prices are not simply included as a macroeconomic benchmark (as derived from the study of Reinhart and Rogoff (2009)), but also represent the underlying portfolios of REITs. Early research shows that REITs are highly linked to the unsecuritized real estate index (Giliberto, 1990) and that REITs and the unsecuritized real estate indices show the same movement trends in the long-‐term (Geltner and Rodriguez, 1998 via Chang et al. (2012)). Clayton and MacKinnon (2003) conduct a thorough study about the fundamentals of REIT returns and try to explain changing REIT variances by stock, bond and real estate performance. By testing the hypothesis whether REITs represent the underlying (unsecuritized) real estate more closely since the REIT boom of the 1990s, they decompose REIT return variability and test their dependence with other assets individually. Their results show that REITs were driven largely by factors also driving large cap stocks during the 1970s and 1980s, but were more strongly related to small cap stocks and real estate-‐related factors in
9 the 1990s. In order to simulate the effect of real estate-‐related factors, a variable needs to be included that captures changes in the value of the underlying real estate portfolios of REITs. Therefore, the variable House Index will be included into the model for both countries. The S&P/Case-‐Shiller Home Price Indices are used as a benchmark of the average house price in the United States. This index tracks the changes in house prices in 20 metropolitan regions across the US, by using the repeat sales pricing technique to measure housing markets. For the United Kingdom, the House Index of Nationwide is used which covers all UK districts.
Bonds
The variable bonds will be included in this study twice and will be used as a different benchmark in the second model. In the first model, it will simply represent one of the three asset classes included in the mixed-‐asset portfolio. Bonds are essential in constructing portfolios, as they have been part of multiple asset portfolios in most portfolio literature. After bonds are used merely as a representation of the whole domestic and international bond market, they will be used as a benchmark,
representing their underlying fundamentals driving its value. The importance of including bonds’ fundamentals becomes apparent in the study of Yang et al. (2012), as the variable default spread turned out to contain significant power in predicting correlation structures among assets. Instead of using the spreads itself, the underlying fundamentals of the significant spread variable will be used for this study. The fundamental driving the spreads is the steadiness of the fixed income-‐streams resulting from long-‐term bonds at different levels of risk. Therefore, capturing stable and long-‐term bonds into the model will probably explain more of the attractiveness of REITs in relation to the other assets. The predictive content of bonds on REITs’ investment performances is underlined by Clayton and MacKinnon (2003). They argue that REITs performances are due to the relatively fixed nature of the cash flows derived from income-‐property with long-‐term leases and high-‐credit quality tenants, related to the same fundamentals that drive bond performances. For this reason, the high-‐ credit quality fixed-‐income flow will be represented by government bonds from developed countries with a 10-‐year horizon.
Crisis
Although attention is paid to the interaction between the independent variables and the REIT optima at times of different economic market conditions, extra attention should be paid to distressed periods. As addressed earlier, asset markets become more integrated at times of bearish markets, as has been documented by Garcia and Tsafack, (2011), Poon et al. (2004), Longin and Solnik (2001), Mashal and Zeevi (2002) and Ning (2010). Sudden financial distress, however, cannot be compared to a general declining stock market as the aftermath of a stock market crash is more serious in terms of depth. The consequences of a crisis have been captures in the study of Yang et al. (2012). In this
10 study a shift in the fundamentals is found that drive correlations among the asset markets after the recent financial crisis of 2007. Beginning in early August, the stock market volatility lost its predictive power and instead, the term spread became more prominent.
Hartmann et al. (2004) capture similar extreme linkages in stock returns during periods of financial turmoil. By using a measure from statistical extreme-‐value analysis, the authors capture the dependence structure of multivariate distributions far away from the center, making it possible to capture market linkages in crisis periods directly. This way, there is no need to analyze correlations first, therefore omitting the before mentioned inaccuracies which are accompanied with correlation-‐ analysis. Hartmann et al. (2004) find that the stock market effects are not present in the bond market. On the contrary, rallies into the bond markets are witnessed at times of financial turmoil as a flight-‐ to-‐quality arises from stocks into bond markets. Unfortunately, this study focuses on the years 1887 to 1999 and therefore only marginally overlaps the time span of this study. However, findings are useful as both United Kingdom and United States are included in their study as well.
11 III. Methodology
In order to find out to what extent real estate stock performances depend on other financial markets and the macroeconomic environment, a two-‐step approach is needed. First, the question “how much of the market portfolio should have been allocated to real estate stocks?” should be addressed by constructing optimal portfolios for every month of the study’s timespan. Subsequently, the interaction between these optima and a selection of variables should be analyzed, with special attention paid to the relationship at times of economic prosperity and economic downturns.
Constructing the dependent variable; optimal portfolios
The first step is to generate optimal portfolios on a monthly basis in order to obtain data on the optimal levels of real estate stocks. Portfolios are constructed by optimizing the mean-‐variance ratio, which means that portfolios containing the highest Sharpe ratio of every month will be selected. Since historical data is used and portfolios are constructed in retrospect, this study focuses solely on the actual returns instead of expected returns. Putting in other words, by using ex-‐post data, only historical performances are taken into account and therefore any influence arising from future expectations are excluded. Although future expectations play a crucial part in the investment decision – the importance is represented by the abundant literature addressing this topic – omitting these influences is necessary if one wants to measure the (changing) composition of the
fundamentals of REITs.
Portfolios are constructed using six different asset classes for every country, covering domestic and international real estate stocks, domestic and international stocks and domestic and international government bonds. The countries that are analyzed are derived from the literature and cover the United Kingdom and the United States. Both the international and domestic indices are summarized in the table of exhibit 2 below.
Exhibit 2, data summary Domestic RE
stocks International RE stocks Domestic stocks International stocks governmenDomestic t bonds International government bonds UK FTSE EPRA /Nareit UK FTSE EPRA /Nareit Developed FTSE (mid-caps included)
MSCI World 10-y bonds
UK
10-y bonds average of 22 developed countries US FTSE EPRA /Nareit US FTSE EPRA /Nareit Developed
S&P 900 MSCI World 10-y bonds
US
10-y bonds average of 22 developed
countries
12 All price indices in the table listed above are expressed in the country’s own currency, meaning that returns are unhedged. The only exception being the FTSE EPRA/Nareit UK index, which is given in dollars, due to limited data access.
The daily index values of the assets are retrieved from Datastream. Portfolios are constructed, starting in 1995 since this is the year where most mid cap indices and the Nareit index went public, up to the end of 2013. By using the actual daily price index values, the optimal amount of domestic and international real estate stocks will be constructed for every month of the study’s timespan. For each country, the value of domestic real estate stocks is represented by the domestic FTSE EPRA/Nareit indices. The content of the international real estate stock performance – which is captured in the FTSE EPRA/Nareit Developed Price Index – is limited to real estate data of the developed countries. The markets of emerging countries are often immature, which results in less integrated financial markets in comparison to mature markets. Therefore, the financial markets of emerging countries show more diversifying potential and cannot simply be compared to developed markets without controlling for this. Another reason for narrowing down the definition of
“international” is to maintain consensus among the data. Both the data on international stocks and international bonds are limited to developed markets as well. Therefore, excluding information on real estate of emerging markets creates a more homogenous dataset and generates more accurate comparisons among the asset classes.
In order to obtain data on the domestic stocks, the largest stock index of every country is selected, combined with the performance of the domestic mid caps. The variable domestic stock
market of the United Kingdom consists of a combination of the FTSE 100 and the UK mid caps, which
together amount 622 constituents. For the United States the S&P 900 is selected, which consists of 900 large and mid cap companies. Since data on the S&P 900 was published for the first time in June 1995, the first optimal portfolios of the United States are constructed starting from July 1995. Portfolio construction of the UK starts at January 1995.
The MSCI World Index represents the international stocks. This index covers large and mid cap companies across 23 developed markets. The index consists of 1612 constituents and covers approximately 85% of the free float-‐adjusted market capitalization in each country1.
13 As explained in chapter two, 10-‐year government bonds are selected for both the domestic and international asset classes. These steady long-‐term government bonds are used as two different measures in this study. In the first regression this asset class is used as a representation of the bond market. Afterwards, it is used as a benchmark for the shared fundamentals that bonds have in common with REITs. In order to capture the performance of international bonds into the model, a variable is created which is based on the WGBI Citigroup international bonds index. This latter index covers the government bonds of different maturities of more than 20 developed countries. Since this index only contains monthly data, it is not used for this study. In order to construct optimal portfolios on a monthly basis, detailed information (i.e. daily data) is needed to calculate monthly variances of the assets accurately. Therefore, a different index is created which is based on the Citigroup bonds index. The variable International bonds contain indices of 10-‐year government bonds of the countries listed in the table below.
Exhibit 3, countries included in indices Nareit
Developed MSCI Citigroup International bonds
Common countries Norway, Sweden, Finland, France, Spain, Italy, Greece, Portugal, Germany, Netherlands, Belgium, Switzerland, Austria, United Kingdom, United States, Canada, Australia, Japan
Additional countries
South-Korea Singapore, Hong Kong, Israel, New
Zealand
Ireland, Singapore, Hong Kong, Israel,
New Zealand South-Africa, Malaysia, Mexico, Poland, Singapore South-Korea, Ireland, New Zealand
The new international bond index is more appropriate for this study because it offers daily data. Furthermore, the Citigroup index uses government bonds of different maturities, while the new index focuses solely on 10-‐year maturity bonds, just like the domestic bond indexes. Additionally, the selection of countries of the new index is a better composition than the Citigroup index. The
countries South-‐Africa, Malaysia, Mexico and Poland are not considered as developed by the other two international indexes of this study and are therefore excluded from the newly generated international bond index. Hence, omitting these countries will benefit unity among the data.
Data frequency
Two parameters of each individual variable are required to generate optimized mean-‐variance portfolios; the variance, as well as the return of the asset. In order to capture the interaction
between real estate and the macro-‐economy in detail, portfolios will be constructed frequently, that is, on a monthly basis. Focusing on higher-‐frequency dynamic linkages is important in order to capture in-‐depth dynamics (Yang et al., 2012). The advantage of constructing portfolios on a monthly basis instead of (for example) a quarterly basis is that the short-‐term (or direct) effects of a variable, caused by a change in value of another variable, can be measured more precisely. After the data
14 of interest is generated, attention will be paid to the long-‐term environmental influences on REIT performances as well. The real estate optima will be regressed on several macroeconomic variables and their lags, in order to capture effects beyond the scope of one month.
The variance and returns are constructed on the last trading day of the month. In order to construct the variance, all daily returns of the concerning month are taken into account. This results in the variance of the S&P 900 of the 31st of January 1996 being based on the daily observations of the
month January. The returns are presented by the percentage change of the index of the last day of the month of interest, in comparison to the last day of the previous month. As not every month counts an equal amount of trading days, both variance and return are constructed based on the information of the last 21 trading days, which equals approximately one month. The average amount of trading days in one year is 250 (in 2013 this was 252)2. This means that on average a month
includes (250/12) 20.8 trading days. As a consequence, using the daily information of the previous 21 trading days will generate parameters that show a close resemblance of the monthly activities.
Sharpe
After the monthly variances and returns of the individual asset classes have been constructed, a bordered variance-‐covariance matrix can be composed. This matrix calculates the variance of the portfolio, which is required to construct Sharpe ratios. Using Excel and more specifically the Solver program, optimal portfolios will be constructed from January 1995 up to November 2013. This means that 227 results will be generated for the United Kingdom. Since the data on the S&P 900 of the United States starts from July 1995, 221 optimal portfolios will be constructed for this country. In this study, it is assumed that no transaction costs exist and short selling is not allowed.
Subperiods
In order to reveal the time-‐varying composition of the fundamentals of REITs, the regression will be run several times, covering different subperiods. The sample period is divided into periods of economic growth and economic downturns so as to create a comparison of the estimators at times of different market conditions. The benchmark in determining the turning points in time will be the performance of the stock index of the specific country. The highs and lows of the S&P 900 and FTSE will be used for the US and UK respectively. The course of the stock indices is pictured in exhibit 4.
15
Exhibit 4, Price Index of the S&P 900 and the FTSE with mid-‐caps included
07-'99! 10-'02! 08-'07! 03-'09! 0! 500! 1000! 1500! 2000! 2500! 3000! 3500!
S&P 900 Price Index!
03-'03! 08-'00! 06-'07! 03-'09! 0! 500! 1000! 1500! 2000! 2500! 3000! 3500! 4000!
16 Turning points arise approximately at the same time for both countries, except for the first two periods. Economic growth in the US ended at the end of June ’99 as the S&P 900 reached its highest point. Subsequently, an economic downturn occurred, starting from July ’99 up to the beginning of the recovery period, which started in the first part of October ’02. The flourishing economy reached its all time high peak at the end of July ’07. In August 2007 the credit crunch officially erupted, reaching its lowest point at the beginning of March ’09. After this, the economy started to recover and continued its growth up to the end of the sample period. The FTSE Index of the UK followed a similar course to the S&P 900. The first growth period lasted slightly longer, up to the last day of August ’00. Economic distress continued up to March ’03 and started again in the beginning of July ’07. The recovery of the credit crunch started at the beginning of March ’09.
REITs’ dependence on stocks and bonds
As mentioned earlier, asset market integration at times of economic distress is widely recognized. However, no study has approached this topic by using portfolio optima as the dependent variable. A multifactor model will be used to construct the effects of stock and bond returns on the optima of REITs first. The independent variables are limited to stocks and bonds, since only these assets are included in the portfolios. As mentioned earlier, it is expected that REITs are affected by both stock and bond fundamentals, therefore significant estimators are expected. The following regression model will be conducted for the countries individually:
(1) 𝐎𝐩𝐭𝒊,𝒕= 𝛂 + 𝛃𝒊,𝟏∗ 𝒓𝐬𝐭𝐨𝐜𝐤𝒊,𝒕+ 𝛃𝒊,𝟐∗ 𝒓𝐁𝐨𝐧𝐝𝐬𝒊,𝒕+ 𝒖𝒊,𝒕
With 𝒊 indicating the country and 𝒕 indicating the exact month. The variables 𝒓𝐬𝐭𝐨𝐜𝐤𝒊,𝒕 and 𝒓𝐁𝐨𝐧𝐝𝐬𝒊,𝒕
capture the stock and bonds returns respectively of the specific month. The error term 𝒖𝒊,𝒕
represents the unexplained portion of the REIT optimum. It is assumed that the expected value of 𝒖𝐢,𝐭 is zero and not dependent on any other values included in order to generate consistent and unbiased estimators. Depending on the results, the model will be extended by adding lags of the independent variables. Since the values of the variables are measured at a monthly frequency, it is plausible that the performance of the assets of the previous month(s) contain predictive power as well. By modeling the equation from general to specific, the number of lags will be chosen, based on significance.
Model (1) will be first applied to the full study period, therefore making it difficult to reveal short-‐ term interactions. In order to capture time-‐varying fluctuating effects of the independent variables, model (1) should be applied separately to shorter-‐term periods as well. The turning points illustrated in exhibit 5 will be used to mark the beginning and ending of subperiods. After applying model (1) to these subperiods, the equation will be extended. First, a dummy-‐variable is created which takes on
