The relationship between residential real
estate prices and stock prices
Evidence from the United States
Michael F.A. Mijlof
10666532
June 2016
Bachelor of Science Thesis
Thesis coordinator:
Dr. P.J.P.M. Versijp
Thesis supervisor:
Dr. M.I. Dröes
University of Amsterdam
Faculty of Economics and Business
Specialization: Finance
Table of contents
1. Introduction 4 2. Literature review 6 2.1 Characteristics of real estate 6 2.2 Characteristics of stock prices 7 2.3 Relationship between real estate and stock prices 7 2.4 Hypotheses 10 3. Data 11 3.1 Main explanatory variables 11 3.2 Control variables 13 4. Methodology 15 4.1 Regression 15 5. Results 18 5.1 Regression analysis 18 5.2 VAR-analysis 21 5.3. Impulse response functions 23 6. Conclusion 25 7. Reference list
Abstract
Real estate was one of the major causes for the last financial crisis. Due to very complex mortgage derivatives, everyone was able to purchase a house. After a while, the bubble crushed and many people just left their house. As a result of this housing problem, many stock markets worldwide collapsed. These houses are categorized as residential real estate, which means that they are not used for a business purpose. In this thesis, the relationship between stock prices and residential real estate will be examined. This research focuses on the diversification effect of real estate investments for the stock portfolio. However, there will be a simultaneous causality between stocks and real estate and therefore, not only two regressions with different dependent variables are done but also a vector autoregression is used. Concluding, it can be stated that there is a multidirectional effect between stock prices and residential real estate prices. The effect of stock prices on residential real estate prices has stronger statistical evidence compared with the effect of residential real estate prices on stock prices, where the statistical evidence is weak. On the long run, which can be seen in the impulse response functions, the same pattern occurs. It can also be stated that there is indeed a lagged effect in residential real estate. This result is in line with momentum strategy in real estate markets, which is examined in earlier research. Statement of originality This document is written by, M.F.A. Mijlof, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business of the University of Amsterdam is responsible solely for the supervision of completion of the work, not for the contents.
1. Introduction
In the recent financial crisis in the United States, real estate was one of the major causes. Especially financing real estate by mortgages and the complexity of the mortgages derivatives traded by investment banks were the main factors of the financial crisis. The mortgages were repacked in other financial products and traded to gain huge profits. These repacked mortgage derivatives were called Collaterized Debt Obligations (CDOs). Though, these derivatives became too complex after a while that even the brokers at the investment banks did not know what these CDOs exactly were. This led to a massive real estate bubble and, as a result, this led to one of the greatest financial crises in human history. Almost all the stock markets worldwide collapsed due to the crushed bubble in the real estate market. The real estate market is one of the most feasible kinds of investments. Stocks, bond, options and other derivatives are mostly intangible where real estate is tangible. A lot of investors will invest in stocks of notable companies worldwide or in bonds issued by safe countries but only a few investors are using real estate as an investment. The majority of those investors are using real estate as a diversification method to hedge the idiosyncratic risk of companies. However, it is not exactly clear if there really is a diversification effect or what kinds of real estate investments are the most suitable to get this diversification effect. Many investors are using indirect real estate such as Real Estate Investment Trusts (REITs) or direct commercial real estate. For instance, Ling and Narajo (1999) investigated the relationship between commercial real estate prices and stock markets. Specifically, they investigated the integration of commercial real estate markets and other asset markets. This integration is very important for portfolio diversification strategies. Another example is the research of Lee et al. (2012), who investigated the interrelationship between stocks and REITs for the market of Taiwan. Their findings were that there is a relationship between REITs and the stock market, which can be seen by the fact that all the variables indicate break points, reflecting shocks, for example, the Subprime Mortgage Crisis. To use real estate investments as diversification effect, there should be a low or zero correlation between stocks and real estate. These REITs and commercial real estate are mainly used for a business purpose. However, there is a lack of research on using residential real estate as a diversification. Residential real estate contains houses, so it can be defined as real estate that is not used for a business purpose.
According to a recent news article published by CNBC, the U.K. investment bank Barclays is issuing mortgages of 100% (Barnato, 2016). These risky mortgages were, as mentioned before, one of the main causes of the global financial crisis in 2008. When looking at the global stock markets, the prices went up since the recent financial crisis. For instance, the S&P500 notated an index price of $968.75 in October 2008 and $2049.64 in May 2016 (Yahoo, 2016). Another example can be given from the Eurozone, namely that the FTSE100 notated an index price of $4377.30 in October 2008 and $6098.48 in May 2016 (Yahoo, 2016). Due to these examples, it can be seen that the stock prices are rising since the crisis again. The investment bank Barclays is also issuing full mortgages again. The S&P500 is even on their highest price level. As a result of all these current events in the real estate and stock market, the main research question of this thesis will be:
‘what are the effects of stock prices and residential real estate prices on each other in the United States?’
Many databases are used to extract the data that are needed in this research. One of the main explanatory variables, residential real estate prices, is obtained from the Federal Housing Finance Agency. It contains monthly data. This database is an index where the base year is set on January 1st 1991. The other main explanatory variable,
stock prices, is acquired from the CRSP Stock Market indexes. It contains monthly absolute values of the S&P500. The other variables in this research are used as control variables to get a more unbiased answer. These control variables are population, construction costs, gross domestic product, inflation rate and mortgage rate, which are assumed to be exogenous. These variables contain monthly data besides gross domestic product. The time period for the research starts at January 1st 1993 until January 1st
2016. Lastly, all the variables are calculated in first differences after converted into a logarithmic scale.
The research question will be answered by an empirical analysis using a multiple regression model. The dependent variable will be residential real estate prices and the main explanatory variable will be stock prices and vice versa. Reason for this is the simultaneous causality that appears between the two main variables. These regressions are all computed with robust standard errors. Moreover, to get a more unbiased conclusion, a VAR-analysis will also be executed. VAR-analysis means vector
autoregression and it is an econometric technique where interdependence between two variables over time is controlled.
In order to answer the main question, there will be a literature review to explain the factors that are important for the research. After that, the econometric analysis will be explained in more detail. The regression, hypothesis and all the variables will be specified. Subsequently explaining the econometric analysis, the results will be discussed extendedly. Finally, the research question will be answered in the conclusion.
2. Literature review
In this section, the two main components of the research, which are stock prices and real estate, will be defined. First, their characteristics will be explained and second, the relationship between the two components will be examined. Finally, the hypotheses for this research will be stated.
2.1 Characteristics of real estate
According to a research by Kuryj-Wysocka et al. (2014), real estate value is a concept that reflects both price and market characteristics. It is a multidimensional category, which contains spatial, economic and investment dynamics. These dynamics present the value and potential of real estate. Particular elements of a market may change not only under the influence of the interdependence, which exists between them, but also under the influence of extrinsic factors that constitute the environment of the market. The real estate market is therefore the result of many factors in this system, either external or internal (Kuryj-Wysocka et al., 2014). Dynamics of the real estate market can have different values, which depend on the trade cycle, product life cycle and macroeconomic environment. Based on the time needed for planning and construction of real estate, the largest investors try to act in advance and start a construction before their competitors observe an economic recovery and report the demand for commercial and residential surfaces (Kuryja-Wysocka et al., 2014). As a result, many factors affect real estate prices but most importantly, the effects are delayed due to long construction time of real estate.
Lieser and Groh (2015) found in a recent study that a productive economy positively affects the demand for real estate assets. It is also intuitive that real estate is related to the general economic activity of a region or country. Hoskin et al. (2014)
found that gross domestic product (GDP), inflation rate and interest rates are correlated with real estate returns. They also found evidence that due to real estate supply characteristics, the real estate cycle lags behind movements of macroeconomic variables. As a result, it is not only important to incorporate lags in the variables when analyzing real estate but also to incorporate main macroeconomic factors that affect the economy as a whole.
Mulder (2006) found that the relationship between population and housing is two-sided. On the one hand, population change leads to changing demand in housing. Population growth, particularly the growth in the number of households, leads to growth in the housing demand. Population decline could, in the long run, lead to a decrease in housing demand. But at the same time, the supply of housing influences the opportunities for population increase through immigration and the opportunities for people to form new households (Mulder, 2006). Therefore, population size is an important factor for residential real estate prices.
2.2 Characteristics of stock prices
According to the seminal work of Fama and Burton (1970), the primary role of the capital market is allocation of ownership of the economy’s capital stock. The ideal is a market in which prices provide accurate signals for resource allocation. This is a market in which firms can make production-investment decisions and investors can choose among the securities that represent ownership of firms’ activities under the assumption that security prices at any time fully reflect all available information. The market is called efficient when that is the case (Fama & Burton, 1970). As a result, stock prices are also affected by internal and external factors but the effects are not delayed, which is the case for real estate prices.
In a recent empirical study, Bhargava (2014) found by estimating dynamic models with maximum likelihood that external firms’ fundamentals such as interest rates affect quarterly stock prices for approximately 3000 firms in the United States. In addition, other macroeconomic variables such as unemployment rates in different sectors of the economy reflect the demand for firms’ products and services. Also, higher interest rates increase the cost of borrowing, especially for high leveraged firms. Thus, shocks to the economic system reflected by macroeconomic variables are likely to play an important role in explaining stock prices (Bhargava, 2014).
Birz & Lott (2011) investigated whether economic news, such as changes in gross domestic product, affects stock returns. By examining the effect by performing a regression analysis, they found that news about GDP growth and unemployment significantly affects stock returns (Birz & Lott, 2011). For this reason, it is important to incorporate macroeconomic variables such as interest rates and gross domestic product to control for, when analyzing stock prices. 2.3 Relationship between stock prices and real estate Many authors of previous researches about the relationship between real estate prices and stock prices argued that commercial real estate has a diversification effect because of the low correlation with generally used stock price indices such as the S&P500 (Quan & Titman, 1999). According to Quan and Titman (1999), these low correlations are surprising due to the fact that the level of economic activity and interest rates affects them both. For example, stock prices may increase because of more investment opportunities and this increase could in turn lead to an increase in real interest rates. As a result, this could reduce the value of commercial buildings even if the rental prices are rising. Other factors that may cause a negative relation between real estate prices and stock prices are changes in the cost of labor. Furthermore, Quan and Titman (1999) stated that the low correlation found by earlier researchers could be an artifact of the data. The reason for this is because real estate trades infrequently which causes the researches to rely on indices on estimated or inferred real estate prices. Due to this inferring process, such indices are often smoothed and they thus underestimate the true volatility of the commercial real estate as well as the covariance between real estate price changes and stock returns. Hence, commercial real estate may provide less diversification benefit than indicated by former researchers. The study of Quan & Titman (1999) provided some new evidence on the relation between stock returns and real estate prices changes by analyzing real estate price indices, stock prices and macroeconomic data from 17 countries. These countries include the largest industrialized economies as well as the smaller emerging economies. In contrast to other studies, Quan and Titman (1999) found a positive relation between stock returns and changes in commercial real estate values. They also estimated additional regressions to provide some insights into why these two returns series are correlated. Their analysis suggests that the correlation found between real estate values and stock
prices arises because of current economic fundamentals and not because of expectations about future growth. Moreover, they found that rental rates, which are the primary determinant of real estate values, are strongly correlated with GDP growth rates as well as stock returns. The only limitation that Quan and Titman (1999) gave is that there is likely to be some correlation between the measurement errors in the real estate prices series and the corresponding measurement errors in the rental rate series. This could lead to a bias in the final regressions that examine the effect of stock prices on real estate prices. In this research, rental prices are not used and therefore, the bias will not occur.
The study of Okunev et al. (2000) examined the causal relationship between the real estate market and trends within the stock markets. Their objective is to determine any real and significant relationships exists between these two markets and what implications they can have for investors, policymakers and other stakeholders. The general motivation of the research is the fact that if it is possible to determine the causal relationship between the two markets, it can yield a number of insights that can aid investors and speculators to forecast future performance. The empirical test is executed by a number of causality tests that are conducted for monthly returns on Real Estate Investment Trusts (REITs) and the S&P500 for sample period of more than twenty years from 1972 to 1998. They investigated the dynamic relationship by both linear and nonlinear causality tests (Okunev et al., 2000). The results show that there is some causality that runs from real estate to stock markets but there is no evidence of any long-run linear relationship. Explanations could be primarily the existence of structural breaks within the time series and a nonlinear relationship between the markets. Furthermore, when a nonlinear causality test is conducted, a strong unidirectional relationship running from the stock market to the real estate market is evident which is consistent in the presence of any breaks (Okunev et al., 2000). The limitation given by Okunev et al. (2000) is that their research shows that the stock market affects and determines returns in the real estate market but the way in which it does so is not as clear cut as it might be with other financial assets.
Li et al. (2015) provided some insights on the linkages between the U.S. housing and stock markets. These markets are the two largest and principal components of wealth in the U.S. economy. Movements in their market values can dramatically affect the economic condition of families and business and, hence, affect the overall growth of
the U.S. economy. Booms and busts have always played an important role in the U.S. business cycle history. The most recent financial crisis and Great Recession created an economy-wide housing bubble burst followed by a remarkable stock market crash, causing the U.S. and the world economies to suffer huge financial losses. The focus of Li et al. (2015) is from the perspective of macroeconomic policy makers who want to use movements in these markets to analyze the business cycle. This differs from other existing literature that focus on the relationship between the real estate markets and stock markets from the financial perspective of investors who want to diversify their portfolios. According to Li et al. (2015), the nature and direction of causality between the two markets can aid policymakers and investors to forecast future performance from one market to another. First, the wealth effect indicates that a rise in stock prices and, hence, an unexpected gain in stock returns causing a boost in real estate prices, while the second, credit-price effect, suggests that a rise in real estate can, in turn, lead to an increase in stock market prices. Li et al. (2015) applied the novel wavelet analysis. That is, since the presence of structural breaks made the result of non-causality between these two assets returns from standard linear causality test invalid, they needed to adopt a time-varying approach. Wavelet analysis allows a simultaneous assessment of co-movement and causality between the two returns in both the time and frequency domain. They find that the co-movement between the two returns varies across frequencies and evolves with time. However, they did not find any stable causal link between U.S. housing and stock returns for the whole sample but only substantial time and frequency effects were found. In other words, macroeconomic policy makers cannot rely on the stock or housing market movements as the predicting factors of the business cycle.
The paper of Ling & Naranjo (1999) tested whether commercial real estate markets are integrated with stock markets using multifactor asset pricing models. The results of their research support the hypothesis that the market for exchange-traded real estate companies, including REITs, are integrated with market for exchange-traded (non-real-estate) stocks. The degree of integration even increased significantly during the 1990s. However, when appraisal-based returns (adjusted for smoothing) are used to construct real estate portfolio returns, the results fail to support the integration hypothesis, although this may be able to reflect the inability of those estimated private market return to accurately proxy for commercial real estate returns. This result
suggests that models of commercial real estate returns and stock price returns that exclude consumption risk are misspecified.
2.4 Hypotheses
According to the literature, real estate prices are affected by internal and external factors. They depend on macroeconomic situations such as gross domestic product, interest rate and demographic situations such as population but all these effects are lagged. Also, according to the literature, stock prices are, just as real estate, affected by internal and external factors. For instance, they also depend on macroeconomic situations such as gross domestic product and interest rates.
Earlier work already investigated the relationship between stock prices and real estate prices but they were mainly focused on commercial real estate or indirect real estate investments such as REITs. This thesis will focus on the relationship between residential real estate and stock prices from a financial perspective. Due to these differences, this thesis will contribute to the existing literature.
Concluding, the first hypothesis will be: ‘there is a direct effect between stock
prices and residential real estate prices’. The second hypothesis will be: ‘there is a direct effect between residential real estate prices and stock prices’.
3. Data
In this section, the data that will be used in the research is explained in detail. Specifically, it will be examined where the data is derived from, what kind of data it is, more details about the descriptive statistics and at last, why it is incorporated. Firstly, the main explanatory variables will be explained and secondly, the control variables will be explained. 3.1 Main explanatory variables
Firstly, one of the two main variables, namely residential real estate prices, will be explained. Residential real estate prices are derived from the Federal Housing Finance Agency (Federal Housing Finance Agency, 2016). The data contains monthly house prices indexes for the United States that are not seasonally adjusted. Within this dataset, the base year was set on January 1st 1991 at an index price of 100. From Table 1, it can
can be derived that residential real estate price were rising since January 1993 till approximately July 2007. After that peak, the residential real estate prices dropped, especially, during the crisis between 2008 and 2010. When the crisis was over, the prices of real estate started rising again. Secondly, the other main variable, stock prices will be explained. Stock prices are derived from the CRSP Stock Market Indexes (The Center for Research in Security Prices, 2016). The data contains monthly absolute values of the S&P500. Reason for using the S&P500 is that the index already is diversified for all the individual risks of the firms and it only contains market risk. One firm can have more effect on residential real estate prices and vice versa, this could lead to a biased analysis. Therefore, using a well-diversified portfolio, will lead to a more unbiased analysis. According to Figure 2, the stock prices were falling during the crisis, which was also the case for the residential real estate prices.
Table 1
Descriptive statistics
Variable #Observations Mean Std. Dev. Min Max
Residential Real Estate Prices 277 170.2444 40.92452 104.07 229.48 Stock Prices 277 1165.442 413.1714 438.78 2107.39 Population 277 292713.9 18680.42 258679 322997 Construction costs 277 29364.45 10635.97 12141 60866 Gross domestic product 277 12288.45 3387.899 6748.2 18221.1 Inflation rate 277 191.7906 30.06381 142.8 238.302 Mortgage rate 277 6.129061 1.485511 3.35 9.2
3.2 Control variables
At first, one of the control variables, namely population, will be explained. Population is derived from the database of the Economic Research, Federal Reserve Bank of St. Louis and the source is the U.S. Bureau of the Census. It contains monthly data of the total population of the United States. All the values are in units of thousands (U.S. Bureau of the Census, 2016). The population is constantly rising. The minimum value of 258.679.000 is the first observation, namely on January 1st 1993, and the maximum
value of 322.997.000 is the last observation, namely on January 1st 2016. This control
variable is incorporated because when the population is rising, the demand for housing should also be rising. Due to economic intuition, it can be stated that there will be a positive effect of population on residential real estate prices. According to Table 2, the effect of population on residential real estate prices is quite high as well. The coefficient is 0,8948, which means that there is a strong correlation.
Second, another control variable, namely construction costs, will be explained. Construction costs are derived directly from the U.S. Bureau of the Census. It provides the monthly estimates of the total dollar value of construction work done in the United States with a focus on private residential real estate. The units of the data are in millions of dollars (U.S. Bureau of the Census, 2016). This control variable is incorporated because higher construction costs will lead to higher residential real estate prices. Reason is that when construction costs are higher, the firms have to sell the house for a higher price to maintain their profit marge or to not make a loss. In this case, it can also be stated that there will be a positive effect of construction costs on residential real estate prices. According to the correlation matrix in Table 2, the effect of construction costs on residential real estate prices is indeed positive. The coefficient is 0.5952, which means that there is a moderate correlation.
Third, the control variable gross domestic product will be explained. Gross domestic product is again derived from the database of the Economic Research, Federal Reserve Bank of St. Louis and the source is the U.S. Bureau of Economic Analysis. It contains quarterly data of the gross domestic product of the United States. Gross domestic product is the market value of the goods and services produced by labor and property in the United States (U.S. Bureau of Economic Analysis, 2016). The units are in billions of dollars. Reason of incorporating gross domestic product is because it is a measure of the macro-economic situation of the United States. When gross domestic
product is high, it means that the economy is doing well as a whole and this will definitely have an effect on residential real estate prices. According to Table 2, the effect of the gross domestic product on residential real estate is positive and very high. The coefficient is 0.91, which means that there is an almost perfect relationship between the two variables. Fourth, inflation rate, another control variable, will be explained. Inflation rate is derived from the database of the Economic Research, Federal Reserve Bank of St. Louis and the source is the U.S. Bureau of Labor Statistics. It contains monthly data consumer price index for all items. More defined, it is a measure of the average monthly change in price for goods and services paid by consumers between any two-time periods (U.S. Bureau of Labor Statistics, 2016). This variable is also almost constantly rising, only with some minor exceptions. Inflation rate is incorporated due to the fact that when the inflation rate is high, people will forward their purchase of goods, services and also real estate. As a result, the inflation rate will affect the residential real estate prices because when people are forwarding their purchase of real estate, the demand will increase and prices of residential will also increase. According to the correlations in Table 2, the effect of inflation rate on residential real estate is highly positive. The coefficient is 0.8816, which again means that there is strong correlation.
Fifth and as last, the mortgage rate, also a control variable, will be explained. Mortgage rate is also derived from the database of Economic Research, Federal Reserve Bank of St. Louis and the source is Freddie Mac. It contains monthly data of the average 30-years mortgage rate in the United States (Freddie Mac, 2016). The mortgage rate is almost constantly decreasing since October 1st 2008, when the mortgage had an average
of 6.20% till January 1st 2016, when the mortgage rate had an average of 3.87%. The
reason for this is obviously the last financial crisis. Furthermore, the variable is incorporated because the mortgage rate is much more related to the residential real estate prices than, for instance, the real interest rate. The mortgage rate will negatively affect the residential real estate prices, because when mortgage rates are rising, demand of housing will decrease. As a result, people have to pay more interest for their mortgage and housing prices will also decrease. According to Table 2, the effect of mortgage rate on residential real estate prices is highly negative. The coefficient is -0.7422, which means that the correlation is quite strong.
Table 2
Correlation matrix
RREP SP POP CC GDP IR MR
RREP 1 SP -0.0798 1 POP 0.8948 -0.0525 1 CC 0.5952 -0.0646 0.2629 1 GDP 0.9100 -0.0545 0.9953 0.2877 1 IR 0.8816 -0.0543 0.9950 0.2222 0.9956 1 MR -0.7422 -0.0134 -0.9081 -0.0995 -0.8982 -0.9095 1 Furthermore, the time period for the data is from January 1st 1993 till January 1st 2016,
so, the research is for 23 years. Also, the data, excluding gross domestic product and inflation rate, are not seasonally adjusted because in this case, we can also give a conclusion about the seasonal component of the variables. When there is a conclusion for the seasonal component, we can forecast future house prices or stock prices in a more precise way.
4. Methodology
This section will explain which method is used and why this method is applied in this research. Specifically, the regression analysis will be explained and their variables. 4.1 Regression To answer the research question: ‘what are the effects of stock prices and the residentialreal estate prices on each other in the United States?’ a regression analysis is executed.
The regression analysis will be a multiple regression with endogenous variables and exogenous variables. Residential real estate prices and stock prices are assumed as the endogenous variables where the control variables are assumed to be the exogenous variables. To test the multi-causality between the stock prices and residential real estate prices the coefficients β1 and γ1 are of main interest tested in this research. The
regression equations are the following:
𝟏) 𝜟𝒍𝒏(𝑹𝑹𝑬𝑷𝒕) = 𝜷𝟎+ 𝜷𝟏𝜟𝒍𝒏(𝑺𝑷𝒕!𝟏) + 𝜷𝟐𝚫𝒍𝒏(𝑹𝑹𝑬𝑷𝒕!𝟏) + 𝜷𝟑𝜟𝒍𝒏(𝑷𝑶𝑷𝒕) + 𝜷𝟒𝜟𝒍𝒏(𝑪𝑪𝒕) +
𝜷𝟓𝜟𝒍𝒏(𝑮𝑫𝑷𝒕) + 𝜷𝟔𝜟𝑰𝑹𝒕+ 𝜷𝟕𝚫𝑴𝑹𝒕+ 𝚫𝜺𝟏,𝒕
𝟐) 𝜟𝒍𝒏(𝑺𝑷𝒕) = 𝜸𝟎+ 𝜸𝟏𝚫𝒍𝒏(𝑹𝑹𝑬𝑷𝒕!𝟏) + 𝜸𝟐𝜟𝒍𝒏(𝑺𝑷𝒕!𝟏) + 𝜸𝟑𝜟𝒍𝒏(𝑷𝑶𝑷𝒕) + 𝜸𝟒𝚫𝒍𝒏(𝑪𝑪𝒕) +
These regressions will be used to test the following hypothesis to an answer the research question. Mathematically, the main hypotheses will be:
𝐻0: 𝛽!𝛥𝑙𝑛 (𝑆𝑃!!!) & 𝛾!𝛥 𝑙𝑛 𝑅𝑅𝐸𝑃!!! = 0 and 𝐻1: 𝛽!𝛥𝑙𝑛 (𝑆𝑃!!!) & 𝛾!𝛥𝑙𝑛 (𝑅𝑅𝐸𝑃!!!) ≠ 0 Table 3 List of variables RREPt Residential real estate prices at time t SPt Stock price index of the S&P500 at time t SPt-1 Stock price index of the S&P500 lagged with one month RREPt-1 Residential real estate prices lagged with one month POPt Population of the United States at time t CCt Constructions costs at time t GDPt Gross domestic product of United States at time t IRt Inflation rate of the United States at time t MRt Mortgage rate in the United States at time t
Trend breaks appear in time series, and unit root tests therefore need to make allowance for these if they avoid the serious effects that not comparable trend breaks have on power of the model (Harvey et al., 2013). In Table 4, a unit root test, specifically a Dickey Fuller test, is performed to test if it is unit root or stationary. If variables that have unit root are regressed on each other, this will lead to spurious regression results. Within this test, the null hypothesis involves that there is a unit root and therefore, first differences should be taken into account. According to the Table 4 (1), all variables, except population, are not significant which means that there is unit root so first differences are needed. In Table 4 (2), all variables are significant which means that there is no unit root. This is a favorable answer because in the second model, all variables are first differences and therefore it can be concluded that they are used in a suitable way. According to the significance of population in their robust way and their adjusted way, it can be stated that it does not matter if you take the first difference or the absolute values of population.
The coefficients are first converted into a logarithmic scale and then the first differences were calculated. To elaborate this a little bit more, the formula for one of the variables will be examined: 𝛥𝑙𝑛 (𝑅𝑅𝐸𝑃!) = 𝑙𝑛 𝑅𝑅𝐸𝑃! − 𝑙𝑛 (𝑅𝑅𝐸𝑃!!!) All other variables, excluding mortgage rate and inflation rate are calculated in the same way. For the mortgage rate and inflation rate, only the first difference is calculated but they are not converted into a logarithmic scale. As a result, all variables are percentage
changes and therefore, all variables can be implemented in the same way, namely as an elasticity. All the first difference variables are notated with a delta (Δ). Table 4 Unit root tests (Dickey-Fuller) (1) (2) Not-adjusted data First-differenced data Residential real estate prices -0,837 -6,770*** (0.8079) (0.0000) Stock prices -0,897 -15,272*** (0.7891) (0.0000) Construction costs -2,170 -10,321*** (0.2173) (0.0000) Inflation rate -0,615 -10,508*** (0.8676) (0.0000) Mortgage rate -0,899 -12,465*** (0.7882) (0.0000) Gross domestic product 0,338 -5,056*** (0.9790) (0.0000) Population -12,511*** -4,209*** (0.0000) (0.0006) Notes: p-values in parentheses; *p<0.10, **p<0.05, ***p<0.01 Moreover, the regression analysis will also be tested the other way around, meaning that the dependent variable RREPt and the independent variable SPt will be switched. Reason
is the simultaneous causality that is supposed to appear. When doing only one regression in a case of simultaneous causality, the estimators will be biased and inconsistent and it leads to correlation between the main variable and error term (Stock & Watson, 2015). Lastly, the lagged terms of the stock prices and residential real estate prices are used due to smoothing and lagging. According to Fu (2003), real estate prices typically reflect changes in market conditions and fundamentals slowly rather than immediately. This is the case because of the illiquidity and high transaction costs of real estate as well as the high cost of gathering information on heterogeneous real estate preventing investors from quickly acting on market news. This lag in price to market news renders observed prices indices less informative and hinders an accurate measurement of real estate market performance.
The regression method used in this research is Ordinary Least Squares. The linear multiple regression is used because when using only a single linear regression model
and the main explanatory variable is correlated with a variable that is not in the model but has an effect on the dependent variable, the estimators will be biased (Stock & Watson, 2015). This is called omitted variable bias. To test the significance of the model and all the single variables, the F-test and t-tests are used. The F-test will test the significance of the model as a whole while the t-tests will test all variables separately.
Additionally, in this thesis, a vector autoregression (VAR) with two time series variables is executed as well. This regression will take the simultaneous causality of the main variables into account. A vector autoregression extends the univariate autoregression to a list of time series variables (Stock & Watson, 2015). Instead of doing two separate regressions, the VAR analysis will regress both variables as dependent variable at one time. The dependent variables are RREPt and SPt. The regressors are
lagged values of both variables. Specifically, they are lagged with one time period, which is one month in this case. The coefficients of the vector autoregression are estimated by estimating each of the equations by OLS (Stock & Watson, 2015). Reason to use VAR-analysis in this research is due to the fact that stock prices and residential real estate prices are interrelated. This is also often the case with other macroeconomic variables. The majority of the economists agree that fluctuations in these macroeconomic variables are interrelated and therefore a way of estimating for these time series variables is needed (Sims, 1980). In this research, we are looking for some causal inference and as a result, structural VARs are used. In structural VARs, VARs coupled with restrictions derived from economic and financial theory are used to examine the effects of structural shocks on key variables (Poskitt, 2016).
5. Results
In this section the statistical results of the regression will be explained by discussing all the outcomes of the tests that are calculated. First, the two multiple regression will be discussed. Second, the VAR-analysis will be debated. Last, some impulse response functions will be disputed. 5.1 Regression analysis The results of the first regression where RREPt is the dependent variable can be found below in Table 5 (1). For this model, the adjusted R2 is 0.604. This means that the model explains 60.4% of the sample variance of the residential real estate prices. The adjusted
R2 is used instead of R2 because R2 will increase when a new variable is added, but that
does not mean that the goodness of fit of the model will improve. The adjusted R2 is a
modified version of the R2 that does not necessarily increase when a new variable is
added (Stock & Watson, 2015, p. 243). First, the model is tested as a whole where the null hypothesis assumes that all coefficients are zero. F (7, 267) = 45.83, p<0.01 meaning that with a significance level of 1%, the null hypothesis can be rejected and that at least one of the variables is different from zero thus it has an effect on the residential real estate prices. Second, the separate coefficients will be discussed. The coefficient of the lagged stock price with one month is 0.0160 meaning that a one-percentage change in lagged stock prices will lead to a 0.0160% change in residential real estate prices. The effect is low but significant at a 10% significance level. It can be stated that lagged stock prices have a direct effect on residential real estate prices. The coefficient of the lagged residential real estate prices with one month is 0.552 meaning that a one-percentage change in lagged residential real estate prices will lead to a 0.552% change in current residential real estate prices. This is effect is moderately high but it is significant at a 1% significance level. Lagged residential real estate prices do have an effect on the current residential real estate prices, which can be explained by the lagging effect of real estate. The coefficient of population is -4.792 meaning that a one-percentage change in population will lead to -4.792% change in residential real estate prices. The effect is also significant at a 5% significance level. In more detail, this negative effect means that when population is rising, residential real estate prices are falling. This effect is strange because when population is rising, more people need housing, which will increase the demand for real estate and due to the increasing demand and stick supply of real estate on the short run, the price of residential real estate should rise likewise. An explanation for this unfavorable effect could be omitted variables bias. For instance, housing supply is not taken into account and therefore this odd effect appears. That is also the reason why the constant is significant. The coefficient of construction costs is 0.0178 meaning that a one-percentage change in construction costs will lead to a 0.0178% change in residential real estate prices. This effect is highly significant, namely at a 1% significance level. In more detail, when construction costs are rising, the residential real estate prices are rising as well. This effect is correct because when it will take more costs to build a house, the firms who built the house also want to be compensated and therefore, the price of housing will go up. The coefficient of gross domestic product is 0.454 meaning
that a one-percentage change in gross domestic product will lead to a 0.454% change in residential real estate prices. The positive effect is significant at a 5% significance level. Specifically, when gross domestic product is rising meaning the economy is doing better as a whole, people are getting wealthier and therefore can afford more expensive houses or buy another house. The other variables, inflation rate and mortgage rate, are not significant. It can be concluded that these control variables are not significant due to multicollinearity. Multicollinearity means that two independent variables are correlated with each other. According to the correlation matrix above where the coefficient is -0.91, it can be concluded that these variables indeed are related. Unfortunately, one of the variables cannot be deleted to solve the multicollinearity because omitted variable bias will occur. The results of the second regression where SPt is the dependent variable can be found below in Table 5 (2). For this model, the adjusted R2 is 0.064. This means that the model explains only 6.4% of the sample variance of stock prices. Again, first, the model is tested as a whole where the null hypothesis states that all coefficients are zero. F (7, 267) = 2.37, p<0.05 meaning that with a significance level of 5%, the null hypothesis can be rejected and that at least one of the variables is different from zero and having an effect on stock prices. Again, as second, the separate coefficients will be discussed. The coefficient of the lagged stock price with one month is 0.022 meaning that one-percentage change in lagged stock prices will lead to a 0.022% change in current stock prices. This effect is not significant. The coefficient of the lagged residential real estate prices with one month is -0.890 that means that a one-percentage change in lagged residential real estate prices will lead to a -0.890% change in current stock prices. This effect is significant at a 10% level. Therefore, it can be stated that real estate does have a direct effect on stock prices. But, the effect is very low and also negative and, as a result, it could still be used as an addition in an investment portfolio to diversify the firm-specific risk. The coefficient of gross domestic product is 6.156 meaning that a one-percentage change in gross domestic product will lead to a 6.156% change in stock prices. This effect is very significant, explicitly at a 1% significance level. This effect is favorable because the gross domestic product is an important indicator of the state of the economy and therefore, when it will rise, people are expecting values to grow and as a result, stock prices will go up. The other variables, population, construction costs, inflation rate and mortgage rate are neither significant.
Table 5 Regression analysis: equation-by-equation estimate (1) (2) Δln(Residential Real Estate Prices (t)) Δln(Stock Prices (t)) Δln(Stock prices (t-1)) 0.0160* 0.0220 (0.00724) (0.0754) Δln(Residential real estate prices (t-1)) 0.552*** -0.890* (0.0525) (0.469) Δln(Population (t)) -4.792** -14.19 (1.500) (14.16) Δln(Construction costs (t)) 0.0178*** 0.0224 (0.00306) (0.0313) Δln(Gross domestic product (t)) 0.454** 6.156*** (0.140) (1.730) ΔInflation rate (t) 0.000208 -0.000262 (0.000492) (0.00541) ΔMortgage rate (t) -0.000741 -0.0107 (0.00127) (0.0131) Constant 0.00327* -0.00308 (0.00134) (0.0118) Number of observations 275 275 R-square 0.614 0.088 Adjusted R-square 0.604 0.064 F-statistic 45.38 2.37 Notes: robust standard errors in parentheses; *p<0.10, **p<0.05, ***p<0.01 5.2 VAR-analysis In Table 6 (1), which is the first part of the VAR analysis, where residential real estate prices is the dependent variable, both endogenous regressors, lagged residential real estate prices and lagged stock prices are significant. The coefficient of the lagged residential real estate prices is significant at 1% significance level. It can be concluded that, as mentioned before, there is a lagging effect in residential real estate prices because the past residential real estate prices have a great direct effect on the current residential real estate prices. The coefficient of lagged stock prices is significant at a 5% significance level. It can similarly be concluded that stock prices have a direct effect on residential real estate prices. As a result, stock prices can be used as a forecasting for residential real estate. However, the effect of stock prices on residential real estate is low, so there is some doubt about the actual forecasting effect. Moreover, due to this low
effect, it can be stated that there is a possibility for diversification when using real estate and stock prices. The significant effects of population and construction costs have the same reasoning as mentioned in the previous section. Furthermore, the R2 in this part is
61.4%, which means that the model fits quite well. Therefore, it can be stated that the control variables used are sufficient to estimate residential real estate.
In Table 6 (2), the second part of the VAR-analysis, where stock prices are the dependent variable, one of the endogenous regressors is not significant namely, lagged stock prices. The other endogenous variable, residential real estate prices, is significant at a 10% significance level. This result supports the conclusion that real estate and stocks are a method to diversify the idiosyncratic risk of a portfolio because the effect is low, negative and not very significant. The coefficient of gross domestic product is again significant and the reasoning is the same as mentioned in the previous section. Moreover, the R2 in this part is only 8.8%, which means that the model does not fit very well but this is due to omitted variables that can explain stock prices in a better way. Table 6 Vector autoregression: joint estimate Δln(Residential Real Estate Prices (t)) Δln(Stock Prices (t)) (1) (2) Δln(Residential real estate prices (t-1)) 0.552*** Δln(Residential real estate prices (t-1)) -0.890* (0.0439) (0.458) Δln(Stock prices (t-1)) 0.0160** Δln(Stock prices (t-1)) 0.0220 (0.00579) (0.0603) Δln(Population (t)) -4.792*** Δln(Population (t)) -14.19 (1.446) (15.08) Δln(Construction costs (t)) 0.0178*** Δln(Construction costs (t)) 0.0224 (0.00312) (0.0325) Δln(Gross domestic product (t)) 0.454*** Δln(Gross domestic product (t)) 6.156*** (0.124) (1.289) ΔInflation rate (t) 0.000208 ΔInflation rate (t) -0.000262 (0.000445) (0.00464) ΔMortgage rate (t) -0.000741 ΔMortgage rate (t) -0.0107 (0.00128) (0.0134) Constant 0.00327** Constant -0.00308 (0.00115) (0.0120) Number of observations 275 Number of observations 275 R-square 0.614 R-square 0.088 Notes: standard errors in parentheses; *p<0.10, **p<0.05, ***p<0.01
5.3 Impulse response functions
To examine the dynamic response between residential real estate prices and stock prices, impulse response functions are calculated. Impulse response functions will examine the shocks on the endogenous variables.
The first IRF function, 1(a), is showing a shock of one standard deviation in residential real estate prices and the effect of that shock on residential real estate prices. It can be derived from the graph that a shock in one standard deviation leads to an immediate increase in residential real estate prices but it diminishes until approximately four months and then it will be at the base level again. The second IRF function, 1(b), shows a shock of one standard deviation in residential real estate prices and the effect of that shock on stock prices. It can be derived from the graph that a shock in one standard deviation leads to immediate decrease in stock prices that will last approximately one month. After that, it will go up again to the base level approximately six months after. The third IRF function, 1(c), shows a shock of one standard deviation in stock prices and the effect of that shock on residential real estate prices. It can be derived from the graph that a shock does not affect residential real estate. The illiquidity of real estate could be a reason behind this. The fourth, and last IRF function, 1(d), shows a shock of one standard deviation in stock prices and the effect of that shock on -2 -1 0 1 -2 -1 0 1 0 2 4 6 8 0 2 4 6 8
IRF 1(a), RREP/RREP IRF 1(b) RREP/SP
IRF 1 (c), SP/RREP IRF 1 (d), SP/SP
95% CI impulse-response function (irf) step
stock prices. It can be derived from the graph that there will be an immediate increase in stock prices but this decreases again for about one month before it returns at the base level again. Figure 3: orthogonalized IRF of stock prices on real estate A better way to examine a shock in one of the endogenous variables is by using an orthogonalized impulse response function. In this function, the most endogenous variable must be determined, which in this case is residential real estate prices. The reason is that residential real estate prices are more affected by stock prices but this is not the case when considering it the other way around. The regression results discussed before support this. The effect of stock prices on residential real estate is more significant than the effect of residential real estate prices on stock prices. According to Figure 3, stock prices have a direct effect on residential real estate till approximately one month after the shock. After that month, the effect will diminish until six months, before it returns to the base level. For approximately four months, the effect is also significant at a 5% significance level because zero is not within the 95% confidence interval, which is the grey area. According to Figure 4, residential real estate prices also have a direct effect on stock prices till, again, approximately one month after the shock, but this shock is smaller. After that month, the effect will diminish much until four months after the
0 .0005 .001
0 2 4 6 8
Orthogonalized IRF, SP on RREP
95% CI orthogonalized irf
period
shock, which is a shorter time period. For the entire period, the effects are not significant at a 5% significance level because zero is within the 95% confidence interval. These outcomes are in line with the results of the regressions. Figure 4: orthogonalized IRF of real estate on stock prices
6. Conclusion
In this thesis, the relationship between stock prices and residential real estate prices has been investigated. The research was based on 23 years for the country of the United States. This thesis contributed to existing research by investigating residential real estate instead of commercial real estate. Furthermore, the time period of 1993 till 2016 is relatively recent and therefore, it is also adding value to existing research. The main research question in this thesis has been: ‘what are the effects of stock prices andresidential real estate prices on each other in the United States?’
To answer this question, a literature review of existing research was done. First, according to existing research, the determinants of both stock prices and real estate were described. Second, the existing literature about the relationship between real estate and stock prices is discussed. The literature review resulted in two hypotheses namely: 1) there is a direct effect between stock prices and residential real estate prices -.01 -.005 0 .005 0 2 4 6 8
Orthogonalized IRF, RREP on SP
95% CI orthogonalized irf
step
and 2) there is a direct effect between residential real estate prices and stock prices. Third, the relationship was tested empirically by doing a regression analysis and a VAR-analysis. Fourth, the results show that there is a small direct effect of stock prices on residential real estate prices but this effect is very significant. The first null hypothesis is therefore rejected at a 1% significance level. There is also a direct effect of residential real estate prices on stock prices but this effect is not very significant. The second null hypothesis is therefore rejected at a 10% significance level. The effect of stock prices on residential real estate prices has stronger statistical evidence in comparison with the effect of residential real estate prices on stock prices, where the statistical evidence is weak. As mentioned in the beginning, many investors use real estate investments as a diversification method to hedge themselves against the idiosyncratic risk of companies. Therefore, it can indeed be concluded that real estate and stock prices can be used in an investment portfolio to get a diversification effect. It can also be concluded that due to the low correlation and small direct effect, residential real estate prices cannot be used to predict stock prices.
One of the limitations of this research is that multicollinearity occurs between two control variables and that more control variables could be included. Another improvement could be if the population coefficient can be included in some other way because in this thesis, the result of this particular coefficient is abnormal. Further research could include these limitations. Also, further research can include more lagged variables to maybe tell something about cycling effects in real estate. At last, further research can use another regression analysis to test if the relationship is non-linear.
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