Amsterdam Business School Faculty of Economics and Business
Master of Science in
Business Economics: Real Estate Finance
Master Thesis
European Office Markets:
Analysis of Co-Integration and Convergence
Name: Fabian Wieser Student ID: 10825681
Address: Waldfriedhofstraße 45, 81377 München, Germany Submitted to: Dr. Marcel Theebe
Statement of Originality
This thesis is written by student Fabian Wieser, 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 Economic and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
The idea behind this paper is to examine, whether or not European office markets still offer potential for diversification. Tests for long-term Co-Integration are supposed to show, whether markets are already co-integrated, tests for convergence give a sign of markets converging towards each other or towards a common market. Positive results in any of the tests would indicate a decrease of diversification potential. However, results showed, that Co-Integration is not found for any combination of cities,
neither in the rental, nor in the investment markets.
Convergence was partly visible, which is supporting the theory that multiple markets are converging towards a common market in the future.
The final conclusion drawn from this research is that there is still is diversification potential between the tested European office markets. While the markets might have gotten closer together in recent years, there are enough exclusive factors that prohibit those markets from merging.
Content
List of Tables ... i
List of Figures ... ii
1. Introduction ... 1
2. Literature Review ... 4
2.1. The Foundation of Diversification Research ... 4
2.2. Economic Factors ... 5
2.3. European Co-Integration around the Euro-Adaption ... 6
2.4. London and New York City as global players ... 7
2.5. Recent Research on European Office Markets ... 9
3. Methodology ... 12
3.1. Testing for Co-Integration ... 13
3.2. Testing for Convergence ... 15
4. Data & Descriptive Statistics ... 18
4.1. Data ... 18 4.2. Descriptive Statistics ... 19 5. Results ... 25 5.1. Co-Integration ... 25 5.2. Convergence ... 27 5.3. Economic Interpretation ... 43
6. Limitations of this Paper ... 46
6.1. Limitations of Dataset ... 46
6.2. Limitations of Statistical Approach ... 46
6.3. General Limitations ... 47
7. Conclusion ... 48
References ... 50
List of Tables
Table 1. Summary Statistics for Nominal and Real Yields 19
Table 2. Summary Statistics for Nominal and Real Rents 20
Table 3. Summary Statistics for Total Returns 21
Table 4. Correlation Matrixes between Nominal Rents and Yields 22 Table 5. Correlation Matrixes between Real Rents and Yields 23
Table 6. Correlation Matrixes between Total Return Indices 23
Table 7. EG-ADF Test Results for Nominal Rents 25
Table 8. EG-ADF Test Results for Real Rents 26
Table 9. EG-ADF Test Results for Yields and Total Returns 26
Table 10. PCA Results for Real Rents 31
Table 11. PCA Results for Real Rents First Half of Sample 31
Table 12. PCA Results for Real Rents Second Half of Sample 31
Table 13. PCA Results for Real Yields 32
Table 14. PCA Results for Real Yields First Half of Sample 33
Table 15. PCA Results for Real Yields Second Half of Sample 33
Table 16. PCA Results for Real Total Returns 34
Table 17. PCA Results for Real Total Returns First Half of Sample 34 Table 18. PCA Results for Real Total Returns Second Half of Sample 35
Table 19. Beta Convergence Results for Nominal Rents 36
Table 20. Beta Convergence Results for Nominal Rents 37
Table 21. Beta Convergence Results for Nominal Yields 37
Table 22. Beta Convergence Results for Real Yields 38
Table 23. Beta Convergence Results for Nominal Total Return Indices 38 Table 24. Beta Convergence Results for Real Total Return Indices 39
List of Figures
Figure 1. Dynamic Correlation of Real Rents for London 28
Figure 2. Dynamic Correlation of Nominal Yields for London 29
Figure 3. Dynamic Correlation of Real Total Returns for Paris 30
Figure 4. Sigma Convergence of Real Rents 40
Figure 5. Sigma Convergence of Real Yields 41
Figure 6. Sigma Convergence of Real Total Returns 41
Figure 7. Sigma Convergence of Nominal Total Returns 42
1. Introduction
Diversification is an important part of any portfolio strategy. One way of achieving a certain degree of diversification is by splitting investments regionally, for example buying shares of companies that are located and operate in different regions. While in today’s globalizing world, regional diversification for stock investments might become less relevant, in the world of real estate, the focus is still on location. Firms may operate across borders and continents, yet real estate stays in the exact spot where it has been erected. Due to the growth of some communities, some real estate markets merge and become a new, combined market. Yet, this only happens if two markets are really adjacent to each other. Otherwise, real estate markets cannot merge or become similar, or can they?
As any market, both the rental and the investment real estate market are basically a function of demand and supply. Demand and supply again are dependent on multiple factors, some of which are very market specific, some others are rather globally. Now if two markets are driven mainly by the same factors, they develop a kind of co-movement over time. Due to the high complexity and the very high number of influencing factors on the movement of each market, it is difficult to identify such a market co-movement. Yet, if two or more markets start to move alike, they lose part of their potential for diversification. This reduction in diversification potentially leads to an unnoticed increase in portfolio risk for all investors that are invested in the affected markets. Due to this fact, it is highly important for any investor to deeply understand the markets he is invested in. Furthermore, a constant observation of market changes in relation to other markets is necessary, in order to be able to react accordingly. The more a portfolio’s diversification strategy is focused on regional diversification, the more it might be affected by the described effect. Of course, there are multiple other options for portfolio diversification, such as diversification of usage classes or diversification of asset classes.
There are different kinds of co-movement. If two markets behave very similar over a long time horizon, they might be co-integrated. That means, that they are both driven by very comparable or even partly identical factors. If their behavior becomes more and more similar over time, they are converging, which basically describes the fact that common influences become more powerful and therefore the subject markets are not moving exactly parallel (as they would in case of co-integration) but rather towards each other, decreasing the gap between them. A weaker phenomenon would be the pursuit of a
common trend, a common influence that drives both markets into the same direction. Among multiple other possibilities, it is also possible that two or more markets are not converging towards each other but towards a common parameter.
Any of the described possibilities has a negative influence on portfolio diversification and risk if they stay unnoticed. Therefore, in the past, quite some researchers have analyzed different kinds of combinations of markets in order to test for forms of similarity and co-movement.
While existing literature has focussed on more global relationships in the past and the last comparable analysis of European cities was conducted with data only until 2009 (Lee & Srivatsa, 2012), this paper aims on providing an overview of potential market similarity between five important European office markets, namely London, Frankfurt, Paris, Madrid and Milan.
Past researchers were already partly successful in proving the existence of market similarities on a general level, therefore, this paper aims to explore the potentially existing co-integration as well as convergence within European cities by analysing a new dataset consisting of recent data. To analyse the relations between these relatively transparent markets quarterly nominal rent and yield data from Q1 1993 to Q1 2015, provided by Cushman & Wakefield LLP, is used.
The main question asked is whether diversification is still achievable for any investor that focuses only on prime office segment real estate investments in the given cities. Besides using a fresh and privately collected dataset, also the statistical approach is partly different to those used in prior other papers. To test for co-integration, this paper will apply the methodology developed by Engel and Granger (Engle & Granger, 1987) and mentioned by Jackson et al. (Jackson, Stevenson, & Watkins, 2008). The so called “Engle-Granger Augmented-Dickey-Fuller” test will yield results that allow for interpretations concerning the degree of co-integration between the subject markets. Finally, while many past publications did not have access to yield data but had to make estimations concerning the yield co-integration (compare e.g. (Jackson, Stevenson, & Watkins, 2008)) this paper is able to run a full analysis on yield data. This might yield new insights and may help to back up or object existing opinions in this field of research. Furthermore, the test for convergence might yield insights concerning the question if markets are coming closer together due to growing similar influences or not. Here, the methodology applied is based
on Lee and Srivatsa (Lee & Srivatsa, 2012), who analysed beta- and sigma-convergence of rents and yields. In order to add further insight to the research, the convergence analysis of this paper is extended to total returns, and thereby combining the information included in rents and yields.
Course of investigation
The first chapter of this paper will give an overview of the relevant literature and the prior applied methodologies. While in general, many researchers have worked on the topics of co-integration and convergence, there are substantial differences. First of all, due to a generally higher interest in the big financial centers, many studies focus on only few very large markets such as New York City. Secondly, most likely because it is easier to collect data, a lot of work done in the past was based on listed real estate. The literature review is supposed to show the development over time which was made in the area as well as the differences of the results achieved. At the end of the review, the research question of this paper is discussed.
The second part of the paper is going to focus on the data, the descriptive statistics and the applied methodology. In general, the statistical approach is to be seen in three steps. The first step is mainly about the data set and the information it contains which lead to the choice of methods to analyze co-integration and subsequently convergence. The second step explains the procedure of the co-integration analysis, the third and final step focuses on the main part of this paper, the convergence analysis.
The following part is about the results achieved by the different statistical approaches. Apart from the explanation of the procedure and the results, the economic meaning of the results is explained. This way, the results do not stand on their own but are put into context, which is elementary for their practical use.
The final part of this paper is supposed to discuss the limitations of the research, conclude the findings, and summarize the approach and the implications for further research as well as for practical use.
2. Literature Review
2.1. The Foundation of Diversification Research
As mentioned above, the interest in questions concerning regional diversification in real estate research is existing for some time now. The foundation for this kind of questions lies in Markowitz’ work concerning the structuring of the optimal portfolio (Markowitz, 1952). Since then, many researchers have focussed on optimal portfolio allocation and the different ways to diversify ones investments. While all the studies that are part of this literature review do have a focus on the similarity of markets, they differ to a certain extent. Some search for long term similarity, while other focus on short term developments. Some analyse listed real estate, which behaves, at least partly, differently than non-listed real estate. While the latter group is probably more relevant for this paper, analysis of listed real estate is also regarded in the literature review. The existence of similarity in listed real estate markets does not guarantee the existence of similarities in non-listed markets, the results of the research are still adding inside to the general understanding of the topic and therefore are definitely valuable concerning this paper’s scope. Per definition, listed real estate is comparable to other listed assets such as stocks and bonds. Examples for listed real estate would be shares of a real estate company or a real estate investment trust (REIT). Due to legal obligations, many forms of listed real estate are more transparent than non-listed or direct real estate. Also, for small investors, it is easier to invest in listed real estate, as the size of a single investment is theoretically independent of the underlying value (e.g. a single property or real estate portfolio). In comparison to that, non-listed real estate often requires a higher degree of effort from the investor. Potential investments are not to be compared that easily. While investment in non-listed funds for example is also independent from the volume of the underlying property, direct real estate investments usually demand for a certain substantial investment volume. In general, it is to be assumed that listed real estate offers more information and a higher liquidity to investors. Therefore, it is easier for investors to enter and leave such a market. This again results in potentially faster adaptions to changes for markets of listed real estate. Concluding, it is expected, that while listed markets might change faster, also non-listed markets react, as the underlying asset – real estate – is the same for both categories. These observations should be kept in mind when comparing the different approaches and results mentioned in the literature review.
One of the first to analyse ways of diversification especially for real estate portfolios was Piet Eichholtz et al. in 1995 (Eichholtz, Hoesli, MacGregor, & Nanthakumaran, 1995). Their work discussed the different diversification opportunities in real estate, namely property type and region. Different property types underlie different driving factors, which makes them less correlated. For example, the performance of office buildings is more dependent of the development of the demand for working space than the performance of retail properties. Earlier scientists mostly focussed on those two possibilities.
2.2. Economic Factors
Yet there are certain economic effects that affect regions rather than a certain property type (Eichholtz, Huisman, Koedijk, & Schuin, 1998). Already in 1982, the existence of underlying economic factors that influence real estate was discussed (Miles & McCue, 1982). So when looking for an optimal diversification strategy for a real estate portfolio, it is necessary to look not only for different regions and asset classes but to also make sure that there is no general economic driving force that undermines the diversification. For data from securitized real estate in the period between 1984 and 1996, Eichholtz et al. however found that, while the continental factors they found where strong within the U.S. and Europe, they were not significant in the Asia-Pacific region. With the adaption of the single currency within the European Union in 2001 however, the continental effect for Europe might have grown since. Also, the ongoing globalization could be a reason for the continental effect to grow.
That divergence in European real estate markets might still be possible is the outcome of a study by Brounen and Huisman (Brounen & Huisman, 2007), who took Eichholtz’ continental theory and analysed the European factor in a time frame from 1997 to 2007. Probably in order to be able to compare their results with those of Eichholtz, they choose a dataset with similar basic conditions. What they find is essentially, that not all European countries have developed identically. While some countries (Austria, Belgium, The Netherlands, Spain and the UK) have become less related to the European factor, some others (France, Germany, Italy and Sweden) have become more related to it. Their results indicate, that convergence is not simply to be expected due to the existence of a general factor. In fact, it seems that at least for some countries, independent influences have a much higher proportion than expected.
In 2003, De Wit and van Dijk found that such economic factors do not naturally have to be continent based. The factors they found were influencing direct office real estate performance in a number of countries around the globe which is another proof for the existence of those underlying forces. Yet it has to be said that while e.g. GDP, unemployment rate, vacancy and available stock do influence real estate markets, it does not mean that all factors do influence all markets at the same time. It only means that those variables do potentially influence certain markets. (De Wit & van Dijk, 2003).
These findings of both Brounen and Huisman as well as De Wit and van Dijk are a good example to show that the general concepts of trends influencing real estate markets apply to both, listed and non-listed markets.
2.3. European Co-Integration around the Euro-Adaption
In the same year Lizieri, McAllister and Ward (Lizieri, McAllister, & Ward, 2003) published their work on the ongoing convergence trends in European real estate equities. They analysed monthly data from securitized real estate markets with multiple statistical approaches. In combination with (McAllister & Lizieri, Monetary Integration and Real Estate Markets: The Impact of Euro on European Real Estate Equities , 2006), they published their findings on the ongoing co-integration of European office markets. A key fact in their research is the development before and after the introduction of the single currency within the EU. While there is a noticeable convergence in stock market results, the real estate markets behaved slower and less strong. Due to their size and their rather local holding structure, market convergence was not as strong as for stock market equities. Lizieri et al. find a difference between countries within the single currency union and those outside the union. In their opinion, the rather slow convergence of real estate markets in comparison to stock markets is to be explained by market size and the mostly local investors.
In 2005, a few years after the introduction of the EMU (Economic and Monetary Union of the European Union), Yang et al. (Yang, Kolari, & Zhu, 2005) studied the integration of European real estate markets. They looked at daily data from publicly traded real estate stock price indices from Germany, France, the Netherlands, Spain, Italy, Belgium, the UK, Switzerland and Denmark. What they find is that large countries within the EMU co-integrate more than smaller countries within the monetary Union. The countries outside the EMU showed none or diminishing integration effects. The authors conclude
that the implementation of the single currency has been beneficial for the more developed markets within the Union as they now show a higher co-integration. If and how this is really beneficial however stays unanswered.
Stephen L. Lee also attributed multiple papers to the topic of growing similarity of markets. In 2007 (Lee S. , European Real Estate Diversification, 2007) Lee proved an increase in the average correlation between European direct real estate markets, especially in the office segment. His findings include that the single currency is an important factor when looking at co-integration, as the countries which are part of the monetary union showed a much higher correlation with each other than with countries that are not within the union. Also, those countries (UK, Denmark & Sweden) showed significantly smaller correlation with each other as well as with the EMU countries. Besides the three already mentioned, Lee analysed data from Austria, Belgium, France, Germany, Ireland, Italy, The Netherlands, Spain and Portugal.
In 2008, Andrews and Lee (Andrews & Lee, 2008) presented a paper at the Asian Real Estate Society meeting in Shanghai, China which was concerned with the extent of global and regional integration of European real estate securities markets. They found that the general level of co-integration has risen since 1990, with big markets like France and the UK showing a higher global and local integration than smaller markets like Germany, Belgium or Spain. Those smaller markets did not show a high integration, neither globally nor with other countries in Europe. The researchers state that those smaller markets are mainly driven by local influences and therefore less connected. Finally some countries within Europe show co-integration, but rather globally than within Europe. Examples were the Netherlands, Italy, Sweden or Denmark. The used dataset had a timeframe from 1990 to 2007 and consisted of monthly observations. While the timeframe is comparable to other papers mentioned here, the results do somehow go in a different direction. On the other side, it makes sense that bigger markets attract more international investors which again makes them more sensitive to international changes and developments. The following work of Lee therefore focuses on the special position of the UK.
2.4. London and New York City as global players
While many important European financial centres lie within the EMU, London, the most important one, does not. How the English and especially the London real estate market behaves in comparison with the rest of Europe was analysed by Lee in 2009 (Lee S. , Is
the UK real estate market converging with the rest of Europe? , 2009). His findings say that, while the London real estate market was more influenced by the US between 1990-1998, it was closer to European development from 1998-2004. Yet, since 2004 the London market has again started to diverge from most other European markets. Due to its size and international importance, the London real estate market has a special position in comparison to other, more local markets.
Lee is not the only scientist whose focus is or was on the special position of London. For example, Brooks and Tsolacos (Brooks & Tsolacos, 2007) in 2007 analysed the relationship between the CBD-office markets of New York, London and Paris. They find that while New York and London are closely linked, Paris is more autonomous and does not react strongly on changes in the other markets. Yet, in the long run all three markets move similar, which lets the authors conclude that diversification benefits can only be realized in the short run.
As they were probably fascinated by the special relationship between New York and London, Brooks and Tsolacos analysed the relationship again in 2008, taking the Tokyo office market into consideration (Brooks & Tsolacos, 2008). They find that the three cities form a long run equilibrium relationship, with London reacting more strongly to deviations from the long run path than New York or Tokyo. They performed a Johansen test that clearly indicated the co-integration of the three office markets. Their further findings include the theory that, as London and especially Tokyo real estate prices are lying above the equilibrium and New York prices are significantly below, New York real estate owners might be able to profit from increasing prices in the future.
This paper is dominantly focussing on the aspect of regional diversification while taking the explained economic driving forces into account. Useful prior research in this particular area was conducted by Jackson et al. who were researching the degree of co-integration between the office markets of New York and London (Jackson, Stevenson, & Watkins, 2008). What they found was that there was no strong correlation of the rental markets. Further, they expected the investment markets both to be influenced from the same factors as they found co-integration between total returns but not within rents. They conclude that investors might face a dilemma as it seems difficult to invest in many independent markets that all have a certain liquidity level. To yield a high general liquidity, markets need a broad range of investors, which again gives them an international focus. Other (smaller) markets are often less liquid, because their main
investors are smaller on average and have only local interests. Yet, these local markets might be the ones that are less connected to the overall real estate economy and therefore could yield higher diversification benefits.
2.5. Recent Research on European Office Markets
In the same year as Jackson et al. there was another study by Patrick McAllister (McAllister, Integration and Convergence in European Office Markets: An empirical Analysis, 2008). He analysed convergence effects in 24 office markets within Europe. To test the level of convergence, he used beta- and sigma-convergence models, which tested the level and speed of the convergence. To have a benchmark for his results, he performed the same tests for a sample of 27 office markets within the US. McAllister’s results were not totally explicit. While he did not find a significant decrease in the standard deviation of the rental levels, his results indicated, that when one removes the non-euro countries, it becomes clear that the remaining markets have moved closer together. After modifying his approach by including the “natural” dispersion that is given due to the differences between the office markets, the results showed a clearer picture and indicated, that the subject office markets indeed are converging.
In a follow up study, Lee and Srivatsa (Lee & Srivatsa, 2012) modify McAllisters approach and test 7 European office markets in the period from 1982 to 2009. They find, that while there is no significant beta-convergence between any cities at any time, there is a significant sigma-convergence throughout the entire data set. Also, they argue, as many others do, that the introduction of the single currency within most EU-countries has led to an increase in convergence, especially in the continental core markets. Their conclusion is that diversification, due to low degree of beta-convergence in both rents and yields, is still a viable option for investors.
After careful review of the existing literature, it becomes clear, that while there is extensive information published on the general topic, the different approaches, data settings and purposes of research make it difficult to compare results without acknowledging their different setups. In general, the similarity of the markets is, at least in 2009, when the last studies horizon ended, not yet at a point where diversification is not possible anymore. While there are some combinations of markets where co-integration is already visible, the European cities within and outside of the EMU have
shown connections in the past that have not been strong enough to pose a real thread to the diversification potential.
The results of past research have furthermore proven, that both listed and non-listed real estate behave in a comparable manner. While velocity of change and liquidity of markets might be different, both types of real estate seem to react on the same factors. As this paper is using a data set which is sourced from direct observations of rental and investment transactions within the subject markets, the prior research concerning non-listed real estate might be a little more comparable. Yet, the idea behind research concerning co-integration and convergence of listed real estate is identical and therefore those results are not to be ignored.
In the further course of this paper, two main phenomena shall be investigated. The author wants to test first for long run co-integration within the data set. This analysis is performed in accordance with the approach of Jackson et al. (Jackson, Stevenson, & Watkins, 2008), who performed a comparable co-integration analysis for their data set.
In a subsequent analysis, the paper is going to focus on convergence effects. Do markets show tendencies to move closer together? Here, the statistical analysis is conducted according to the approaches of McAllister (McAllister, Integration and Convergence in European Office Markets: An empirical Analysis, 2008) as well as Lee & Srivatsa (Lee & Srivatsa, 2012).
With the knowledge of the mentioned previous studies, this paper will try to proof either co-integration or convergence within the subject European office markets for a more recent dataset. As fully co-integrated markets cannot converge towards each other anymore, a possible outcome would be a high degree of co-integration and no convergence. The more likely opposite would be limited to zero proof of co-integration, as markets and market participants are still very heterogeneous, but a certain degree of convergence, as markets within the European economy are expected to eventually converge towards each other and form a common European real estate market. In case neither co-integration nor convergence can be proofed, this would be a sign for the early stage of the described similarity process in which the subject markets are currently in. The co-integration test is configured to test for pair-wise co-integration, as it is expected that the likelihood of two cities being integrated is bigger than all cities being co-integrated. For the convergence test however, it makes more sense to test, if the European
markets under investigation converge towards a common market, which might lie between the different current markets. The results achieved this way are supposed to have a higher explanatory power, as the general existence of convergence would be a sign for potential co-integration of single markets in the future.
To be able to find the potentially existing relationship, this paper makes use of a new, privately assembled data set, which has never been analysed in a comparable way before. This, in combination with a test for co-integration and convergence has never before been done for the continental European office markets. The results hopefully give an interpretation of the development of the European real estate markets over the recent years.
What sets this paper apart from prior research is the idea systematically test for co-integration and convergence. If it is possible to proof the above described situation that co-integration is not yet existing on a statistical significant level but convergence is, this might an argument supporting the theory that co-integration can, but not necessarily has to be, an after-effect of convergence.
While convergence has been proven within European markets in prior studies, the same data set has never before been used to also test for co-integration. Also as differences between two sets of data concerning non-listed real estate can exist, the existence of convergence within only one data set does not state a strong enough proof to generally accept this phenomenon for further research. That is why it seems legitimate, to test for convergence again.
3. Methodology
In the previous part, multiple possible approaches and a great amount of studies and results have been discussed. What this paper intends to do in detail is the following.
The main question to be determined is whether there is still diversification potential within European real estate markets. To find a suitable answer to this question, this paper will evaluate the relationship between five major European office markets. These markets are Frankfurt in Germany, London in Great Britain, Paris in France, Milan in Italy and Madrid in Spain. One way to clarify if and how much diversification potential is existing, is to analyse the degree of co-integration between these mentioned markets. If they are co-integrated with each other, their development in the future will be identical and hence they would not suit any investor who desires diversification for his real estate portfolio. It is important to clearly differentiate between co-integration, which is a long run phenomenon and convergence, which is rather short term and does not allow for conclusions concerning the long run connection of markets. Yet, convergence is a very interesting phenomenon itself, as its existence can explain connections within markets, e.g. if and how they are affected by the same factors. Furthermore, existing convergence is a sign for growing market similarity. If two markets become more similar over time, eventually they will show signs of co-integration.
There are other ways to test for the existence of diversification potential, for example the cross-sectional-approach (Solnik & Roulet, 2000) or the integration-score-approach (Akdogan, 1996), yet the test for co-integration yields some advantages which are useful in this case. The cross-sectional approach does not need a long data history, it allows for results without many past observations and has produced similar results as comparable co-integration tests in other studies. Yet, due to the fact that for this analysis, a long enough data stream is available, it seemed unnecessary to forego this fact. The integration-score-approach, which uses regressions of country returns on an overall index could have been performed with the data set used for this paper but seemed less rewarding. Both approaches, as well as multiple more, might also be suitable to analyse the subject problem. They have their share in the existing literature and were useful in the past. What was of help for this study was not only the mentioning of the co-integration approach by Jackson et al. (Jackson, Stevenson, & Watkins, 2008) but also the very clear explanation and reasoning given by Stock and Watson (Stock & Watson, 2011), which in the end might have tipped the scales in favour of the co-integration approach. Most
important is the fact that the interpretation of the results is straight forward. Either there is a significant co-integration between some or all of the cities or there is none. A potential weakness of the co-integration approach lies in the fact that it can only be applied in cases where there is a trend in the data set. In total, it seems legitimate to choose the co-integration approach, which will be explained in detail in the following.
3.1. Testing for Co-Integration
In order to perform a co-integration test, there has to be a sufficient amount of data available that fulfils certain criteria. As co-integration is a long term effect, the observation period should be rather long. Commonly, at least 50 observations should be available for an analysis. Also, it is helpful if all data comes from the same source, otherwise, there might be issues such as lagging data or different kinds of measurements. For example, it is not efficient to compare prime yields of city A with average yields of city B. The one source approach makes sure that the data set in itself is coherent and ready to use. There are multiple indicators that one can observe and measure when analysing a real estate market, examples would be rent, yields, total returns, vacancy, net addition, growth etc. This paper will only test for co-integration within nominal rents, real rents, yields and total returns. These parameters are comparatively simple to measure and probably most relevant to investors, as they already include many information from different parameters.
To test for co-integration, some necessary procedures with the obtained data have to be undertaken first. In the beginning, the simple time series of all available categories (nominal rents, real rents, yields, total returns) for all five cities were plotted. After that, all the autocorrelation curves were plotted to produce a first indication whether or not the given data was stationary or non-stationary. It is crucial for the co-integration analysis that the dataset is non-stationary, otherwise it is impossible to test for co-integration. As all time-series showed a first lag autocorrelation which was close to one, the first weak evidence for non-stationarity was found.
The next important step is to find out if all variables are integrated to the same order. This is to be tested by generating the first differences, and again plotting their autocorrelation curves. If the first differences are stationary, e.g. their first lag is not close to one, this means that the actual variables might be non-stationary, a second weak evidence is found.
In the third step, the real test for non-stationarity is performed. To do so, each variable is tested either with a Dickey-Fuller test (which comprises of only one lag) or an Augmented-Dickey-Fuller test (which comprises of multiple lags). In order to find out which of the two possibilities is the better choice, a so called AIC criterion has to be calculated. An AR(p) model with variables for the first ten lags is developed (equation 1). The AIC is calculated by addition of the sum of squared residuals of the AR(p) model. The model with the smallest SSR gives the number of lags to be used for the (Augmented)-Dickey-Fuller test. All ADF-tests (equation 2) where done with and without inclusion of a time trend. In cases the trend proofed to be significant, it was included, in all other cases, it was excluded again. Intercepts were not excluded but automatically estimated and integrated by the statistical software used.
Equation 1. AR(p) Model with p Lags
𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴𝑡 = 𝛽0+ 𝛽1∗ 𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴𝑡−1+ ⋯ + 𝛽𝑝∗ 𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴𝑡−𝑝+ 𝜀𝑡
Equation 2. Augmented Dickey Fuller Test
△ 𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴 𝑡= 𝛽0+ 𝛿 ∗ 𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴 𝑡−1
+𝛽1∗ △ 𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴 𝑡−1+ ⋯ + 𝛽𝑝∗ △ 𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴 𝑡−𝑝+ 𝜀𝑡
The final result of the above explained processes is that the given data set can be used to calculate the potential co-integration between the cities. All variables are non-stationary and integrated to the same order, namely one.
To perform the co-integration test, this paper uses the so called “Engle-Granger Augmented-Dickey-Fuller” test, which was originally developed by Engle & Granger in 1987 (Engle & Granger, 1987) and is furthermore mentioned as an equivalent alternative to their tests by Jackson et al. (Jackson, Stevenson, & Watkins, 2008). In order to perform this test, one first has to calculate an OLS-regression of e.g. “Nominal Rent A” on “Nominal Rent B”. The resulting residuals have to be saved and then tested on stationarity by using the Augmented-Dickey-Fuller test again (equation 3).
Equation 3. EG-ADF Test
𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐴𝑡 = 𝛽0+ 𝛽1∗ 𝑁𝑜𝑚𝑖𝑛𝑎𝑙_𝑅𝑒𝑛𝑡_𝐶𝑖𝑡𝑦𝐵𝑡+ 𝜀𝑡 𝜀𝑡 = 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙𝑠
△ 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙𝑡 = 𝛽0+ 𝛿 ∗ 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙𝑡−1+ 𝛽1∗△ 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙𝑡−1
3.2. Testing for Convergence
After the completion of the co-integration analysis, a convergence analysis is performed. In order to do so, in a first step, a dynamic correlation analysis is performed.
To gain an initial impression of how the association between the different markets develop over time, correlations between the different indices are estimated using a rolling window. To balance the need of estimating the correlation at a particular point in time and the need to have a sufficiently large sample to estimate reliably, a window of 16 quarterly observations is used.
As a second step, the paper investigates the presence of a common factor in the different variables. Principle Component Analysis (PCA) is used to do so. PCA is a standard statistical method that is used to extract linear combinations of the variables which account for the largest fraction of variance in the data. It is based on a decomposition of the correlation matrix of the variables. An important assumption for PCA to work well is that the underlying variables should be normally distributed.
Should a common European factor which drives real estate returns across the continent exist there would be a principle component which can account for a large variation of the variance in the indices. Moreover, each index for each country should have a strong loading of the same size for this component. This would indicate that this represents an underlying economic factor that is responsible for a common component in real estate returns across the continent.
To investigate whether the potential common factor is persistent through time, a PCA is estimated separately for the first and second half of the sample. If the nature of the
common factor has not changes through time then the loadings in the two subsamples should be similar to the loadings of the full sample, as well as to each other.
Finally, the actual test for convergence, namely beta- and sigma-convergence is performed.
In order to estimate beta-convergence, the following fixed-effects panel regression is estimated:
Equation 4. Beta-Convergence Estimation
𝛥𝑅𝑖,𝑡 = 𝛼𝑖+ 𝛽𝑅𝑖,𝑡−1+ ∑ 𝛾𝑖,𝑡−1𝛥𝑅𝑖,𝑡−1+ 𝜀𝑖,𝑡 𝐿
𝑙=1
Where 𝑅𝑖,𝑡represents the return spread in a specific market 𝑖 to a European benchmark index at time t and Δ is the first-difference operator (ΔR𝑖,𝑡 = R𝑖,𝑡− R𝑖,𝑡−1). As the primary dataset does not contain a benchmark index for European real estate returns, the first principle component constructed in the prior section is used. This component was shown to account for a large fraction of the common variation and appears to be a common driving factor for the indices. As a robustness check, also the regression using the arithmetic average of the individual indices is estimated as a benchmark.
The optimal lag length L is determined by using the BIC criterion defined as:
Equation 5. BIC Criterion
𝐵𝐼𝐶 = −𝐿𝐿𝑜𝑔 + 𝑘 𝑙𝑛 𝑛
The minimal BIC indicates the optimal trade-off between in-sample fit and the number of parameters required to obtain this estimation.
Beta-convergence is indicated by the data when the β coefficient in the regression is statistically significant and negative. Values between 0 and -1 indicate monotone convergence whereas values between -2 and -1 show that the convergence is fluctuating with successive overshooting.
A further analysis on the convergence of European real estate markets is done using sigma-convergence. This measure is calculated as the cross-section standard deviation of the indices using the following formula:
Equation 6. Sigma Convergence Estimation
𝜎𝑡= √ 1 𝑁 − 1∑[𝑙𝑛(𝑦𝑖,𝑡) − 𝑙𝑛(𝑦̅𝑡)] 2 𝑁 𝑖=1
Where 𝑦𝑖,𝑡 is the observation of index i at time t and 𝑦̅𝑡 is the average of the indices at time t. This index is calculated for each point in time in the sample. A decrease in the index indicates convergence as the variation of the indices over time around their common mean decreases.
4. Data & Descriptive Statistics
4.1. Data
For an analysis of this kind, a data set is needed that fulfils the criteria mentioned above and furthermore has a certain length. Co-integration is a long time effect and only measurable in a long enough time sequence. The subject data set consists of quarterly observations of the two variables nominal rents and yields of the prime CBD locations in the five cities, namely London, Frankfurt, Paris, Milan and Madrid, in a time period from Q1 1992 to Q1 2015. The data set was provided especially for this paper by the European Research Department of Cushman & Wakefield LLP. The nominal rents were collected in Euro, with the London rent transformed from GBP to Euro using the then current exchange rate. This has a small negative influence. It is not possible to calculate or explain the exact currency effect that might be the reason for some portion of the overall influence of the London market. Unfortunately, the single exchange rates used each quarter to transfer the GBP measures in Euro are not part of the data set and cannot be exactly reproduced, which is why this small error has to be accepted.
To make it possible to see whether the different national inflations have an influence on the co-integration between the rental markets, the nominal rents were converted to real rents using quarterly inflation data from all subject countries in the time 1993 to 2015. The inflation rates are publicly available and in this case were obtained from the specific national institutions (For a full list of sources please refer to the appendix.) Furthermore, the respective total returns were calculated by combining the existing rent and yield information. To do so, values were brought down to a quarterly level and the following formula (equation 7) was used to calculate total returns:
Equation 7. Construction of Total Returns
𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 = 𝐼𝑛𝑐𝑜𝑚𝑒 𝑅𝑒𝑡𝑢𝑟𝑛 + 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐺𝑟𝑜𝑤𝑡ℎ 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐺𝑟𝑜𝑤𝑡ℎ = (𝑌𝑖𝑒𝑙𝑑𝑅𝑒𝑛𝑡𝑡 𝑡) − ( 𝑅𝑒𝑛𝑡𝑡−1 𝑌𝑖𝑒𝑙𝑑𝑡−1) (𝑌𝑖𝑒𝑙𝑑𝑅𝑒𝑛𝑡𝑡−1 𝑡−1)
4.2. Descriptive Statistics
Before explaining the results of the statistical analyses, the part of descriptive statistics is supposed to give an overview of the used data set, its condition and the potential information that might be expectable after the analyses.
The descriptive statistics describe all independent variables under investigation. Starting with nominal yields, as well as generated real yields, the part continues with nominal and real rents and ends with nominal and real total returns. After that, the Pearson correlation is calculated for each variable and city-pairing, in order to give a first brief view on how the markets might be correlated.
Table 1. Summary Statistics for Nominal and Real Yields
Nominal Yields Paris Frankfurt Milan Madrid London
Mean 5,35% 5,20% 4,98% 5,77% 4,78% Standard Error 0,09% 0,04% 0,05% 0,09% 0,08% Standard Deviation 0,83% 0,38% 0,45% 0,85% 0,77% Skewness -0,42 0,10 0,19 -0,63 -0,03 Kurtosis 1,74 1,69 3,75 3,14 2,27 Number of Observations 90 90 90 90 90
Real Yields Paris Frankfurt Milan Madrid London
Mean 4,95% 4,77% 4,36% 5,08% 4,25% Standard Error 0,10% 0,06% 0,07% 0,12% 0,10% Standard Deviation 0,91% 0,60% 0,64% 1,14% 0,96% Skewness -0,49 -0,89 -0,07 -0,66 0,06 Kurtosis 2,26 5,31 2,96 3,20 2,37 Number of Observations 90 90 90 90 90
The calculated summary statistics consist of mean, standard error, standard deviation, skewness, kurtosis and the number of observations. Table 1 starts with results for nominal and real yields. The nominal mean yields lie between 4,78% for London and 5,77% for Madrid. The inflation revised values are slightly smaller, as inflation was mainly positive over the observation period. Standard deviation and error are generally larger for real yields than for nominal ones, which is to be explained by the broader spread of the amount of real growth in comparison to nominal growth. The values for skewness lie slightly above and below zero, which indicates a slight left respectively right skewness. As the values are rather small, the deviations from the mean should not be essentially bigger on one side or the other. The highest skewness value observed here is from real yields in
Frankfurt. The value of -0,89 indicates a left-skewed distribution of the data, which again means that deviations from the mean are larger below it than above it. The kurtosis of all regarded data streams does not deviate a lot from 3, which implies a normal distribution. The lowest value was found for the nominal yields in Frankfurt (1,69), the highest value for real yields in Frankfurt (5,31). This rather large change suggest a significant influence from the inflation. While values below zero usually indicate that all results lie close to the mean, values above three indicate are broader distribution of values. Overall the descriptive statistics proof that the values are distributed rather normally.
Table 2. Summary Statistics for Nominal and Real Rents
Nominal Rents Paris Frankfurt Milan Madrid London
Mean 0,27% -0,13% 0,20% 0,18% 1,53% Standard Error 0,48% 0,35% 0,51% 0,60% 0,73% Standard Deviation 4,49% 3,29% 4,78% 5,69% 6,88% Skewness 1,06 -0,37 0,36 0,20 -0,84 Kurtosis 5,84 5,61 7,64 4,37 6,48 Number of Observations 89 89 89 89 89
Real Rents Paris Frankfurt Milan Madrid London
Mean -0,10% -0,53% -0,38% -0,47% 1,01% Standard Error 0,48% 0,36% 0,51% 0,60% 0,72% Standard Deviation 4,54% 3,39% 4,86% 5,70% 6,84% Skewness 0,97 -0,56 0,26 0,16 -0,72 Kurtosis 5,59 6,63 7,48 4,17 6,06 Number of Observations 89 89 89 89 89
Table 2 gives a summary of the descriptive statistics for nominal and real rents of the data set. The nominal mean growth of rents lies between -0,13% for Frankfurt and 1,53% for London. Considering inflation, the market in the British capital is the only one that shows a real rental increase over time. Rather high standard deviations and errors over all data streams are a sign for the rather large fluctuations within the rental markets over the years. Due to rental cycles within each market, the alternation of excessive and insufficient demand and supply, rent levels rise and fall more than e.g. yields. The values for skewness are heterogeneous, ranging from 1,06 for nominal rents in Paris to -0,84 for nominal rents in London. The average kurtosis is rather high, all values, for nominal and real data lie significantly above 3 which again is a sign for broad distributions of the values above and below the mean. It is visible that the data is distributed more heterogeneous that the yield data.
Table 3. Summary Statistics for Total Returns
Total Returns Paris Frankfurt Milan Madrid London
Mean 1,43% 1,38% 1,31% 1,49% 1,37% Standard Error 0,02% 0,01% 0,01% 0,02% 0,02% Standard Deviation 0,22% 0,11% 0,11% 0,21% 0,21% Skewness -0,35 0,21 0,08 -0,58 -0,02 Kurtosis 1,73 1,81 3,63 3,13 2,03 Number of Observations 90 90 90 90 90
Real Total Returns Paris Frankfurt Milan Madrid London
Mean 1,06% 0,96% 0,71% 0,83% 0,85% Standard Error 0,05% 0,05% 0,05% 0,08% 0,06% Standard Deviation 0,45% 0,45% 0,43% 0,81% 0,57% Skewness -0,43 -1,67 -0,24 -0,09 -0,14 Kurtosis 2,83 9,41 3,43 2,92 2,94 Number of Observations 90 90 90 90 90
The statistics for both nominal and real total returns (table 3) show a narrow range in the average annualized quarterly total return between the countries. For the nominal data stream, the smallest mean return is recorded in Milan with a value of 1,31% and the largest in Madrid with a value of 1,49%. The standard deviations of these returns are comparatively small with values between 0,11% and 0,22%. Thus, the standard errors of the mean returns are very small. This indicates that the returns are statistically significantly positive. The skewness of the returns is negative in Paris (-0,35) and Madrid (-0,58) indicating a left-skewed distribution. This implies that deviations from the mean are larger below the mean than above it. For Frankfurt, the skewness is slightly positive with a value of 0,21 while for Milan (0,08) and London (-0,02) the skewness is essentially zero. The kurtoses of the returns are comparatively small. The largest value is from Milan, 3,63 which is only slightly above the value of 3 for the normal distribution. For London, Paris, and Frankfurt the kurtosis is below 3 indicating a platykurtic distribution with most values highly concentrated around the mean and very thin tails.
Comparing the real total returns, it is visible that the all means are decreasing, which is logical as real returns equal nominal returns minus inflation. Standard deviation and error are a little higher, which might be due to the fact that inflation rates vary over time and therefore a broader range of results is achieved. Now, the skewness for all results is negative, while the values for kurtosis behave heterogeneous. The value for Frankfurt is
relatively high (9,41) which implies a broader distribution of the generated values. For the other markets under investigation, the value lies around 3, which is a sign for a relative normal distribution of values. These figures suggest that the total returns of the real estate market under consideration are very stable over time.
To understand the association and gain an initial insight into potential diversification benefits, the Pearson-correlation matrix between the total return indices is presented in Tables 4-6.
Table 4. Correlation Matrixes between Nominal Rents and Yields
Nominal Rents Paris Frankfurt Milan Madrid London Paris 1,00 0,43 0,45 0,51 0,34
Frankfurt 0,43 1,00 0,41 0,48 0,18
Milan 0,45 0,41 1,00 0,32 0,19
Madrid 0,51 0,48 0,32 1,00 0,40
London 0,34 0,18 0,19 0,40 1,00 Nominal Yields Paris Frankfurt Milan Madrid London Paris 1,00 0,56 0,65 0,65 0,77
Frankfurt 0,56 1,00 0,53 0,39 0,21
Milan 0,65 0,53 1,00 0,61 0,34
Madrid 0,65 0,39 0,61 1,00 0,49
London 0,77 0,21 0,34 0,49 1,00
Both for nominal rents and yields there are only positive correlations. In the rents section, Paris and Madrid have the highest overall correlation, while London has the lowest. In general, the values are rather low, the strongest correlation is visible also between Paris and Madrid with 0,51.
The yield section shows a slightly different picture. Again, Paris hat the overall highest correlation, yet concerning the investment market, Frankfurt is the city that seems least connected. The highest correlation is visible for London and Paris.
Table 5. Correlation Matrixes between Real Rents and Yields
Real Rents Paris Frankfurt Milan Madrid London Paris 1,00 0,44 0,46 0,51 0,33
Frankfurt 0,44 1,00 0,43 0,48 0,17
Milan 0,46 0,43 1,00 0,31 0,19
Madrid 0,51 0,48 0,31 1,00 0,38
London 0,33 0,17 0,19 0,38 1,00 Real Yields Paris Frankfurt Milan Madrid London Paris 1,00 0,49 0,47 0,45 0,68
Frankfurt 0,49 1,00 0,46 0,23 0,14
Milan 0,47 0,46 1,00 0,40 0,21
Madrid 0,45 0,23 0,40 1,00 0,36
London 0,68 0,14 0,21 0,36 1,00
After including the relevant inflation rates for each market, the image changes. While Paris is still the most correlated, the overall correlation for rents decreases significantly. This is to be expected, as each country has its own inflation rate and especially before the introduction of the EMU, these rates could differ widely.
For yields however, the change is a lot less drastic. In fact, no market changes its average correlations by more than 0,01.
Table 6. Correlation Matrixes between Total Return Indices
Total Returns Paris Frankfurt Milan Madrid London Paris 1,00 0,69 0,70 0,68 0,76
Frankfurt 0,69 1,00 0,62 0,47 0,32
Milan 0,70 0,62 1,00 0,66 0,34
Madrid 0,68 0,47 0,66 1,00 0,41
London 0,76 0,32 0,34 0,41 1,00 Real Total Returns Paris Frankfurt Milan Madrid London Paris 1,00 0,54 0,48 0,36 0,43
Frankfurt 0,54 1,00 0,42 0,26 0,25
Milan 0,48 0,42 1,00 0,36 0,22
Madrid 0,36 0,26 0,36 1,00 0,36
London 0,43 0,25 0,22 0,36 1,00
After combination of rents and yields, the first thing that is visible is that all cities show positive correlations. The values for nominal total returns range from 0,32 between London and Frankfurt to 0,76 between London and Paris. In general, Paris has the highest average correlation, while London shows the weakest connection to the other cities. Regarding the real total returns, as to be expected, the combined influence of rents and
yields becomes visible. In general, the correlation decreases, which is due to the influence of rents. Yet the decrease is not as drastic as for the rents themselves, which again is due to the stabilizing effect of the yields.
It is noticeable, that Paris consistently has the highest correlation while London is most cases has the lowest one. In the case of London, this is not so remarkable, as the literature review already predicted, that London as one of the world’s biggest markets for office space is partly driven by global influences that do not affect the smaller markets of continental Europe with the same intensity. Furthermore, the above described potential inaccuracy concerning the moving transformation from GBP to Euro might be responsible for part of the low connection.
5. Results
5.1. Co-Integration
Before going into the single results of the co-integration analysis, it is necessary to explain the critical values of the Engle-Granger Augmented-Dickey-Fuller test. The table below states values that have to be reached for results to be at least 90%, respective 95% or 99% significant.
In order to show a solid and broad base of results, the categories rents and yields were not only tested over the whole data set but also tested only for the time since the introduction of the single currency. The following tables are supposed to give an overview of the single results.
Unfortunately, none of the run co-integration tests have yielded a result that would give a proof for an existing co-integration between two or more of the cities. This is the case for nominal rents as well as for real rents, yields and total returns. Therefore, this paper has not found a co-integration between cities, at least not to a degree of significance of 90% or higher. While results below this 90% are not scientifically resilient, there are certain patterns that are of interest.
Table 7. EG-ADF Test Results for Nominal Rents
Results Nominal Rents Nominal Rents from 1999 - 2015 Paris - Frankfurt -0,743 -2,824 Paris - Milan -2,181 -2,099 Paris - Madrid -1,07 -2,51 Paris - London -2,24 -2,584 Frankfurt - Milan -1,731 -1,408 Frankfurt - Madrid -1,998 -1,299 Frankfurt - London -1,983 -1,058 Milan - Madrid -1,188 -2,85 Milan - London -1,676 -2,748 Madrid - London -1,208 -0,75
Table 7 shows the results of the Engle-Granger Augmented-Dickey-Fuller test for nominal rents using the whole data range as well as the above explained data range since
90% 95% 99%
-3.12 -3.41 -3.96
the introduction of the Euro. While the results all have in common, that they are not statistically significant, there are interesting differences between the two time-windows. While for the longer time horizon, the results are rather far away from being significant, with the smaller horizon, some values increase drastically and indicate that there might be a connection. The highest value measured is for the combination Paris – Frankfurt, which suits the findings in the descriptive statistics part.
Table 8. EG-ADF Test Results for Real Rents
Results
Real Rents
Real Rents from 1999 - 2015 Paris - Frankfurt -1,9 -3,093 Paris - Milan -2,12 -2,238 Paris - Madrid -1,546 -3,083 Paris - London -2,629 -2,522 Frankfurt - Milan -0,75 -0,942 Frankfurt - Madrid -1,422 -1,81 Frankfurt - London -0,771 -1,01 Milan - Madrid -1,662 -2,288 Milan - London -2,262 -1,924 Madrid - London -1,816 -0,673
For the analysis of real rents, a similar picture is presented. The shorter time horizon yields higher values. Yet again, no significant results. The introduction of the single European currency seems to have a positive impact on the results of this co-integration analysis. Again the value for Paris and Frankfurt is the highest observed, it is only slightly smaller than the 90% significance value of -3,12.
Table 9. EG-ADF Test Results for Yields and Total Returns
Results Yields Total Returns Paris - Frankfurt -1,622 -1,612 Paris - Milan -1,053 -0,667 Paris - Madrid -0,81 -0,401 Paris - London -2,394 -1,762 Frankfurt - Milan -2,021 -0,302 Frankfurt - Madrid -2,086 -0,206 Frankfurt - London -1,935 -1,586 Milan - Madrid -2,259 -1,283 Milan - London -2,2052 -0,419 Madrid - London -1,213 -0,602
Finally, the results for yields and total returns show a quite heterogeneous pattern. As none of them is close to being significant, there is no need for a further explanation of the results. The fact that other researchers were able to partly proof co-integration is in contrast to this papers findings. One possible reason is the fact that especially with private, manually collected data concerning non-listed real estate, a wide diversity of correct but divergent data can be collected within each market.
5.2. Convergence
As the results for the performed co-integration analysis were not significant, it is impossible to derive a conclusion concerning the relationship between the different markets just yet. But if co-integration is not yet given, a test for convergence could yield information concerning the movement of the markets in relation to each other. For example if it is provable, that all markets converge towards a common basis, it is only a question of time, until co-integration becomes visible.
One way to test for convergence is by looking for beta- and sigma-convergence. As mentioned in the literature review, Lee and Srivatsa (Lee & Srivatsa, 2012) were the first to test for beta- and sigma-convergence in European office markets. This papers methodology strongly leans on their statistical approach, yet differentiates itself in certain areas.
Dynamic Correlation Analysis
Bevor the actual test of convergence, a dynamic correlation analysis is performed. As explained in the methodology section, a rolling window of 16 observations is used. The following graphs depict the dynamic correlation over time and support the first impressions gained during the interpretation of the descriptive statistics. The dynamic correlation was calculated for all cities and all independent variables. As the general patterns were mostly similar, only one graph per variable is explained in detail. The dynamic correlation analysis was first and foremost conducted to achieve an understanding of the general behaviour of the different data streams. The results indicated, that the following testing procedure was eligible and significant results could be expected.
Starting with rents, figure 1 depicts the rolling correlation of London’s real rents with the other cities. While in the beginning, the correlation seems unstable, it somewhat stabilizes over time. As already estimated from the results of the descriptive statistics, London holds a special position, as it is not strongly connected to any of the other cities. Eventually correlations all run below 0,5.
All other cities showed slightly higher dynamic correlations to each other and significantly lower correlations to London over time. Furthermore noticeable is the fact, that inflation has not had a trend-changing influence on the dynamic correlations. Results of nominal and real rents were quite similar for all cities.
Figure 2. Dynamic Correlation of Nominal Yields for London
To show the patterns of dynamic correlations of yields, again an example from London was chosen. For all other cities, the pattern showed low to medium correlation for the continental European markets, while London does not play a role in approx. the first half of the observation period. This seems to be in line with the results of Lee in 2009 (Lee S. , Is the UK real estate market converging with the rest of Europe? , 2009), mentioned in the literature review. However in the second part of the observation period, London yields become more correlated to continental Europe again. Yet its special position is visible over time as correlations never reach resilient levels.
Again, results for nominal and real values were not prominently different from each other. For the total return series however, they were. Figure 3 shows the results for the dynamic correlations of total returns for Paris. As before, the correlation with the other continental cities is rather constant over time, London first does not correlate at all (value around 0), yet increases over time and reaches a comparable level as the other cities in the last third of the observation period. For the nominal results, the fluctuation in correlation over time
is higher, the overall outcome seems less stable. This leads to the estimation that inflation might have a bigger impact on total returns as expected before.
Figure 3. Dynamic Correlation of Real Total Returns for Paris
Principal Component Analysis
To further investigate the relationship between the different markets, a principal component analysis is conducted. As mentioned before, this analysis is a rather standard procedure to test for a common factor within the data set. As before, the test was performed for all available variables. In a second step, the data streams were split into a first and a second half of the data and then were analysed separately in order to test if the common factor was persistent over time. Due to the fact that the overall difference of nominal and real values is rather small, only the results of the real rents, yields and total returns will be explained in detail. The nominal test results can be found in the appendix.
Table 10. PCA Results for Real Rents
Real Rents PCA 1 PCA 2 PCA 3 PCA 4 PCA 5 Standard Deviation 1,584 0,950 0,810 0,714 0,649 Proportion of Variance 0,502 0,181 0,131 0,102 0,084 Cumulative Proportion 0,502 0,682 0,633 0,604 0,586 Loadings Paris -0,503 0,027 0,130 -0,716 0,465 Frankfurt -0,461 0,365 -0,440 0,532 0,421 Milan -0,426 0,440 0,664 0,186 -0,387 Madrid -0,487 -0,204 -0,508 -0,184 -0,655 London -0,340 -0,794 0,300 0,370 0,164
The PCA results for real rents paint a clear picture. The first factor is able to explain approx. half of the total variance within the data. As all cities show loadings of the same sign for the first component. This indicates that a common trend might be within the rental data.
Table 11. PCA Results for Real Rents First Half of Sample
Real Rents PCA 1 PCA 2 PCA 3 PCA 4 PCA 5 Standard Deviation 1,686 0,886 0,764 0,666 0,589 Proportion of Variance 0,568 0,157 0,117 0,089 0,069 Cumulative Proportion 0,568 0,725 0,685 0,657 0,638 Loadings Paris -0,501 -0,161 0,197 -0,279 0,779 Frankfurt -0,456 -0,144 -0,598 0,640 0,058 Milan -0,418 -0,647 0,372 -0,051 -0,515 Madrid -0,455 0,360 -0,425 -0,611 -0,329 London -0,398 0,636 0,533 0,369 -0,127
Table 12. PCA Results for Real Rents Second Half of Sample
Real Rents PCA 1 PCA 2 PCA 3 PCA 4 PCA 5 Standard Deviation 1,341 1,089 0,952 0,806 0,678 Proportion of Variance 0,360 0,237 0,181 0,130 0,092 Cumulative Proportion 0,360 0,597 0,541 0,489 0,452 Loadings Paris -0,488 0,324 -0,391 0,639 0,310 Frankfurt -0,339 -0,655 -0,339 -0,358 0,462 Milan -0,305 -0,484 0,680 0,456 -0,056 Madrid -0,622 0,022 -0,166 -0,234 -0,728 London -0,410 0,482 0,492 -0,448 0,396
