July 4, 2016
Analyzing Real Estate Performance: Using a
Pure-Property Index to Assess Liquidity Risk
Willem Vlaming 6050689
Supervisor: prof. dr. Marc Francke
MSc Business Economics
Track: Finance and Real Estate Finance Amsterdam Business School
2 Statement of Originality
This document is written by Willem Vlaming 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 is responsible solely for the supervision of completion of the work, not for the contents.
3 Acknowledgements
I would like to express my sincere gratitude to multiple parties that were willing to share their data to make this thesis possible. Firstly I want to thank Kristian Elonen, who provided me the data of his research. This made it possible for me to test the first versions of the model. Secondly I would like to thank SNL Financial, in particular Kevin Lindemann and Imran Tahir, for
providing transaction and holding data of European REITs. Lastly I would like to thank Bob White and Yiqun Wang from Real Capital Analytics (RCA). RCA provided both pricing data and transaction-based indices, which were vital components of this research.
I would also like to thank my supervisor Marc Francke and his colleague Alex van de Minne for their support during the writing of this thesis, in particular for their assistance in coding the state space model.
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Table of Contents
Acknowledgements
1. Introduction ---5
2. Literature Review ---7
2.1 The Risk Premium Puzzle ---7
2.2 Liquidity Risk ---9
2.3 Comparing private real estate and public REITs --- 11
3. Methodology --- 15
3.1 REIT Index Model ---15
3.2 REIT Index Estimation --- 17
3.3 Comparing Return Series --- 18
4. Data ---19
4.1 Transaction-based Indices --- 19
4.2 REIT Index Construction ---21
4.3 Comparability ---23
5. Results ---25
5.1 REIT Indices --- 25
5.1.1 Country Indices Diagnostics --- 26
5.1.2 Sector Reweighting --- 28
5.2 Comparison Results ---30
6. Conclusion ---33
References --- 35
5 1. Introduction
Real estate is an attractive asset class for investors. The risk and return characteristics of real estate are positioned between those of bonds and stocks and more importantly the returns have a low correlation with other asset classes (Quan and Titman, 1999). This makes real estate an essential asset class in an investor’s portfolio. But how much exactly to allocate to real estate has been subject of discussion for decades. Early literature suggests an allocation in the range of 20 to 30 percent. This is however rarely observed in practice. US institutional investors’ allocations have risen to just 7.4% percent from even lower allocations according to Preqin (2014). Globally institutional investors have an allocation of 8.5% to real estate (Hodes Weill, 2015). Although investors are increasing the allocation of real estate in their portfolios, it remains significantly lower than the suggested 15% to 25% (Hoesli, 2005). This is one of the most widely discussed puzzles in real estate literature.
Multiple studies have researched this puzzle and most of the proposed explanations are related to the illiquid nature of real estate. The sector is being characterized by high transaction costs and low liquidity. For investors liquidity can be very important as market conditions can change rapidly, making it necessary to sell off assets quickly. This can easily be done for stocks and bonds, but not for real estate. This is an extra risk component in real estate that is hard to quantify in traditional risk and return measurements. These metrics are based on observed transactions and do not factor in the liquidity risk. If liquidity risk could be enclosed in the performance of real estate, it could well be that investors do not underinvest in real estate after all. The goal of this study is to provide an estimate of the liquidity premium in real estate. If there is a significant liquidity premium present in real estate performance, the classic return and risk characteristics of real estate are positively biased in comparison to stocks and bonds. This would imply that the optimal allocation to real estate should be lower than previously believed.
The approach taken in this is study is to compare two types of real estate price indices that differ only in liquidity. If the underlying of both indices is equal the difference in returns and risk can be attributed to liquidity risk. In contrast to stocks the price of real estate is not readily observable. Construction of price indices is therefore not straightforward. There are multiple accepted types of indices, all with their pros and cons. Transaction-based indices, like hedonic and repeat-sales indices, are hard to construct for commercial real estate. Commercial real estate
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is very heterogeneous and is not repeatedly sold often. The other option, appraisal-based indices, suffers from smoothing. De-smoothing procedures used in other studies can be rather arbitrary and so it is hard to compare appraisal-based indices to other types of indices. The final option is a REIT index, based on publicly traded REITs. These indices suffer from leverage and a diverse pool of underlying assets, therefore making it hard to extract pure real estate returns. In this study the comparison is performed on transaction-based repeat-sales indices and self-constructed REIT indices. The transaction-based indices are provided by Real Capital Analytics (RCA). The REIT indices are newly constructed with European REIT data. The focus of this study is Europe, because liquidity risk is expected to be larger in comparison to the United States. The transaction indices represent the illiquid private market. The constructed REIT indices represent a fully liquid market. The returns and risks of these full liquidity indices can be compared to the traditional indices to assess the size of the liquidity premium.
After equalizing both types of indices, the differences in risks and returns can be analyzed. The main question answered in this study is: How large is the liquidity premium in
real estate?
Some of the existing literature on liquidity and optimal allocations is discussed in the literature review of chapter 2. In chapter 3 the methodologies of the index construction and the comparison of risk and returns are presented. All data used in this study is described in chapter 4. The results of the index construction and the formal comparison between both indices are
discussed in chapter 5. The final chapter of this study concludes all findings and presents an answer to the main question.
7 2. Literature review
The literature review is divided into three parts. In the first part the risk premium puzzle is discussed. The second part continues with liquidity in real estate. In this section first the
components of liquidity risk are discussed, next literature that incorporates liquidity risk into real estate returns is reviewed. The final section concludes with literature that covers REIT index construction, in particular pure-property indices, and literature that compares public and private real estate.
2.1 The Risk Premium puzzle
Modern portfolio theory (MPT) has provided great insights into the optimal allocation of assets in a diversified portfolio. The theory has evolved significantly since the introduction of MPT by Markowitz (1952), but the core remains valid today. For a given return, an investor can lower the risk of his portfolio by adding assets that have a low correlation with other assets in his portfolio. This theory is especially interesting for real estate since it generally has a low correlation with stocks and bonds (Quan and Titman, 1999). Investors therefore can sharply decrease the risk of their investment by adding real estate into their portfolio. The optimal allocation weights have been researched for decades. Early research from the 80’s suggested very high allocations to real estate. Suggested ranges of 20 to 30 percent were not uncommon (Ziobrowski, 1997). Hartzell et al. (1986) even concluded that the investment industry conducted ‘naive diversification’. They argued that the benefits of real estate are so significant that allocation to this sector should be sharply increased. Not all accepted these high theoretical allocations. Criticism focused on the unusual high inflation during the 70’s, which made real estate as an inflation hedge very attractive, and the use of appraisal-based return series. It has been repeatedly proven that appraisal-based return series suffer from excessive smoothing (Hoesli, 2003). Therefore risks will be underestimated using an appraisal-based index. But also studies from more recent years suggest high allocations. Hoesli et al. (2003) present optimal allocations in the 15 to 20% range and Hudson-Wilson et al. (2005) even suggest allocations up to 50%.
Surprisingly these allocations are never observed in reality. Hoesli et al. present
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range for American institutions. Although allocations have been growing the last couple of years, there still remains a big discrepancy between suggested and actual allocations to real estate.
This puzzling reality has led to a number of studies that try to explain the gap. Chun et al. (2004) present a thorough research covering the allocation paradox. Unfortunately they do not find a compelling explanation. The authors find that real estate diversification pays off when it is most needed, because during economic downturns real estate reacts less heavy in comparison to stocks and bonds. The authors also find that real estate returns are predictable. Various
components of REIT characteristics, like the price-dividend ratio, were used to predict real estate returns. Especially at longer horizons, which are most common in real estate, a substantial
amount of the returns can be predicted by these characteristics. For investors this predictability leads to lower risk. Other findings are that real estate performs well with the liabilities of
institutions and that large losses are unlikely. All these findings leads the authors to conclude that there is no compelling reason for the low observed allocations to real estate. To eliminate market risk they suggest allocations up to 12%.
Hoesli et al. (2003) also present possible explanations for the observed gap. Real estate is very illiquid compared to the other asset classes and the transaction costs are high. Liquidity risk is not captured in traditional real estate indices. Therefore the risk and return measurements could be positively skewed. This significantly affects the optimal allocation to real estate. Other proposed reasons are the high management burden of real estate and the significant investment amounts for single properties. The latter means that it is hard to invest in the ‘market’ and that investors always have property specific risks.
Riddiough et al. (2005) take a different approach and focus on differences between return series. They compare the returns of private and public real estate. In theory the returns should be equal as the underlying, real estate, is same for both. To answer their research question they compare a private appraisal based index with a public REIT index. They start off by adjusting the REIT index to make the underlying as equal as possible to the appraisal-based index. The most important steps are de-levering and adjusting the sector weights. The results were
surprising as public real estate outperformed private real estate. The authors proposed a couple of reasons that could explain the difference. The first and most obvious explanation is that the risks in both indices are not equal. If REITs tend to invest in more risky assets this would clarify the
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higher returns earned from public real estate. The second possibility could be liquidity. Investing in public real estate provides greater liquidity than investing in private real estate. But since investors prefer liquidity it should lead to private real estate outperforming public real estate and not the other way around.
2.2 Liquidity Risk
One facet of real estate that is part of every study is the effect of liquidity, especially in comparison to other asset classes. Adjusting real estate performance to reflect liquidity risk could very well be the solution to the allocation paradox. The amount of liquidity is typically defined by three factors: The amount of time it takes to sell an asset, the impact of a transaction on the asset price and the amount of buyers and sellers in the market. The first factor is the most important for this study. The amount of time it takes to sell an asset can be very important for a real estate investor. If a companies’ cash holdings drops to dangerously low levels or a great buying opportunity appears, the investor may need to sell one of its asset quickly to generate cash. In the public REIT market an investor can easily sell of his shares. In the private market however it is very hard to sell an asset quickly. The extra amount of time it takes to sell an asset induces costs for an investor and is one of the components of liquidity risk. On top of this there is the actual uncertainty in the amount of time it takes to sell an asset. This so-called marketing period risk leads to even more risk and is another component of liquidity risk. The second factor is often used in the stock market to describe the effect the sale of stocks has on the stock price. In a fully liquid market, the impact of stock sales on the price is small. In an illiquid market
however the share price will drop significantly when shares are being sold. In real estate the reasoning is the same. As more properties in a certain market are being sold, this has a
significant impact on the price of other properties in that same market. This again adds extra risk to real estate which is less present in fully liquid markets as bond and stock markets. This second risk factor should however be present in both the private and the public market and therefore has no value in a comparison between private and public market real estate. Multiple studies have addressed liquidity risk in real estate and have tried to incorporate liquidity risk in real estate performance.
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Fisher et al. (2003) recognize that liquidity differences are not captured in traditional transaction or appraisal-based indices. They provide a new econometrical model to create so called constant-liquidity indices. In up-markets it is easier to sell real estate than in
down-markets. This is due the fact that buyers tend to react faster to news than sellers. Since liquidity is a measure of ‘ease to sell’ or time on market (TOM) it is positively correlated with the market. In principle this means that in an up-market one can sell real estate at a given price quicker than in a down-market. Or by reasoning the other way around an investor can sell his real estate in an up-market at a higher price given the TOM. The authors adjust this variability in TOM by keeping the transaction volume fixed, therefore creating a constant-liquidity index. Fisher and others apply their model to the National Counsel of Real Estate Investment Fiduciaries (NCREIF) transaction based index and compare the constant-liquidity index with existing indices. The constant-liquidity index is significantly more volatile than its variable-liquidity counterpart. It has almost the same volatility as the National Association of Real Estate Investment Trust (NAREIT) index that is made up from public REITs. To conclude their study they use their new index in a mean-variance portfolio to see whether it has significant effects on the optimal allocation to real estate. Starting with the variable-liquidity index, the optimal allocation to real estate in a five-asset class portfolio is 32.56%. This drops to 9.27% using the constant-liquidity index. This finding only strengthens the conjecture that liquidity affects the attractiveness of real estate as an asset class.
In line with Fisher’s article future research focuses on the illiquidity of real estate. Lin et al. (2007) continue on the work of Fisher, but in a more theoretical way. Where Fisher proposes an econometric correction of observed prices, Lin discusses the process of price risk and TOM risk. This allows them to access the full range of options including a full liquidity scenario, which is different than a constant-liquidity index. Only then is real estate fully comparable to other asset classes. Lin’s addition to the liquidity literature is the notion of ex ante risk. With traditional real estate indices the risk and returns are based on ex post prices. Since ex post there is no uncertainty in the selling time, there is no so-called marketing period risk. The only risk is price risk. This is however not realistic because ex ante an investor does not know when he will be able to sell and so there is an extra marketing period risk. To circumvent this problem the authors introduce a new ex ante risk measure that includes the marketing period risk. They apply their model to both the residential and the commercial market to put the effect of liquidity in
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perspective. For longer holding periods the risk adjustment is lower, because the risk can be amortized over a longer period. For a 10-year holding period, which is realistic for an
institutional investor, risk increases by 30% and 40% for the residential and commercial market respectively. This is a severe bias that again partly explains the lower than expected allocation to real estate.
There is one caveat in Lin’s article and that is the assumption that real estate returns are independent and identically distributed (i.i.d.) over time. Many have found contradicting results and conclude that there is strong evidence of serial correlation in real estate returns (e.g. Englund et al., 1999). Cheng et al. (2013) introduce the liquidity risk factor (LRF), which is calculated by dividing the risk of an illiquid asset with the risk of a liquid asset. A low LRF means there is a small difference between the risk of liquid and illiquid assets. The addition to Lin’s article is that the authors do not assume that the returns are i.i.d. They use three different return distributions and present the results for all. The first distribution is i.i.d. in which the variance increases linear with the holding time. The second return distribution is one in which the variance of the returns increases with the square of the holding time. In the final used distribution they assume that the variance increases somewhere between the first two. Using the first i.i.d. assumption they find the same risk factor as Lin. When using the other two more realistic variance assumptions the risk factor increases and so does the difference between the risk of liquid and illiquid assets. The effect strongly depends on the market and on the holding period. A poor market and a short holding period lead to a high liquidity risk factor.
2.3 Comparing private real estate and public REITs
All three liquidity articles adjust private market real estate to fully reflect the risk of liquidity. In this study a different approach is taken, more similar to Riddiough’s (2005) approach. A fully liquid REIT index, based on the pure-property methodology, is constructed and compared to an illiquid private market index. In this subsection first studies about the pure-property methodology are discussed. This subsection concludes with a study that mirrors the approach of Riddiough.
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In an earlier study of Geltner and Kruger (1998) new REIT-based pure-play portfolios are constructed. Normally REITs are invested in a number of sectors. It is therefore hard for an investor to only invest in one sector via REITs. With the new pure-play technique an investor can invest in his desired sector by taking different long and short positions in REITs. This way the desired exposure can be achieved. The paper focuses on explaining and analyzing the new technique. More interesting for this study is their comparison of the constructed pure-play REIT indices and the appraisal-based NCREIF index. Both constructed indices were national sector indices. More granular indices were not feasible due to data constraint. The REIT indices are unlevered and the NCREIF index is unsmoothed. Still the REIT indices outperformed the
NCREIF index. The returns tended to be higher during the whole sample period of 1987 to 1996. The volatility of the REIT indices was also somewhat higher. The results are in line with the results of Riddiough et al. (2005).
Due to data constraints, especially the holdings of REITs, the pure-property methodology has not been used in practice until quite recently. Horrigan et al. (2009) were the first to apply the methodology in a broader sense to the US REIT market. Overall their results were very satisfactory. The indices showed comparable risk characteristics as their transaction-based Commercial Property Price Indices (CPPI) counterparts. The indices also tended to lead the CPPI.
Kristian Elonen (2013) is the only one up to now to attempt to construct the pure-property indices for European markets. The author tried to construct both country and sector indices. In limited cases Elonen estimated country specific sector indices. The results were mixed. For some countries the methodology produced reliable indices. Reliable in the sense that the returns and risk are reasonable and somewhat comparable to existing appraisal- or
transaction-based indices. For other countries however the results were unsatisfactory. The indices showed very high volatilities and occasionally even negative autocorrelations. These mixed results for the European market can most likely be attributed to the scarce amount of observations. The REIT market in Europe is still relatively small in comparison to the United States. Especially the countries where the results were unrealistic tend to have very small REIT markets.
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In line with Riddiough’s approach, a study from Pagliari et al. (2005) also compares public real estate with private real estate. The authors compare the private appraisal-based NCREIF index with a restated NAREIT index. The most important step in such a comparison is equalizing the underlying of both indices. In making them comparable the researchers take a few extra steps than Riddiough et al. Because the investment focus of REITs is different than the content of the NCREIF index, all the REITs need to be labeled to get an overview. For example a REIT invested for 80% in apartments is labeled an apartment REIT. REITs invested in special sectors, like golf courses, are dropped. After labeling all REITs, it is easy to calculate the sector weights of the restated NAREIT index. Next the NCREIF property-type returns can be
reconfigured to match the content of the restated NAREIT index. The second step is de-levering the REIT returns, because the NCREIF returns are unlevered. De-levering is done using the WACC identity, debt ratios and debt costs. The final step is adjusting the NCREIF index for appraisal smoothing. Appraisal smoothing leads to a dampened volatility and needs to be removed as it not present in the market-based NAREIT index. After all these steps the two indices have the same underlying. The sectors are equally represented and the indices are unlevered and unsmoothed. The authors finish their paper by testing for differences between both indices. The difference in returns is tested utilizing a paired-comparison t-test. They do not find a significant difference between the returns of both indices. They explain that this result is likely partly explained by the noisy return differential during the sample time. The difference in volatility is tested with an F-test. While using the smoothed appraisal index they do find a significant difference in volatility of both indices. However they do not find a significant
difference in volatility between the unsmoothed NCREIF index and the restated REIT index. The results of Pagliari contradict the findings of both Geltner and Riddiough.
A caveat in both Pagliari’s and Riddiough’s study is that there is no control for the actual riskiness of properties in both indices the authors are comparing. This is largely a data issue that is very hard to solve. It is impossible to assess whether REITs tend to invest in more or less risky assets than those assets present in the private market index. In general however it is believed that REITs invest in more risky assets than institutions (Barkham and Geltner, 1995). This could potentially bias their results in favor of the REITs.
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In this chapter previous research regarding the risk premium puzzle and liquidity were discussed. Chun et al. (2004) and Hoesli (2003) analyze actual real estate returns and did not find compelling reasons for the perceived under allocation to real estate. Fisher et al. (2003), Lin et al. (2007) and Cheng et al. (2013) add a liquidity risk component to real estate returns and all find that real estate performance significantly drops when adding such an additional risk component. Riddiough et al. (2005) and Pagliari et al. (2005) compare private and public real estate to research whether there are difference in the risk and returns. Riddiough finds that public real estate outperforms private real estate, which is in line with Geltner and Kruger’s (1998) pure-property study. Pagliari however finds no significant difference between both return series. This study will combine the approaches of Riddiough and Pagliari with the pure-property
methodology of Geltner and Kruger. A newly constructed public market REIT index is compared to a private market transaction-based index.
15 3. Methodology
In this study the liquidity premium is estimated by comparing two different types of real estate indices. The first index is a transaction-based private market index, the other is a newly
constructed public market REIT index. In the first part of this chapter the process of constructing the REIT indices is described. In the second section the methodology of the comparison is elaborated.
3.1 REIT Index Model
The REIT indices are based on the pure property methodology, firstly introduced in a study of Geltner and Kluger (1998). The issue of REIT indices is that REITs are both diversified and levered. It is therefore very hard to create sector and/or location indices out of REITs. The solution of the pure property methodology is to regress de-levered REIT returns on the exposures of the REIT holdings. This way one can extract purely the property returns out of REITs. As an example the returns can be regressed on the property holdings divided into the country
exposures. The resulting coefficients of the regression represent the country returns. This can be clarified by the following example:
𝑟𝑜𝑎𝑖,𝑡 = 𝑏𝑁𝐿,𝑡𝑥𝑁𝐿,𝑖,𝑡+ 𝑏𝐷𝐸,𝑡𝑥𝐷𝐸,𝑖,𝑡+ 𝑏𝑈𝐾,𝑡𝑥𝑈𝐾,𝑖,𝑡+ 𝑒𝑖,𝑡 (1)
In this example the REITs only have investments in either the Netherlands, Germany or the United Kingdom. The indices constructed in this study are all quarterly, but in theory it could be done daily. The dependent variable is the return on assets, which are the de-levered REIT returns. The x’s are the independent variables and represent the portion of the total investments of the REIT invested in a specific country. For every period these holdings vary, but the sum of the x components always adds up to one. The b’s are the regression coefficients and reflect purely the country’s real estate returns. The error term is e. This model uses an unbalanced panel.
De-levering the REIT equity returns is done using the weighted average cost of capital (WACC) identity:
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Tax effects are neglected as REITs tend to pay out all earnings to avoid paying taxes. After running the regressions of equation (1) it is easy to construct country specific indices.
In recent years the pure-property methodology has been revitalized by both Horrigan (2009) and Elonen (2013). Both authors use the classic ordinary least squares (OLS) approach to estimate the returns in equation (1). This generally works when there is a sufficient amount of observations, as in the United States. However when there is a limited amount of REITs separate regressions for every period can lead to very volatile indices. This is shown by Elonen for the Netherlands and France. There is no modelled relation of the returns over time, which can lead to indices that move up and down every quarter. In general it is believed however that real estate markets do not act in such a volatile way. In this study another approach is taken to construct European pure property indices. To provide better indices for the European markets the
regression will be based on a state-space model. In this state-space model the return parameters are time-varying and follow a random walk. Modelling the returns in a random walk will lead to less volatile indices, since the returns are not able to move heavily period by period. Specifying real estate returns in a random walk is also not unrealistic as multiple studies have shown serial correlation is common in real estate returns.
The model used in this study is an example of a structured time series model. All separate OLS regressions are replaced by one regression. In this model the returns follow a random walk. The returns are allowed to vary over time, but not unbound as in a period by period regression. The estimation process includes the Kalman filter (1960) and therefore, if past returns are very informative, new observations that strongly differ from the trend will only affect the result to a small extent. A big outlying jump in a quarterly return is therefore restricted to a smaller deviation. This all can be visualized by the following model, which builds on the previous example:
𝑟𝑜𝑎𝑖,𝑡 = 𝑏𝑁𝐿,𝑡𝑥𝑁𝐿,𝑖,𝑡+ 𝑏𝐷𝐸,𝑡𝑥𝐷𝐸,𝑖,𝑡+ 𝑏𝑈𝐾,𝑡𝑥𝑈𝐾,𝑖,𝑡+ 𝑒𝑖,𝑡 𝜀𝑡~ 𝑁𝐼𝐷(0, 𝜎𝜀2) (3)
𝑏𝑁𝐿,𝑡 = 𝑏𝑁𝐿,𝑡−1+ 𝜂𝑁𝐿,𝑡 𝜂𝑁𝐿,𝑡~ 𝑁𝐼𝐷(0, 𝜎𝜂,𝑁𝐿2 ) (4)
𝑏𝐷𝐸,𝑡 = 𝑏𝐷𝐸,𝑡−1+ 𝜂𝐷𝐸,𝑡 𝜂𝐷𝐸,𝑡~ 𝑁𝐼𝐷(0, 𝜎𝜂,𝐷𝐸2 ) (5)
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In this model all country returns follow a random walk. The country returns are unobserved and equations (4) to (6) are called the state equations. The addition of the state equations is the large contribution of this study to previous studies. The returns are related through time, which will prevent negative autocorrelation and excessive volatility in the returns.
3.2 REIT Index Estimation
The model is estimated with a forward pass through the data, the Kalman filter (1960), and a backward pass, a recursive algorithm regularly called state and disturbance smoother. The Kalman filter is used with the forward pass through the data and provides estimates based only on past values of the observed time series, the REIT returns. The state and disturbance smoothers are required for smoothing. It provides the estimates of the state and disturbance vectors based on all observations.
The hyperparameters, the observation and state disturbance variances, are estimated in an iterative process in which a log-likelihood function is maximized. Most important factors in this likelihood function are the prediction errors and their variances, which both are minimized. The prediction error is the difference between the observed return and the predicted return, which in a random walk is the return of t-1. How much a new observation is allowed to influence the
previous state, depends on the variance of the filtered state, the information in past observations, and the variance of the one-step ahead prediction errors, the information in new observations. The ratio of the previous two variances is called the Kalman gain. The larger the Kalman gain, the larger the influence new observations have on the new state.
For readers with further interest in state space models and the Kalman filter I would recommend Koopman and Commandeur’s book: “An introduction to State Space Time Series Analysis” (2007). In appendix A1 a generalized version of the state space model is provided with an applied example of the REIT indices for this study. The estimation is conducted through OxProfessional and SffPack.
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3.3 Comparing Return Series
After the REIT indices are estimated, a comparison is made between the returns in the REIT indices and RCA’s transaction-based indices. The underlying of the REIT indices is made as equal as possible to that of RCA’s private market indices. The goal of this research is to estimate liquidity premium, which in theory would be the only difference remaining in both indices. Therefore two tests are performed. First a test to access if there is a significant difference in the mean quarterly return between the two indices. Due the additional liquidity risk in private-market real estate, the returns of the REIT indices are hypothesized to be lower than the private market-based indices’ returns to compensate for the lack of liquidity risk.
The null hypothesis is therefore: H0: 𝒓𝒑𝒖𝒃𝒍𝒊𝒄 – 𝒓𝒑𝒓𝒊𝒗𝒂𝒕𝒆 ≥ 𝟎
The alternative hypothesis is: H1: 𝒓𝒑𝒖𝒃𝒍𝒊𝒄 – 𝒓𝒑𝒓𝒊𝒗𝒂𝒕𝒆 < 𝟎
A simple paired-comparison t-test is used to test this hypothesis.
The second test covers the difference in risk between both indices. Again the hypothesis is that the volatility in public real estate is higher than the volatility in private real estate to compensate for the lack of liquidity in the private market.
The null hypothesis is: H0: 𝛔𝐩𝐮𝐛𝐥𝐢𝐜𝟐 ≤ 𝛔𝐩𝐫𝐢𝐯𝐚𝐭𝐞𝟐
Versus the alternative: H1: 𝛔𝐩𝐮𝐛𝐥𝐢𝐜 𝟐 > 𝛔𝐩𝐫𝐢𝐯𝐚𝐭𝐞𝟐
This hypothesis is tested with an F-test.
In this chapter fist the methodology of constructing the REIT indices was discussed. The contribution of this thesis is the state space model used to estimate the indices. Returns are related through time in this model opposed to the unrelated returns in the period by period regressions from previous studies. This will aid the efforts to remove negative autocorrelation and excessive volatility. Next the tests were discussed which will be used to compare both indices. A paired-comparison t-test will be used to test differences in the returns and the difference in volatility will be tested with an F-test.
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4. Data
This research is based on two types of real estate indices, a private market-based transaction index and a public REIT index. In this chapter first the private market-based transaction indices are shown and summarized. Next all data necessary to develop the public REIT indices is discussed.
4.1 Transaction-based Indices
The comparison is carried out from the beginning of 2010 to the end of 2014. Real Capital Analytics (RCA) provided their recently introduced transaction indices for Europe. RCA’s Commercial Property Price Indices (CPPI) are constructed using the repeat-sales methodology. Because the European commercial real estate market is too thinly traded to create the indices with a standard repeat-sales model, a hierarchical trend model is defined to estimate the European indices (Francke and Vos, 2004). This hierarchical model is an enhanced version of the structured time series model used to create the REIT indices. The production of the indices starts in 2007 and is updated monthly. The indices displayed below have an index value of 100 in 2010 for comparability purposes.
Figure 1: RCA Country Indices
40 50 60 70 80 90 100 110 120 130 140 2010 2011 2012 2013 2014
20
In table 1 the summary statistics are given. The average returns and standard deviations are on a quarterly basis. The worst performer is the Netherlands and the Nordic countries have the highest 5-year return.
Table 1: Summary statistics RCA’s CPPI (2010-2014)
Country Average Quarterly Return Standard Deviation of Returns 5-Year Return Netherlands -2.54% 3.23% -42.93% France 1.27% 1.47% 24.74% UK 1.28% 2.15% 24.03% Italy -0.46% 0.99% -10.01% Germany 0.24% 2.69% 4.07% Nordics 1.55% 3.19% 33.02%
One important element in the comparison are the weights of different property types in these indices. So next to these country indices RCA provided indices split by both country and
property type. These indices can be used to composite new country indices that match the sector exposures of the REIT indices. Since some of the sectors have too few observations to construct an index, this set is not complete for every country. The German index for example is impossible to split. In figure 2 the UK indices are shown and in table 2 their summary statistics. In appendix A2 all available indices are shown.
Table 2: Summary statistics RCA’s UK Sector Indices (2014)
Sector Average Quarterly Return Standard Deviation of Returns 5-Year Return Office 1.63% 2.69% 35.02% Retail 0.39% 2.16% 7.15% Apartment 1.31% 2.24% 27.54% Industrial 1.31% 2.68% 27.29% Hotel 0.95% 2.25% 19.02%
21
Figure 2: RCA UK Sector Indices
4.2 REIT Index Construction
The public REIT indices are newly created for this research and use data from multiple sources. The REITs are selected out the FTSE NAREIT developed Europe index (FTSE NDEI). The REITs have to be operational for the entire time period, since a balanced panel is chosen for this study. The starting list of REITs is a combination of the 2010 and 2015 FTSE NDEI. The necessary data consists of two parts: de-levered REIT returns and the REIT holdings.
The REIT stock returns and dividends are retrieved from DataStream. The stock returns are unadjusted for dividends and therefore represent pure capital gains. The dividends can be added to calculate total REIT returns. Since RCA’s CPPI do not contain income returns, dividends are left out.
Debt ratios are also collected from DataStream. The ratio is defined as total debt divided by total capital. Numerous ratios were unavailable for the second half of 2014. These missing ratios are gathered from the financial statements of the REITs.
The final REIT data necessary to calculate the unlevered returns is the cost of debt. Multiple approaches can be taken to estimate the cost of debt. In this study bond data is retrieved and used to approach the cost of debt. Raw bond data is gathered from DataStream. These are all
80 90 100 110 120 130 140 2010 2011 2012 2013 2014
22
REIT bonds outstanding during the start of 2015. Bonds that matured before the start of 2015 are not used in this analysis. Unfortunately for 40 REITs bond data is unavailable. Therefore in line with previous research of Elonen (2013), one cost of debt per year is estimated and applied to all REITs. This is obviously not ideal, but since the variability in cost of debt among REITs is quite low this approach suffices for this study. The yearly cost of debt is estimated by first calculating the average yield to maturity (YTM) by REIT from all their outstanding bonds. Secondly the YTM’s are equal weighted across companies to estimate the average cost of debt by period.
In table 3 yearly summary statistics for the REITs are given. The average quarterly return is the equal-weighted asset return of the REITs, so these returns already have been de-levered using the WACC-identity. In line with table 1 and 2 the average quarterly asset return over the entire period is 1.64% and the standard deviation is 2.21%.
Table 3: REIT summary statistics (Based on final 73 REITs)
Year Average Quarterly
Return on Assets
Average Debt Ratio Debt Cost
2010 1.99% 49.31% 4.90%
2011 -0.35% 49.52% 3.80%
2012 1.64% 50.23% 4.30%
2013 3.07% 48.86% 3.99%
2014 1.83% 46.05% 2.73%
The second part of the data is the holdings of the REITs. Unfortunately there is no historic database of the REIT holdings. Only the current holdings of REITs are stored in the database of SNL Financial (SNL). Transaction data however can be used to recreate the historic holdings of the REITs. SNL provided all their transaction data for the selected REITs. The starting point of such a recreation is the current portfolio of the REIT, which is readily available. From this portfolio you can go back in time processing all transactions. A sell at a certain point in time implies that before that date the property was part of the portfolio. For a buy the opposite is true, before that date the property was not part of the portfolio. Going through this process for every single REIT leads to a database of the holdings per period.
The data SNL provides is in square feet. Because this does not give a fair representation of the value of a property, pricing data needs to be used to estimate property values. RCA’s
23
database covers all commercial real estate transactions above five million. This database is used to calculate an average price per square foot for the entire period per property type and
submarket. When transactions are too scarce on a submarket level to calculate a reliable average, market or even country averages are used. Multiplying the size of the properties with the average price per square foot gives an estimate of property values.
The data SNL provided was not without gaps. A good amount of transactions had missing data points and numerous assumptions have been made to recreate the holdings as accurate as possible. In appendix A3 a detailed description of all assumptions is given.
As noted before the starting list of REITs is a combination of the 2010 and 2015 FTSE NDEI and amounts to 96 REITs.There are however multiple reasons to drop REITs from this list and not use them to create the indices. The first reason is that some of the REITs were not active for the entire time period. This study uses a balanced panel, so these REITs cannot be used. Secondly for some REITs holdings data is not available. Since this is a vital part of the data these REITs need to be excluded. A final reason for exclusion is that some of the REITs are very specialized. The methodology does not benefit from a REIT that, as an example, is invested for 90% in self-storage. REITs that invested over 30% in an ‘other’ category are dropped. This also removes speculative REITs that invest in land. A complete overview of all the REITs and the reason for exclusion can be found in Appendix A4.The final balanced panel is a set of 73 REITs.
4.3 Comparability
A disadvantage of comparing two real estate indices is that the underlying assets differ. Therefore there is always a risk that any of the finding can be attributed to a difference in the underlying. An argument often made is that REITs tend to invest in more risky assets than institutions, which would bias REIT-based performance measurements upwards and would make them incomparable to a private-market based index.
The private-market index used in this study however is not only based on institutional investors, but on all types of investors. These can be wealthy individuals or non-traded funds, even transactions with REITs as one of the players in the deal are present in the private-market based index. Next to this REITs that invest a significant portion outside of the traditional real estate types are excluded, so REITs that invest in development sites or land are not used. A final measure taken is the use of a balanced panel. Only REITs that existed for the entire period are
24
used. This will filter out bankrupted REITs and newly started REITs, which have a higher probability of being involved in risky real estate. This is by no means a perfect solution to the problem, but it will filter out the most obvious differences in riskiness of assets between the REIT index and the transaction-based index.
25 5. Results
In this the chapter the results of the various regressions are presented. First the estimation results of the REIT indices are discussed. Next the exposures of these indices to different sectors are described. The exposures differ from RCA’s indices, which makes them crucial for comparison purposes. With these results RCA’s indices are restated to reflect the same sector exposures as the REIT indices. In the final part the results of the comparison tests are discussed.
5.1 REIT indices
The European REIT indices have been constructed in three ways: a split by geographical area, a split by sector and a split by both geographical area and sector. The structured time series methodology produces stable indices for the country and sector splits. Regressions by both country and sector however were rarely successful. The model only produced successful sector indices for the United Kingdom. This is still the result of the scarce amount of data. The number of REITs in Europe is too low to produce property type indices for countries other than the UK. Below the resulting country indices are shown in figure 3. The sector indices and the UK sector index can be found in Appendix A5.
Figure 3: REIT-based Market Indices
40 60 80 100 120 140 160 180
26
5.1.1. Country Indices Diagnostics
To stabilize the estimation of the country indices both the state and observations standard errors were set equal across countries, the states, and REITs, the observations. The state standard error is 17% and the observations standard error is 21.9%. This translates into a state variance of 2.89% and an observation variance of 4.79%. The value of the maximized log-likelihood function is 2248.6.
The results of the Kalman filter are shown in figure 4. The one-step prediction errors do, with Germany as the exception, not provide reason for concern. The errors tend to be stable and centered around zero, which is a desired outcome for the prediction errors. The high positive errors for Germany starting in 2012 however are not desirable. Modelling the returns in a random walk might be not be suitable for Germany. For reason others than these errors the German index is actually not used in the comparison.
Figure 4: Prediction Errors
The final diagnostics showed on the country indices are how accurate they have been estimated. Below in figure 5 the returns with their 95% confidence bounds are shown for the UK and the Netherlands, the other results can be found in appendix A6. The UK is the country which has the most data available and therefore is estimated most accurately with an average standard error of less than 1%. The confidence bounds for the Netherlands are significantly wider due the scarce
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
27
amount of REITs invested in the Netherlands. The 2.6% average standard error leads to wide 95% confidence bounds.
Figure 5: 95% Confidence Bounds
The added value of the state-space model can especially be seen when compared to the same analysis in a period by period OLS estimation. The resulting country indices estimated in an OLS framework can be found in figure 6. The indices are significantly more volatile and occasionally even show negative autocorrelation, e.g. The Netherlands. This is a result of thin data in the European REIT market and does not give a realistic representation of the European real estate markets. Modelling the returns in a structural time series model solves for this excessive volatility.
Figure 6: REIT-based Market Indices in an OLS framework -8.0% -6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% United Kingdom -15.0% -10.0% -5.0% 0.0% 5.0% 10.0% 15.0% Netherlands 40 60 80 100 120 140 160 180
28
In the estimated country indices the Netherlands is again the worst performer among the European real estate markets with a loss of more than 20% over 5 years. A striking difference with the transaction-based indices is the performance of Germany, which has the best return in the REIT indices. A big portion of these return differences can be attributed to the sectors that are represented in the price indices. The average apartment sector exposure of REITs in Germany is 25%, while the transaction-based index is almost completely based on the office sector. As a result of these sector differences the transaction-based indices are re-weighted to match the sector exposures of the REITs. All other summary statistics of the REIT indices can be found in table 4.
Table 4: REIT indices summary statistics
Country Average Quarterly Return Standard Deviation of Returns 5-Year Return Netherlands -1.21% 2.17% -22.05% France 0.69% 2.56% 14.08% UK 1.81% 2.35% 42.51% Italy 0.63% 2.87% 12.56% Germany 2.64% 2.32% 67.83% Nordics 2.00% 2.05% 47.98% 5.1.2 Sector reweighting
To remove the differences in sector exposures, the by country and sector transaction-based indices are composited to match the exposures of the REIT indices. As an example the REIT exposures to different sectors in the UK are shown in figure 7. The REITs focus on the three traditional commercial real estate sectors and barely rebalance their sector investment over time. Next these weights are used to reweight the returns of the UK sector series of figure 2. The result is a transaction-based country price index that has the same weights in different sectors as the REIT-based indices.
29
Figure 7: REITs UK Sector Exposures
Because the sectors of the REIT indices differed slightly from the transaction-based indices, some assumptions had to be made. The exposures to the multi-use sector are split equally between the three traditional commercial sectors, office, retail and industrial. Exposures to the ‘other’ sector are equally divided over all sectors. Unfortunately the re-weighting leads to the loss of Germany and Italy as markets for the comparison. The German transaction-based index is almost purely office and therefore not suitable to split in sectors. The Italian transaction-based index has zero exposure to apartments. Therefore it was not possible to match the
exposures of the REITs, which do have investments in the Italian apartment sector.
The final performance comparison will be done for the four remaining markets: the Netherlands, United Kingdom, France and Nordics. Below in figure 8 all indices are shown in one graph. The Netherlands is the only country where value was lost over the last five years. Another easy observation is that except for France, all REIT-based indices outperformed their transaction-based counterparts. In the next section the formal tests on the returns of both indices are discussed. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
30
Figure 8: REIT indices vs Transaction-based Indices
5.2 Comparison results
The first set of test is a paired-comparison t-test on the quarterly returns. The alternative hypothesis is that public REIT returns are significantly lower than the private transaction-based returns. If this proves to be true the favorable liquidity in public real estate would translate into lower returns. The null hypothesis however cannot be rejected for any market. The mean difference is actually positive in 3 out of 4 countries. For France the mean difference was
-0.72%, but not low enough to accept the alternative hypothesis. All results can found in table 5.
Table 5: Paired-Comparison t-tests on quarterly returns
Market Mean Difference Standard Deviation p-value Null Hypothesis
Netherlands 0.75% 3.56% 82.2% Not Rejected
United Kingdom 0.67% 2.99% 83.6% Not Rejected
France -0.72% 2.90% 13.9% Not Rejected
Nordics 0.53% 3.97% 72.3% Not Rejected
50 60 70 80 90 100 110 120 130 140 150
31
Although there is no statistical difference in returns, public real estate could still show higher risk. The next step is to assess if there is difference in risk between the public- and private-based indices. An F-test is used to assess whether the variance ratio of private and public real estate is lower than 1. The alternative hypothesis is therefore that public real estate is riskier than private real estate.
For 3 out of 4 markets the null hypothesis cannot be rejected. Risk in the private real estate market is not significantly lower than in the public market. For France however the variance in private market returns is significantly lower than the variance in public real estate returns. All variance ratios and p-values can be found in table 6.
Table 6: F-test to compare variances
Market Ratio of Variances p-value Null Hypothesis
Netherlands 1.41 76.9% Not Rejected
United Kingdom 0.98 47.8% Not Rejected
France 0.26 0.2% Rejected
Nordics 2.12 94.5% Not Rejected
The results of the comparison indicate there are no significant differences in the risk and returns of public and private real estate. This would imply there is no compensation for the extra liquidity risks in private-market real estate or that liquidity risks are negligible for real estate investors. The long holding periods of real estate could diminish liquidity risk significantly, making investors indifferent between public and private real estate. The other potential explanation would be that the REIT index, even with precautionary measures taken, still has more risky assets as the underlying which biases the returns and risks upwards. France is the only country where the REIT index both underperformed the private market index and proved to be more risky than the private market index. This not so much the result of a very volatile REIT index, but more so of a very stable private market index. This is a prime example of the
difficulties in equalizing the underlying assets of two different indices. The private market index is almost made up completely of Paris properties, which has seen a stable growth in property prices over recent years. The REITs however are geographically strongly diversified. This explains the lower and more volatile performance of the French REIT index.
32
As a final check both tests are applied to a pooled dataset with all countries.
Unsurprisingly the results are reconfirmed. The REIT indices have both a higher return and a lower variance than the transaction-based index. The mean difference is 0.31% in favor of the REIT index and the variance ratio is 1.12 again in favor of the REIT index. Both null hypotheses cannot be rejected for the pooled dataset.
This chapter started off with the results of the REIT index estimation. After restating the private market indices, which led to the loss of Germany and Italy, comparative tests were discussed on the differences between the public and private market indices. Except for the variance in the French returns, no significant differences between both indices can be found. Unfortunately there can be multiple explanations for these results. As shown for France there is no geographical control within countries, because there are no transaction-based indices on such a granular level. The first and most obvious explanation for the findings is that REITs tend to invest in more speculative markets than the investors in the private-market index. This has led to higher returns in every country except France, which is just the result of the very high exposure to Paris in the private-market index. Other possible explanations are errors in the assumptions discussed in appendix A3 or misspecification of the returns. The latter seems less likely given the diagnostics and prior knowledge on real estate return behavior. A final explanation would be that there is no sufficient compensation for liquidity risk in the private real estate market and
33 6. Conclusion
The attractiveness of real estate as an asset class has been subject of discussion for decades. Theory suggests allocations over 15% in an optimally diversified portfolio, but this is rarely observed in reality. This perceived under allocation to real estate has been labeled the risk premium puzzle. Since a persistent under allocation should be regarded as unlikely in a rational market, there might be other risks not observable in traditional performance measurements that would explain the lower than expected allocation to real estate.
The lack of liquidity is often labeled as one of the elements that make real estate riskier than other asset classes. A liquidity premium might already be included in the performance measurements and could be the solution to the risk premium puzzle. The main question of this study therefore is: How large is the liquidity premium in real estate?
To answer this questions two real estate indices were compared, a private market transaction-based index and a newly-created public market REIT index. The private market index represents the illiquid real estate market and the REIT index represents a fully liquid real estate market. Both are unlevered real estate indices and the exposures to sectors and countries are equal.
Differences in returns and risks were tested, but no significant differences were found. This implies that there is either no liquidity premium or that liquidity premium could not be extracted in this study. This second less satisfactory result could be explained by that, even after taken some precautionary measures, the assets underlying the REIT index remain riskier than the assets underlying the private market index. This would explain the better performance of the REIT indices. In this study there is unfortunately no way to test this due to data constraints. This is the largest limitation of this study. Both the exposures to countries and sectors are equalized, but there is no way to assess the riskiness of individual assets in both indices. Future research should focus on filtering out these differences. More granular market indices would filter out geographical differences within countries and average occupancy levels and leasing terms could be used to assess the riskiness of individual assets.
34
For now the risk premium puzzle remains unsolved as no proof was found for a significant liquidity premium. Liquidity could still to be the cause for the perceived under allocation to real estate, but no evidence was found in this study.
35 References
Barkham, R. and Geltner, D. (1995). Price Discovery in American and British Property Markets. Real Estate Economics. Vol. 23, No. 1, pp. 21-44.
Cheng, P., Zehnguo, L. and Yingchun, L. (2013). Is There a Real Estate Allocation Puzzle? The Journal of Portfolio Management. Special Real Estate Issue 2013.
Cheng, P., Zehnguo, L. and Yingchun, L. (2013). Liquidity Risk of Private Assets: Evidence from
Real Estate Markets. The Financial Review. Vol. 48, pp. 671-696.
Commandeur, J.J.F. and Koopman, S.J. (2007). An introduction to State Space Time Series Analysis. Oxford University Press 2007.
Elonen, K. (2013). Tracking and Trading Commercial Real Estate through REIT-Based Pure-
Play Portfolios: The European Case. Thesis MSc in Real Estate Development at MIT.
Englund, P., Gordon, T.M. and Quigley, J.M. (1999). The Valuation of Real Capital: A Random
Walk down Kungsgatan. Journal of Housing Economics. Vol. 8, No. 3, pp. 205-216.
Fisher, J., Gatzlaff, D. Geltner, D. and Haurin, D. (2003). Controlling for the Impact of Variable
Liquidity in Commercial Real Estate Price Indices. Real Estate Economics. Vol. 32, No.
2, pp. 269-303.
Francke, M.K. and de Vos, G.A. (2004). The Hierarchical Trend Model for Property Valuation
and Local Price Indices. Journal of Real Estate Finance and Economics. Vol. 28, No. 2,
pp. 179-208.
Geltner, D. and Kluger, B. (1998). REIT-Based Pure-Play Portfolios: The Case of Property
Types. Real Estate Economics. Vol. 6, No. 4, pp. 581-612.
Goetzmann, W.N. and Dhar, R. (2005). Institutional Perspectives on Real Estate Investing: the
Role of Risk and Uncertainty. Yale ICF Working Paper. No. 05-20. August 2005.
Hartzell, D., Hekman, J. and Miles, M. (1986). Diversification Categories in Investment Real
Estate. AREUEA Journal. Vol. 14, No. 2.
Hoesli, M. Lekander, J. and Witkiewicz, W. (2003). Real Estate in the Institutional Portfolio: A
Comparison of Suggested and Actual Weights. The Journal of Alternative Investments.
Vol. 6, No. 3, pp. 53-59. Winter 2003.
Horrigan, H., Case, B., Geltner, D. and Pollakowski, H. (2009). REIT-Based Property Return
36 Portfolio Management. Vol 35.5, pp. 80-91.
Hudson-Wilson, S., Gordon, J.N., Fabozzi, F.J., Anson, M.J.P. and Giliberto, M.S. (2005). Why
Real Estate. The Journal of Portfolio Management. Vol. 31, No. 5, pp. 12-21.
Lin, Z. and Vandell, K, D. (2007). Illiquidity and Pricing Biases in the Real Estate Market. Real Estate Economics. Vol. 35, No. 3, pp. 291-330.
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance. Vol. 7, No. 1, pp. 77-91. March 1952.
Kalman, R.E. (1960). A New Approach to Linear Filtering and Prediction Problems. J. Basic Engineering, Transactions ASMA Series D. Vol 82, pp. 35-45.
Pagliari, J.L., Scherer, K.A. and Monopoli, R.T. (2005). Public versus Private Real Estate
Equities: A More Refined, Long-Term Comparison. Real Estate Economics. Vol. 33,
No.1, pp. 147-187.
Preqin Real Estate Online (2014). Institutional Investors in Private Real Estate. The Preqin Quarterly Update: Real Estate, Q1 2014.
Riddiough, T.J., Moriarty, M. and Yeatman, P.J. (2005). Privately Versus Publicly Held Asset
Investment Performance. Real Estate Economics. Vol. 33, No. 1, pp. 121-146.
Quan, D.C. and Titman, S. (1999). Do Real Estate Prices and Stock Prices Move Together? An
International analysis. Real Estate Economics. Vol. 27, No.2, pp. 183-207.
Ziobrowski, B.J. and Zioibrowski, A.J. (1997). Higher Real Estate Risk and Mixed-Asset
Portfolio Performance. Journal of Real Estate Portfolio Management. Vol. 3, No. 2, pp.
37 Appendix
A1: State Space REIT index
General description of State Space Model: Observation equation:
𝑦𝑡= 𝑍𝑡𝛼𝑡+ 𝜀𝑡 𝜀𝑡 ~ 𝑁𝐼𝐷(0, 𝐻𝑡) (1) State equation:
𝛼𝑡+1= 𝑇𝑡𝛼𝑡+ 𝑅𝑡𝜂𝑡 𝜂𝑡 ~ 𝑁𝐼𝐷(0, 𝑄𝑡) (2) Initial state distribution:
𝛼1~𝑁(𝛼1, 𝑃1) (3)
Application to REIT index:
General
m = Number of REITs
k = Number of States (Countries or Sectors) n = Number of Periods
Equation (1)
𝑦𝑡 = m * 1 vector of observed time series (REIT returns, observed)
𝑍𝑡 = m * k matrix that links the state vector (𝛼𝑡) with the observation vector (𝑦𝑡) (state exposures, observed)
𝛼𝑡 = k * 1 state vector (state returns, unobserved)
𝜀𝑡 = m * 1 vector of observation disturbances. Assumed to have mean zero and an unknown variance-covariance structure represented by a variance matrix 𝐻𝑡 of order m * m
38
Equation (2)
𝑇𝑡 = k * k transition matrix (Identity matrix 𝐼𝑘)
𝑅𝑡 = Identity matrix 𝐼𝑘
𝜂𝑡 = k * 1 vector that contains state disturbances. Assumed to have mean zero an unknown variances and covariances in variance matrix 𝑄𝑡 of order k * k
Example
In this example we have data on 4 REITs that invest in 2 countries (the Netherlands and Germany).
The observation equation:
𝛼𝑡 = (𝛽𝑡 𝑁𝐿 𝛽𝑡𝐷𝐸) , 𝑍𝑡= ( 𝑋𝑡𝑁𝐿,1 𝑋𝑡𝐷𝐸,1 𝑋𝑡𝑁𝐿,2 𝑋𝑡𝐷𝐸,2 𝑋𝑡𝑁𝐿,3 𝑋𝑡𝐷𝐸,3 𝑋𝑡𝑁𝐿,4 𝑋𝑡𝐷𝐸,4)
These two matrices lead to the four following observation equations: 𝑦𝑡(1) = 𝛽𝑡𝑁𝐿∗ 𝑋𝑡𝑁𝐿,1+ 𝛽𝑡𝐷𝐸 ∗ 𝑋𝑡𝐷𝐸,1+ 𝜀𝑡 (1) 𝑦𝑡(2) = 𝛽𝑡𝑁𝐿∗ 𝑋𝑡𝑁𝐿,2+ 𝛽𝑡𝐷𝐸 ∗ 𝑋𝑡𝐷𝐸,2+ 𝜀𝑡(2) 𝑦𝑡(3) = 𝛽𝑡𝑁𝐿∗ 𝑋 𝑡𝑁𝐿,3+ 𝛽𝑡𝐷𝐸 ∗ 𝑋𝑡𝐷𝐸,3+ 𝜀𝑡 (3) 𝑦𝑡(4) = 𝛽𝑡𝑁𝐿∗ 𝑋𝑡𝑁𝐿,4+ 𝛽𝑡𝐷𝐸 ∗ 𝑋𝑡𝐷𝐸,4+ 𝜀𝑡(4)
Where 𝜀𝑡 is NID and has a zero mean and a variance-covariance structure of 𝐻𝑡 =
( 𝜎𝜀2(1) 𝑐𝑜𝑣(𝜀(1), 𝜀(2)) 𝑐𝑜𝑣(𝜀(1), 𝜀(2)) 𝜎𝜀2(2) 𝑐𝑜𝑣(𝜀(1), 𝜀(3)) 𝑐𝑜𝑣(𝜀(1), 𝜀(4)) 𝑐𝑜𝑣(𝜀(2), 𝜀(3)) 𝑐𝑜𝑣(𝜀(2), 𝜀(4)) 𝑐𝑜𝑣(𝜀(1), 𝜀(3)) 𝑐𝑜𝑣(𝜀(2), 𝜀(3)) 𝑐𝑜𝑣(𝜀(1), 𝜀(4)) 𝑐𝑜𝑣(𝜀(2), 𝜀(4)) 𝜎𝜀2(3) 𝑐𝑜𝑣(𝜀(3), 𝜀(4)) 𝑐𝑜𝑣(𝜀(3), 𝜀(4)) 𝜎 𝜀(4) 2 )
The state equation: 𝑇𝑡 = (1 0
0 1), 𝑅𝑡 = ( 1 0 0 1)
39
These two matrices lead to the two following state equations: 𝛽𝑡+1𝑁𝐿 = 𝛽𝑡𝑁𝐿+ 𝜂𝑡(𝑁𝐿) 𝛽𝑡+1𝐷𝐸 = 𝛽
𝑡𝐷𝐸+ 𝜂𝑡 (𝐷𝐸)
Where 𝜂𝑡 is NID and has a zero mean and a variance-covariance structure of 𝑄𝑡 =
( 𝜎𝜂(𝑁𝐿)
2 𝑐𝑜𝑣(𝜂(𝑁𝐿), 𝜂(𝐷𝐸))
𝑐𝑜𝑣(𝜂(𝑁𝐿), 𝜂(𝐷𝐸) 𝜎 𝜂(𝐷𝐸)
40 A2: Indices by Country and Sector
40 60 80 100 120 140 160 2010 2011 2012 2013 2014
RCA - Country-Sector Indices
NL-Office NL-Retail NL-Apartment NL-Industrial NL-Hotel France-Office
France-Retail France-Apartment France-Industrial France-Hotel UK-Office UK-Retail
UK-Apartment UK-Industrial UK-Hotel Italy-Office Italy-Retail Italy-Industrial
41 A3: Holdings data manipulation and assumptions
SNL provided all transaction data of the REITs required for the indices. The data includes the location of the property, the acquisition date, the disposition date, the property type, the
percentage interest and the size in square feet. Unfortunately the dataset had quite some missing observations, which needed to be estimated. In this appendix all data manipulations and
assumptions are described.
Disposition and Acquisition dates
Since SNL provided transaction data, not all observations have both acquisition and disposition dates. If the property is still in a portfolio it only has an acquisition date. If the property was newly developed or transacted before SNL’s coverage started it will not have an acquisition date. There are even cases where a property has no acquisition or disposition date. In these cases SNL only knows the property is part of the portfolio.
If there is no disposition date the assumption in this research is that the property is still part of the company’s portfolio. In case there is no acquisition date the assumption is that the property was acquired before the start of 2010. In the situation that both the acquisition and disposition date are blank the assumption is that the property has been part of the portfolio from 2010 till today.
Sizes
The sizes of the properties are very important to determine the geographical and sectorial exposures of the REITs, as they are used to estimate the value of the properties. Unfortunately not all properties have available sizes, so an assumption driven rule-based scheme has been made to determine these missing sizes.
First the dataset is filtered to only keep properties that have the location, square feet and property type available. Next three calculations are made:
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1. The average size of the properties by company, sector and country 2. The average size of the properties by country and property type 3. The average size of the properties by sector
All properties that have an unavailable size first get assigned the size calculated in step 3. If the size at step 2 is calculated with at least 30 properties, the properties get assigned the size at step 2. Finally if the size at step 1 is calculated by at least 5 properties the properties get assigned that average size. The steps are ordered, so if both the sizes calculated at step 2 and 1 qualify the property gets the size assigned of step 1.
Prices
The final step in the data preparation is the price estimation of all the properties. The prices are determined by location and sector and are then connected to the correct properties. The average prices are calculated with data from RCA. All transactions from 2008 to 2015 are used to calculate an average price per square foot. The same system as with sizes is used to create an average price that is based on a sufficient amount of observations. This time the average price is calculated on four levels:
1. The average price per square foot by submarket and property type 2. The average price per square foot by market and property type 3. The average price per square foot by country and property type 4. The average price per square foot by property type
The same logic applies to the final assignment of the prices. First all properties are linked to the price calculated at step 4. Next if there are more than 5 observations used to calculate step 3 the price is replaced by the price calculated at step 3. If at least 3 properties are used to calculate the average price at step 2, this price replaces whatever price currently is assigned to the property. Finally if at least 2 properties are used to calculate the price at step 1, this price replaces the currently assigned price.
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This is a lengthy process and subject to inaccurate allocations. As a final step all prices are checked to secure the integrity of the price estimation. When there are obvious mismatches these prices have been corrected.
