The effect of property type and country type on risk diversified real estate portfolios : an empirical investigation of the 2008 financial crisis

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THE EFFECT OF PROPERTY TYPE AND

COUNTRY TYPE ON RISK DIVERSIFIED

REAL ESTATE PORTFOLIOS

An empirical investigation of the 2008 financial crisis

Nathan Kon

Abstract

This thesis examines and tests the merits of risk diversifying portfolios of real estate securities internationally and by property types. The analysis covers the period of December 2003 through December 2017 which is divided in periods before, during and after the 2008 financial crisis. Using data from the GPR General Index we obtain monthly

prices for 21 countries. The GPR 250 Index provides monthly prices for four property types inside Europe. At first an analysis is conducted of country and property type differences in real estate security returns. Thereafter the variance of returns across countries (within-country variation vs. between-country variation) and sector classes (within-sector variation vs. between-sector variation) is tested. This information is used

to create the optimal risky portfolios of property and country types. Results suggests that Germany was the safest country during the 2008 financial crisis and confirms that

the residential sector was the most volatile. Although there are differences in returns observed, the ANOVA p-values do not provide significance. We find that all risk diversified portfolios suffered a loss in the 2008 financial crisis, combined with the highest risk relative to the periods surrounding the crisis. Although the highest benefits from risk diversification are gained during the time frame of the 2008 financial crisis. In addition, we find that country diversification was more efficient in risk diversification

than property type diversification during the 2008 financial crisis.

University of Amsterdam

Supervisor: Simas Kučinskas

Study: Economie en Bedrijfskunde BSc

Track: Financiering & Organisatie

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Statement of Originality

This document is written by Student Nathan Kon who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are 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.

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1. Introduction

1.1 Introduction to indirect real estate market

According to the latest research of Savills world research (2016) the value of all developed real estate in the world amounts to approximately $217 trillion US Dollars. This implies that the world owns real estate assets of nearly 300% of its annual income. The concept of real estate as a financial investment asset has a history that exceeds any other asset class within finance. Investing in real estate has innovated from direct outright purchases to the indirect investment market.

The US Congress was the first to establish the Real Estate Investment Trust (REIT). Which is comparable to a mutual fund, however REITs are federally obligated to invest only in real estate. The fund issuing companies receive income from a portfolio of real estate properties such as: apartment complexes, hospitals, office buildings, warehouses, hotels and shopping malls. Individuals can invest in real estate securities by purchasing shares directly on an open exchange or by investing in a mutual fund that specializes in public real estate. The task of investment managers is to design a portfolio of properties that takes advantage of a wide range of opportunities across the international

investment landscape. Practitioners rely on a decomposition of portfolio risk into factors to guide investment decisions.

This thesis examines and tests the merits of risk diversifying portfolios of real estate securities internationally and by property types. During the 2008 financial crisis and the years surrounding. We analyze to which extent the real estate securities market risk and returns reacted in the years surrounding the 2008 financial crisis. Specifically: how did the country specific risk and returns reacted? And more so, inside Europe how did property specific risk and return reacted? This provides the opportunity thereafter to investigate which property types and which countries were able to form the best optimal risky portfolio. Subsequently it is feasible to compare similarities and

differences of optimal risky portfolios before, during and after the 2008 financial crisis. What most academic literature has in common is that results conclude that country factors and property type factors provides investors with the strongest diversification benefits. However which specific countries and property types operate as optimal

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- 2 - portfolio is not defined. Moreover does no academic research to real estate securities involve the 2008 financial crisis. Because research is very limited to real estate portfolio diversification at this period, this thesis contributes to the scientific environment by adding complementary information. These outcomes provides new information to portfolio diversification strategies of real estate investment trusts . Moreover, it gives insight to the 2008 financial crisis from a different perspective.

Real Estate Finance is a an essential academic field that needs international efforts to better understand the underlying dynamics. Abrupt changes in real estate prices can cause threatening problems for the population worldwide. A recent example described by Mishkin(2011), is the price decline at the low end of the U.S. housing market during spring of 2007 which caused a global credit crisis.

The data is from Global Property Research (GPR). GPR is a research center investigating real estate security issuing companies worldwide. GPR includes companies investing in different property types and countries and provides a market-weighted total return index that is available on a monthly/daily basis. For the period “before the crisis” December 2003 till December 2006 is observed. “During the crisis” indicates the period January 2007 till March 2009 and “after the crisis” the period April 2009 till December 2017.

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2. Literature review

2.1 Factors that determine real estate securities risk and returns

In order to investigate the merits of diversification, the factors that determine risk and return need to be specified. Numerous studies have revealed different factors that are associated with the risk and return. However, the utmost extent perceives the property and country type the company invests in as key factors.

Heston and Rouwenhorst (1995) used industry factors like: transportation, finance, and energy to measure return on real estate securities. They compared the returns from industry factors, with the outcomes from country factors. They found that country factors were the dominant determinant of real estate security returns.

Case et al. (2000) broadened this research by investigating other factors. They found global real estate returns to be heavily related to fundamental economic variables like GDP. Their study of 22 real estate markets in 21 countries from 1987 to 1997 revealed that country-specific GDP changes could explain the variations in returns. These country-specific GDP changes are taken into this thesis by observing country specific returns.

Pai and Geltner (2007) applied the Fama and French model to conclude that real estate risk-premiums were caused by the size and type of the investment. They concluded that apartments were found to be the riskiest investment and they required the highest risk premium, to be followed by retail and offices. These factors are taken into the analysis of this thesis, by observing returns from different property classes.

Hin et al (2015) focused on differences in real estate returns across specific countries. By using a pooled- panel multi-factor least squares model, the find that the real estate risk premiums for North and South Asia are higher than that for the US.

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2.2 Country type and property type diversification

In the previous section, academic literature gave empowerment that county type and property type explain real estate securities returns After almost all-previous appointed research, further investigation was conducted to the most efficient factor for portfolio diversification. This information offers expectations to the effects on risk diversified portfolios examined in this thesis.

In a cross sectional variance analysis of country and property types on a time frame of 1990-2002, Glascock and Kelly (2005) shows that property type effects are smaller relative to country effects. In their analyzed period Australia, Spain, and the US have the highest return and the US has the lowest risk. Property type specialization explains four percent of the variance of national real estate securities index returns. Since property type effects are smaller, country diversification is a more effective tool for achieving risk reduction than property type diversification. However Fisher and Liang (2000) and Lee (2001) create pure property type and geographic indices for the US and the UK,

respectively, they find that property type diversification is more effective than geographic diversification.

Throughout the time frame of February 1990 to December 2001 Bond et al (2003) find a large variation in monthly real estate returns and standard deviations across countries. Where the highest mean return (1.205%) also belonged to the United States.

By using various global and country-level factor models, they find that there is evidence of a strong global market risk component

Also Ling and Naranjo (2002) find evidence of a strong worldwide factor in international real estate returns. Furthermore, even after controlling for the effects of worldwide systematic risk, the country-specific factor is highly significant. This strong global market risk component suggests that real estate securities may provide international diversification opportunities.

Also according to Hartzell et al (1996) real estate securities provide great potentials for international diversification. REIT diversification across continents provides more diversification benefits than international common stocks.

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- 5 - All of the existing literature answers the question which type of diversification is the most beneficial. However none of them provides an actual optimal portfolio of country types and property types for a given time frame. Even though most research suggests that country type is the best factor to diversify internationally, it is still worthwhile to composite a portfolio of best performing country types and property types. Which will give a view on how a different diversification tools can form an efficient portfolio. Moreover does no research contain real estate security portfolio diversification during the 2008 financial crisis.

2.3 Real estate securities during the 2008 financial crisis.

In the previous section, academic literature gave empowerment to the benefits of

diversification. However this does not provides evidence of real estate security portfolio diversification during the 2008 financial crisis. In order to investigate this in this thesis, risk and return are analyzed. Expectations of risk and return are formed by academic literature on risk and return during the 2008 financial crisis. This section provides academic literature that involve the 2008 financial crisis effects.

A recent study by Damodaran (2016) classified the crisis of 2008 as unprecedented in terms of its impact on worldwide equity risk premiums. This caused equity risk premiums to expand more during 2008 than in any one of the prior 50 years. The expansion happened in a fifteen-week time period towards the end of the year. While much of the increase dissipated in 2009, as equity risk premiums returned to pre-crisis levels, equity risk premiums have remained more volatile since 2008. This research suggests that the volatility of real estate securities were higher during the 2008 financial crisis and did not return back to normal level after. This thesis complements this study, by comparing the volatility of real estate securities in the periods before, during and after the financial crisis. To analyze if the results found on worldwide equity, also implied to the real estate security market.

According to Mishkin(2011), the price decline at the low end of the U.S. housing market during spring of 2007 caused the global credit crisis. This thesis investigates whether this effect is also transferred to the residential sector of real estate securities.

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- 6 - In the years surrounding the financial crisis, the share prices of equity Real Estate

Investment Trusts (REITs) were extremely volatile according to Titman et al (2013). REITs were even more volatile than the underlying commercial real estate prices. They did an investigation for the direct and indirect real estate market in the US. The NAREIT All Equity REITs Index fell from 10,256 in January 2007 to a low of 3,337 in February 2009. A cumulative loss of 67%, with the largest falls of 60% between

September 2008 and February 2009. The fall on the US index is in line with the fall of the world market capitalization in figure 1. This research suggests that during the financial crisis the average return of real estate securities investigated in this thesis decreased substantial compared to the period before for the crisis as well. Also the mentioned “extremely volatile” would suggest that there were benefits of a risk diversified portfolio.

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3. Data

3.1 Data source

In order to perform a regression analysis of international real estate securities returns that also makes distinction between property types, a specific data set is required. This data set needs distinctive rules for company inclusion in order to serve as a proxy of the national specific indirect real estate market.

The Global Property Research (GPR) database provides this indirect international property data. The database consist of international real estate stocks and includes for each company information i.e. the country of origin, the type of fund and the main property type in which the company invest. The database provides property type information for the following sectors, office, retail, residential, industrial, hotel, health care, other and diversified.

A company needs at least $50 million free float market capitalization in order to be included in the index. Furthermore to be allocated to a sector type 60% operational turnover from one specific sector is required. If this is not the case, the data will be classified as: diversified.

Country allocation works through the rule that 75% operational turnover from one country is required.

GPR main indexes are the GPR general index and the GPR 250 index. The differences can be found in the size of the companies taken into the index. The GPR General Index

contains all listed real estate companies that comply with their consistently applied rules. The GPR 250 Index is composed of the 250 most liquid listed property securities in the world.

GPR provides different customized indexes, which they vend to companies e.g. RBS and J.P Morgan. This makes the GPR index composition of sector allocation within a specific country type limited by accessibility. However GPR was willing to provide the GPR 250 index sector allocation for Europe as a whole. Which makes it possible to examine the exact time frame as the GPR General Index country returns.

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- 8 - Figure 1

Market capitalization of the world real estate securities over time.

3.2 Data manipulation

3.2.1 Time frame split from original index

The GPR General Index has 31 December 1983 as base date and the GPR 250 index has a base date of 29 December 1989. Both indexes have a base value of 100. The index in this thesis is monthly observed, by observing the index at the last day of the month. In order to investigate the dynamics of the market surrounding the 2008 financial crisis, the index is split up in 3 different periods. As can be seen in figure 1 the highest decline in the market capitalization of real estate securities was from 31-01-2007 till the first quarter of 2009. Thereafter the market capital started to rise again. To capture the negativity of 2008 financial crisis as preeminent as possible, the end date of the crisis in this thesis is taken as the end of the first quarter in 2009 (31-03-2009) . Table 1

provides the exact start and end dates of the time frames observed in this thesis. 0 200 400 600 800 1000 1200 1400 1600 1800 2000

Bi

lli

ons

o

f E

ur

os

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- 9 - Table 1

Time frame severance

Period

Start date End date Total Observations

Before crisis 31-01-2003 30-11-2006 47 During crisis 31-01-2007 31-03-2009 26 After crisis 30-04-2009 31-12-2017 105

3.2.2 Country specific data manipulation

Not every country conforms the previous mentioned monthly inclusion rules set by GPR. This means that during the three different time frames, not every country is available in the GPR general index. The countries that are included in the index from 01-31-2003 till 12-31-2017 are: Australia, Austria, Belgium, Canada, Finland, France, Germany, Hong Kong, Italy, Japan, Malaysia, Netherlands, New Zealand, Norway, Philippines, Singapore, South Africa, Sweden Switzerland, United Kingdom and the United States. Which

represents an adequate global distribution of countries across continents.

Furthermore is the normal GPR general index given in USD. In order to compare results from the country specific data to the property specific, indexes are measured in EUR.

3.2.3 Property specific data manipulation

GPR 250 index European property data was obtained as daily returns. To make a more exact comparison with the country specific index, the returns are monthly observed. After 2004 no European company had 60% operational turnover from the hotel sector. The hotel sector is therefore not available in the index and excluded from the analysis. The same applies to the healthcare sector. Several companies cannot be categorized into a single property type index, however they do meet the other inclusion rules set by GPR. GPR named this category: Diversified. Because there is no adequate information about the origin of the property types is this category, it is excluded from the analysis. The residual property types are: Industrial, Office, Residential and Retail, who are perceived as the global main property types real estate companies invest in.

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4. Method

4.1 Return from index

To abstract the return from the index, the following formula is used: 𝑅𝑅 = 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}𝑡𝑡−𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝑡𝑡−1

𝑡𝑡−1

Where 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝑡𝑡 is the index on the last day of the month 𝑡𝑡 and 𝑡𝑡 − 1 is the index on the

last day the previous month. The return 𝑅𝑅 is measured in percentages per month. To analyze the risk and return of real estate securities, a decomposition of the mean and standard deviation of the index is made.

The mean of the observed time period is equal to the average return of that specific country or property type. It is therefore a useful statistical tool to explain the return for that country/property type, in any given period.

To quantify the amount of variation or dispersion of the index, the standard deviation is used. A large dispersion indicates how much the return on the security is deviating from the normal returns. The greater the standard deviation of a security, the greater the variance between each price and the mean. The standard deviation can therefore be seen as an indicator of risk. To compare risk and return characteristics of specific country/property types the Sharpe ratio is analyzes.

4.1 ANOVA

To specify the factor on return a country/property type has compared to others, merely the summary statistics are not sufficient. In order to compare influences, the mean and variance have to be compared relative to each other. To analyze the variance of returns across countries (within-country variation vs. between-country variation) and asset classes (within-class variation vs. between-class variation), a one- way Analysis of Variance (ANOVA) is executed. ANOVA is a statistical method used to test differences between two or more means. The inferences about the means are made by analyzing the variance. This is done by calculating the sum of squares within groups and the sum of squares between groups. Adding these up will provide the total sum of squares.

Within the analysis of countries, a specific country is seen as a group. With property type analysis, a specific property type is seen as a group. The degrees of freedom are

calculated by subtracting the total of groups with 1.

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- 11 - This thus provides a statistical measurement to analyze differences in means of returns

not only within a group, but also between groups. In order to test the 𝐻𝐻0 the 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼

is examined.

4.1 Optimal risky portfolio

For the portfolios with risk diversification, we construct the optimal risky portfolios. The optimal risky provides the lowest possible risk for any given level of expected return. In order to calculate the weights of the optimal risky portfolio of multiple assets (10 countries or 4 property types) we first need to analyze a portfolio with the mean and variance of the portfolio with equal weights.

The variance of the portfolio is a weighted sum of covariances, and each weight is the product of the portfolio proportions of the pair of assets in the covariance term. Since the portfolio consists of multiple assets, at first a variance - covariance matrix of the returns needs to be constructed. The covariance matrix ∑ as seen in Bodie et al (2011) and Markowitz (1954), is modified to construct a portfolio with 𝑘𝑘

country/property types. 𝑊𝑊 = ⎣ ⎢ ⎢ ⎢ ⎡𝑊𝑊_𝑊𝑊1₂ 𝑊𝑊3 … 𝑊𝑊𝑘𝑘⎦ ⎥ ⎥ ⎥ ⎤ 𝜇𝜇 = ⎣ ⎢ ⎢ ⎢ ⎡𝐸𝐸(𝑅𝑅_{𝐸𝐸(𝑅𝑅}1) 2) 𝐸𝐸(𝑅𝑅3) … 𝐸𝐸(𝑅𝑅𝑘𝑘) ⎦ ⎥ ⎥ ⎥ ⎤ ∑ = ⎣ ⎢ ⎢ ⎢ ⎡𝜎𝜎_𝜎𝜎11₂₁ 𝜎𝜎31 … 𝜎𝜎𝑘𝑘1 𝜎𝜎12 𝜎𝜎22 𝜎𝜎32 … 𝜎𝜎𝑘𝑘2 𝜎𝜎13 𝜎𝜎23 𝜎𝜎33 … 𝜎𝜎𝑘𝑘3 …. 𝜎𝜎1𝑘𝑘 𝜎𝜎2𝑘𝑘 𝜎𝜎3𝑘𝑘 … 𝜎𝜎𝑘𝑘𝑘𝑘⎦ ⎥ ⎥ ⎥ ⎤

And inferring that the covariance between i.e. asset 1 and 2 is calculated by the formula.

𝜎𝜎

₁₂₌1

𝑛𝑛∗∑(1𝑖𝑖−1�)∗(2𝑖𝑖−2�)

This means that the return on an asset needs to be subtracted by the average. After formulating the variance-covariance matrix, the function “Solver” is used to construct the optimal weights, by imposing a minimum on the portfolio standard deviation and fluctuating the portfolio weights.

In the final portfolio, expected return is 𝐸𝐸�𝑅𝑅𝑝𝑝� = 𝑊𝑊𝑇𝑇 𝜇𝜇

And the portfolio standard deviation 𝜎𝜎𝑝𝑝 = �𝑊𝑊𝑇𝑇 ∑𝑊𝑊

𝑊𝑊 is the weight of the country/property types in the portfolio. All weights together need to sum up to 1. Since in this thesis we do not allow short selling, the weight of all types 𝑘𝑘 need to be ≥ 0.

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- 12 - To compare the portfolio’s average return earned per unit of risk over different time frames, the ex-post Sharpe ratio introduced by William Sharpe (1966) is analyzed .

The Sharpe ratio is calculated as: 𝑆𝑆ℎ𝑣𝑣𝑎𝑎𝑝𝑝𝐼𝐼 =_𝜎𝜎𝜇𝜇_𝑝𝑝

.

Since this thesis consists of an

time-series analysis of countries and thus currencies worldwide , the risk free rate we would obtain at any point in time can vary. It is therefore left out in the formula. This should not give different outcomes, since we would subtract all mean returns with the same risk free rate.

4.4 Hypotheses

To analyze the effect of property type and country type on risk and return of real estate securities in the years surrounding the 2008 financial crisis, the following multiple forms of hypotheses are outlined. The hypotheses are ordered from broad hypothesis to

more portfolio precise ones. The 𝐻𝐻1is the alternative hypothesis.

I. The US had the least volatile market during the 2008 financial crisis.

𝐻𝐻0

: 𝜎𝜎

𝑈𝑈𝑈𝑈 2007−2009

< 𝜎𝜎

𝑚𝑚𝑚𝑚𝑘𝑘𝑡𝑡 2007−2009

𝐻𝐻1

: 𝜎𝜎

𝑈𝑈𝑈𝑈 2007−2009

</ 𝜎𝜎

II. The European residential property sector was the most volatile sector market during the 2008 financial crisis.

𝐻𝐻0:

𝜎𝜎

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅𝑅𝑅 2007−2009

> 𝜎𝜎

𝐻𝐻1:

𝜎𝜎

/> 𝜎𝜎

III. The means of country type returns are equal in every period (ANOVA).

𝐻𝐻0: 𝜇𝜇𝐴𝐴𝐴𝐴𝑅𝑅𝑡𝑡𝑚𝑚𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝜇𝜇𝐴𝐴𝐴𝐴𝑅𝑅𝑡𝑡𝑚𝑚𝑅𝑅𝑅𝑅 = ⋯ = 𝜇𝜇𝑈𝑈𝑅𝑅𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅 𝑅𝑅𝑡𝑡𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅

𝐻𝐻1: 𝐴𝐴𝑡𝑡 𝑣𝑣𝐼𝐼𝑣𝑣𝑡𝑡𝑡𝑡 𝑜𝑜𝐼𝐼𝐼𝐼 𝑝𝑝𝑣𝑣𝑝𝑝𝑎𝑎 𝑜𝑜𝑜𝑜 𝑚𝑚𝐼𝐼𝑣𝑣𝐼𝐼𝑡𝑡 𝑣𝑣𝑎𝑎𝐼𝐼 𝐼𝐼𝑝𝑝𝑜𝑜𝑜𝑜𝐼𝐼𝑎𝑎𝐼𝐼𝐼𝐼𝑡𝑡 𝑜𝑜𝑎𝑎𝑜𝑜𝑚𝑚 𝐼𝐼𝑣𝑣𝑒𝑒ℎ𝑜𝑜𝑡𝑡ℎ𝐼𝐼𝑎𝑎

IV. The means of property type returns are equal in every period (ANOVA).

𝐻𝐻0: 𝜇𝜇𝐼𝐼𝑅𝑅𝑅𝑅𝐴𝐴𝑅𝑅𝑡𝑡𝑚𝑚𝑅𝑅𝑅𝑅𝑅𝑅 = 𝜇𝜇𝑂𝑂𝑂𝑂𝑂𝑂𝑅𝑅𝑂𝑂𝑅𝑅 = ⋯ = 𝜇𝜇𝑅𝑅𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅𝑅𝑅

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- 13 - V. The benefits of risk diversification were for country/property type diversification

higher during the financial crisis, than the period before and after the 2008 financial crisis.

𝐻𝐻0

: ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2007−2009}

> ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2003−2006,}

𝑜𝑜𝑎𝑎 ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2009−2017}

𝐻𝐻1

: ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2007−2009}

/> ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2003−2006}

𝑜𝑜𝑎𝑎 ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2009−2017}

VI. The average return from portfolios of country/ property types are negative during the 2008 financial crisis.

𝐻𝐻0

: 𝜇𝜇

_{𝐸𝐸𝐸𝐸.𝑃𝑃𝑎𝑎𝑡𝑡𝑜𝑜 2007−2009}

< 0

𝐻𝐻1

: 𝜇𝜇

</0

VII. The volatility of country/property portfolios is higher during the financial crisis than before/ after the crisis.

𝐻𝐻0:

𝜎𝜎

𝑃𝑃𝑎𝑎𝑡𝑡𝑜𝑜 2007−2009

> 𝜎𝜎

𝑝𝑝𝑎𝑎𝑡𝑡𝑜𝑜 2003−2006, 2009−2017

𝐻𝐻1:

𝜎𝜎

> 𝜎𝜎

𝑝𝑝𝑎𝑎𝑡𝑡𝑜𝑜 2003−2006, 2009−2017

VIII. Country diversification is a more effective tool than property type diversification inside Europe during the financial crisis.

𝐻𝐻0

: ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.𝐶𝐶𝑜𝑜𝑣𝑣𝐼𝐼𝑡𝑡𝑎𝑎𝐶𝐶 2007−2009}

> ∆

�𝜇𝜇_𝜎𝜎�_{𝑅𝑅.𝑃𝑃𝑎𝑎𝑜𝑜𝑝𝑝𝐼𝐼𝑎𝑎𝑡𝑡𝐶𝐶2007−2009}

𝐻𝐻1

: ∆

/> ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.𝑃𝑃𝑎𝑎𝑜𝑜𝑝𝑝𝐼𝐼𝑎𝑎𝑡𝑡𝐶𝐶2007−2009}

IX. The benefits of diversification through the optimal risky portfolio are higher than that of investing in one country/property during the 2008 financial crisis.

𝐻𝐻0

:

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.𝑝𝑝𝑜𝑜𝑎𝑎𝑡𝑡𝑜𝑜𝑜𝑜𝑣𝑣𝑝𝑝𝑜𝑜 2007−2009}

>

�_𝜎𝜎𝜇𝜇�_{𝑡𝑡𝑝𝑝𝐼𝐼𝑒𝑒𝑝𝑝𝑜𝑜𝑝𝑝𝑒𝑒 𝑝𝑝𝑎𝑎𝑜𝑜𝑝𝑝𝐼𝐼𝑎𝑎𝑡𝑡𝐶𝐶,𝑒𝑒𝑜𝑜𝑣𝑣𝐼𝐼𝑡𝑡𝑎𝑎𝐶𝐶 2007−2009}

(17)

- 14 -

5. Results

This section summarizes the obtained results from the analysis of the country specific GPR general index and the GPR 250 property specific index. Thereafter the differences and similarities between countries and property types are examined. Followed by the ANOVA, who assesses the differences in average return between countries/properties and within. At last the optimal portfolios are analyzed and compared.

5.1 Country specific risk and return.

This section summarizes the obtained results from the GPR general index. As mentioned before, the index is divided into specific countries worldwide. The main differences and similarities between country types during the observed periods are reviewed.

5.1.1 Before the crisis.

Table 2 summarizes the performance of the twenty-one countries in the period 2003-2006. This is the period prior to the financial crisis. The table shows that there are differences across countries in terms of average monthly returns. By looking at the column of the “mean” it is possible to conclude which country has the highest/lowest average return and thus the highest/lowest average performance in the period. The standard deviation shows the most/least volatile country

It is clear that Singapore is the top performer followed by Sweden and South Africa. The lowest average return is from Germany, however the mean is not negative. This implies that even the lowest performing country still had positive average returns during the period of 2003-2006. Furthermore had Germany also the lowest volatility, with a substantial difference between other countries. It is therefore the safest country to invest in real estate securities. This

(18)

- 15 - Table 2

Summary statistics of countries before the crisis (2003-2006)

Mean (𝜇𝜇)

St. Dev

_(𝜎𝜎)

Sharpe Ratio (

𝜇𝜇_𝜎𝜎

)

Australia 1.837 % 3.142 % 0.58 Austria 1.015 % 1.209 % 0.84 Belgium 1.224 % 1.938 % 0.63 Canada 2.143 % 4.114 % 0.52 Finland 2.862 % 4.755 % 0.60 France 2.851 % 3.811 % 0.75 Germany (*)**** 0.326 % 0.285 % 1.14 Hong Kong 1.997 % 6.619 % 0.30 Italy 2.466 % 4.846 % 0.51 Japan 2.570 % 7.623 % 0.34 Malaysia 1.372 % 6.367 % 0.22 Netherlands 2.136 % 3.381 % 0.63 New Zealand 1.306 % 3.290 % 0.40 Norway 2.870 % 5.136 % 0.56 Philippines ** 2.289 % 8.459 % 0.27 Singapore *** 3.309 % 5.385 % 0.61 South Africa 2.996 % 7.758 % 0.39 Sweden 3.064 % 5.276 % 0.58 Switzerland 0.543 % 1.475 % 0.37 United Kingdom 2.656 % 3.780 % 0.70 United States 1.986 % 4.173 % 0.48 * Lowest risk ** Highest risk *** Highest return **** Lowest return

(19)

- 16 -

5.1.2 During the crisis+ answering hypothesis I

Table 3 summarizes the individual country performance during the financial crisis period of 2007-2009. This period indicates 26 monthly observations. The table shows that there are again differences across countries in terms of average returns and the volatility of returns. However, all countries have in common that they all suffered an average loss during the financial crisis. This can be seen in the column “mean” which is for every country a negative value.

It is possible to conclude that Switzerland was the top performer and suffered the least on her returns during the financial crisis. During the 2008 financial crisis Switzerland almost suffered no loss, but also did not obtain returns. Creating the Sharpe ratio equal to 0.

Austria had an the biggest loss with 6% per month. Combined with the highest volatility. The country with the lowest volatility is Germany once again. Germany is in this period around 21 times less risky than Austria. Germany is compared to all the other observed countries by far one of the safest countries during the financial crisis. They also follow Switzerland up with the second lowest loss on returns.

The United States almost doubled their volatility and went from an average return of almost 2% per month, to an average loss of 9% per month.

Where an investor in the Netherlands used to get an average return of 2% per month, suffered in the crisis an average loss of almost 3% per month.

This information allows to answer hypothesis I:

I. The US had the least volatile market during the financial crisis

𝐻𝐻₀

: 𝜎𝜎

_{𝑈𝑈𝑈𝑈 2007−2009}

< 𝜎𝜎

_{𝑚𝑚𝑚𝑚𝑘𝑘𝑡𝑡 2007−2009}

𝐻𝐻1

: 𝜎𝜎

𝑈𝑈𝑈𝑈 2007−2009

</ 𝜎𝜎

One can observe that during the period of the 2008 financial crisis the standard deviation of the United States equaled 9.1%. It is compared to the other countries not the country with the lowest volatility. Germany is the country with the lowest volatility

The 𝐻𝐻0 is for this reason rejected. This is not in line with previous findings of research

from Glascock and Kelly (2005) in the period 1990-2002. Where the United States used to be the market with the lowest volatility.

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- 17 - Table 3

Summary statistics of countries during the crisis (2007-2009)

Mean (𝝁𝝁)

St. Dev

_(𝝈𝝈)

Sharpe Ratio (

𝝁𝝁_𝝈𝝈

)

Australia -4.371% 8.508% -0.51 Austria **(****) -6.099% 17.437% -0.35 Belgium -1.227% 4.622% -0.27 Canada -2.331% 7.159% -0.33 Finland -4.548% 8.371% -0.54 France -2.741% 6.680% -0.41 Germany * -0.265% 0.824% -0.32 Hong Kong -1.055% 8.893% -0.12 Italy -3.968% 9.538% -0.42 Japan -2.998% 7.393% -0.41 Malaysia -0.786% 5.992% -0.13 Netherlands -2.830% 6.524% -0.43 New Zealand -2.100% 5.662% -0.37 Norway -3.865% 10.450% -0.37 Philippines -1.732% 8.916% -0.19 Singapore -2.902% 7.926% -0.37 South Africa -0.317% 9.276% -0.03 Sweden -2.843% 7.894% -0.36 Switzerland *** -0.003% 2.655% 0.00 United Kingdom -5.990% 7.029% -0.85 United States -3.962% 9.137% -0.43 * Lowest risk ** Highest risk *** Highest return **** Lowest return

(21)

- 18 -

5.1.3 After the crisis

Table 4 contains the summary of the country performance during the period after the crisis up till the end of 2017.

This period indicates 105 monthly observations. The table gives gives insight how countries have restored after the financial crisis. Germany is in this last period once more the country with the lowest volatility. What interesting is to notice, is that the volatility is actual higher than in the period of the financial crisis . Germany is also 5 times more volatile than in the period before the crisis. The fact that it still is the country with the lowest volatility lies in the fact to the relative performance of the other

countries. In chapter 5.3 the volatility within a country is compared to the volatility between countries, this provides further insight to the relative performance. No country has a negative average return in the period after the crisis. The highest return is from the Philippines combined with a relative high volatility. The highest Sharpe ratio is from New Zealand. When arguing from a finance perspective, it is the best country to invest in real estate securities. Canada is the following up country after new Zealand. Because Italy had such a high volatility, it had the lowest Sharpe ratio. This makes Italy the least attractive country.

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- 19 - Table 4

Summary statistics of countries after the crisis (2009-2017)

Mean (𝝁𝝁)

St. Dev

_(𝝈𝝈)

Sharpe Ratio (

𝝁𝝁_𝝈𝝈

)

Australia 1.438% 4.633% 0.31 Austria 1.565% 7.348% 0.21 Belgium 0.914% 2.752% 0.33 Canada 1.381% 3.992% 0.35 Finland 1.231% 6.602% 0.19 France 1.284% 5.114% 0.25 Germany (*)**** 0.355% 1.078% 0.33 Hong Kong 1.318% 5.570% 0.24 Italy ** 1.140% 8.143% 0.14 Japan 1.029% 5.210% 0.20 Malaysia 1.211% 3.911% 0.31 Netherlands 0.774% 5.120% 0.15 New Zealand 1.543% 4.209% 0.37 Norway 1.141% 5.705% 0.20 Philippines *** 2.148% 6.944% 0.31 Singapore 1.348% 5.009% 0.27 South Africa 1.263% 5.921% 0.21 Sweden 1.746% 5.546% 0.31 Switzerland 0.975% 3.388% 0.29 United Kingdom 1.182% 4.945% 0.24 United States 1.468% 4.756% 0.31 * Lowest risk ** Highest risk *** Highest return **** Lowest return

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- 20 -

5.2 Property specific risk and return.

This section summarizes the obtained results from the GPR 250 index. As mentioned before, the index is divided into specific property types inside the EU. The main differences and similarities between property types and time periods are reviewed.

5.2.1 Before the crisis

Figure 2 illustrates the distribution graph of the standard deviation and the mean return of the four different asset classes in the period before the crisis. Underneath the

property type data label, is the Sharpe ratio specified. These results suggest that the office sector has the lowest volatility with a comparable average return to retail and industrial. The Sharpe ratio is therefore also higher than these sectors. Residential has the highest volatility, but also the highest average return. Retail and industrial seem to have unnecessary high risk compared to their return.

Figure 2

Summary statistics of property types before the crisis (2003-2006)

IND

0.72

OFF

0.95

RES

0.83

RET

0.78 0,0% 0,5% 1,0% 1,5% 2,0% 2,5% 3,0% 3,5% 0,0% 0,5% 1,0% 1,5% 2,0% 2,5% 3,0% 3,5% 4,0% 4,5%

M

ea

n

Standard Deviation

Before the crisis 2003-2006

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- 21 -

5.2.2 During the crisis + answering hypothesis II

Figure 3 shows the statistics of the four specific property types in Europe in the period during the financial crisis. Retail is in this period the best sector relative to invest in. It is mentioned as “relative”, because all property types have a negative return. If one had the information ex-post of the crisis, no one would invest in any property type specific real estate security, since it gave an average loss of at least 3.5 % per month. Even though this table provides information which sector suffered the lowest loss. Residential had the highest volatility, however not the highest loss on return.

II. The European residential property sector was the most volatile sector market during the financial crisis

𝐻𝐻0:

𝜎𝜎

> 𝜎𝜎

𝐻𝐻1:

𝜎𝜎

/> 𝜎𝜎

The standard deviation of the residential sector is exactly 20.0%, which is the highest of

the asset classes. This can be observed from the x-axis. Therefore the 𝐻𝐻0 is accepted and

can be concluded that the residential sector is the most volatile sector during the 2008 financial crisis. This is in line with the fact that the 2008 financial crisis was initiated by the collapse in the housing price bubble in 2007 mentioned by Mishkin (2011). Since the residential sector can be seen as the sector including the houses with the subprime mortgages, this hypothesis is accepted as academic literature would .

An important limitation of this thesis is that the property specific index is given for Europe as a whole. This makes it limited to compare the relative effect between country type and property type. However results suggests that the country with the lowest volatility and with the highest Sharpe ratio are both European countries (Germany and Switzerland respectively). These results can be combined with the European property market outcomes. This suggests that she safest real estate security during the 2008 financial crisis was from a German company investing in the retail sector. And the real estate security with the most beneficial risk and return would be from a company investing in residential real estate in Switzerland.

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- 22 -

IND

0.26

OFF

0.27

RES

0.32

RET

0.23 0,0% 0,5% 1,0% 1,5% 2,0% 2,5% 0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 6,0% 7,0% 8,0%

M

ea

n

Standard Deviation

After the crisis 2009-2017

Figure 3

Summary statistics of property types during the crisis (2007-2009)

5.2.3 after the crisis

Figure 4 shows the graph of the standard deviation and the average return of the four specific property types in Europe in the period after the crisis. Office is still the asset class with a very low risk. However when comparing the Sharpe ratios with each other, residential is the asset class with the highest Sharpe ratio. Where it used to be the least efficient investment in the financial crisis. It now has the highest Sharpe ratio.

Figure 4

Summary statistics of property types after the crisis (2009-2017)

IND

-0.49

OFF

-0.65

RES

-0.22

RET

-0.56 -7,0% -6,0% -5,0% -4,0% -3,0% -2,0% -1,0% 0,0% 0,0% 5,0% 10,0% 15,0% 20,0% 25,0%

M

ea

n

Standard Deviation

During the crisis 2007-2009

(26)

- 23 -

5.3 Country/ Property specific ANOVA + answering hypothesis III and IV

Tables 5-10 contain the results from the ANOVA tests. The input for the ANOVA is from the return of different countries and property types. For answering the hypothesis we observe the 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼.

III. The means of country type returns are equal in every period (ANOVA)

𝐻𝐻0: 𝜇𝜇𝐴𝐴𝐴𝐴𝑅𝑅𝑡𝑡𝑚𝑚𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝜇𝜇𝐴𝐴𝐴𝐴𝑅𝑅𝑡𝑡𝑚𝑚𝑅𝑅𝑅𝑅 = ⋯ = 𝜇𝜇𝑈𝑈𝑅𝑅𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅 𝑅𝑅𝑡𝑡𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅

IV. The means of property type returns are equal in every period (ANOVA)

𝐻𝐻0: 𝜇𝜇𝐼𝐼𝑅𝑅𝑅𝑅𝐴𝐴𝑅𝑅𝑡𝑡𝑚𝑚𝑅𝑅𝑅𝑅𝑅𝑅 = 𝜇𝜇𝑂𝑂𝑂𝑂𝑂𝑂𝑅𝑅𝑂𝑂𝑅𝑅 = ⋯ = 𝜇𝜇𝑅𝑅𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅𝑅𝑅

By looking at the underlined integer of the 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼 of tables 5-10 , one can observe the 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼 during the three different time period. The 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼 is used to provide the smallest level of significance at which the null hypothesis would be rejected. Due to the

high 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼𝑡𝑡, tables 5-10 suggest that by using a significance level 𝛼𝛼 = 0.05 , the 𝐻𝐻0 is

not rejected in any period. So we conclude that given a significance level of 95% there is not enough evidence for differences in means of return between countries nor property types. In the period before the crisis, it was possible to conclude with a significance level of 87.4% that at least one pair of means from country types was different. This is the highest level of significance presented by the ANOVA tables to explain differences in means, but not worthy to mention as significant. The period of financial crisis, increased the 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼 for property and country type, indicating more similarities in return. For countries the 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼 further increased in the next period, where for property types the 𝑝𝑝 − 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝐼𝐼decreased thereafter.

The fact that the 𝐻𝐻0 is not rejected, does not imply that all mean returns are equal.

There is no statistical significance evidence for differences between all groups.

Nonetheless is it possible to conclude which countries or properties had the most or the least similarities.

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- 24 - Table 5

ANOVA of country types before the crisis (2003-2006)

Source of

Variation SS df MS F P-value F crit

Between Groups 0.0662 20 0.0033 1.3735 0.1261 1.5817 Within Groups 2.2781 945 0.0024

Total 2.3444 965

Table 6

ANOVA of country types during the crisis (2007-2009)

Source of

Total 3.7603 545

Table 7

ANOVA of country types after the crisis (2009-2017)

Source of

Total 6.0402 2183

Table 8

ANOVA of property types before the crisis (2003-2006)

Source of

(28)

- 25 - Table 9

ANOVA of property types during the crisis (2007-2009)

Source of

Total 1.6283 103

Table 10

ANOVA of property types after the crisis (2009-2017)

Source of

Total 1.5041 419

5.4 Country diversified optimal risky portfolio’s

This section shows the optimal risky portfolios statistics over time. These portfolios diversify by making use of real estate securities across different countries

Figure 5 displays the optimal risky portfolio weight distribution of countries in different time frames. The graph of the equally weighted portfolio (appendix figure B) would imply equal weights in every period. Since there are 21 observed countries, the equally

weighted portfolio would imply that every country participate with ₂₁1 = 4.8% .

However Figure 5 shows the weight distribution of the portfolio with the lowest standard deviation, As can be seen right away, Germany always has been a big contribution to the portfolio. Over time the importance of Germany only increased. While Germany was 43,5% of the optimal risky portfolio before the crisis, it was after the crisis up till the end of 2017 even 82,5%. Austria was in the period before the crisis an useful country to take upon in the portfolio, however in the next following periods it was not taken into the portfolio. The United Kingdom played in the crisis a big role in the portfolio. Even while it did have the lowest Sharpe ratio and the highest loss (table 5). This can be explained by the fact that we are looking at the optimal portfolio with the lowest standard deviation and the United Kingdom had a relative low volatility. New

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- 26 - Zealand is a country that has in every period a small contribution to the optimal

portfolio. Malaysia was in the period after the crisis also a country to take in the optimal portfolio. Countries that have never been a part of the optimal portfolio are: Belgium, Finland, Netherlands and the United States.

Tables 11-13 present the statistics obtained from the equally weighted portfolio and the optimal risky portfolio diversifying across countries. The tables also include the country with the highest Sharpe ratio, to compare diversification with country specific

investment, The results are comparable to tables 2-4, however these statistics are now from the formed portfolio. The ∆ shows the difference between the Sharpe ratios of the optimal risky portfolio and the equally weighted portfolio. This is used as measure for risk diversification benefits. One can observe that the standard deviation of the

portfolios decreased compared to the equally weighted portfolio. However this does not say enough about the benefits of the diversification. The Sharpe ratio is used to compare the change in a portfolio's overall risk-return characteristics, by comparing the standard deviation with the average return. The Sharpe ratio increased in the period before the crisis, indicating a successful portfolio diversification. In the period of the 2008 financial crisis the Sharpe ratio decreased, which is initiated by the fact that the mean return is negative. Both the equally weighted as the optimal portfolio suffered a loss in the 2008 financial crisis. However the optimal risky portfolio did provide diversification benefits, by creating a lower average loss and lower volatility. In the period after the crisis the Sharpe ratio decreased using the optimal risky portfolio. Even though the risk

decreased, the average return decreased even more. Arguing from a financial

perspective, is the equally weighted portfolio more beneficial than the optimal risky portfolio.

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- 27 - 0,0% 10,0% 20,0% 30,0% 40,0% 50,0% 60,0% 70,0% 80,0% 90,0% W ei gh t i n po rtf ol io

Optimal risky portfolios

Before During After

Figure 5

Graph of optimal risky portfolio’s using country types in all periods

Table 11

Statistics of portfolios of countries and best performing country before the crisis (2003-2006)

Mean (𝝁𝝁)

_{St. Dev}

_(𝝈𝝈)

_{Sharpe Ratio (}

𝝁𝝁_𝝈𝝈

₎

Equally weighted 2.087% 2.353% 0.89

Optimal risky 1.057% 1.140% 0.93 ∆=0.04

(31)

- 28 - Table 12

Statistics of portfolios of countries and best performing country during the crisis (2007-2009)

Table 13

Statistics of portfolios of countries and best performing country after the crisis (2009-2017)

Mean (𝝁𝝁)

_{St. Dev}

_(𝝈𝝈)

_{Sharpe Ratio (}

𝝁𝝁_𝝈𝝈

₎

Optimal risky 0.482% 1.453% 0.33 ∆=0.06

New Zealand 1.543% 4.209% 0.37

5.6 Optimal risky property portfolio’s + answering hypotheses

V- IX

This section shows the optimal risky portfolios over time. These portfolios diversify by making use of real estate securities across different properties inside Europe.

Figure 6 shows the weights of the four property types in the optimal risky portfolios

during the 3 different time frames. The equally weighted portfolio, consists of 1₄= 25%

weight of each property type, in every period (appendix figure A). What can be

concluded right away, is that the office sector has as very dominant place in the optimal portfolio in every observed period. All property types have played a role in the total investigated period of 2003-2017. However the residential sector only had a weight of 1,1% in the optimal portfolio in the period before the crisis. Retail played a big role in the 2008 financial crisis. In the period after the financial crisis up till the end of 2017, it seems that the office sector is almost the only real estate security asset class in Europe to provide an optimal risky portfolio.

Mean (𝝁𝝁)

_{St. Dev}

_(𝝈𝝈)

_{Sharpe Ratio (}

𝝁𝝁_𝝈𝝈

₎

Equally weighted -2.711% 5.190% -0.52

Optimal risky -2.019% 3.306% -0.61 ∆=0.09

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- 29 - 14,2% 84,7% 1,1% 55,5% 44,5% 94,4% 5,6% 0,0% 10,0% 20,0% 30,0% 40,0% 50,0% 60,0% 70,0% 80,0% 90,0% 100,0%

IND OFF RES RET

W ei gh t i n po rtf ol io

Optimal risky portfolios

Before During After

Tables 14-16 present the statistics obtained from the equally weighted portfolio, the optimal risky portfolio diversifying across property classes and the property type with the highest Sharpe ratio in the given period. The statistics are comparable to figures 2-4, however these statistics are now from the formed portfolio. The ∆ shows the difference between the Sharpe ratios of the optimal risky portfolio and the equally weighted portfolio. The Sharpe ratio increased before the financial crisis with the optimal risky portfolio. This implies a diversification benefit. During the 2008 financial crisis, the Sharpe ratio is also negative. However with the optimal risky portfolio, the average return increased and the volatility did too. This implicates that the optimal portfolio also provided diversification benefits. In the period after the crisis, up till the end of 2017 the optimal risky portfolio did not provide diversification benefits. The Sharpe ratio

decreased from 0.30 with the equally weighted portfolio to 0.26 in the optimal risky portfolio.

Figure 6

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- 30 - Table 14

Statistics of portfolio of properties and best performing property before the crisis (2003-2006)

Mean (𝝁𝝁)

_{St. Dev}

_(𝝈𝝈)

_{Sharpe Ratio (}

𝝁𝝁_𝝈𝝈

₎

Optimal risky 2.549% 2.632% 0.97 ∆= 0.02

Office 2.533% 2.662% 0.95

Table 15

Statistics of portfolio of properties and best performing property during the crisis (2007-2009)

Mean (𝝁𝝁)

_{St. Dev}

_(𝝈𝝈)

_{Sharpe Ratio (}

𝝁𝝁_𝝈𝝈

₎

Equally weighted -4.4101% 10.0225% -0.44

Optimal risky -3.7068% 6.1360% -0.60 ∆=0.06

Retail -3.354% 6.001% -0.56

Table 16

Statistics portfolio of properties and best performing property after the crisis (2009-2017)

Mean (𝝁𝝁)

St. Dev

(𝝈𝝈)

Sharpe Ratio (

𝝁𝝁_𝝈𝝈

)

Optimal risky 1.204% 4.566% 0.26 ∆=0.04

Residential 2.104% 6.666% 0.32

V. The average return from portfolios of country/ property types are negative during the 2008 financial crisis.

𝐻𝐻0

: 𝜇𝜇

< 0

𝐻𝐻1

: 𝜇𝜇

</0

One can observe by looking at table 12 and 15, that the mean is negative for both

country type diversification as for property type diversification with both portfolios. The

𝐻𝐻0 is therefore accepted and it is concluded that all the portfolios suffered a loss in the

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- 31 - VI.

The benefits of risk diversification were for country/property type diversification higher during the financial crisis, than the period before and after the crisis.

𝐻𝐻0

: ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2007−2009}

> ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2003−2006,}

𝑜𝑜𝑎𝑎 ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2009−2017}

𝐻𝐻1

: ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2007−2009}

/> ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2003−2006}

𝑜𝑜𝑎𝑎 ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.2009−2017}

As can be concluded from table 11-13 and 14-16, the difference in Sharpe ratio from risk diversification (∆) is the highest for the period of the financial crisis. (0.09>0.04 or 0.06)

and (0.09>0.04 or 0.02). This provides sufficient evidence for the 𝐻𝐻0 and is therefore

accepted. It is thus possible to conclude that risk diversification was the most efficient during the 2008 financial crisis.

VII. The volatility of country/property risk diversified portfolios is higher during the financial crisis than before/ after the 2008 financial crisis.

𝐻𝐻0:

𝜎𝜎

> 𝜎𝜎

𝑝𝑝𝑎𝑎𝑡𝑡𝑜𝑜 2003−2006, 2009−2017

𝐻𝐻1:

𝜎𝜎

> 𝜎𝜎

𝑝𝑝𝑎𝑎𝑡𝑡𝑜𝑜 2003−2006, 2009−2017

One can observe by looking at table 11-13 and 14-16 that in the financial crisis the standard deviation of the optimal risky portfolio is higher during the financial crisis than in the other periods (3.306%>1.140% or 1.453%) and (6.1360%>2.632% or 4.566%).

This makes it possible to conclude that the financial crisis was the most volatile period, even when risk diversifying.

VIII. Country diversification was a more effective tool than property type diversification inside Europe during the 2008 financial crisis.

𝐻𝐻0

: ∆

> ∆

�𝜇𝜇_𝜎𝜎�_{𝑅𝑅.𝑃𝑃𝑎𝑎𝑜𝑜𝑝𝑝𝐼𝐼𝑎𝑎𝑡𝑡𝐶𝐶2007−2009}

𝐻𝐻1

: ∆

/> ∆

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.𝑃𝑃𝑎𝑎𝑜𝑜𝑝𝑝𝐼𝐼𝑎𝑎𝑡𝑡𝐶𝐶2007−2009}

This hypothesis is answered by observing table 12 and 15. To conclude that country risk diversification is a more effective tool than property risk diversification, the change in

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Sharpe ratio ∆ is witnessed. One can observe that the ∆ in table 12 is higher than in table

15 (0.09>0.06). This provides evidence for the 𝐻𝐻0 , which implies that country risk

diversification was a more effective tool than property type risk diversification. This is in line with research from Glascock and Kelly (2005), who concludes that country diversification is a more effective tool for achieving risk reduction than property type diversification in the period 1990-2002.

IX. The benefits of diversification through the optimal risky portfolio are lower than that of investing in one country/property.

𝐻𝐻0

:

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.𝑝𝑝𝑜𝑜𝑎𝑎𝑡𝑡𝑜𝑜𝑜𝑜𝑣𝑣𝑝𝑝𝑜𝑜}

<

�_𝜎𝜎𝜇𝜇�_{𝑡𝑡𝑝𝑝𝐼𝐼𝑒𝑒𝑝𝑝𝑜𝑜𝑝𝑝𝑒𝑒 𝑝𝑝𝑎𝑎𝑜𝑜𝑝𝑝𝐼𝐼𝑎𝑎𝑡𝑡𝐶𝐶,𝑒𝑒𝑜𝑜𝑣𝑣𝐼𝐼𝑡𝑡𝑎𝑎𝐶𝐶}

𝐻𝐻1

:

�_𝜎𝜎𝜇𝜇�_{𝑅𝑅.𝑝𝑝𝑜𝑜𝑎𝑎𝑡𝑡𝑜𝑜𝑜𝑜𝑣𝑣𝑝𝑝𝑜𝑜}

</

�_𝜎𝜎𝜇𝜇�_{𝑝𝑝𝐼𝐼𝑒𝑒𝑝𝑝𝑜𝑜𝑝𝑝𝑒𝑒 𝑝𝑝𝑎𝑎𝑜𝑜𝑝𝑝𝐼𝐼𝑎𝑎𝑡𝑡𝐶𝐶,𝑒𝑒𝑜𝑜𝑣𝑣𝐼𝐼𝑡𝑡𝑎𝑎𝐶𝐶}

The answer for hypothesis IX is found by observing tables 11 till 16. The Sharpe ratio of the optimal risky portfolio is compared to the country/property with the highest Sharpe ratio in that period. This provides insight to the question whether investing in one specific country or property type could have served as a better alternative than the optimal risky portfolio. Comparing all values in tables 11 (0.93< 1.14) till table 16 (0.26< 0.32) shows that only table 14 provides an opposite observation (0.97>0.95). Risk diversification through property types was during the period prior to the 2008 more effective than investing in one specific sector. This gives not enough evidence to

accept the 𝐻𝐻0, since it is not true in all observed periods. Acquiring the lowest possible

risk with the optimal risky portfolio, does not mean a lower Sharpe ratio in every observed period.

6. Robustness check

This chapter contains a reviews the robustness check performed

6.1 Alternative index

In this section the correlation between the GPR General index and an alternative index, the Dow Jones Select Real Estate Securities Index is observed. This index is fit as

alternative index, because of the highly similar inclusion rules. The same period is analyzed as the GPR General index in this thesis (31/01/2003 till 31-12-2017). The

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- 33 - index is also observed on a monthly basis. What can be concluded from the correlation in table 17, is that the indexes are highly correlated. This would imply that if the Dow Jones Select Real Estate Securities Index was observed, it would provide similar outcomes.

Table 17

Correlation of GPR and DJ index.

7. Conclusion

This thesis examines and tests the merits of risk diversifying portfolios of real

estate securities internationally and by property type over the period December 2003 through December 2017. We divide this period to analyze the effect of the 2008 financial crisis and the years surrounding. Using data from twenty-one countries from the GPR General Index and four European property sectors from the GPR 250 Index. We analyze country and property type sources of variation in real estate security returns. This analysis rejects our hypothesis formed by previous research of Glascock and Kelly (2005) concerning that the lowest volatility originated from the United States. Germany however had the lowest volatility, but Switzerland the highest We confirm that the residential sector was the most volatile market during the 2008 financial crisis. This hypothesis was formed by the collapse of the housing price bubble mentioned by Mishkin (2011).

We examine the variance of returns across countries (within-country variation vs. between-country variation) and properties (within-sector variation vs. between-sector variation). We find with a significance level of 95%, not enough evidence to conclude variance across countries nor properties.

Next, we compare the benefits of risk diversification of portfolios of real

estate securities along country and property types over the three different time frames. We use the Sharpe ratio as comparison benchmark. We find that the highest benefits

GPR

DJ

GPR

1

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- 34 - from risk diversification are gained during the time frame of the 2008 financial crisis. This is in line with our expectations.

Moreover we confirm previous finding by Glascock and Kelly (2005) that country diversification is a more effective tool for achieving risk reduction than property type diversification. Enlightened by the relative increases in Sharpe ratios.

Finally results suggests that the benefits from the best specific country/property were not always higher than the optimal risky portfolio.

An important limitation of this thesis is that the property specific index is given for Europe as a whole. This makes it limited to compare the relative effect between country type and property type.

A natural extension of this thesis would be to identify the origin of the country/sector benefits. Or else the comparison of movements between real estate securities and the direct real estate market.

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The effect of property type and country type on risk diversified real estate portfolios : an empirical investigation of the 2008 financial crisis