Acknowledgments I am greatly indebted to my supervisor, Associate Professor Ho Kim Hin, David He has been a tremendous source of support, ideas, and useful advice during the three years we worked together His energy and keen interest in challenging problems have been an example and a constant inspiration for me I would like to acknowledge gratefully the financial support of the National University of Singapore (NUS) for granting me the prestigious NUS Research Scholarship I am also thankful to Professor Ong Seow Eng, Associate Professor Fu Yuming, Associate Professor Sing Tien Foo and Associate Professor Tu Yong, for their concern, willingness to listen, and their constant efforts to make some suggestions My friends at NUS have helped me in numerous ways To Li Yun, Chen Zhiwei – I thank you The love of my family has been my greatest blessing, and it has helped me to go on in my most difficult moments I fondly thank my parents, who have always been an example of ambition and hard work but also of devotion, caring, and humanity I am grateful to my sister for her efforts to support me and take care of my parents Your encouragement gave me the strength to pursue my professional goals, and your very existence reminded me that there is so much more to life I thank you with all my heart I Contents Acknowledgments I Contents II Summary V List of Tables VI List of Figures VII Chapter Introduction 1.1 Background and Motivation 1.1.1 Background 1.1.2 Motivation 1.2 Research Question and Issues 1.3 Objectives 1.4 Data and Methodology 1.5 Scope of the Research 1.6 Potential Results and Contributions 1.7 Structure of This Dissertation 10 Chapter Literature Review 12 2.1 Real Estate 12 2.1.1 Definition of Real estate 12 2.1.2 Characteristics of real estate 13 2.1.3 The real estate investing process 13 2.1.4 The benefits of real estate investing 15 2.1.5 Why choose international and direct real estate investing, and not the real estate investment trust (REITs)? 16 2.2 Direct Real Estate Asset Allocation 18 2.2.1 Asset allocation 18 2.2.2 Direct real estate asset allocation 20 2.2.3 Asset Allocation Models 37 2.2.4 Shortcomings of traditional asset allocation approaches 43 2.3 Fuzzy Set Theory and Fuzzy Decision Making 45 II 2.3.1 Fuzzy set theory 45 2.3.2 The fuzzy logic benefit 46 2.3.3 Why must computer software programs enable decision to be made? 46 2.3.4 Why fuzzy logic? 47 2.3.5 Fuzzy logic’s underlying principle 47 2.3.6 Why is there a need for an “Inference Engine”? 48 2.3.7 The Extension Principle 49 2.3.8 Probability theory and fuzzy set theory 50 2.3.9 Popularity of Fuzzy Set Theory Application Research 50 2.3.10 Fuzzy decision making 50 Chapter The Fuzzy Strategic Asset Allocation (FSAA) Model 52 3.1 Introduction 52 3.2 FSAA 53 Chapter Fuzzy Tactical Asset Allocation (FTAA) Decision Making Models 62 4.1 Expert judgement and fuzziness 63 4.2 Optimization in the fuzzy environment 65 4.3 Definition of the fuzzy decision (Bellman and Zadeh) 65 4.4 Flexible Model: Zimmerman’s Symmetric Fuzzy Linear Programming Model 67 4.4.1 Zimmermann’s Symmetric Fuzzy Linear Programming model 67 4.4.2 Fuzzy optimizer 73 4.5 FTAA Robust Model: Ramik and Rimanek’s Robust Programming Model 74 Chapter Validation of the Fuzzy Asset Allocation Models 77 5.1 The Data 77 5.1.1 JLL Data Source 77 5.1.2 The Required Data 78 5.1.3 Some Key definitions used in by JLL REIS-Asia 80 5.2 Calculation of Total Return Correlation Coefficient 84 5.3 The Fuzzy Asset Allocation Models 86 5.4 Comparisons with the Traditional and Fuzzy Asset Allocation Models 88 Chapter Conclusion and Future Studies 90 6.1 Review of Research Objectives 90 III 6.2 Summary of Key Findings 90 6.3 Conclusion and Implications 92 6.4 Theoretical Contributions 93 6.5 Practical Contributions and Policy Implication 93 6.6 Limitations of This Research 93 6.7 Recommendations for Future Studies 96 References 97 Appendix A fuzzyTECH 5.12e (08-Mar-2000) 103 AppendixB MPT and Efficient Frontier 109 Appendix C The Fuzzy Tactical Asset Allocation Models 114 IV Summary Although the classical Markowitz mean-variance asset allocation framework can be used to enable decision-making in international and direct real estate investing, and that many institutional investors have used it to support their decision-making, such a meanvariance framework still needs to be enhanced in order to capture the multi-causal factors influencing international and direct real estate investing A fuzzy decision-making approach can be a more intuitive and a rigorous alternative in this regard The aim of this dissertation is to enhance the classical Markowitz mean-variance asset allocation framework through making it more appropriate for decision-making in international and direct real estate investing This dissertation is concerned with the model formation and estimation of the institutional investors’ fuzzy strategic asset allocation (FSAA) and fuzzy tactical asset allocation (FTAA) The dissertation utilizes the Jones Lang Lasalle Real Estate Intelligence-Asia office-sector dataset in order to integrate the fuzzy decisionmaking approach with the classical Markowitz’s asset allocation mean-variance framework to provide institutional investors, engaged in international and direct real estate investing, with a more intuitive way of uniquely and rigorously capturing their expert judgement in optimal asset allocation The findings indicate that the new and estimated FSAA model and FTAA models can be the appropriate ones to enhance decision-making in international and direct real estate investing Keywords: Direct real estate, fuzzy set theory, fuzzy strategic asset allocation, fuzzy tactical asset allocation, Zimmermann’s fuzzy linear programming, Ramik & Rimanek’s fuzzy optimization V List of Tables Table 1.1 Portfolio size of institutional investors across the globe (in billions of US$) Table 1.2 Estimates of the size of the investible institutional real estate portfolio in 2000 Table Project Statistics 53 Table Linguistic Variables 55 Table 3 Base Variables 55 Table Interfaces 56 Table Definition Points of MBF "EconGthProsp" 57 Table Definition Points of MBF "MktLiquidity" 57 Table Definition Points of MBF "MktTransparency" 58 Table Definition Points of MBF "MktVacancy" 58 Table Definition Points of MBF "MktPerformance" 59 Table 10 Rules of the Rule Block "RB1" 60 Table 11The fuzzy strategic asset allocation results 61 Table Historical TRs 2000-2005 79 Table Historical Correlations among Asian Country TRs (2000-2005) 79 Table Forecast (Ex ante) TRs, 2006-2010 80 Table Ex-ante Correlations among Asian Country TRs (2006-2010) 80 Table 5 General information of ten Asian real estate market 85 Table Correlation Coefficients 86 Table Covariance Matrix 86 Table Zimmerman's FTAA Flexible Programming Model Coefficients 87 Table Zimmerman's FTAA Flexible Programming Model Results 87 Table 10 The Ramik & Rimanek FTAA Robust Programming Model Coefficients 87 Table 11 Ramik & Rimanek FTAA Robust Programming Model Results 87 Table 12 Comparision of the different asset allocation models 88 Table 5.13 Portfolio Risk and Return Comparisons……………… ….…….………… 89 VI List of Figures Fig 1 Structure of this Dissertation 10 Fig The Real Estate Investing Process 14 Fig 2 Participants in the real estate investment 15 Fig Opportunity set of portfolios 40 Fig Risk indifference curves for investors A and B 41 Fig Risk indifference curves for investors A and B with changes in the rate of interest 41 Fig Risk indifference curves and the opportunity set 42 Fig Structure of the Fuzzy Logic System 54 Fig Membership Function of 'temperature' 55 Fig3 MBF of "EconGthProsp" 56 Fig 4: MBF of "MktLiquidity" 57 Fig MBF of "MktTransparency" 57 Fig 6: MBF of "MktVacancy" 58 Fig 7: MBF of "MktPerformance" 59 Fig Decision-making in fuzzy environment 66 Fig Efficient frontier of ten Asian real estate market 85 VII Chapter Introduction “Precision is not truth.” Henri Matisse, Impressionist Painter 1.1 Background and Motivation 1.1.1 Background Real estate investing is a complex human cognitive process involving decision-making regarding possible uncertain future returns In an ill-defined and complex environment, human cognition is often overloaded with many interdependent facets of that environment, resulting in many instances, a sub-optimal judgment Investment analysis comprises several key analytical techniques, namely the discounted cash flow (DCF) model, portfolio theory and risk analysis that are essentially structured frameworks, which enable a more precise and certain evaluation of an investment However, the success of investment analysis still relies greatly on the reliability and quality of the inputs to the analytical techniques In investment analysis, the precise and crisp result of any of its techniques (models) is derived on the assumption that the variables in the analysis are deterministic or probabilistic in nature This assumption is pseudo accurate and it fails to take into account unexpected shocks or perturbations that are possible in the real world Therefore, investors who rely on sophisticated analytical techniques are not placed in a better position but are in fact subject to substantial risk Expert judgment offers an acceptable alternative to non-naïve models as that judgment, which itself is limited by uncertainty, is attributable to the vagueness and imprecision inherent to the associated expert’s ex ante information Such a limitation is known as cognitive uncertainty or fuzziness As a result, ‘Fuzzy Set Theory’ is incepted to allow a natural and intuitive way of representing cognitive uncertainty Fuzzy set theory relaxes the crispness and precision to enable a robust summary of expert knowledge The incorporation of fuzzy set theory has made significant inroads relating to the generalization of traditional investment analysis and its techniques, thereby opening up a new frontier in structured frameworks for evaluating the investment market 1.1.2 Motivation Institutional investors like the insurance companies, banks, corporations and pension funds, are the primary capital players in today’s investment environment The corresponding and teeming volume of funds interested in international real estate investing is highlighted in Table 1.1 Table 1.1 Portfolio size of institutional investors across the globe (in billions of US$) US Japan UK Canada Netherlands Switzerland Australia Germany France Ireland Hong Kong Total Pension funds (1998 data) 7,400 2,285 1,159 585 470 350 205 363 77 46 21 12,961 Insurance companies(1999 data) 3,996 2,216 1,651 164 230 252 179 950 712 38 10,391 Source: Henderson Investors (2000) Table 1.2 Estimates of the size of the investible institutional real estate portfolio in 2000 Regions North America UK Continental Europe Asia Australasia South America Total Institutional real estate (US$ billions) 1,598 361 1,262 825 103 131 4,280 Percentage of global portfolio 37.3% 8.4% 29.5% 19.4% 2.4% 3.1% 100.0% Source: Henderson Investors (2000) As observed in Table 1.1, the estimated value of the global investment market (i.e insurance companies and pension funds around the world) in year 2000 is about US$23 trillion (Henderson Investors, 2000) The estimated total invested institutional direct real estate market is much smaller at about US$1.3 trillion, which includes the direct real estate holdings of insurance companies, pension funds and real estate companies in the major economies Recently, industry studies by major investment advisors, including Henderson Investors (2000), Prudential (1988 and 1990), Jones Lang LaSalle, Lend Lease and AIG, have all advocated international real estate investing to be the next frontier for institutional investors, and international real estate to be an alternative and viable investment asset class Given the potentially immense volume of funds that is interested in international real estate investing, it is not surprising that there has been a significant amount of research focused on the potential benefits of an international real estate investment strategy Investment management and advisory firms clearly support and promote the diversification benefits of international real estate investing The diversification benefits have been instrumental for teeming research, which has amassed many studies and rich Waiscott, C.B “The Stock-Bond Correlation and its Implication for Asset Allocation,” Financial Analysts Journal, July/August, 1990, pp 55 Webb, J R., Rubens, J H., 1989 “Diversification Gains from Including Foreign Real Estate in Mixed Asset Portfolios”, Presented as a working paper at the American Real Estate Society Annual Meeting, San Francisco Wers, B M., “Aggregation Models in Mathematical Programming,” in G Mitra (Ed.) Mathematical Model for Decision Support, 1988, pp.295-305 Worzala, E M., 1992 “International Direct Real Estate Investments as Alternative Portfolio Assets for Institutional Investors: An Evaluation”, unpublished PhD dissertation, University of Wisconsin-Madison Worzala, E M., 1994 “Overseas Property Investments: How Are They Perceived By the Institutional Investor?” The Journal of Property Valuation and Investment, 12, 3, pp 3147 Yager, R.R., “On a General Class of Fuzzy Connectives,” Fuzzy Sets and Systems, Vol 4(3), 1980, pp 235-242 Zaded, L A., “Fuzzy Sets,” Information and Control, 8, 1965, pp 338-352 Zimmermann, H J., “Description and Optimization of Fuzzy Systems,” International Journal of General System, Vol 2, 1976, pp 209-215 Zimmermann, H J., “Fuzzy Mathematical Programming,” Computer & Operational Research, Vol 10, No 4, 1983, pp 291-298; Zimmermann, H J., Fuzzy Sets, Decision Making and Expert Systems, Kluwer Academic Publishers, Boston, 1987; etc Zimmermann, H J., and Zysno P., “Decisions and Evaluations by Hierarchical Aggregation of Information,” Fuzzy Sets and Systems, Vol 10 (3), 1983, pp 243-260 Zimmermann, H J., Fuzzy Set Theory- and Its Applications, Kluwer Academic Publishers, Second Edition, 1991 Ziobrowski, A.J., Curcio, R.J., 1991 “Diversification Benefits of US Real Estate to Foreign Investors”, Journal of Real Estate Research, Vol 6, No Ziobrowski, A.J., B.J Ziobrowski and S Rosenberg 1997 Currency Swaps and International real Estate Investment Real Estate Economics 25(2): 223–251 102 Appendix A fuzzyTECH 5.12e (08-Mar-2000) The fuzzyTECH website http://www.fuzzytech.com/ The process of fuzzy logic application Fuzzification Inference Defuzzification Fuzzy Logic Design Fuzzy Logic Development Tools Because a key element of fuzzy logic is its characteristic trait which transforms the binary world of digital computing into a computation based on continuous intervals, true fuzzy logic must be emulated by a software program on a standard microcontroller/-processor Initial attempts at this software emulation proved to be very inefficient Even a small fuzzy logic system required approximately one second to compute on a standard 8051 microcontroller For most real-time control applications, this was much too slow Some vendors looked into hardware acceleration of fuzzy logic by designing fuzzy 103 coprocessors Today, such hardware acceleration devices are available from many vendors including Fujitsu, Siemens, SGS-Thomson, and VLSI While fuzzy coprocessors can compute fuzzy logic systems in only fractions of a millisecond, a coprocessor design can be much more expensive than a software-only solution on a standard microcontroller How can you get both high performance and low cost at the same time? In 1992, Intel Corp.'s microcontroller group teamed up with Inform Software Corp., a U.S./German software firm that has pioneered the fuzzy logic development tool market with its "fuzzyTECH microkernel" software architecture that provides implementations of fuzzy logic much more efficiently than previous emulation technologies Now, the same example of a small fuzzy logic system running on a standard 8051 requires about one millisecond to compute, an acceleration of about 1000 times This computational performance is sufficient for many real-time control systems, and renders the use of expensive fuzzy coprocessors unnecessary in most applications Since 1992, the fuzzyTECH microkernel solution has been licensed by most other MCU vendors including Microchip, Texas Instruments, Siemens, SGS-Thomson, Mitsubishi, and Motorola The fuzzy logic systems used for this benchmarking range from a simple position controller (Bench0) to one of the most complex fuzzy logic embedded systems ever implemented (Bench4); consisting of 500 rules, input, and output variables The source code for these benchmarks can be downloaded from this site How does the fuzzyTECH microkernel accomplish an increase in software computational efficiency of 1000 times? The key is to incorporate as many computational steps as possible into the fuzzy compiler, thus the microcontroller must compute very little at runtime For example, at compile time, fuzzyTECH clusters the rule base into segments, requiring the microcontroller to evaluate only a small fraction of the rule base at runtime In case of a rule base containing 500 rules, the microcontroller first determines which of the segments contain rules that apply to the current input conditions This can reduce the number of rules that need to be evaluated at runtime to perhaps 100 Rules that not apply to the current input conditions in the fuzzy computation not influence the result and would only add unnecessary cycles to the fuzzy computation In another step, the microcontroller determines which of the rules are dominated by others These dominated 104 rules also play no part in influencing the result and are thus eliminated from the computation as well This subsequent step can reduce the number of rules that must be computed at runtime to around 25, sometimes fewer Typically, only 5% of the rules in a fuzzy logic system actually need to be computed This two-step determination of a rule segment, containing the influencing rules before actually computing an inference result, is quite fast at runtime because it uses a segmentation made at compile time Another key technique implemented in the fuzzyTECH microkernel is resolution analysis In a microcontroller implementation of fuzzy logic, computations in the defuzzification step often consume most of the total inference time This occurs because a straightforward implementation of the defuzzification in 8-bit resolution involves a 32-bit by 16-bit division By analyzing the information flow in a fuzzy logic system during compilation, the fuzzyTECH development software can split up the final 32/16 bit division into a number of 8/8 bit divisions before the defuzzification and one 16/8 bit division afterwards This operation is considerably faster, yet delivers the same accuracy Hence, the major reason for the fast execution of fuzzy logic on standard microcontrollers using the fuzzyTECH microkernel techniques lies in the identification and definition of intelligent shortcuts during compile time on the development PC Because even very small modifications of the fuzzy logic system definition may require completely different shortcuts, this analysis must be performed by the fuzzyTECH compiler on each compile This analysis is what makes hand-coding the fuzzy logic algorithm is so impractical Any time even a small modification of the fuzzy logic system is made by the designer, very significant modifications in the assembly code may become necessary Not only tools like fuzzyTECH provide optimal implementations of fuzzy logic, they also speed system design by relieving the developer from writing fuzzy logic code The more advanced tools available today incorporate extensive GUIs which not only provide the developer with a graphical representation of the system structure, but also highly interactive optimization tools to help the user gain a deeper understanding of how their inference is computing a given solution If designers are to create fuzzy systems which 105 draw on intuition and experience, they are best served by tools which provide informative feedback to help them understand the details of the fuzzy logic inference process Figure Fuzzy Design Wizards in fuzzyTECH Guide Designers Through All Major Steps of Standard Development Methodology Development Methodology The fuzzy logic development methodology as currently under standardization involves five steps: Design: Specification of linguistic variables Definition of inference structure Formulation of fuzzy rules Debugging: Off-line analysis, testing and verification On-line optimization A fuzzy logic system implements a control strategy by "if-then" fuzzy rules that use fuzzily defined expressions such as "pretty_low" or "relatively_high" The specification of these expressions is provided by the linguistic variables More succinctly, the linguistic 106 variables are the "vocabulary" that the fuzzy rules use to express the strategy State-of-the art fuzzy logic software development tools automate the specification of linguistic variables and automatically generate the documentation of the design process For example, fuzzyTECH features the Fuzzy Variables Wizard that creates the complete definition of linguistic variables based on the standardized development methodology Many fuzzy logic systems consist of multiple components For example, one component may estimate a process variable for which a sensor does not exist by utilizing related input signals Based on this fuzzy estimation and other inputs, another component could define the actual control strategy Each component of a fuzzy logic system contains a subset of the complete fuzzy rule set and is thus called a "rule block" To connect rule blocks to each other, intermediate linguistic variables are used Because these variables are never fuzzified or defuzzified, no membership functions are required Connecting rule blocks with input, output, and intermediate linguistic variables defines the inference structure of the fuzzy logic system State-of-the-art fuzzy logic development tools support visual definition of this inference structure (Figure 2) The rule blocks in the fuzzy logic design contain the actual control strategy Fuzzy rule design falls into two steps The first is the formulation of initial rule blocks, and the second is to optimize the rules based on analysis and testing in the last two design steps The formulation of initial rule blocks in fuzzyTECH is made easier by the Fuzzy Rule Wizard that uses a structured audit approach to create complete rule blocks automatically While the first three steps of a fuzzy logic development - definition of variables, structure, and rules - are the design phase of the development, the next two steps cover the debugging phase In the debugging phase, analyzers and editors are used to visualize the computation of the fuzzy logic inference For example, the fuzzy rules are checked for consistency and completeness In interactive debugging, the designer simulates specific input conditions for the fuzzy logic system and evaluates its reaction If the performance is not satisfactory, the analyzers point the designer toward the respective rules and variables that require tuning Depending on the application, process simulations and recorded process data may also be used in this fourth development step 107 Figure Analyzer and Editor Windows in fuzzyTECH During System Optimization In some applications, the final tuning and verification of the fuzzy logic system can only be completed when the fuzzy logic system controls the process in real time A technique known as "on-line" debugging lets designers connect the microcontroller to the PC running fuzzyTECH by a serial cable or in-circuit emulator The designer may then conduct the same analyses on-line that were performed off-line in the previous development step By optimizing linguistic variables and fuzzy rules "on-the-fly", the reaction of the process under control relative to the modified fuzzy logic controller can be studied 108 AppendixB MPT and Efficient Frontier How to calculate the MPT asset allocation results and how to draw the efficient frontier? In this dissertation, we use the Microsoft Excel Solver to calculate the asset allocation results Table The Main Asia Office Market Historical and Forecasting Data Office Market Beijing Shang hai Central + Major Business Districts Country China China HK South Korea Japan Philippines Indonesia Singapore Malaysia Thailand BJ SH HK SL TK MN JK SG KL BK Seoul Tokyo Manilar Jakarta Singap pore (Raffles Place) Kuala Lumpur Bangkok 1989 70.53% 50.36% 39.40% 19.53% 1990 37.61% 101.80% 135.80% 91.13% 1991 -8.99% 18.16% 48.41% 50.31% 1992 7.96% 20.78% -0.77% -3.62% 1993 39.94% 25.50% -8.12% -2.25% 10.06% 0.07% 1994 1995 45.89% 20.67% 11.69% 3.10% 9.23% 4.72% 20.60% 32.67% 4.37% 40.26% 13.78% 9.66% 1996 -16.99% 19.93% -0.25% 19.84% 10.70% 9.77% 7.26% 61.86% 21.73% 7.20% 17.57% 10.53% 9.00% 4.03% -20.30% 3.27% 6.43% 0.87% 9.60% -22.06% -1.69% -39.71% -4.98% -0.83% -52.45% 3.40% 39.12% -13.62% -9.53% 1997 1998 1999 2000 12.45% 13.93% 24.95% -3.08% 17.77% 5.80% 3.59% -0.62% 23.26% 4.24% 10.22% 3.60% 2001 50.53% 4.59% 12.39% 43.38% 6.07% -8.58% 8.78% 7.22% 13.91% 2002 8.11% 8.04% -0.56% 43.66% 2.58% 3.93% 6.01% 9.27% 2003 7.56% 10.08% -13.30% 16.31% 1.70% 13.86% -9.13% 6.42% 11.98% 2004 9.61% 11.34% -6.93% 13.91% 2.95% 16.03% 14.53% 11.47% 14.84% 7.59% 11.41% -2.38% 7.33% 31.41% 2005 9.82% 11.98% 61.18% 18.30% 21.15% 14.85% 9.96% 4.17% 8.25% 43.39% 2006 16.89% 27.31% 43.42% 24.18% 63.22% 36.44% 23.47% 10.88% 11.91% 32.33% 2006 9.94% 21.59% 13.34% 15.05% 48.38% 42.72% 25.70% 18.11% 17.14% 20.11% 2007 2.28% 17.36% -7.06% 18.44% -0.85% 21.87% 10.69% 15.09% 19.82% 10.61% 2008 13.13% 18.08% -26.85% 18.40% 5.91% 15.59% 12.99% 11.10% 2.15% 14.48% 2009 16.51% 12.37% -2.02% 12.46% 8.64% 17.35% 17.83% 7.69% 8.61% 8.30% 2010 12.55% 12.54% 39.95% 14.95% 13.76% 15.34% 17.53% 6.20% 11.03% 7.96% 109 Table Forecasting Data Central + Major Business Districts Seoul Tokyo Manilar Jakarta China HK South Korea Japan Philippines Indonesia Singapore (Raffles Place) Singapore BJ 9.94% 2.28% 13.13% 16.51% 12.55% 10.88% SH 21.59% 17.36% 18.08% 12.37% 12.54% 16.39% HK 13.34% -7.06% -26.85% -2.02% 39.95% 3.47% SL 15.05% 18.44% 18.40% 12.46% 14.95% 15.86% TK 48.38% -0.85% 5.91% 8.64% 13.76% 15.17% MN 42.72% 21.87% 15.59% 17.35% 15.34% 22.57% JK 25.70% 10.69% 12.99% 17.83% 17.53% 16.95% SG 18.11% 15.09% 11.10% 7.69% 6.20% 11.64% 5.35% 3.93% 24.94% 2.56% 19.30% 11.56% 5.76% 4.98% Office Market Beijing Shang hai Country China 2006 2007 2008 2009 2010 Mean Std Dev Kuala Lumpur Bangkok Malaysia Thailand KL 17.14% 19.82% 2.15% 8.61% 11.03% 11.75% BK 20.11% 10.61% 14.48% 8.30% 7.96% 12.29% 7.01% 5.09% Table Descriptive Statistics Mean BJ 10.88% SH 16.39% HK 3.47% SL 15.86% TK 15.17% MN 22.57% Median 12.55% 17.36% -2.02% Maximum 16.51% 21.59% 39.95% 15.05% 8.64% 18.44% 48.38% Minimum 2.28% 12.37% -26.85% 12.46% Std Dev 5.35% 3.93% 24.94% Skewness Kurtosis -0.8098 0.11357 2.48844 1.59781 Jarque-Bera 0.60097 Probability 0.74046 Sum Sum Sq Dev JK 16.95% SG 11.64% KL 11.75% BK 12.29% 17.35% 17.53% 11.10% 11.03% 10.61% 42.72% 25.70% 18.11% 19.82% 20.11% -0.85% 15.34% 10.69% 6.20% 2.15% 7.96% 2.56% 19.30% 11.56% 5.76% 4.98% 7.01% 5.09% 0.36543 -0.1175 1.22281 1.3226 0.53367 0.2029 -0.1896 0.71979 2.13042 1.61331 2.90939 2.98267 2.17647 1.52984 1.7671 2.04342 0.42036 0.26881 0.41211 1.24775 1.4578 0.37863 0.48459 0.34663 0.62238 0.81044 0.87423 0.81379 0.53586 0.48244 0.82753 0.78482 0.84087 0.73258 0.5441 0.8194 0.1736 0.793 0.7584 1.1287 0.8474 0.5819 0.5875 0.6146 0.01144 0.00618 0.24885 0.00262 0.14899 0.05348 0.01325 0.00993 0.01967 0.01034 5 5 5 5 5 Observations Table Correlation Coefficient BJ BJ 1.00 SH -0.46 HK 0.08 SL -0.67 TK 0.11 MN -0.28 JK 0.35 SG -0.64 KL -0.77 BK -0.16 SH -0.46 1.00 -0.33 0.49 0.57 0.78 0.30 0.93 0.32 0.94 HK 0.08 -0.33 1.00 -0.50 0.40 0.16 0.50 -0.27 0.36 -0.21 SL -0.67 0.49 -0.50 1.00 -0.35 -0.10 -0.63 0.41 0.05 0.24 TK 0.11 0.57 0.40 -0.35 1.00 0.88 0.95 0.52 0.30 0.76 MN -0.28 0.78 0.16 -0.10 0.88 1.00 0.75 0.83 0.59 0.83 JK 0.35 0.30 0.50 -0.63 0.95 0.75 1.00 0.27 0.19 0.55 SG -0.64 0.93 -0.27 0.41 0.52 0.83 0.27 1.00 0.60 0.82 KL -0.77 0.32 0.36 0.05 0.30 0.59 0.19 0.60 1.00 0.16 BK -0.16 0.94 -0.21 0.24 0.76 0.83 0.55 0.82 0.16 1.00 110 Table Covariance Matrix BJ SH HK SL TK MN JK SG KL BK Sumproduct BJ 0.23% 0.04% 0.09% 0.09% 0.23% 0.14% 0.14% 0.08% 0.07% 0.09% SH -0.04% HK 0.09% SL 0.09% TK -0.23% MN -0.14% JK -0.14% SG -0.08% KL -0.07% BK 0.09% 0.21% -0.22% 0.13% 0.05% 0.39% 0.17% 0.15% 0.02% 0.60% -0.22% 0.13% 4.98% 0.58% 0.58% 0.27% 0.50% 0.06% 0.37% 0.40% -0.27% 0.06% -0.26% 0.05% -0.25% -0.07% 1.52% 0.84% 0.05% 0.50% 0.06% 0.39% 0.38% 0.17% 0.07% 0.01% 0.32% 0.39% 0.37% 0.40% 0.38% 1.07% 0.38% 0.28% -0.02% 1.58% 0.17% -0.27% 0.06% 0.17% 0.38% 0.20% 0.15% 0.04% 0.40% 0.15% -0.26% 0.05% 0.07% 0.28% 0.15% 0.12% 0.04% 0.35% 0.02% -0.25% -0.07% 0.01% -0.02% 0.04% 0.04% 0.05% -0.14% 0.60% 1.52% 0.84% 0.32% 1.58% 0.40% 0.35% -0.14% 2.98% -0.0523% 0.134198% 0.075268% 0.099512% 0.100274% 0.320576% 0.132700% 0.101969% 0.007094% 0.435656% Table the caculation results Proportion BJ 12.51% Portfolio Risk Portfolio SD Portfolio return 16.00% Expected return 16.00% SH 0% HK 0% SL 17% TK 0% MN 0% JK 70% SG 0% KL 0% BK 0% Total 100% 0.10% 3.22% You can find the Solver in the Microsoft Excel Tools 111 You can change the Expected Return in the Excel and you will get some more asset allocation results as shown in Table Table Simulation of the expected returns and the asset allocation results 112 PRisk Preturn P-SD Expected return BJ SH HK SL TK MN JK SG KL BK Total 100% 0.13% 3.6% 10.0% 10.0% 29.6% 0.0% 17.8% 0.0% 0.0% 0.0% 0.0% 20.3% 32.3% 0.0% 0.05% 2.3% 10.5% 10.5% 27.9% 0.0% 11.9% 0.0% 0.0% 0.0% 0.0% 16.4% 43.7% 0.0% 100% 0.01% 1.2% 11.0% 11.0% 26.2% 0.0% 6.1% 0.0% 0.0% 0.0% 0.0% 12.5% 55.1% 0.0% 100% 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.04% 0.05% 0.08% 0.10% 0.14% 0.18% 0.23% 0.28% 0.34% 0.7% 0.3% 0.4% 0.8% 1.2% 1.6% 1.9% 2.3% 2.8% 3.2% 3.7% 4.2% 4.7% 5.3% 5.8% 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0% 15.5% 16.0% 16.5% 17.0% 17.5% 18.0% 18.5% 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0% 15.5% 16.0% 16.5% 17.0% 17.5% 18.0% 18.5% 29.1% 0.0% 33.6% 34.6% 34.8% 35.1% 35.3% 35.5% 30.3% 22.2% 12.5% 2.8% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 2.9% 0.5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 1.5% 9.2% 17.4% 25.6% 23.7% 18.4% 13.1% 7.8% 7.2% 17.0% 18.8% 16.7% 14.7% 12.6% 10.5% 5.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 5.5% 13.4% 21.2% 29.1% 0.0% 0.0% 7.8% 18.8% 29.9% 40.9% 52.0% 62.9% 68.6% 70.1% 71.6% 70.8% 68.2% 65.7% 63.1% 5.3% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 55.4% 48.9% % 48.9 38.8% 29.6% 20.4% 11.2% 2.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 0.40% 6.3% 19.0% 19.0% 0.0% 0.0% 0.0% 2.5% 0.0% 37.0% 60.5% 0.0% 0.0% 0.0% 100% We can use the portfolio returns and portfolio standard deviations to draw the efficient frontier as shown in Fig Asian Real Estate market investment asset allocation 20.0% 18.0% 16.0% n r u t e R o i l o f t r o P 14.0% 12.0% TAA 10.0% 8.0% 6.0% 4.0% 2.0% 0.0% 0.0% 2.0% 4.0% 6.0% Portfolio Risk 8.0% Fig Efficient frontier of Asia Office market 113 Appendix C The Fuzzy Tactical Asset Allocation Models For the fuzzy tactical asset allocation models, the most important thing is to identify all the parameters used in each model Zimmerman's FTAA Flexible Programming Model Coefficients RISKp+λp1 Rp -λp2 Whole proportion+λp3 18.00% 12.00% ≤d1+p1 ≥d2-p2 18.00% 12.00% d1 d2 16.00% 16.00% p1 p2 2.00% 4.00% 120.00% ≤d3+p3 120.00% d3 100.00% p3 20.00% Source: Author, 2007 114 Zimmerman's FTAA Flexible Programming Model Results BJ 1.28% Proportion Portfolio Risk Portfolio SD Portfolio return Expected return SH 1% HK 3% SL 0% TK 46% MN 25% JK 4% SG 17% KL 1% BK 1% λ Total 100% 0.33% 5.70% 16.00% 16.00% Source: Author, 2007 The Ramik & Rimanek FTAA Robust Programming Model Coefficients mx nx αx βx 14.48% 16.48% 2.00% 2.00% p q γ δ 14.50% 17.50% 3.00% 3.00% εl δl εr δr 0.00% 2.00% 2.00% 4.00% _εl(α l(αx-γ) _δl(α l(αx-γ) εr(β r(βx-δ) δr(β r(βx-δ) 0.00% 0.02% -0.02% 0.00% ≤p-mx ≤p-mx ≤q-nx ≤q-nx 0.02% 0.02% 1.02% 1.02% Source: Author, 2007 The membership function of this fuzzy TAA model µ i ( x ) m-α m n n-β 115 Ramik & Rimanek FTAA Robust Programming Model Results Proportion Portfolio Risk Portfolio SD Portfolio return Expected return BJ SH HK SL TK MN JK SG KL BK Total 0.00% 5% 0% 4% 22% 20% 7% 0% 41% 0% 100% 0.14% 3.77% 15.48% 16.00% Source: Author, 2007 116 [...]... real estate) 2 Fuzzy strategic asset allocation (FSAA) and fuzzy tactical asset allocation (FTAA) formulation and estimation 3 Inter-sector portfolio diversification but within a direct real estate portfolio because direct real estate is found to be an effective portfolio diversifier, even more so when both domestic and international real estate sectors (assets) are considered 1.6 Potential Results and... sources of international diversification (such as equities) are superior Regardless, the one thing they all might agree on is the lacking of high quality data on direct and indirect international real estate markets and their past performance It is understandably hard to find reliable and authoritative data sources for major markets of direct and indirect international real estate that are appropriate for... of fuzzy set theory, fuzzy logic and fuzzy optimization to international and direct real estate asset allocation 2.1 Real Estate 2.1.1 Definition of Real estate It is first imperative to properly define real estate itself and according to Graskamp, Real estate is Space and Money over Time.” The space dimension- covering fundamental policy analysis, housing markets (especially user cost and sub-markets)... theory and fuzzy logic can be introduced into the international real estate investing process for direct real estate investments 9 • The study in this dissertation can incorporate human and intuitive thinking into the direct real estate asset allocation process within the international context • New and direct real estate asset allocation models are developed in international real estate investing 1.7 Structure... Dissertation This dissertation consists of six chapters and Fig 1.1 shows the relationships among the chapters The chapters are outlined below Chapter 1 Intruduction Introduction Chapter 2 Direct Real Estate Asset Allocation & Fuzzy Optimization Application to Finance: A Literature Review Chapter 3 Fuzzy Strategic Asset Allocation (FSAA) Decision Making Models Chapter 4 Fuzzy Tactical Asset Allocation. .. Correlation coefficient is low among the direct real estate sectors or assets (the direct real estate sector diversification and the geographical diversification) Pride of direct real estate ownership, locally and abroad Reduce / control operational costs (a financial benefit at the direct real estate project level) Steady rental yield and long-term capital growth (an investment benefits at the direct real. .. data is now more readily available and our understanding of real estate market analysis this sector is improving 2.1.3 The real estate investing process When one investor makes a real estate investing decision, he should systematically analyze the factors and contingencies that impact the value of a real estate investment It is widely accepted by the real estate investment management community that... office annual total returns, comprising annualized rental yields (real estate capitalization rates) and capital value (CV) appreciation on a pre-tax and pre-leveraged basis, are obtained for ten Asian real estate sectors, namely those for the Beijing Central Business District (CBD), Shanghai CBD, Seoul CBD, Tokyo CBD, Hong Kong Central & major business districts, Manila’s Makati CBD, Jakarta CBD, Singapore’s... direct real estate asset allocation in international real estate investing 2 To enable efficient decision- making in international real estate investing for institutional investors, who are interested in direct real estate investments, as the benefits of such investments are well documented (Goetzmann and Ibbotson 1990) Unfortunately, individuals and smaller institutional investors have traditionally had... arguing against international and direct real estate investing, as institutional investors would not have benefited from it during the past twenty years, while Worzala maintained that other authors at the time supported such a case for international and direct real estate inclusion For example, she claims Sweeney (198 9a and 1989b), Asabere et al “(1991), and Worzala (1992) reiterated that “diversification ... the classical meanvariance MPT framework: a unique and rigorous fuzzy strategic asset allocation (FSAA) and a unique and rigorous fuzzy tactical asset allocation (FTAA) Both the FSAA and FTAA should... Jones Lang Lasalle Real Estate Intelligence-Asia office-sector dataset in order to integrate the fuzzy decisionmaking approach with the classical Markowitz’s asset allocation mean-variance framework... Fuzzy Tactical Asset Allocation Models 114 IV Summary Although the classical Markowitz mean-variance asset allocation framework can be used to enable decision- making in international and direct