THE EX ANTE MEASUREMENT AND MODELING OF DIRECT REAL ESTATE INVESTMENT RISK LI YUN M.A. (Finance), Fudan University, 2003 A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF REAL ESTATE NATIONAL UNIVERISITY OF SINGAPORE 2007 ACKNOWLEDGEMENT I am indebted to all those who have assisted in the development and completion of this PhD thesis: Associate Professor (Dr.) David Ho Him Hin, to whom I am most grateful and indebted for the excellent supervision. His patience and availability, thorough editing, and insightful suggestions are exemplary. Thank you very much for your encouragement and the all the inspiring me to a good research and publication! Associate Professor (Dr.) Ong Seow Eng, for his timely reminders and help for the purpose of speeding up my research process, his insightful comments and review of my research, and his wonderful co-supervision for my PhD research. Genuine thanks to your kind help for all the difficulties during my research! Associate Professor (Dr.) Fu Yuming, together with his warm-hearted family, who has all the time shown great concern for my research and PhD study; sincere thanks to you for the research insights, techniques, encouragement, I advice and co-supervision guidance to my thesis writing! Professor (Dr.) John Glascock, with whose provoking thoughts and insightful comments, this thesis is directed to explore the real estate risk measurement from a more meaningful and innovative perspective. Also millions of thanks to him for his kind words, love and concern to me and my family, without which my further PhD work will not possible! My appreciation of his kindness and warm-heartedness is beyond my words. Thanks to my colleagues from Dept of Finance Hong Kong University of Science & Technology, especially Prof Sudipto Dasgupta, Prof John Wei, Prof Kalok Chan, Prof Jonathan Batten, Dr. Junbo Wang and Sophie Ni together with some other scholars for their insightful comments, without which this version of paper will not be possible! Thanks to the anonymous referees, Professor Ko Wang, and Dr. Michael S. Young, for their deep insights and constructive suggestions on my academic journal papers, which are indispensable components of this thesis! Thanks as well to Dr. Clifford A. Lipscomb, Dr. S.G. Sykes, and the discussants and participants at the 2006 American Real Estate Society Annual Meeting in Key West, Florida for their helpful comments on the paper draft. The specific II recommendations on the improvement of this thesis are most appreciated. Thanks to NUS for the opportunity to let me attend the Harvard College China-India Development and Relationships Symposium (CIDRS) and the Doctoral Student Network Asia Pacific Rim University (APRU), which give me a chance to network with academics world widely. Thanks to all the past and present graduate students and research assistants whom I coincided with, for the opportunity to work with you, and to share the difficulties and success of a research. Most especial thankfulness to my wife, Mrs. Fang Le, for her encouragement, support, patience, share of joys and pains of life and love, without which this research would not have been possible; at the same time, I am equally indebted to my parents, in-laws, younger brother and sister, for their unconditional love, encouragement. This work is most lovingly dedicated to them. Deo Omnis Gloria! III TABLE OF CONTENTS Page No Table of contents IV Summary VII References XIII List of Appendices XIII CHAPTER ONE INTRODUCTION 1.1 Background 1.2 Research Questions 1.3 Research Objectives 1.4 Research Contribution 1.5 The Theoretical Framework of Analysis 12 1.6 Research Hypotheses 27 CHAPTER TWO REVIEW OF RELATED LITERATURE 2.1 Traditional Risk Measures 29 2.2 Duration and Convexity 33 2.3 The LPM (Low Partial Moments) and Co-LPM Risks 41 2.4 Value at Risk (VAR) 46 2.5 The Risk Measurement Fitness 45 IV 2.6 Literature Review on Real Estate Duration CHAPTER THREE 47 EMPERICAL MODEL VALIDATION OF DIRECT REAL ESTATE EX ANTE SYSTEMATIC RISK & TOTAL RISK BEHAVIOR UNDER DURATION RISK, TIME-VARYING RISK AND GARCH RISK 3.1 Introduction 52 3.2 The Data Set 55 3.3 The Beta (Systematic Risk) Model Estimations 57 3.4 The Real Estate Asset Total Risk Estimation under the Duration and GARCH Models 65 3.5 Concluding Comments CHAPTER FOUR 68 STRUCTURAL SIMULATION OF EX ANTE, NON-NORMAL DIRECT REAL ESTATE RISK MEASURE & RETURN BEHAVIOR 4.1 Introduction 71 4.2 The Theoretical Frame of Analysis 74 4.3 The Integrated Direct Real Estate Risk Measure Model 78 4.4 The Integrated Risk-measure Model Estimation 87 4.5 Concluding Comments 96 V CHAPTER FIVE CONLUSIONS AND IMPLICATIONS 5.1 Introduction 98 5.2 Conclusions about Research Questions 99 5.3 Theoretical Implications 101 5.4 Limitations and Recommendations for Further Research 102 VI SUMMARY Real estate assets such as office buildings and shopping centers play an important role in the real estate portfolios of institutional investors, although they may well consist of just a small part of such portfolios (Campbell and Viceira 1999 and Ross and Zisler 1991 etc). There are more institutional investors holding the view that real estate assets should form an increasing share in their overall investment portfolios (Chun, Ciochetti and Shilling 2004 and Shoven and Sialm 1998 etc). Compared with the publicly traded securities, such as equities (common stocks) and bonds, which make up the vast majority of most institutional investor’s investment portfolios, real estate assets differ markedly in key respects. While common stocks and bonds are liquid and continuously traded, thereby making their market values readily observable, real estate assets are illiquid and sporadically traded, thereby making real estate market values rather difficult to observe. As for the publicly traded securities, there are well-established time series of returns that can be utilized in the estimation of the expected (future) risks and returns. However, this is not the case for new products in the direct real estate investment markets. Owing to limited and empirical data availability, an ex ante measurement and the modeling of direct real estate investment risk would be significant and can offer promising scholarly investigative research in real estate finance, particularly in such areas as the direct real estate expected return estimation, asset allocation, portfolio management, risk monitoring and performance VII measurement. Investors in real estate, public or private, equity or debt, evaluate their risk-adjusted returns in the pursuit of specific goals. More often the overall approach in practice is to anticipate direct real estate investment returns and not the risk-adjusted investment returns (Ibbotson and Siegel 1994). The reality that practice focuses on returns and not risk–adjusted returns is not because the real estate investor has not read finance theories but because currently there is a lack of appropriate risk measures. Hence, it is important to conduct an investigative research on the ex ante measurement and modeling of direct real estate investment risk. Dechow, Sloan and Soliman (2004) extend the traditional measure of bond duration to equity analysis and develop an algorithm for the empirical estimation of implied equity duration. They show that equity duration represents an important common factor in stock returns; the book-to-market factor advocated by Fama and French (1993) acts as a noisy proxy for an underlying duration factor. Equity duration measure captures the risks of stocks and helps explain the cross section of returns (Pedro, 2004; Dechow, Sloan and Soliman, 2004). An investigation of real estate duration is of significant importance to the real estate asset pricing. Campbell and Vuolteenaho (2003), Brennan and Xia (2003) and Bansal et al. (2002) have tried to explain the value premium in the context of Merton’s Intertemporal Capital Pricing Model (ICAPM). They argue that value firms are actually riskier than VIII growth firms based on the covariance of their returns with changes in the investment opportunity set. Campbell and Vuolteenaho (2003) use a discounted cash flow model to decompose the market’s unexpected returns into news about future cash flows and news about discount rates. In their model, the market may fall because there is bad news about future cash flow or because of an increase in the discount rate. Importantly, in the first case, the market falls but investment opportunities stay the same, whereas in the second case, the market falls but further investment opportunities actually improve due to the higher expected returns going forward. The two components have different impact on long-term investors who hold the market portfolio. Those investors demand a higher premium to hold assets that co-vary with the market’s cash-flow news than to hold assets that co-vary with discount rate news. Therefore cash-flow beta is “bad beta” since it commands a risk premium that is several times larger than the (relatively) “good” discount-rate beta. Note that stocks with high discount-rate (which are similar to stocks with high duration) are still risky for a long–term investor. Campbell and Vuolteenahao (2003) only show that stocks with high cash-flow risk are much riskier. Campbell and Vuolteenhao (2003) find that discount-rate betas are a little greater for value stocks than for growth stocks, but cash-flow betas are much greater for value stocks than for growth stocks. The difference in the premia for each type of risk explains the difference between returns of value and growth stocks. For a similar story to justify the difference in return of high-duration and low-duration stocks, we would need to find that low-duration stocks (low discount-rate beta) have much IX 133 Market Data by JLL 2002 2002 2002 JAN APR JUL END YR QTR HK$/sq.m /yr 833 833 833 HK$/sq.m./ yr 6,382 5,989 5,586 HK$/sq.f t./mth 49.0 46.4 43.2 OUTGOINGS. GROSS RENT GROSS RENT NOMINAL RENTAL SERIES Central Office Market Sector Hong Kong Prime Office Sector Appendix 4.4 4,753 5,156 5,495 HK$/sq .m./yr NET RENT 2.17 2.11 2.11 mths/yr RENT FREE PERIOD 3,200 3,864 4,165 4,462 HK$/sq m/yr 495 534 572 U$/sqm ./yr EFFECTIVE RENT 6,835 7,431 7,565 HK$/sq .ft 64,000 73,571 79,984 81,426 HK$/sq. m. 9,432 10,254 10,439 US$/sq .m. CAPITAL VALUE SERIES 5.0% 5.3% 5.2% 5.5% INITIAL YIELD 6.5% 6.0% 5.8% PASSING YIELD EFFECTIVE NVESTMENT YIELDS 134 Market Data by JLL 2002 2002 2002 JAN APR JUL END YR QTR HK$/sq.m /yr 775 775 775 HK$/sq.m./ yr 3,681 3,522 3,423 HK$/sq.f t./mth 28.5 27.3 26.5 OUTGOINGS. GROSS RENT GROSS RENT NOMINAL RENTAL SERIES Wan Chai Office Market Sector Hong Kong Prime Office Sector Appendix 4.4 2,648 2,474 2,906 HK$/sq .m./yr NET RENT 2.11 2.13 2.02 mths/yr RENT FREE PERIOD 2,100 2,191 2,266 2,420 HK$/sq m/yr 281 291 310 U$/sqm ./yr EFFECTIVE RENT 5,033 5,255 5,386 HK$/sq .ft 52,000 54,175 56,560 57,973 HK$/sq. m. 6,946 7,252 7,433 US$/sq .m. CAPITAL VALUE SERIES 4.0% 4.0% 4.0% 4.2% INITIAL YIELD 5.3% 5.2% 5.1% PASSING YIELD EFFECTIVE NVESTMENT YIELDS Appendix 4.5 Calculations for Current Income and Its Range Singapore Market Sector Raffles Office Market Sector Jan Apr Jul Current Income 5.3% x $12,917 5.5% x $12,378 = 5.7% x $11,948 = = S$685 S$681 S$681 Current Income Range is S$681 – S$685 Shenton Office Market Sector Jan Apr Jul Current Income 5.6% x $9,688 5.8% x $9,365 = 6.1% x $9,042 = = S$533 S$543 S$551 Current Income Range is S$533 – S$551 Hong Kong Market Sector Central Office Market Sector Jan Apr Jul Current Income 5.8% x $81,462 6.0% x $79,984 = 6.5% x $73,571 = = HK$4,725 HK$4,799 HK$4,782 Current Income Range is HK$4,725 – HK$4,799 Wan Chai Office Market Sector Jan Apr Jul Current Income 5.1% x $57,973 5.2% x $56,560 = 5.3% x $54,175 = = HK$2,957 HK$2,941 HK$2,871 Current Income Range is HK$2,871 – HK$2,957 135 Appendix 4.6 Treasury Bill Rates from SGS End of Period Average Buying Rates of Govt Securities Dealers Average Buying Rates of Govt Securities Dealers 5-Year Bond Yield (.25) 3.36 3.11 3.2 2.97 2.95 2.78 2.6 2.46 2.43 1.89 1.74 1.58 1.43 1.48 1.48 1.32 1.41 2.06 2.58 2.5 3.1 3.11 2.74 2002 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2-Year Bond Yield (.75) 1.93 1.69 1.79 1.6 1.57 1.46 1.26 1.21 1.35 1.3 1.19 1.07 2003 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 0.99 0.86 0.87 0.83 0.71 0.74 1.2 1.41 1.15 1.26 1.28 - Weighted Average for years 2.29 2.05 2.14 1.94 1.91 1.79 1.6 1.52 1.62 1.48 1.37 1.24 1.14 1.0 1.01 0.99 0.86 0.91 1.42 1.70 1.49 1.72 1.74 * Figures before 2000 are the modes of closing bid prices quoted by SGS primary dealers. * Figures after 2000 are the average of closing bid rates quoted by SGS primary dealers. * Overnight repo rates are closing offer rates quoted by SGS primary dealers. * Yield is quoted as % p.a. * Price is quoted in S$ per $100 of principal amount. Source: Singapore Government Securities (http://www.sgs.gov.sg) *Weighted Average year values are calculated based on author’s assumptions. 136 Appendix 4.7 Hong Kong Exchange Fund Bill Rates As at end of -year As at end of 3-year 2002 Jan Feb 4.25 3.89 2003 Jan Feb 2.505 2.230 Mar 4.61 Mar 2.062 Apr 4.09 Apr 2.274 May 3.97 May 1.722 Jun 3.46 Jun 1.778 Jul 3.15 Jul 2.347 Aug 2.53 Aug 2.567 Sep 2.38 Sep 2.077 Oct 2.67 Oct 2.308 Nov 2.82 Nov 2.375 Dec 2.359 Dec 2.033 * * Before 16 Dec 2002, yield figures are calculated as the arithmetic mean of quotes collected from designated banks. Following the introduction of the HKMA EFBN Fixings on 16 Dec 2002, the yield figures are calculated as the arithmetic mean of the middle quotes, after excluding the highest and lowest quotes collected from 12 designated banks. Yield figures powered by Reuters. Source: Hong Kong Monetary Authority (http://www.info.gov.hk/hkma/) 137 Appendix 4.8 Crystal Ball Simulation Report for Raffles Simulation started on 7/21/04 at 20:20:00 Simulation stopped on 7/21/04 at 20:25:08 Forecast: Raffles Modified Duration Cell: C21 Summary: Display Range is from 19.05 to 19.85 years Entire Range is from 19.05 to 19.85 years After 1,000 Trials, the Std. Error of the Mean is 0.01 Statistics: Value 1000 19.43 19.44 --0.18 0.03 0.00 2.19 0.01 19.05 19.85 0.80 0.01 Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Forecast: Raffles Modified Duration 1,000 Trials FrequencyChart 1,000 Displayed .023 23 .017 17.25 .012 11.5 .006 5.75 .000 19.05 19.25 19.45 19.65 19.85 years 138 Forecast: (cont'd) Raffles Modified Duration Cell: C21 Percentiles: years 19.05 19.20 19.26 19.33 19.38 19.44 19.48 19.53 19.60 19.67 19.85 Percentile 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Sensitivity Chart Target Forecast: Raffles Modified Duration Raffles Equivalent yield -.97 Raffles Rental Value .18 Raffles Current income -.04 Raffles Target Return -.03 Raffles Riskless Return .02 -1 -0.5 0.5 Measured by Rank Correlation End of Forecast 139 Forecast: Raffles Returns < Target Cell: I9 Summary: Display Range is from 0.0% to 31.0% Entire Range is from 0.0% to 55.4% After 1,000 Trials, the Std. Error of the Mean is 0.3% Statistics: Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 1000 9.7% 7.2% 2.2% 8.4% 0.7% 1.56 6.03 0.87 0.0% 55.4% 55.4% 0.27% Forecast: Raffles Returns < Target 1,000 Trials FrequencyChart 974 Displayed .033 33 .025 24.75 .017 16.5 .008 8.25 .000 0.0% 7.7% 15.5% 23.2% 31.0% 140 Forecast: Raffles Returns < Target (cont'd) Cell: I9 Percentiles: Value 0.0% 1.6% 2.8% 4.2% 5.4% 7.2% 9.4% 12.0% 15.4% 21.6% 55.4% Percentile 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Sensitivity Chart Target Forecast: Raffles Returns < Target Raffles Target Return .92 Raffles Equivalent yield -.29 Raffles Current income -.03 Raffles Riskless Return .02 Raffles Rental Value -.00 -1 -0.5 0.5 Measured by Rank Correlation End of Forecast 141 Cell: I11 Forecast: Raffles Returns < Riskless Summary: Display Range is from 0.0% to 4.5% Entire Range is from 0.0% to 5.8% After 1,000 Trials, the Std. Error of the Mean is 0.0% Statistics: Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Value 1000 1.6% 1.4% 0.6% 1.1% 0.0% 0.94 3.57 0.69 0.0% 5.8% 5.8% 0.04% Forecast: Raffles Returns < Riskless 1,000 Trials FrequencyChart 985 Displayed .094 94 .071 70.5 .047 47 .024 23.5 .000 0.0% 1.1% 2.3% 3.4% 4.5% 142 Forecast: Raffles Returns < Riskless (cont'd) Cell: I11 Percentiles: Value 0.0% 0.4% 0.6% 0.8% 1.2% 1.4% 1.6% 2.0% 2.6% 3.2% 5.8% Percentile 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Sensitivity Chart Target Forecast: Raffles Returns < Riskless Raffles Equivalent yield -.81 Raffles Riskless Return .25 Raffles Rental Value .05 Raffles Target Return -.04 Raffles Current income -.03 -1 -0.5 0.5 Measured by Rank Correlation End of Forecast 143 Assumptions Assumption: Cell: C4 Raffles Current income Normal distribution with parameters: Mean $683 Standard Dev. $1 Raffles Current income Mean = $683 Selected range is from $681 to $685 Assumption: $680 $682 $683 $685 $686 Cell: C3 Raffles Equivalent yield Normal distribution with parameters: 5% - tile 5.0% 95% - tile 5.2% Raffles Equivalent yield Mean = 5.1% Selected range is from 5.0% to 5.2% 4.9% 5.0% 5.1% 5.2% 5.3% Cell: C5 Assumption: Raffles Rental Value Normal distribution with parameters: Mean $636 Standard Dev. $12 Raffles Rental Value Mean = $636 Selected range is from $604 to $668 Assumption: $600 $618 $636 $654 Raffles Riskless Return $672 Cell: C14 Beta distribution with parameters: 5% - tile 1.2% 95% - tile 2.3% Scale 3.5% Raffles Riskless Return Mean = 1.8% 0.8% 1.3% 1.8% 2.3% 2.8% Selected range is from 1.2% to 2.3% Assumption: Raffles Target Return Cell: C13 Beta distribution with parameters: 5% - tile 1.5% 95% - tile 10.0% Scale 17.1% Raffles Target Return Mean = 5.3% 0.0% 3.6% 7.1% 10.7% 14.3% 144 Selected range is from 0.0% to +Infinity End of Assumptions 145 Appendix 4.9 Crystal Ball Simulation Report for Shenton Simulation started on 7/21/04 at 23:01:08 Simulation stopped on 7/21/04 at 23:03:03 Forecast: Shenton Modified Duration Cell: C21 Summary: Display Range is from 17.68 to 18.45 years Entire Range is from 17.65 to 18.47 years After 1,000 Trials, the Std. Error of the Mean is 0.00 Statistics: Value 1000 18.05 18.05 --0.15 0.02 0.07 2.49 0.01 17.65 18.47 0.82 0.00 Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Forecast: Shenton Modified Duration 1,000 Trials FrequencyChart 997 Displayed .031 31 .023 23.25 .016 15.5 .008 7.75 .000 17.68 17.87 18.06 18.26 18.45 years 146 Forecast: Shenton Modified Duration (cont'd) Cell: C21 Percentiles: years 17.65 17.85 17.92 17.97 18.00 18.05 18.09 18.13 18.20 18.26 18.47 Percentile 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Sensitivity Chart Target Forecast: Shenton Modified Duration Shenton Equivalent Yield -.95 Shenton Rental Value .35 Shenton Current Income -.07 Shenton Target Return .05 Shenton Riskless Return -.02 -1 -0.5 0.5 Measured by Rank Correlation End of Forecast 147 Forecast: Shenton Return < Target Cell: I9 Summary: Display Range is from 0.0% to 38.5% percentage Entire Range is from 0.0% to 60.4% percentage After 1,000 Trials, the Std. Error of the Mean is 0.4% Statistics: Value 1000 8.4% 3.2% 0.0% 11.6% 1.4% 1.83 6.02 1.38 0.0% 60.4% 60.4% 0.37% Trials Mean Median Mode Standard Deviation Variance Skewness Kurtosis Coeff. of Variability Range Minimum Range Maximum Range Width Mean Std. Error Forecast: Shenton Return < Target 1,000 Trials FrequencyChart 959 Displayed .251 251 .188 188.2 .126 125.5 .063 62.75 .000 0.0% 9.6% 19.3% 28.9% 38.5% perc entage 148 [...]... combining the specific direct real estate equivalent-yield valuation model The achieved ex ante direct real estate investment risk model provides a meaningful insight on direct real estate investment risk behavior under a modified duration model Further modeling of other real estate investment risks like the low partial moment (LPM), the systematic risk, the total risk and the GARCH risk are explored on the. .. investigation of the non-linear exposure measurements of direct real estate systematic risk and direct real estate total risk under the ex ante duration risk, the time-varying beta risk and the GARCH (generalized autoregressive conditional heterogeneity) risk In this chapter, the author first reviews several traditional definitions and measures of direct real estate investment risk and then proposes... shed light on the pricing of underlying direct real estate assets consisting of a mortgage asset pool 1.3 Research Objectives The Four main objectives of this research consist of the following: • To rigorously model an ex ante risk measure of the direct real estate systematic risk and the direct real estate total risk, in terms of the non-linear exposure to movements in the direct real estate yield;... real estate systematic risk modeling, while the second part is concerned with the parametric modeling of a unique and rigorous ex ante direct real estate risk measure and return estimation Thus, the first part of the theoretical framework of analysis covers the following: The modified duration Model, the direct real estate duration and the direct real estate return volatility relative to a market index;... Estimation of the volatility of the real estate (or sector) return, relative to the market, via equation (1.11), offers us some meaningful insights Equation (1.11) reveals that the β of a direct real estate asset’s return depends on the relative size of the duration of the direct real estate asset and the real estate market as well as the volatility of changes in the real estate yields The importance of the. .. captures the risks of stocks and helps explain the cross section of stock returns Can the duration measure of direct real estate investment assets capture the risks of the real estate investment? Answering these questions offers good potential in a number of areas such as real estate expected return estimation, asset allocation, portfolio management, risk monitoring and performance measurement and will... discussed The corresponding risk measurement fitness problem is also discussed In the end of this chapter, literature review on the real estate duration and equity duration is made Chapter three presents a theoretical and empirical investigation of the non-linear exposure measurements of direct real estate systematic risk and direct real estate total risk under the ex ante duration risk, the time-varying... overcome the limited data availability for direct real estate investments and the poor quality (i.e the temporal lagging error) of appraisal-based real estate return data, the investigative research proposes a unique ex ante modeling of direct real estate risk To investigate such ex ante modeling, this research makes use of well-defined financial theory (viz the duration and convexity together with the. .. estimate the direct real estate duration 8 beta and the time-varying beta, within the context of Singapore’s real estate market that comprises the luxury residential, the prime office and the retail sectors; • To restructure the resulting and ex ante direct real estate modified duration model in order to estimate the direct real estate total risk, which in turn is assessed in comparison with the GARCH... four, a new parametric modeling of the ex ante direct real estate risk measure and the corresponding return estimation is discussed However, comparatively the direct real estate risk modeling in Chapter three does not make any strict requirement of the real estate return distributions, Chapter four’s parametric modeling takes the Beta distribution function to represent the direct real estate return distribution . Similarly, an exploration of real estate duration under an ex ante analysis is of the essence and will surely direct us to a better understanding of real estate investment risk and real estate asset. products in the direct real estate investment markets. Owing to limited and empirical data availability, an ex ante measurement and the modeling of direct real estate investment risk would be. non-linear exposure measurements of direct real estate systematic risk and direct real estate total risk under the ex ante duration risk, the time-varying beta risk and the GARCH (generalized autoregressive