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Why volatility is (still) an inappropriate risk measure for real estate

Why volatility is (still) an inappropriate risk measure for real estate. OUTLINE. Background. by Moritz Müller, Carsten Lausberg, and Stephen Lee prepared for the 18th Annual Conference of the European Real Estate Society, June 15-18, 2011 in Eindhoven. Literature. Appropriateness

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Why volatility is (still) an inappropriate risk measure for real estate

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  1. Why volatility is (still) an inappropriate risk measure for real estate OUTLINE Background by Moritz Müller, Carsten Lausberg, and Stephen Lee prepared for the 18th Annual Conference of the European Real Estate Society,June 15-18, 2011 in Eindhoven Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion

  2. Motivation: General motivation is to improve the current real estate risk measures This paper wants to contribute to this objective by assessing whether volatility is an appropriate measure for real estate risk Approach: Overview of existent literature that deals with volatility as a real estate risk measure Assessment of the general appropriateness of volatility as a risk measure Review whether volatility’s assumptions do apply in the real estate context Empiricalanalysis of return distributions of 223 German properties NEW: Empirical analysis of return distributions of 939 German properties (including the fitting of theoretical distributions to the observed frequency distributions) Comment about possible alternatives as real estate risk measures Motivation and approach for this study Background Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion

  3. History of volatility as a real estate risk measure Background • Pioneering works: • Questioning of the normality assumption • Application of downside risk measures • Forward looking approach • Friedmann (1971) • Phyrr (1973) • Webb/Rubens (1987) • Firstenberget al. (1988) • Geltner (1989) • Myer/Webb (1992/1994) • Young/Graff (1995) • Maurer et al. (2004) • Young et al. (2006) • Sivitanides (1998) • Sing/Ong (2000) • Hamelink/Hoesli(2004) • Wheaton et al. (1999/2001a/2001b/2002) Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion

  4. Appropriateness of volatility as a risk measure Background • Various sets of axioms exist to assess the general appropriateness of risk measures • The most important set of axioms was defined by Artzneret al. (1997/1999) • Definition of four axioms that a risk measure has to satisfy in order to be considered appropriate: • Subadditivity • Positive homogeneity • Translation invariance • Monotonicity Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Volatility does not satisfy the axiom of monotonicity and therefore cannot be considered an appropriate risk measure

  5. Underlying assumptions of volatility Background • The use of historical volatility as a risk measure is generally based on several assumptions • The most important assumptions are: • Significant data base • Market efficiency and random-walk • Definition of risk as the variation of returns • Normally distributed returns Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Do these assumptions apply in a real estate context?

  6. (1) Significant data base Background Historical real estate return data has to be sufficient regarding quantity and quality It is frequently argued that historical real estate return series do not cover a whole real estate cycle Smoothing occurs when appraisal-based data is used which leads historical volatility to understate the actual real estate risk No existing model to desmooth appraisal-based data is perfect Liquidity risk is not captured when the volatility is calculated based on historical returns Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Available data is another major problem when historical volatility is used as a risk measure

  7. (2) Market efficiency and random-walk Background Using historical volatility as a proxy for real estate risk is based on the assumption that real estate markets are efficient and returns are not predictable Various studies reveal that real estate returns are partly predictable Due to autocorrelation of historical real estate returns, an increasing number of academics questions the random-walk hypothesis Real estate markets are–at best–weak form efficient since sufficient real estate data is rarely available and transactions occur infrequently on local markets Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion It is questionable to use historical volatility as a risk measure since the random-walk hypothesis is unlikely to apply for real estate returns

  8. (3) Definition of risk as the variation of returns Background • The definition of risk as a positive and negative deviation of an expected return is increasingly questioned • Investors are more concerned with the chance to sustain a loss rather than with the chance to realize excess profit of the same amount • Due to psychological effects and explainable by the diminishing marginal utility Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Employing volatility as a risk measure that captures upside as well as downside potential is not in line with most investors’ intuition

  9. (4) Normally distributed returns Background • Normal distribution of real estate returns was not questioned until the early 1990s • Based on empirical studies, various authors found evidence that real estate returns are likely to be not normally distributed, for example: • Normality has to be rejected for individual property returns and for most market indices • Only when longer holding period data is analyzed, it seems more likely for the returns to follow a normal distribution Literature Appropriateness of volatility • Myer/Webb (1992/1994) • King/Young (1994) • Byrne/Lee (1997) • Brown/Matysiak (2000) • Lizieri/Ward (2001) • Maureret al. (2004) • Young et al. (2006) Underlying assumptions Empirical study Conclusion It is precarious to assume normality for real estate return distributions and to use volatility as a real estate risk measure

  10. Analysis of German RE return distributions (1/2) Background • Analysis–on individual property and index level–whether German real estate returns are normally distributed • Data: • Individual returns provided by IPD Germany for all 939 German properties with return histories of at least 10 years: • 523 office • 189 retail • 152 residential • 75 others • Market data provided by BulwienGesa and IPD Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion

  11. Analysis of German RE return distributions (2/2) Background • Analyses: • Time-series analysis of individual properties returns • Cross-sectional analysis of individual properties returns • Analysis of German real estate market returns • Approach • Estimation of skewness and kurtosis figures • Calculation of various normality tests: • JarqueBera (JB) test • Kolmogorov-Smirnov (K-S) test • Lilliefors (L) test • Shapiro-Wilk (S-W) test • Anderson-Darling (A-D) test • Cramer-von-Mises (C-M) test • Watson (W) test • Fitting of theoretical distributions to observed frequency distributions Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion

  12. Time-series analysis of property returns (1/2) Background Analysis of total return for 939 properties for the period 1996-2009 Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Table 1: Distributional characteristics of total returns of 939 properties in the IPD databank

  13. Time-series analysis of property returns (2/2) Background When considering all properties, normality cannot be rejected in more than 50% of the cases for all tests The time-series analysis reveals that normality cannot be rejected for the majority of the properties Due to the relatively short period and comparably few data points, the significance of these results is questionable Literature Appropriateness of volatility Underlying assumptions Table 2: Number of properties with normally distributed returns for portfolio Empirical study Conclusion

  14. Cross-sectional analysis of property returns (1/3) Background Determination of distributional characteristics of total returns Returns are not normally distributed for all years under observation The distributions are negatively skewed and leptokurtic Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Table 3: Distributional characteristics as well as JB and K-S statistics of total returns per year: All properties

  15. Cross-sectional analysis of property returns (2/3) Background Further normality tests give the same results The same results are obtained when individual sub-sectors are analysed Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Table 4: Further normality tests for total returns per year: All properties

  16. Cross-sectional analysis of property returns (3/3) Background Illustration of the properties’ return distribution and Q-Q Plot when all returns for the whole period are combined Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Figure 1: Density function and QQ-Plot of log annual total returns for all properties over the period 1996-2009

  17. Analysis of German RE market returns (1/2) Background Time-series analysis of return distributions of the DIX market index by the IPD Investment Property Databank and the GPI index by BulwienGesa Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Table 5: Distributional characteristics of the German IPD index (1996-2010) and the GPI Index (1995-2010)

  18. Analysis of German RE market returns (2/2) Background Normality cannot be rejected for the GPI index and the IPD All property index as well as most sub-subsectors Same results are apparent when examining the Q-Q Plots of the IPD index These results are in line with other studies that analyze return distributions of annual market returns Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Figure 2: Q-Q Plots for IPD index returns: All property and sub-indices office and retail

  19. Models of return distributions (1/3) Background According to three different goodness of fit tests, the Logistic distribution is the most likely theoretical distribution to fit the time-series return data of individual German properties Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Table 6: Frequency of theoretical distributions to be ranked as the most likely distribution – All property

  20. Models of return distributions (2/3) Background Similarly, the Logistical distribution was ranked as the most likely theoretical distribution to fit the empirical cross-sectional data in thirteen out of fourteen years--according to the Chi-Square test (similar results where obtained from the A-D test and the K-S test) Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Table 7: Three most likely theoretical distributions to fit the cross-sectional data – All property

  21. Models of return distributions (3/3) Background The Chi-Square test suggest that the Logistic distribution is most likely to be the best fit for the IPD All Property market index and most appropriately fits the sub-indices for residential, industrial and other properties In contrast, the Triang distribution is most likely to be the best fit for the GPI market index Similar results where obtained for the Kolmogorov-Smirnov and the Anderson-Darling test Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion Table 8: Three most likely theoretical distributions to fit the IPD and the GPI market index data

  22. Results Annual property returns: normality cannot be rejected Property returns using cross-sectional analysis: normality is likely to be rejected Annual market returns: normality cannot be rejected Distribution fitting: Logistic distribution is most likely to be best fit for all of the above Limitations Few data points Only annual total returns Normality is more likely to be rejected when shorter holding periods for a longer overall given period are analysed Results and limitations of our study Background Same results as in Müller/Lausberg (2010) Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion

  23. Conclusion Background • Volatility is not an appropriate risk measure for real estate, at least not for individual properties • Alternatives: • A set of different risk and return measures • Downside risk measures, e.g., VaR, MVaR, LPM, MDD • Qualitative risk measures, e.g., scores and rating grades, … ideally combined with quantitative measures • State of the art: Real estate lending ratings that meet the criteria of the advanced approach of the Basel Accord. Example: • Quantitative: probability estimation derived from a Monte Carlo simulation of future cash flows • Qualitative: subjective opinion on the location quality of a property • Our research shows that real estate industry does not meet this standard Literature Appropriateness of volatility Underlying assumptions Empirical study Conclusion A lot of work ahead!

  24. Many Thanks to… BulwienGesa AG IPD Investment Property Databank GmbH Background Literature Appropriateness of volatility Underlying assumptions Questions or Comments? Empirical study Conclusion

  25. Contact: Cass Business School 106 Bunhill Row, London, EC1Y 8TZ UK Moritz Müller MSc Real Estate Investment Programme moritz.mueller@ondos.de Stephen Lee Faculty of Finance Stephen.Lee.1@city.ac.uk Contact: Campus of Real Estate Nürtingen-Geislingen University Parkstr. 4 73312 Geislingen, Germany Carsten Lausberg Professor of Real Estate Banking carsten.lausberg@hfwu.de

  26. References (1/2) Background Artzneret al. (1997): Artzner, P., Delbaen, F., Eber J.-M. and Heath, D., ThinkingCoherently, in: Risk Magazine, Vol. 10, No. 11, 1997, pp. 68–71. Artzneret al. (1999): Artzner, P., Delbaen, F., Eber J.-M. and Heath, D., Coherent Measures of Risk, in: Mathematical Finance, Vol. 9, No. 3, 1999, pp. 203-228. Brown/Matysiak (2000): Brown, G.R., Matysiak, G.A., Real Estate Investment - A Capital Market Approach, Harlow (UK) u.a.: Financial Times Prentice Hall, 2000. Byrne/Lee (1997): Byrne, P., Lee, S.L., Real Estate Portfolio Analysis underConditionsof Non-Normality - The Case of NCREIF, in: Journal of Real Estate Portfolio Management, Vol. 3, No. 1, 1997, pp. 37-46. Firstenberg et al. (1988): Firstenberg, P.M., Ross, S.A., Zisler, R.C., Real estate: The wholestory, in: Journal of Portfolio Management, Vol. 14, No. 3, 1988, pp. 22-34. Friedman (1971): Friedman, H.C., Real Estate Investment and Portfolio Theory, in: Journal of Financial and Quantitative Analysis, Vol. 6, No. 2, 1971, pp. 861-874. Geltner (1989): Geltner, D., Estimating Real Estate's Systematic Risk from Aggregate Level Appraisal-Based Returns, in: Real Estate Economics, Vol. 17, No. 4, 1989, pp. 463-481. • Gleißner (2006): Gleißner, W., Risikomaße, Safety-First-Ansätze und Portfoliooptimierung, in: Risiko Manager, No. 13, 2006, pp. 17-23. • Hamelink/Hoesli (2004): Hamelink, F.; Hoesli, M., Maxi-mum Drawdown and the Allocation to Real Estate, in: Journal of Property Research, Vol. 21, No. 1, 2004, pp. 5-29. • Jarque/Bera (1987): Jarque, C.M., Bera, A.K., A test for normality of observations and regression residuals, in: International Statistical Review, Vol. 55, No. 2, 1987, pp. 163-172. • King/Young (1994): King, D.A. Jr., Young, M.S., WhyDiversificationDoesn’t Work – Flaws in Modern Portfolio Theory turn Real Estate Portfolio Managers back toold-fashionedUnderwriting, in: Real Estate Review, Vol. 24, No. 2, 1994, pp. 6-12. • Lizieri/Ward (2001): Lizieri, C., Ward, C., The Distribution of Commercial Real Estate Returns, in: Knight/Satchell (2001), pp. 47-74. • Maurer et al. (2004): Maurer, R., Reiner, F., Sebastian, S., Characteristicsof German Real Estate Return Distributions: Evidencefrom Germany andComparisontothe U.S. and U.K., in: Journal of Real Estate Portfolio Management, Vol. 10, No. 1, 2004, pp. 59-76. • Müller/Lausberg (2010): Müller, M., Lausberg, C., Why volatility is an inappropriate risk measure for real estate; Conference Paper, ERES Conference in Milan, June 2010. Literature Appropriateness of volatility Underlying assumptions Empirical study Outlook Conclusion

  27. References (2/2) Background • Myer/Webb (1992): Myer, F.C. N., Webb, J.R., Return Properties of Equity REITs, Common Stocks, and Commercial Real Estate: A Comparison, in: Journal of Real Estate Research, Vol. 8, No. 1, 1992, pp. 87-106. • Myer/Webb (1994): Myer, F.C. N., Webb, J.R., Statistical Properties of Returns: Financial Assets versus Commercial Real Estate, in: Journal of Real Estate Finance and Economics, Vol. 8, No. 3, 1994, pp. 267-282. • Phyrr (1973): Phyrr, S.A., A Computer Simulation Model to measure the Risk in Real Estate Investment, in: Journal of the American Real Estate & Urban Economics Association, Vol. 1, No. 1, 1973, pp. 48-78 • Sing/Ong (2000): Sing, T.F., Ong, S.E., Asset Allocation in a Downside Risk Framework, in: Journal of Real Estate Portfolio Management, Vol. 6, No. 3, 2000, pp. 213-223. • Sivitanides (1998): Sivitanides, P.S., A Downside-Risk Approach to Real Estate Portfolio Structuring, in: Journal of Real Estate Portfolio Management, Vol. 4, No. 2, 1998, pp. 159-168. • Webb/Rubens (1987): Webb, J.R., Rubens, J.H., How much in real estate? A surprising answer, in: Journal of Portfolio Management, Vol. 13, No. 3, 1987, pp. 10-14. • Wheaton et al. (1999): Wheaton, W.C., Torto, R.G., Sivitanidis, P. and Southard, J., EvaluatingRisk in Real Estate, in: Real Estate Finance, Vol. 16, No. 2, 1999, pp. 15-22. • Wheaton et al. (2001a): Wheaton, W.C., Torto, R.G., Sivitanidis, P. andSouthard, J., Hopkins, R.E. and Costello, J.M., Real Estate Risk: A Forward-Looking Approach, in: Real Estate Finance, Vol. 18, No. 3, 2001, pp. 20-28. • Wheaton et al. (2001b): Wheaton, W.C., Torto, R.G., Southard, J.A. and Hopkins, R.E., Real Estate Risk: Evaluating Real Estate Risk: DebtApplications, in: Real Estate Finance, Vol. 18, No. 3, 2001, pp. 29-41 • Wheaton et al. (2002): Wheaton, W.C., Torto, R.G., Southard, J.A. andSivitanides, P.S., Real Estate Risk: Evaluating Real Estate Risk: Equity Appli-cations, in: Real Estate Finance, Vol. 18, No. 4, 2002, pp. 7-17. • Young/Graff (1995): Young, M.S.; Graff, R.A.: Real Estate Is Not Normal: A Fresh Look at Real Estate Return Distributions, in: Journal of Real Estate Finance and Economics, Vol. 10, No. 3, 1995, pp. 225-259. • Young et al. (2006): Young, M.S.; Lee, S.L.; Devaney, S.P.: Non-Normal Real Estate Return Distributions by Property Type in the UK, in: Journal of Property Research, Vol. 23, No. 2, 2006, pp. 109-133 Literature Appropriateness of volatility Underlying assumptions Empirical study Outlook Conclusion

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