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

Why volatility is (still) an inappropriate risk measure for

real estateby

Moritz Müller, Carsten Lausberg, and Stephen Leeprepared for the 18th Annual Conference

of the European Real Estate Society,June 15-18, 2011 in Eindhoven

OUTLINE

Literature

Appropriatenessof volatility

Underlying assumptions

Empirical study

Conclusion

Background

Motivation and approach for this studyMotivation:- 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- Empirical analysis 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

Literature



Empirical study

Background

© Müller/Lausberg/Lee 2011, p. 2

Conclusion

History of volatility as a real estate risk measurePioneering works:

Questioning of the normality assumption

Application of downside risk measures

Forward looking approach

- Friedmann (1971)- Phyrr (1973)- Webb/Rubens (1987)- Firstenberg et 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



Empirical study

Background

Conclusion


Appropriateness of volatility as a risk measureVarious sets of axioms exist to assess the general appropriateness of risk measures

The most important set of axioms was defined by Artzner et 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



Empirical study

Background

Volatility does not satisfy the axiom of monotonicity and therefore cannot be considered an appropriate risk measure

Conclusion


Underlying assumptions of volatilityThe use of historical volatility as a risk measure is generally based on several assumptions

The most important assumptions are:(1) Significant data base(2) Market efficiency and random-walk(3) Definition of risk as the variation of returns(4) Normally distributed returns

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Empirical study

Background

Do these assumptions apply in a real estate context?

Conclusion


(1) Significant data baseHistorical real estate return data has to be sufficient regarding quantity and qualityIt is frequently argued that historical real estate return series do not cover a whole real estate cycleSmoothing occurs when appraisal-based data is used which leads historical volatility to understate the actual real estate riskNo existing model to desmooth appraisal-based data is perfectLiquidity risk is not captured when the volatility is calculated based on historical returns

Literature



Empirical study

Background

Available data is another major problem when historical volatility is used as a risk measure

Conclusion


(2) Market efficiency and random-walkUsing 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 predictableDue to autocorrelation of historical real estate returns, an increasing number of academics questions the random-walk hypothesisReal estate markets are–at best–weak form efficient since sufficient real estate data is rarely available and transactions occur infrequently on local markets

Literature



Empirical study

Background

It is questionable to use historical volatility as a risk measure since the random-walk hypothesis is unlikely to apply for real estate returns

Conclusion


(3) Definition of risk as the variation of returnsThe definition of risk as a positive and negative deviation of an expected return is increasingly questionedInvestors are more concerned with the chance to sustain a loss rather than with the chance to realize excess profit of the same amountDue to psychological effects and explainable by the diminishing marginal utility

Literature



Empirical study

Background

Employing volatility as a risk measure that captures upside as well as downside potential is not in line with most investors’ intuition

Conclusion


(4) Normally distributed returnsNormal distribution of real estate returns was not questioned until the early 1990sBased 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 indicesOnly when longer holding period data is analyzed, it seems more likely for the returns to follow a normal distribution

Literature



Empirical study

Background

It is precarious to assume normality for real estate return distributions and to use volatility as a real estate risk measure

Conclusion

- Myer/Webb (1992/1994)- King/Young (1994)- Byrne/Lee (1997)

- Brown/Matysiak (2000)- Lizieri/Ward (2001)- Maurer et al. (2004)

- Young et al. (2006)


Analysis of German RE return distributions (1/2)Analysis–on individual property and index level–whether German real estate returns are normally distributedData:- 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



Empirical study

Background

Conclusion


Analysis of German RE return distributions (2/2)Analyses:- Time-series analysis of individual properties returns- Cross-sectional analysis of individual properties returns- Analysis of German real estate market returnsApproach- Estimation of skewness and kurtosis figures- Calculation of various normality tests:

• Jarque Bera (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



Empirical study

Background

Conclusion


Time-series analysis of property returns (1/2)Analysis of total return for 939 properties for the period 1996-2009

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Empirical study

Background

Table 1: Distributional characteristics of total returns of 939 properties in the IPD databank

Conclusion


Time-series analysis of property returns (2/2)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 propertiesDue to the relatively short period and comparably few data points, the significance of these results is questionable

Literature



Empirical study

Background

Table 2: Number of properties with normally distributed returns for portfolio

Conclusion


Cross-sectional analysis of property returns (1/3)Determination of distributional characteristics of total returns

Returns are not normally distributed for all years under observationThe distributions are negatively skewed and leptokurtic

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Empirical study

Background

Table 3: Distributional characteristics as well as JB and K-S statistics of total returns per year: All properties

Conclusion


Further normality tests give the same results

The same results are obtained when individual sub-sectors are analysed

Cross-sectional analysis of property returns (2/3)

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Empirical study

Background

Table 4: Further normality tests for total returns per year: All properties

Conclusion


-50

-40

-30

-20

-10

0

10

20

30

40

50

-240% -200% -160% -120% -80% -40% 0% 40% 80%

Total returnQ

uant

iles

of N

orm

al

-100% -90% -80% -70% -60% -50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70%

Total returnsTheoretical normal distribution

10% 20% 30% 40% 50% 60% 70%0%-10%-20%-30%-40%-60% -50%-70%

Cross-sectional analysis of property returns (3/3)Illustration of the properties’ return distribution and Q-Q Plot when all returns for the whole period are combined

Literature



Empirical study

Background

Figure 1: Density function and QQ-Plot of log annual total returns for all properties over the period 1996-2009

Conclusion


Time-series analysis of return distributions of the DIX market index by the IPD Investment Property Databank and the GPI index by BulwienGesa

Analysis of German RE market returns (1/2)

Literature



Empirical study

Background

Table 5: Distributional characteristics of the German IPD index (1996-2010) and the GPI Index (1995-2010)

Conclusion


Statistic p-value Normality? Statistic p-value Normality? Statistic p-value Normality? Statistic p-value Normality?IPD All Prop. 0.14 > 0.1 not rejected 0.37 0.43 not rejected 0.05 0.48 not rejected 0.05 0.52 not rejected

Office 0.12 > 0.1 not rejected 0.34 0.50 not rejected 0.04 0.62 not rejected 0.04 0.64 not rejectedRetail 0.14 > 0.1 not rejected 0.26 0.71 not rejected 0.05 0.58 not rejected 0.05 0.53 not rejectedResidential 0.20 > 0.1 not rejected 0.56 0.15 not rejected 0.10 0.13 not rejected 0.08 0.15 not rejectedIndustrial 0.25 0.02 rejected 1.28 0.00 rejected 0.21 0.00 rejected 0.18 0.01 rejectedOther 0.17 > 0.1 not rejected 0.64 0.10 not rejected 0.10 0.11 not rejected 0.09 0.15 not rejected

GPI Index 0.16 > 0.1 not rejected 0.46 0.26 not rejected 0.08 0.23 not rejected 0.07 0.21 not rejected

Anderson Darling Cramer-von Mises WatsonSector

Lilliefors

Statistic p-value Normality?IPD All Prop. 15 3.43% 3.82% 5.41% 0.61% 1.50% -0.56 2.23 1.15 0.56 not rejected

Office 15 2.98% 3.05% 5.64% -0.75% 2.03% -0.49 2.26 0.93 0.63 not rejectedRetail 15 4.54% 4.23% 6.79% 2.54% 1.18% 0.06 2.26 0.35 0.84 not rejectedResidential 14 4.48% 4.99% 6.24% 1.30% 1.43% -0.90 2.92 1.88 0.39 not rejectedIndustrial 14 4.98% 5.90% 7.40% -2.94% 2.88% -1.74 5.26 10.07 0.01 rejectedOther 15 3.43% 3.72% 4.93% 0.05% 1.33% -1.19 3.87 3.99 0.14 not rejected

GPI Index 16 5.94% 6.63% 10.62% 0.00% 3.26% -0.29 1.78 1.21 0.55 not rejected

SD Skewness KurtosisJarque Bera Test

SectorObser-vations Mean Median Max. Min.

Normality cannot be rejected for the GPI index and the IPD All property index as well as most sub-subsectorsSame 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

Analysis of German RE market returns (2/2)

Literature



Empirical study

Background

Conclusion


Figure 2: Q-Q Plots for IPD index returns: All property and sub-indices office and retail

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

Models of return distributions (1/3)

Literature



Empirical study

Background

Conclusion


Table 6: Frequency of theoretical distributions to be ranked as the most likely distribution – All property

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



Empirical study

Background

Conclusion


Table 7: Three most likely theoretical distributions to fit the cross-sectional data – All property

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 propertiesIn 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



Empirical study

Background

Conclusion


Table 8: Three most likely theoretical distributions to fit the IPD and the GPI market index data

Results and limitations of our studyResults- 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 aboveLimitations- 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

Literature



Empirical study

Background

Conclusion


Same results as in Müller/Lausberg (2010)

Volatility is not an appropriate risk measure for real estate, at least not for individual propertiesAlternatives:- 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 measuresState 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

Conclusion

A lot of work ahead!

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Empirical study

Background

Conclusion


Many Thanks to…

BulwienGesa AGIPD Investment Property Databank GmbH

Questions or Comments?

Literature



Empirical study

Background

Conclusion


Contact:

Campus of Real EstateNürtingen-Geislingen University Parkstr. 473312 Geislingen, Germany

Carsten LausbergProfessor of Real Estate [email protected]

Contact:

Cass Business School106 Bunhill Row, London, EC1Y 8TZ UK

Moritz MüllerMSc Real Estate Investment [email protected]

Stephen Lee Faculty of [email protected]

References (1/2)

Literature



Empirical study

Outlook

Conclusion

BackgroundArtzner et al. (1997): Artzner, P., Delbaen, F., Eber J.-M. and Heath, D., Thinking Coherently, in: Risk Magazine, Vol. 10, No. 11, 1997, pp. 68–71.Artzner et 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 under Conditions of 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 whole story, 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., Why Diversification Doesn’t Work – Flaws in Modern Portfolio Theory turn Real Estate Portfolio Managers back to old-fashioned Underwriting, 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., Characteristics of German Real Estate Return Distributions: Evidence from Germany and Comparison to the 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.


References (2/2)

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Empirical study

Outlook

Conclusion

BackgroundMyer/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. 48-78Sing/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., Evaluating Risk 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. and Southard, 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: Debt Applications, in: Real Estate Finance, Vol. 18, No. 3, 2001, pp. 29-41Wheaton et al. (2002): Wheaton, W.C., Torto, R.G., Southard, J.A. and Sivitanides, 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


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