francesca battaglia, claudio porzio gabriele sampagnaro

The quality of data of real estate direct market: does the lack of standardization affect the predictability of returns? Francesca Battaglia, Claudio Porzio Gabriele Sampagnaro

Department of research in Business and Finance at University Parthenope, Via Medina 40, Naples 80133, Italy;Email: [email protected] Phone +39 0815474851

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The aim of the paper is an investigation on the reliability of historical returns for the Italian property market, where the quality of information seems not standardized.

In Italy, such as for many other countries, the returns indices for direct markets are provided by several data-sources that differ among them in terms of methodology adopted (appraisal-based vs transaction-based approaches) and in term of indexs composition.

These differences produce a lack of informative standardization that could negatively affects the predictability of market and that can be explained by a strong real estate markets fragmentation, as well as informative and markets organizational inefficiency.

In our paper we examine the implications of this lack of standardisation around some topic such as: IRR of a fund, asset allocation and portfolio management.

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Number of data sources: 4Object of information: property valuesReal estate categories:Geographical/Urban area: 1) Milan2) ItalyData frequency: quarterly (by interpolation)Minimum time interval: 2002-2007Maximum time interval: 1993-2007 Nomisma, OSMI, Tecnocasa, Scenari ImmobiliariMilanResidentialCommercialIndustrialOffice*

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Table 1. Real estate time series length and urban areaReal Estate market: ItalyReal Estate CategoryDataSource#1DataSource#2DataSource#3DataSource#4Residential1988-20071997-2007n.a2002-2007Commercial1988-20071997-2007n.a2002-2007Office1988-20071997-2007n.a2002-2007Industrialn.a.1997-2007n.a2002-2007Real Estate market: MilanReal Estate CategoryDataSource#1DataSource#2DataSource#3DataSource#4Residential1965-20071993-20071995-2007n.aCommercial1965-20071993-20071997-2007n.aOfficen.a.1993-20071997-2007n.aIndustrialn.a.1993-20071997-2007n.aSemiannual data are interpolated to provide quarterly data

Geographical Area: ITALYTime interval: 2002-2007*The table shows a significant difference among the average values of the indices and among the real estate categories covered. This result can be considered as a preliminary indication of a lack of data sources, although they are referring to the same phenomenon (the italian real estate market).

ResidentialOfficeCommercialIndustrialTime Series#1MEAN 223.1** Standard Deviation (69.5)180.9** (46.7)168.6** (40.9)N. A.Time Series#2218.3** (82.8)127.6 ** (27.3)131.0** (27.1)119.2** (18.0)Time Series#3108.5** (6.4)108.2** (4.3)N. A..104.0** (3.1)Time Series#4N. A.N. A.N. A.N. A.

Geographical Area: MilanTime interval: 1997-2007*So we get the same result for the market of Milan. In these cases, the differences are smaller. A possible explanation for this minor discrepancy, it might be provided by the increased centralization of information (for the city of Milan) and a greater homogeneity of the sample of properties underlying each index. In the previous case the indices were constructed with reference to the use of samples belonging to different urban areas.

ResidentialOfficeCommercialIndustrialDataSource#1MEAN 139.0** Standard Deviation (39.8)N. A.144** (32.3)N. A.DataSource#2115.9** (28.2)103.5** (20.4)116.9** (28.4)N. A.DataSource#3128.9** (33.4)136.1** (26.4)135.2** (26.6)108.4** (15.0)DataSource#4161.4** (45.3)N. A.121.6** (25.2)N. A.

Average Correlation= -0.3668Average Correlation= 0.6318*Geographical Area: ITALY

RESIDENTIALDataSource#1DataSource#2DataSource#3DataSource#11DataSource#20.27001DataSource#3-0.6722-0.69821

OFFICEDataSource#1DataSource#2DataSource#3DataSource#11DataSource#20.62331DataSource#30.55080.72121

INDUSTRIALDataSource#2DataSource#30.4401

COMMERCIALDataSource#1DataSource#2-0.0867

Average Correlation = -0.408Average Correlation= 0.169*Geographical Area: MILAN

RESIDENTIALSeries#1Series#2Series#3Series#4Series#11Series#20.452**1Series#3 0.583**0.893**1Series#4-0.2390.2640.497**1

CommercialSeries#1Series#2Series#3Series#4Series#11Series#20.3524**1Series#30.6421**0.4125**1Series#4-0.0188-0.1623-0.2098

OFFICESeries#2Series#30.7484**

To investigate around the severity of the differences among data source we employed a returns ratio test. Specifically, the ratio R was calculated as the ratio between two comparable series: (where:X and Y: are time series provided by different source but related to the same real estate category. m: is the length of time series, Interpretation: the closer the ratio gets to one, the closer the two series analyzed are statistically equal; conversely, the further the ratio gets away from one, the less homogeneous the series are. Since it is certainly important to verify the significance of the relationship between the two series, it was decided to test the null hypothesis H0: ratio = 1 by using the F test

Geographical Area: ITALYTime interval: 2002-2007

*Geographical Area: MILANTime interval: 2002-2007

*The ratio analysis provide an equivalence test among the real estate categories data provided by 4 data source available.The closer the ratio gets to one, the closer the two series analyzed are statistically equal and viceversathe results show a more marked difference for the data pertains to Italy. Probably one of the reasons is the increased centralization of the information provided in a single urban area (milan) are compared with a wider (italy) and more geographically dispersed

Urban AreaIntra-Class Average RatioResidentialCommercialOfficeItaly1.512 1.2501.382Milan1.0551.1731.371

*The results from previous section, especially those referred to the national indices, support the conception of an inefficient informative real-estate market that requires information to become centralized and data collection methods to be standardised.

To confirm this, it would be necessary to implement a further level of investigation and testify the existence of a long-term relationship that.With this aim, we perform a cointegration between the historical series referring to the entire domestic market. In order to take advantage of the wide breadth of property values for each of the historical series, the historical series with observation time-intervals less than seven years were excluded from the cointegration analysis. Imposing this selection criterion, resulted in six historical series originating from two real-estate sources (Source #1-Italy and Source #2-Italy) linked to the residential, shop and office sectors.

*Figure 3. Summary of cointegration analysis results

*Residual-based test for cointegration between DATA-Source #1 and #2

RESIDENTIAL-ITALY

Table 6RESIDENTIALItalia (1997/jan-2008/jan) - data quarterly - Levels/Regression

R2Adj Rt-ratiop-value0.9480.9471.5928.470.000Cointegration AnalysisResidual Based TestTest statisticValueCritical valueCRDWaDW0.0521.03ADFbADF-t-0.744 (lag 1)-3.5136PP cZZt-2.33-1.56-19.42-3.52aCritical Values are reported in Engle and Yoo (1987)bCritical Values for ADF are from MacKinnon (1991). The lag length was chosen according to Schwartz criterioncCritical values are taken from Philips and Ouliaris (1990)

Table 9RESIDENTIALItalia (1997/jan-2008/jan) - data quarterly 1st differences/regression

R2Adj Rt-ratiop-value0.07390.07240.6341.830.074Cointegration AnalysisResidual-based testTest statisticValueCritical valueCRDWaDW0.4951.03ADFbADF-t-2.545 (lag 1)-3.5136PP cZZt-18.2-3.47-19,34-3.52aCritical Values are reported in Engle and Yoo (1987)bCritical Values for ADF are from MacKinnon (1991). The lag length was chosen according to Schwartz criterioncCritical values are taken from Philips and Ouliaris (1990)


OFFICE-ITALY

Table 7Uffici Italia (1997/jan-2008/jan) - data quarterly - Levels/Regression

R2Adj Rt-ratiop-value0.98630.9860.91656.320.000Cointegration AnalysisResidual-based testTest statisticValueCritical valueCRDWaDW0.12611.03ADFbADF-t-3.264 (lag 3)-4.3993PP cZZt-5.91-1.72-19.42-3.52aCritical Values are reported in Engle and Yoo (1987)bCritical Values for ADF are from MacKinnon (1991). The lag length was chosen according to Schwartz criterioncCritical values are taken from Philips and Ouliaris (1990)

Table 10Uffici Italia (1997/jan-2008/jan) - data quarterly 1st differences/regression

R2Adj Rt-ratiop-value0.3880.3740.7455.230.372Cointegration AnalysisResidual-based testTest statisticValueCritical valueCRDWaDW0.8781.03ADFbADF-t-3.195-3.5136PP cZZt-18.1-3.306-19.34-3.52aCritical Values are reported in Engle and Yoo (1987)bCritical Values for ADF are from MacKinnon (1991). The lag length was chosen according to Schwartz criterioncCritical values are taken from Philips and Ouliaris (1990)


COMMERCIAL-ITALY

Table 8Negozi Italia (1997/jan-2008/jan) - data quarterly - Levels/Regression

R2Adj Rt-ratiop-value0.9530.9520.81829.880.000Cointegration AnalysisResidual-based testTest statisticValueCritical valueCRDWaDW0.1041.03ADFbADF-t-2.946 (lag 1)-3.5136PP cZZt-5.03-1.53-19.42-3.52aCritical Values are reported in Engle and Yoo (1987)bCritical Values for ADF are from MacKinnon (1991). The lag length was chosen according to Schwartz criterioncCritical values are taken from Philips and Ouliaris (1990)

Table 11Negozi Italia (1997/jan-2008/jan) - data quarterly 1st differences/regression

R2Adj Rt-ratiop-value0.075-0.0156-0.116-0.570.571Cointegration AnalysisResidual-based testTest statisticValueCritical valueCRDWaDW0.6471.03ADFbADF-t-2.908 (lag 4)-4.76906PP cZZt-16.1-3.13-19.34-3.52aCritical Values are reported in Engle and Yoo (1987)bCritical Values for ADF are from MacKinnon (1991). The lag length was chosen according to Schwartz criterioncCritical values are taken from Philips and Ouliaris (1990)

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National timeseriesCategoryQ test**(correlogram test)ADF test **Lag lengthRt1Rt2RtSeries#1retailsignificantautocorrelation coefficientsstationary //1Series#1officesignificantautocorrelation coefficientsstationary//2Series#1commercialsignificantautocorrelation coefficientsstationary//3Series#2retailsignificantautocorrelation coefficientsnot stationarystationary/3Series#2officesignificantautocorrelation coefficientsnot stationarystationary/3Series#2commercialsignificantautocorrelation coefficientsstationary//1Series#2industrialsignificantautocorrelation coefficientsnot stationarystationary/5Series#3retailsignificantautocorrelation coefficientsnot stationarynot stationarystationary1Series#3officesignificantautocorrelation coefficientsnot stationarystationary/0Series#3industrialsignificantautocorrelation coefficientsnot stationarystationary/0

*We analyze this question through an investigation of two topicsThe implication on the IRR fund calculationThe implication on asset management processes.

To assess the impact upon the management of real estate funds that arises from the existence of divergence among historical time series, we perform be assessed following the performance of a backtesting on the IRRThe starting data of the simulation are formed from 3 historical series relative to valorisation indices of nominal real estate in the commercial sector of Milan and are supplied by 3different providers.The central idea of the simulation is to subject the IRR to a what if analysis.The What if analysis is performed through a variation of the final value of a hypothetical real estate fund according the trend captured by each one of the 3 data source used. The simulation is articulated in 4 steps*

*Backtesting is composed of four logical steps:

1. Identification of the subperiods upon which the simulation is run

2. Evaluation of the properties liquidation values based on the rate of capitalization that is implicit to the historical series used

3. Calculation of the funds IRR for each subperiod

4. Evaluation of the standard deviation of the IRR among periods and among information sources.

Figure 1. Characteristics of the hypothetic (and ultra-simplified) real estate fund. Number of properties: 2 (A e B); Time horizon: 5 ys (t0t5)Unknown variableDate of investmentDate of liquidation Initial PriceAnnual Rental CostsEnd ValueProperty At0t510010?Property Bt0t520020?

1. Identification of the subperiods upon which the simulation is runBacktesting is composed of four logical steps:The simulation provides for the selection of 6 subperiods with a length of five years (each one separated from the previous by one year)1st) Jan/1998Dec/2002;2nd) Jan/1999Dec/2003; 3rd) Jan/2000Dec/2004; 4th) Jan/2001Dec/20055th) Jan/2002Dec/2006; 6th) Jan/2003Dec/2007.2. Evaluation of the properties liquidation values based on the rate of capitalization that is implicit to the historical series usedFor each sub-period we maintain constant the income flows (rents), while we measure the final value of the properties as result of the capitalization rate implicit to that sub period and, much important, to that specific data source*

ExampleJan/1998Dec/2002Property ValuesData Source #1120180T0= 100T5= 150

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Figure 2. Sensitivity analysis of end values and IRR for a hypothetical real estate investment fund. End Values of the FundSub- periodjan/1998-dic/2002jan/1999-dic/2003jan/2000-dic/2004jan/2001-dic/2005jan/2002-dic/2006jan/2003-dic/2007SDSB*Data Source #1 413.3409.1409.3414.2399.2388.92.41%Data Source #2 433.3691.7565.2453.1433.3339.825.47%Data Source #3416.6444.4413.3389.9364.5345.89.19%SDDS**2.5%29.9%19.2%7.6%8.6%7.5%Internal Rate of Return (IRR) of the fundSub periodjan/1998-dic/2002jan/1999-dic/2003jan/2000-dic/2004jan/2001-dic/2005jan/2002-dic/2006jan/2003-dic/2007SDSB*Data Source #118.1%17.9%17.9%18.1%17.5%17.0%2.49%Data Source #219.0%28.3%24.1%19.8%19.0%14.6%22.87%Data Source #318.2%19.4%18.1%17.0%15.8%14.9%9.67%SDDS**2.5%25.6%17.6%7.6%9.0%8.3%*SDSB: Standard Deviation among Sub-Periods **SDDS: Standard Deviation among Data SourcesSDSB and SDDS are expressed as percentage of mean value

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Figure 2. Sensitivity analysis of end values and IRR for a hypothetical real estate investment fund. End Values of the FundSub- periodjan/1998-dic/2002jan/1999-dic/2003jan/2000-dic/2004jan/2001-dic/2005jan/2002-dic/2006jan/2003-dic/2007SDSB*Data Source #1 413.3409.1409.3414.2399.2388.92.41%Data Source #2 433.3691.7565.2453.1433.3339.825.47%Data Source #3416.6444.4413.3389.9364.5345.89.19%SDDS**2.5%29.9%19.2%7.6%8.6%7.5%Internal Rate of Return (IRR) of the fundSub periodjan/1998-dic/2002jan/1999-dic/2003jan/2000-dic/2004jan/2001-dic/2005jan/2002-dic/2006jan/2003-dic/2007SDSB*Data Source #118.1%17.9%17.9%18.1%17.5%17.0%2.49%Data Source #219.0%28.3%24.1%19.8%19.0%14.6%22.87%Data Source #318.2%19.4%18.1%17.0%15.8%14.9%9.67%SDDS**2.5%25.6%17.6%7.6%9.0%8.3%*SDSB: Standard Deviation among Sub-Periods **SDDS: Standard Deviation among Data SourcesSDSB and SDDS are expressed as percentage of portfolio mean value

*We analyze this question through an investigation of two topicsThe implication on the IRR fund calculation

We perform a portfolio optimization with the following five asset class:*

returnsriskFrom A to B : sling effectFrom A to C: raising effectBenefit from inclusion of an asset class not correlatedMinMax*

A Measure of BenefitChange in Mean Risk Adjusted Performance of Frontier (MeRAPF) *

1646121410 81050152025Risk (%)Annualized Return (%)100% DJ EuroSTOXX50100% GBI global index100% Italian Gov. Bond short term100% S&P500100% Residential IndexEfficient frontier with real estate data source#1Efficient frontier with real estate data source#2Efficient frontier with real estate data source#3Efficient frontier with real estate data source#4#1#2#3#4*

Portfolio composition: does the real estate indexes selection affects the asset allocation?Data Source #1RiskRiskPorfolio weightsPorfolio weightsData Source #2*

Portfolio composition: does the real estate indexes selection affects the asset allocation?Porfolio weightsPorfolio weightsData Source #3Data Source #4*

A lower risk than the other asset classA high expected returns, due to the market growth (bubble?)A low correlation with the other asset class*

Efficient frontier with..Benefit from Real Estate inclusion? MeRAPData Source #1YES+76%Data Source #2YES+42%Data Source #3YES+25%Data Source #4YES+39%

*In Italy the providers of real estate data adopt different approaches of construction of the real estate indexes The differences have been investigated with some statistical instruments each of which show a lack of homogeneity among data, especially among the first differences of log value (the returns). The lack of standardization of real estate data produce a potential bias inside the assessment process of real estate investments. In particular, we pay attention to how the lack of homogeneity involve the IRR forecasts of an hypothetical real estate funds and ii) how it impact on the asset allocation decisions in a efficient frontiers framework. All the results of our investigation induce the opinion that the Italian real-estate information systems are not at all adequate and standardized.However, some caveat could be referred to the imperfect synchronization of some data or to the irrational speculative bubble that has charactized some Italian urban area.

*Thank YouGabriele [email protected]

*As it is known, in a general perspective, addition of one (or more) asset class characterized by a low correlation with the others, produces a shift toward left of the frontier, allowing to choice more profitable portfolios at the same risk level.This translation can follow two different paths: a) the inclusion of a new (or more) asset class (scarcely correlated with others) determines a change of corner portfolios of the efficient frontier, i.e. portfolios respectively with minimum and maximum variance, thus generating a raising effect of the frontier itself; b) the addition of a new (or more) asset class (scarcely correlated with others) does not modify the position of corner portfolios on the graph, but produces just an accentuation of curvature level of the frontier determining a sort of sling effect, because it reminds the behaviour of an elastics sling before the throw. These two effects are readily recognizable in figure 3 where A represents the frontier of n asset class, B and C the frontiers generated by the inclusion of a new asset slightly correlated with the others n asset class (the n+1th asset class in frontier B is different from that in C).The frontier A undergoes a sling effect and changes in B after the addition of an asset class characterized by: 1) slight correlation with other asset classes; 2) risk not too different respect to that of the other asset classes in portfolio; 3) a return certainly lower than the highest return of the set of pre-existent asset classes. The assertion sub 3) is related to the circumstance that the portfolio with maximum variance is entirely allocated in the most profitable asset class: on the contrary, the inclusion of an asset class with a return higher than the return of the maximum variance portfolio (i.e., in figure 3), produces a translation from A to C, with a raising effect. In this case, the volatility interval of the frontier is wider or restricted if the new added asset class has respectively a risk higher or lower than the risk of portfolio with max. variance ().

*After the analysis of this positive effect sprang from the inclusion in portfolio of an asset class scarcely correlated with the others, is necessary now to consider how we can measure this benefit of diversification. In case of sling effect, this measure can be provided by the breadth of shift of the new frontier respect to the previous: this shift can be calculated as the change (in the passage between the two set of portfolios) of the mean risk adjusted performance of the frontier. The term mean risk adjusted performance of frontier, synthesised by the acronym MeRAPF, is referred to a very simple measure of profitability represented by the mean of Risk Adjusted Performance of the optimal portfolios. As the number of portfolios that compose an efficient frontier is unlimited, it is obvious that the MeRAPF must be elaborated only for a restricted number of cases. A solution could be provided by the calculation of the decile MeRAPF, i.e. the mean of the return to risk ratio of the decile portfolio, where with this term we indicate the portfolio with a risk equal to a decile of the volatility interval[1] (that is the portfolios PDi with i=110, plotted in figure 3). [1] For example, for a frontier moving along a continue volatility interval between min=5% (minimum variance) and max=15% (maximum variance), the first portfolio decile is that characterized by a standard deviation of p=6%, the second portfolio decile has a volatility of p=7%, and so on until the risk of the tenth portfolio decile that, obviously, will corresponds to the maximum variance (p=15%). With regard to frontiers A and B showed in figure 3, the relation MeRAPFB>MeRAPFA confirms the investors convenience to move toward the new efficient frontier; graphically, the level of MeRAPF is proportional to the breadth of the segments in continuous lines plotted inside the grey area that delimits the differential area of efficiency between frontier A and B. In case of raising effect, the calculation of MeRAPF follows the same methodology used for the sling effect, with just one, but very important, exception: the decile of volatility must be related only to the volatility interval common to the two frontiers[1] (the original and the translated) and this to allow an homogeneous comparison [1] To clarify this concept we can note that, considering figure 3, the common interval correspond to [min - max] of frontier C (i.e., the volatility interval of the two corner portfoliosand ). If the frontier C is presented as a curve with a portfolio of max. variance () and min variance () respectively more and less risky of corner portfolio of the frontier A (and ), then the calculation of MeRAPF is extended to the interval [min - max] of frontier A.

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