ERES conference 2012, Edinburg – working paper

1. ERES conference 2012, Edinburg – working paper Kristin Wellner, Prof. Dr. rer. pol. Fachgebiet Planungs- und Bauökonomie/ Immobilienwirtschaft (Chair of Planning and Construction Economics/ Real Estate) Fakultät VI Planen Bauen Umwelt (Faculty IV Planning Building Environment) Technische Universität Berlin (Technical University of Berlin) Sekr. A57 Straße des 17. Juni 152, 10623 Berlin phone: +49 (0)30-314 21829 +++ fax: +49 (0) 30-314 21826 +++ e-mail: kristin.wellner@tu-berlin.de Using clustering methods for a practicable real estate portfolio allocation process

2. Agenda • Former research • Correlation analysis – empirical study • Clusters • Conclusions for applying

3. Former research: Problems in Transforming MPT to Real Estate • Caused in the assumptions of the Modern Portfolio Theory (MPT) itself • The model restrictions defined by Markowitz (cf. Markowitz 1952,1959) as a pre-requisite for the application of MPT are not executable to real assets, their markets, and the real subjects acting • Caused in the characteristics of the real estate asset class • Property returns are not standard normal distributed • Real estate markets are considered to be extremely non-transparent, inert and dependent on the upstream and downstream markets • real estate is characterized by its long-term use and the substantial investment volume

4. Literature Review • Problems/Critics in applying portfolio theory for real estate • Kaiser, R.: Analyzing Real Estate Portfolio Returns, in: Journal of Portfolio Management, Special Issue, 2005, S. 134-142. • Liang, Y. / Myer, N. / Webb, J.: The Bootstrap Efficient Frontier for Mixed-Asset-Portfolios, in: Real Estate Economics, Vol. 24, 1996, S. 247-256. • Müller, M./ Lausberg, C.: Why volatility is an inappropriate risk measure for real estate, Paper presented at the Annual European Real Estate Society Conference in Milan, 2010. • Forming clusters • Hamelink, F. / Hoesli, M. / Lizieri, C. / MacGregor, B.: Homeogenios commercial property market groupings and portfolio construction in the United Kingdom, in: Environment and Planning A, 32, 2000, pp. 322-344. • Goetzmann, N. / Wachter, M.: Clustering Methods for Real Estate Portfolios, in: Real Estate Economics, Vol. 23, 1995, pp. 280-286. • Jackson, C. / White, M.: Challenging Traditional Real Estate Market Classifications for Investment Decisions, in: The Journal of Real Estate Portfolio Management, Vol. 11, No. 3, 2005, pp. 307-321.

5. Former research: last year paper calculate correlation analyze data find practicable asset allocation forming cluster calculate optimal portfolios Current research aim

6. Data: Annual Total Returns of 76 real estate markets (office/retail) • Data of European office and retail properties (Time frame: 1995-2011) • Source: Property Market Analysis LLP, London, 2011, www.property-m-a.co.uk

7. Data Analysis: Total Return Office • High Return spreads and volatility in: Dublin, Athens, Paris and London markets • Slow results for Germany

8. Data Analysis: Total Return Retail • High Returns und STD in: Athens, Dublin, London and Marseille • Slow results for Germany

9. Forming homogeneous Clusters by Components of Return Analysis • Building homogeneous cluster with similar return risk profiles and co-rotating returns Return Return level (=Average) Risk (=Standard deviation) Amplitude time t Correlation of Returns (=phase difference)

10. Correlation Matrix (extraction) • 76 markets, PMA, retail / office 1995-2011 … extract…

11. Correlation example • With 0,99 highest positive correlation between Paris CBD and Paris Central • Stable correlation – evidence from rolling calculation • Correlation coefficient: PMA Total Return from 1990-2011 in Paris CBD and Paris Central Correlation plot

12. Correlation example II • With -0,56 highest negative correlation between Cologne and Glasgow_Retail • Stable correlation – evidence from rolling calculation • Correlation coefficient: PMA Total Return from 1995-2011 in Cologne and Glasgow_Retail Correlation plot

13. Clustering by using a Dendrogram • A dendrogram • from Greek dendron "tree", -gramma "drawing" • is a tree diagram frequently used to illustrate the arrangement of the clusters produced by hierarchical clustering. Distance

14. Dendrogram of Correlation Distance

15. Cluster – sort by correlation (color) Retail West South Europe Retail South Europe German and German speaking

16. Cluster – sort by correlation (color) Paris Office German Retail North and East Europe UK Office UK Retail London

17. Return Risk Characteristics (76 markets, PMA, retail/office 1995-2011) West Europe Retail East Europe Retail North Europe and London South Europe Paris Office German Retail Middle East Europe UK Retail UK Office German and German speaking office R = Retail

18. Empirical Results – Conclusions for applying • 10 Clusters with similar markets in Europe • Single individual markets within their own cluster (e.g. Dublin) • Evidence of stable correlation over the last 20 years • Using cluster formation for the asset allocation process • Allows a substitution of homogeneous markets • Allows for a pragmatic implementation as several possible markets fulfil conditions, depending on actual availability • Prevents a strict elimination of markets of similar quality at slightly lower returns or minimal higher risk, since in practice, these minimal differences are of no real importance

19. Thank You!!! • Questions?????

20. Back up

21. Investment Spectrum of: Return, Risk, Time, Leverage, Hedging, possible markets … • Return-Risk-Characteristic by market und property type • Theoretical portfolio allocation • Practicable target portfolio • Proof the practicability • Timing and Financial planning • Property data • Financial plans of all properties • Forecasting future development Procedure of Portfolio Management in Practice • Counter-current principle in portfolio management process Investment Strategy Top Down Theoretical Asset Allocation (Research, Portfolio selection) Tactical Asset Allocation Risk Management Synthesis Real Estate Market Competence (Acquisition, Research) Bottom Up Portfolio Controlling / Reporting Real Estate Management (Asset / Property Management, Facilities Management)

22. Application of the Portfolio Selection in Practice • Modified calculation of a model portfolio with: • Forming homogeneous cluster • Determination the maximal portfolio share of 20% • Comparison of historical and forecasted returns • Comparison of rolling calculation step-by-step for 10 years

23. Clusters – Results • O = Office; R = Retail

24. Example: Cluster 28 • Return Time-Frame in cluster 28 • 5 German retail markets and the non weighted mean

25. Efficient Frontier of the 32 Clusters MVP - MinimumVariancePortfolio MRP - MaximumReturnPortfolio MSRP - MaximumSharpRatioPortfolio

26. Optimal Proportion along the Efficient Frontier Only 9 Markets 16 Markets MVP - MinimumVariancePortfolio MRP - MaximumReturnPortfolio MSRP - MaximumSharpRatioPortfolio

27. Optimal Proportion along the Efficient Frontier of the 32 Clusters 7 Cluster with 20 Markets 13 Cluster with 34 Markets MVP - MinimumVariancePortfolio MRP - MaximumReturnPortfolio MSRP - MaximumSharpRatioPortfolio

28. Rolling Calculation within the 16 years of the 32 Clusters

29. Interpretation of empirical Results (II) • Rolling calculations • Show the sensitivity of the selected time-frame • Markets that sustain in multiple calculations, should also be represented in the target portfolio • Make the selection of efficient portfolio building blocks more secure and independent regardless of the selected time-frame • Can make individual influences and statistical outliers visible in the time-frame to eliminate them • Analysis of historical time-frames and their forecasts • Show the sensitivity of the selected time-frame • Markets that sustain in both time-frames (i.e., are good for an optimal portfolio in the past and the future), should also be represented in the target portfolio

30. Conclusions • A 100 percent implementation of the model portfolio is not possible • A single evaluation of an optimal portfolio for the disposal of a real target portfolio would be grossly negligent • A number of simulations to be carried out over the course of time with the help of different raw data, varying indices, ex post and ex ante data • Pragmatic adjustments such as cluster formation and the restriction of maximum shares are making sense • These modifcations couldbringing more attention to the Portfolio Theory in real estate practice in the future

31. 0,8% GB 15,2% 14,9% 1,4% 6,9% 0,0% 1,8% 12,9% 23,6% 2,9% 2,5% 25,3% 16,4% 40,7% 34,8% Approximation the Target Portfolio Market conditions, Offers, market entry barriers …. Theoretical portfolio model (Cluster) Current portfolio (Real Objects) Target portfolio (Real Objects) 6,3% 1,0% 11,6% 17,0% 17,1% 6,8% 2,9% 12,4% 7,3%

32. Proportions in the MSRP Only 9 Markets MVP - MinimumVariancePortfolio MRP - MaximumReturnPortfolio MSRP - MaximumSharpRatioPortfolio

33. Proportions in the MSRP of the 32 Clusters 7 Cluster with 20 Markets MVP - MinimumVariancePortfolio MRP - MaximumReturnPortfolio MSRP - MaximumSharpRatioPortfolio

34. Markowitz Algorithm • Portfolio-Return • Portfolio-Risk • E (R) = expected return of Portfolio • E (ri) = μ = expected return of asset i • n = number of items • ri = rate of return of the item in period n • R = expected return value or • xi = value share of the property's total portfolio • cik = correlation coefficient between asset i and k • COVik = covariance between asset i and k • x = value share of the property's total portfolio • σ = standard deviation of return

35. Efficient Frontier of all 76 Markets