ERES conference 2012, Edinburg – working paper

ERES conference 2012, Edinburg – working paper

Using clustering methods for a practicable real estate portfolio allocation processKristin 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: [email protected]

Slide 2© Prof. Dr. Kristin Wellner, 14.06.2012ERES 2012, Edinburgh

Agenda

1 Former research

2 Correlation analysis – empirical study

3 Clusters

4 Conclusions for applying


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


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.


Former research: last year paper

analyze data

calculate correlation

forming cluster

calculate optimal

portfolios

find

practicable asset

allocation

Current research aim


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

PMA Total Return Office/Retail(R) 1995-2011

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

70

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

To

tal R

etu

rn (

yo

y)

Vienna BrusselsBrussels: OOT* PragueCopenhagen HelsinkiLille LyonMarseille Paris: CBDParis: Central Paris: La DéfenseParis: WBD* BerlinCologne DusseldorfFrankfurt: City Frankfurt: OOT*Hamburg Munich: CityMunich: OOT* StuttgartAthens BudapestDublin MilanRome LuxembourgAmsterdam RotterdamOslo WarsawLisbon BarcelonaMadrid StockholmZurich BirminghamEdinburgh GlasgowLondon: Central London: CityLondon: Docklands London: M25 WestLondon: WEM* ManchesterVienna_R Brussels_RPrague_R Copenhagen_RLille_R Lyon_RMarseille_R Paris_RBerlin_R Cologne_RFrankfurt_R Hamburg_RMunich_R Athens_RBudapest_R Dublin_RMilan_R Naples_RRome_R Amsterdam_RWarsaw _R Lisbon_RBarcelona_R Madrid_RValencia_R Stockholm_RBirmingham_R Glasgow _RLondon_R Manchester_R


Data Analysis: Total Return Office

High Return spreads and volatility in: Dublin, Athens, Paris and London markets

Slow results for GermanyPMA 1995-2011 Total Return Office

-60

-40

-20

0

20

40

60

80

Vie

nn

a

Bru

sse

ls

Bru

sse

ls: O

OT

*

Pra

gu

e

Co

pe

nh

ag

en

He

lsin

ki

Lill

e

Lyo

n

Ma

rse

ille

Pa

ris:

CB

D

Pa

ris:

Ce

ntr

al

Pa

ris:

La

Dé

fen

se

Pa

ris:

WB

D*

Be

rlin

Co

log

ne

Du

sse

ldo

rf

Fra

nkf

urt

: City

Fra

nkf

urt

: OO

T*

Ha

mb

urg

Mu

nic

h: C

ity

Mu

nic

h: O

OT

*

Stu

ttga

rt

Ath

en

s

Bu

da

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st

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n

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: Do

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s

Lo

nd

on

: M2

5 W

est

Lo

nd

on

: WE

M*

Ma

nch

est

er

Mean Min Max STD


Data Analysis: Total Return Retail

High Returns und STD in: Athens, Dublin, London and Marseille

Slow results for Germany

PMA 1995-2011 Total Return Retail

-60

-40

-20

0

20

40

60

80

Vie

nn

a_

R

Bru

sse

ls_

R

Pra

gu

e_

R

Co

pe

nh

ag

en

_R

Lill

e_

R

Lyo

n_

R

Ma

rse

ille

_R

Pa

ris_

R

Be

rlin

_R

Co

log

ne

_R

Fra

nkf

urt

_R

Ha

mb

urg

_R

Mu

nic

h_

R

Ath

en

s_R

Bu

da

pe

st_

R

Du

blin

_R

Mila

n_

R

Na

ple

s_R

Ro

me

_R

Am

ste

rda

m_

R

Wa

rsa

w_

R

Lis

bo

n_

R

Ba

rce

lon

a_

R

Ma

dri

d_

R

Va

len

cia

_R

Sto

ckh

olm

_R

Bir

min

gh

am

_R

Gla

sgo

w_

R

Lo

nd

on

_R

Ma

nch

est

er_

R

Mean Min Max STD


Forming homogeneous Clusters by Components of Return Analysis

Return

time t

Return level

(=Average)

Risk

(=Standard deviation)

Amplitude

Correlation of Returns (=phase difference)

Building homogeneous cluster with similar return risk profiles and co-rotating returns


Correlation Matrix (extraction)

76 markets, PMA, retail / office 1995-2011

… extract…


Correlation example

With 0,99 highest positive correlation between Paris CBD and Paris Central

Stable correlation – evidence from rolling calculation

Correlation coefficient:

-40,00

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

40,00

50,00

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Paris: Central

Paris: CBD

-40

-20

0

20

40

60

-50 0 50

1990-1999 1991-2000 1992-2001 1993-2002 1994-2003 1995-2004 1996-2005 1997-2006 1998-2007 1999-2008 2000-2009 2001-2010 2002-20110,9813 0,9887 0,9919 0,9912 0,9914 0,9905 0,9854 0,9867 0,9878 0,9940 0,9967 0,9972 0,9980

PMA Total Return from 1990-2011 in Paris CBD and Paris Central Correlation plot


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

1995-2004 1996-2005 1997-2006 1998-2007 1999-2008 2000-2009 2001-2010 2002-2011-0,6576 -0,6448 -0,6970 -0,7957 -0,5252 -0,6621 -0,5037 -0,4549

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

40,00

50,00

60,00

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Cologne

Glasgow_R

-10-5

05

1015

2025

-50 0 50 100


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.

Dis

tan

ce


Pa

ris: C

entr

al

Pa

ris: C

BD

Lo

nd

on: W

EM

*

Lo

nd

on: C

entr

al

Pa

ris: L

a D

éfe

nse

Ma

dri

d_

R

Ba

rce

lona

_R

Munic

h: C

ity

Ha

mb

urg

Ro

me

_R

Mila

n_

R

Lyo

n_

R

Lille

_R

Bud

ap

est

Co

pe

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ge

n

Ma

dri

d

Dub

lin

Lyo

n

Lo

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on: C

ity

Fra

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rt: C

ity

Co

log

ne

Zuri

ch

Dusse

ldo

rf

Ro

me

Mila

n

Ma

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ste

r_R

Gla

sg

ow

_R

Ba

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mb

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Be

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_R

Munic

h: O

OT

*

Be

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on:

Dockla

nds

Sto

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lm_

R

Fra

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rt: O

OT

*

Ma

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Pa

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BD

*

Pa

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Ma

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Bir

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Ma

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Lille

Oslo

He

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ki

Am

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25

We

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Bru

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Munic

h_

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Bud

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Bir

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Am

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Pra

gue

_R

Vie

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_R

0,0

1,1

Dendrogram of Correlation

D

ista

nce


Cluster – sort by correlation (color)

MV STD3,1 Barcelona 7,0 17,9

3,1 Lisbon 4,7 13,5

3,2 Lille_R 14,0 13,2

3,2 Lyon 10,5 10,0

3,2 Lyon_R 14,4 19,1

3,3 Dublin 9,8 27,7

3,3 Madrid 8,2 20,9

3,4 Barcelona_R 14,1 14,0

3,4 Madrid_R 14,5 12,6

3,4 Paris_R 12,4 15,2

4,1 Cologne 4,7 8,6

4,1 Dusseldorf 3,2 9,1

4,1 Frankfurt:City 3,5 13,3

4,1 Hamburg_R 3,3 9,1

4,1 Munich:City 4,1 11,9

4,1 Zurich 6,3 14,0

4,2 Stuttgart 3,6 5,6

4,3 Berlin 1,1 10,6

4,3 Munich:OOT* 3,1 8,8

4,3 Vienna 4,0 5,2

MV STD

1,1 Budapest_R 10,7 15,3

1,1 Dublin_R 10,5 23,9

1,1 Valencia_R 13,3 16,6

1,2 Prague_R 14,2 13,0

1,3 Luxembourg 6,8 9,3

1,3 Warsaw 8,5 14,8

1,3 Warsaw_R 13,9 9,2

2,1 Brussels 4,9 5,3

2,1 Milan_R 11,5 14,1

2,1 Naples_R 6,8 12,2

2,1 Rome_R 11,0 13,5

2,2 Lille 9,0 8,2

2,2 Marseille 10,9 9,2

2,2 Milan 8,8 14,0

2,2 Rome 5,7 11,9

Retail

South Europe

West South Europe Retail

German and German speaking


Cluster – sort by correlation (color)MV STD

7,1 Athens 9,0 18,7

7,1 Athens_R 10,0 23,4

7,2 Brussels:OOT* 4,1 6,7

7,3 Amsterdam 7,2 9,3

8,1 Berlin_R 5,4 7,9

8,1 Cologne_R 5,8 5,2

8,1 Frankfurt_R 6,2 5,5

8,1 Hamburg_R 6,3 6,3

8,2 Munich_R 7,0 7,6

9 Vienna_R 8,5 19,2

10 Birmingham 6,5 11,0

10 Edinburgh 6,9 13,8

10 Glasgow 8,3 13,1

10 Manchester 8,2 12,5

11,1 Glasgow_R 9,3 16,1

11,1 London_R 12,1 18,3

11,1 Manchester_R 6,4 16,2

11,2 Birmingham_R 7,5 13,1

11,2 Lisbon_R 7,8 11,6

MV STD5,1 Paris:Central 8,7 17,7

5,1 Paris:DB 8,8 17,5

5,1 Paris:LaDéfense 9,8 21,6

5,1 Paris:WBD* 8,6 17,6

5,2 Amsterdam_R 13,1 12,6

5,2 Frankfurt:OOT* 2,5 8,0

5,2 Marseille_R 14,8 20,2

6,1 Budapest 5,0 10,7

6,1 Copenhagen 5,0 7,7

6,1 Helsinki 6,0 8,2

6,1 Oslo 10,7 17,1

6,1 Prague 5,7 9,6

6,2 London:M25West 7,4 14,8

6,3 Brussels_R 9,7 10,0

6,3 Copenhagen_R 11,2 17,5

6,3 Rotterdam 6,2 8,5

6,4 London:Docklands 12,3 20,1

6,4 Stockholm 9,0 16,7

6,4 Stockholm_R 12,0 12,7

6,5 London:Central 10,0 18,9

6,5 London:City 8,2 20,5

6,5 London:WEM* 10,8 19,5

Paris Office

London

North and East Europe

German Retail

UK Retail

UK Office


Return Risk Characteristics (76 markets, PMA, retail/office 1995-2011)

PMA Total Return 1995-2011

Budapest

Copenhan_R

Dublin

London:M25West

London_RParis_R

Prague

Stuttgart

Warsaw

Zurich

Amsterdam

Amsterdam_R

Athens

Athens_R

Barcelona

Barcelona_R

Berlin

Berlin_R

Birmingham

Birmingham_R

Brussels

Brussels:OOT*

Brussels_R

Budapest_R

Cologne

Cologne_R

Copenhan

Dublin_R

Dusseldorf

Edinburgh

Frankfurt:City

Frankfurt:OOT*

Frankfurt_R

Glasgow

Glasgow_R

Hamburg

Hamburg_R

Helsinki

Lille

Lille_R

Lisbon

Lisbon_R

London:Central

London:City

London:Docklands

London:WEM*

Luxembourg

Lyon

Lyon_R

Madrid

Madrid_R

Manchester

Manchester_R

Marseille

Marseille_R

Milan

Milan_R

Munich:City

Munich:OOT*

Munich_R Naples_R

Oslo

Paris:Central

Paris:DB

Paris:LaDéfense

Paris:WBD*

Prague_R

Rome

Rome_R

Rotterdam

Stockholm

Stockholm_R

Valencia_R

Vienna

Vienna_R

Warsaw_R

0,0

2,5

5,0

7,5

10,0

12,5

15,0

2,5 5,0 7,5 10,0 12,5 15,0 17,5 20,0 22,5 25,0 27,5

Risk (Standarddeviation)

Re

turn

(M

ea

n)

R = Retail

German and German speaking office

German Retail Middle East Europe

UK Office

East Europe

Retail

West Europe Retail

South Europe

North Europe and London

Paris Office

UK Retail


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


Thank You!!!

Questions?????


Back up


Procedure of Portfolio Management in Practice

Risk M

anagement

Top Down

BottomUp

Investment Strategy

Theoretical Asset Allocation (Research, Portfolio selection)

Real Estate Market Competence (Acquisition, Research)

Real Estate Management(Asset / Property Management, Facilities Management)

Tactical Asset AllocationSynthesis

Portfolio Controlling / Reporting

Counter-current principle in portfolio management process

• 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


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


Clusters – Results

O = Office; R = Retail1 Barcelona_R 10 Dusseldorf_O 18 London: Dockl_O 26 Budapest_R1 Madrid_R 10 Frankfurt: City_O 18 Paris_R 26 Oslo_O1 Milan_R 10 Hamburg_O 18 Stockholm_R 26 Prague_R1 Rome_R 10 Munich: City_O 26 Valencia_R

10 Munich: OOT_O 19 Budapest_O 26 Warsaw_R2 Brussels: OOT_O 10 Stuttgart_O 19 Copenhagen_O2 Brussels_O 10 Vienna_O 27 Dublin_R

20 Brussels_R3 Naples_R 11 Zurich_O 20 Copenhagen_R 28 Berlin_R

20 London: M25_O 28 Cologne_R4 Lille_O 12 Paris: CBD_O 28 Frankfurt_R4 Marseille_O 12 Paris: Central_O 21 London: Central_O 28 Hamburg_R

12 Paris: LD_O 21 London: City_O 28 Munich_R5 Milan_O 12 Paris: WBD_O 21 London: WEMT_O5 Rome_O 29 Vienna_R

13 Frankfurt: OOT_O 22 Amsterdam_O6 Cologne_O 22 Lisbon_R 30 Birmingham_R

14 Amsterdam_R 30 Glasgow_R7 Barcelona_O 14 Marseille_R 23 Athens_O 30 Manchester_R7 Lisbon_O 23 Athens_R7 Lyon_O 15 Helsinki_O 31 London_R

15 Rotterdam_O 24 Luxembourg_O8 Lille_R 24 Prague_O 32 Birmingham_O8 Lyon_R 16 Dublin_O 32 Edinburgh_O

25 Warsaw_O 32 Glasgow_O9 Berlin_O 17 Madrid_O 32 Manchester_O

17 Stockholm_O


Example: Cluster 28

Return Time-Frame in cluster 28

5 German retail markets and the non weighted mean

Returns in Cluster 28

-15 -10

-5 05

101520253035

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Berlin_R Cologne_R Frankfurt_R Hamburg_R Munich_R C28


Efficient Frontier of the 32 Clusters

MVP - MinimumVariancePortfolio MRP - MaximumReturnPortfolio MSRP - MaximumSharpRatioPortfolio

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C17

C18

C19

C20C21

C22

C23

C24

C25

C26

C28C29C30

C31

C32

Portfolio

-0,5%

1,5%

3,5%

5,5%

7,5%

9,5%

11,5%

13,5%

2,0% 4,0% 6,0% 8,0% 10,0% 12,0% 14,0% 16,0% 18,0% 20,0%

Risk

To

tal R

etu

rn

MVP MRP MSRP

Portfolio Return: 6,37% 11,63% 8,55%

Portfolio STD: 3,77% 10,64% 4,41%

Portfolio-Sharpe-Ratio: 0,7613 0,7641 1,1451


Optimal Proportion along the Efficient Frontier

16

Ma

rke

ts

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

6,1% 8,7% 9,5% 10,5% 11,5% 12,0% 12,4% 12,7% 13,0% 13,1%

Total Return

Sh

are

Manchester_O

London_R

Frankfurt_RGlasgow_O

Manchester_R

Vienna_R

Valencia_R

Prague_R

Lisbon_RAmsterdam_R

Vienna_O

Lille_R

Marseille_O

Warsaw_RRome_R

Madrid_R

MVP MRP MSRP


Portfolio STD: 2,47% 11,85% 2,97%


Shares in the MSRP

14,2%

3,0%

34,7%

2,2%

13,3%

5,9% 0,0%

0,4%

15,7%

10,6%

Marseille_O

Lisbon_R

Prague_R

Valencia_R

Warsaw_R

Frankfurt_R

Vienna_R

London_R

Glasgow_O

Manchester_O


Only 9 Markets


Optimal Proportion along the Efficient Frontier of the 32 Clusters

13

Clu

ste

r w

ith 3

4 M

ark

ets

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

6,4% 7,7% 8,6% 8,9% 9,4% 9,8% 10,2% 10,6% 10,9% 11,3% 11,5% 11,6% 11,6% 11,6%

Total Return

Sh

are

C1 C8

C2 C26

C14 C4

C31 C6

C18 C22

C28 C29

C32

MVP MRP MSRP


Portfolio STD: 3,77% 10,64% 4,41%


Shares in the MSRP

20,0%

20,0%

4,1%

20,0%

7,0%

20,0%

9,0%

C1 C4

C22 C26

C28 C29

C31


7 Cluster with 20 Markets


Rolling Calculation within the 16 years of the 32 ClustersVeränderliche Anteile durch rollierende Berechnung

PMA 32 Cluster 1995-2010

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1995-2010

1995-2004

1996-2005

1997-2006

1998-2007

1999-2008

2000-2009

2001-2010

Meanall

years

Cluster 2 Cluster 3

Cluster 4 Cluster 5

Cluster 8 Cluster 14







Figures in the MSRP 1995-2010 1995-2004 1996-2005 1997-2006 1998-2007 1999-2008 2000-2009 2001-2010 Mean all yearsPortfolio Return 8,55% 9,40% 9,87% 10,20% 10,78% 10,16% 9,00% 8,80% 9,59%

Portfolio-STD: 4,41% 0,67% 0,41% 0,51% 0,62% 6,30% 6,27% 5,81% 3,13%Portfolio-Sharpe-Ratio: 1,1451 8,8060 15,5366 13,1373 11,7419 1,0571 0,8772 0,9122 6,6517


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


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 could bringing more attention to the Portfolio Theory in real estate practice in the future


Approximation the Target Portfolio

16,4%

2,5%

12,9%

15,2%0,8% GB

6,9%

1,8%

2,9%

40,7%

25,3%

34,8%

23,6%

0,0%1,4%14,9%

12,4%

6,8%

17,0%

1,0% 6,3%

7,3%

2,9%

11,6%

17,1%

Theoretical portfolio model

(Cluster)

Current portfolio

(Real Objects)

Market conditions,Offers,

market entry barriers

….

Target portfolio(Real Objects)


Proportions in the MSRP


Only 9 Markets

MVP MRP MSRP


Portfolio STD: 2,47% 11,85% 2,97%


Shares in the MSRP

14,2%

3,0%

34,7%

2,2%

13,3%

5,9% 0,0%

0,4%

15,7%

10,6%

Marseille_O

Lisbon_R

Prague_R

Valencia_R

Warsaw_R

Frankfurt_R

Vienna_R

London_R

Glasgow_O

Manchester_O


Proportions in the MSRP of the 32 Clusters


7 Cluster with 20 Markets

Shares in the MSRP

20,0%

20,0%

4,1%

20,0%

7,0%

20,0%

9,0%

C1 C4

C22 C26

C28 C29

C31

MVP MRP MSRP


Portfolio STD: 3,77% 10,64% 4,41%



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

n

1ii

n

1iii x)r(Ex)R(E

n

1i

n

1kikkiki

2p cxx

n

1i

1n

1i

n

1ikikkiii COVxx2²²σx


Efficient Frontier of all 76 Markets

Barcelona_RMadrid_R

Milan_RRome_R

Brussels: OOT_O

Brussels_O

Naples_R

Lille_O

Marseille_O

Milan_O

Rome_OCologne_O

Barcelona_O

Lisbon_O

Lyon_O

Lille_R Lyon_R

Berlin_O

Dusseldorf_O Frankfurt: City_OHamburg_OMunich: City_OMunich: OOT_OStuttgart_O

Vienna_O

Zurich_O

Paris: CBD_OParis: Central_OParis: LD_OParis: WBD_O

Frankfurt: OOT_O

Amsterdam_R

Marseille_R

Helsinki_O

Rotterdam_O

Stockholm_O

London: Dockl_OParis_R

Stockholm_R

Budapest_OCopenhagen_O

Brussels_R Copenhagen_R

London: M25_O

London: Central_OLondon: WEMT_O

Amsterdam_OLisbon_R Athens_O

Luxembourg_O

Prague_O

Warsaw _O

Budapest_R

Oslo_O

Prague_R

Valencia_RWarsaw _R

Berlin_RCologne_RFrankfurt_RHamburg_R

Munich_R Vienna_R

Birmingham_R Glasgow _R

Manchester_R

London_R

Birmingham_O Edinburgh_O

Glasgow _OManchester_O

Portfolio

-0,5%

1,5%

3,5%

5,5%

7,5%

9,5%

11,5%

13,5%

2,0% 4,0% 6,0% 8,0% 10,0% 12,0% 14,0% 16,0% 18,0% 20,0%

Risk

To

tal R

etu

rn

MVP MRP MSRP


Portfolio STD: 2,47% 11,85% 2,97%


ERES conference 2012, Edinburg – working paper

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