real estate investment performance introduction. real estate investment performance

Real Estate Investment PerformanceIntroduction

Performance Measurement

o Nominal, Real and Excess Returns

o Measuring Real Estate Risk

o Sharpe’s Reward to Variability Index

o Jensen’s Index of Performance

Global Portfolio Allocations

o CAPM

o Black-Litterman Forward Looking Allocations

Pension Funds

Real Estate Investment Performance

N o m i n a l R e t u r n s

T h e N o m i n a l H o l d i n g P e r i o d R e t u r n ( d u r i n g p e r i o d t ) , R t , i s :

w h e r e P t = e n d o f p e r i o d t p r i c e ; D t = p e r i o d t d i v i d e n d ;

11

1

1

1

t

t

t

tt

t

tttt P

D

P

PP

P

PDPR

P P

PC a p i t a l g a i n y i e l d

D

PD i v i d e n d y i e l d

t t

t

t

t

1

1

1

;


R e a l R e t u r n

T h e r e a l r e t u r n , r , i s t h e i n f l a t i o n a d j u s t e d n o m i n a l r e t u r n .

w h e r e R = n o m i n a l h o l d i n g p e r i o d r e t u r nh = t h e i n f l a t i o n r a t e

T h e F i s h e r E f f e c t : ( 1 + R ) = ( 1 + r ) ( 1 + h )

o r R = h + r + r h

N o t e : r h i s v e r y s m a l l a n d i s f r e q u e n t l y o m i t t e d

rR

h

1

11


Excess Return

The excess return (on an asset or a portfolio) is the portion of the nominal holding period return, R, in excess of the risk free rate of return. The risk free rate of return is usually measured by the return on T-bills, Rf.

Excess Return = R - Rf


C o m p u t i n g A v e r a g e R e t u r n s :A r i t h m e t i c v s G e o m e t r i c

T h e r e a r e ( a t l e a s t ) t w o w a y s t o c o m p u t e a n a v e r a g e r e t u r n .

L e t R t = t h e r e t u r n o n a n a s s e t i n p e r i o d t .

A r i t h m e t i c M e a n =

G e o m e t r i c M e a n =

1

1TR t

t

T

( ) ( ) . . . . . ( )1 1 1 11 2 R R R TT


Equity REITs

Russell 2000 SP 500 Inflation

Arithmetic 1.27% 1.21% 1.14% 0.33%Geometric 1.20% 1.05% 1.05% 0.33%

3.79% 5.53% 4.26% 0.34%2.99 4.56 3.73 1.05

Arithmetic 16.22% 14.80% 14.33% 4.05%Geometric 15.32% 13.97% 13.84% 4.17%

14.63% 17.98% 15.03% 2.88%0.90 1.21 1.05 0.71

Nominal Returns

Monthly: 1979-2006:10Mean

Coef. Of Variation

Mean

Standard Deviation

Standard DeviationCoef. Of Variation

Annual: 1979-2005


Equity REITs

Russell 2000 SP 500

Arithmetic 0.91% 0.91% 0.84%Geometric 0.83% 0.74% 0.74%

3.81% 5.67% 4.42%4.2 6.26 5.28


14.52% 17.54% 15.18%1.19 1.63 1.48

Real Returns


Coef. Of Variation

Mean

Standard Deviation

Standard DeviationCoef. Of Variation

Annual: 1979-2005

Real Estate Investment Performance Excess Returns

Equity REITs Russell 2000 SP 500



Standard Deviation 3.81% 5.54% 4.27%Coef. Of Variation 4.90 7.68 6.55

Annual: 1979-2005Mean


Standard Deviation 14.98% 17.92% 14.81%Coef. Of Variation 1.47 2.05 1.79

Real Estate Investment PerformanceEREITS, Russell 2000, SNP500 and CPI: 1979-2006

Pearson Correlation Coefficients, N = 334 Prob > |r| under H0: Rho=0 EREITs R2000 SP500 CPI EREITs 1.00000 0.59452 0.47255 -0.05864 EREITs <.0001 <.0001 0.2853 R2000 0.59452 1.00000 0.79730 -0.08827 R2000 <.0001 <.0001 0.1074 SP500 0.47255 0.79730 1.00000 -0.10158 SP500 <.0001 <.0001 0.0637 CPI -0.05864 -0.08827 -0.10158 1.00000 CPI 0.2853 0.1074 0.0637

Real Estate Investment Performance Risk Adjusted Performance Indexes

Sharpe Index

The Sharpe Index, SI, evaluates investment performance using total risk:

j

fj RRSI

_ Where Rj = the mean return on portfolio j Rf = the risk free rate of interest (T-bill return) σj = the standard deviation of excess returns on portfolio j.


Equity REITs Russell 2000 S&P 500

Monthly: 1979-2006:10 0.204 0.130 0.153

Annual: 1979-2005 0.679 0.488 0.559

Annual: 1980-1989 0.754 0.423 0.713

Annual: 1990-1999 0.313 0.553 1.048

Sharpe's Index of Performance

Note: the risk-free rate is measured using the monthly average of short- term US Treasury Securities


Jensen’s Index of Performance

Jensen’s Index evaluates performance using market risk. It is based on the Capital Asset Pricing Model (CAPM). CAPM states that, in equilibrium, the expected return on an asset (or portfolio of assets) is related to the risk-free rate of return and the return on the market portfolio:


Jensen’s Index of Performance CAPM:

fmjfj R)R

~E(R)R

~E(

~

where Rj = the random rate of return on portfolio j ~

Rm = the random rate of return on the market Rf = the risk free rate of interest (T-bill return)

βj = the beta coefficient; the risk of the jth asset (or portfolio) relative to the market risk

fm R)R

~E( is the market price of risk



jtmtjjjt rr

Where r jt = the excess return on portfolio j

r mt = the excess return on the market

βj = the beta coefficient or systematic risk

of the jth asset or portfolio

αj = Jensen’s Index of Performance

εjt = the random error term with E(εjt) = 0



A positive alpha indicates a superior performance of the investment fund relative to an unmanaged portfolio of similar market risk. A negative alpha indicates an inferior performance of the investment fund relative to an unmanaged portfolio of similar market risk.

Dependent Variable: Equity REITs Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.11011 0.11011 97.62 <.0001 Error 332 0.37449 0.00113 Corrected Total 333 0.48460 Root MSE 0.03359 R-Square 0.2272 Dependent Mean 0.00777 Adj R-Sq 0.2249 Coeff Var 432.14776 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 0.00500 0.00186 2.69 0.0075 SP500 SP500 1 0.42535 0.04305 9.88 <.0001

Dependent Variable: Russell 2000 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.65491 0.65491 584.96 <.0001 Error 332 0.37170 0.00112 Corrected Total 333 1.02661 Root MSE 0.03346 R-Square 0.6379 Dependent Mean 0.00722 Adj R-Sq 0.6368 Coeff Var 463.70331 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 0.00045211 0.00185 0.24 0.8073 SP500 SP500 1 1.03733 0.04289 24.19 <.0001

Real Estate Investment Performance Portfolio Diversification

Portfolio: group of assets such as stocks and bonds held by an investor. Portfolio weight: the percentage of the portfolio’s total value in a particular asset. Let E{Ri} denote the expected return on asset i for i = 1,.....,N and wi denote the percentage of holdings invested in asset i. Let RP be the return on the portfolio. The expected portfolio return, E{RP}, is: E{RP} = w1E{R1} + w2 E{R2} + ... + wN E{RN}

Real Estate Investment Performance Portfolio Diversification

T h e v a r i a n c e o f t h e p o r t f o l i o r e t u r n i s :

N o t e t h e p o r t f o l i o v a r i a n c e i s n o t s i m p l y a w e i g h t e d a v e r a g e o ft h e i n d i v i d u a l a s s e t r e t u r n v a r i a n c e s .

A n d t h e s t a n d a r d d e v i a t i o n o f t h e p o r t f o l i o i s :

S t D e v { R P } =

V a r R P w V a r R w w C o v R Rii

N

i ij i

N

i

N

j i j{ } { } { , } 2

1 1

2

V a r R P{ }

Efficient frontier with and without REITsStocks, bonds, T-bills, and REITs 1972 – 2005

Source: www.nareit.com

Potential to reduce risk and increase returnStock and bond investors, 1972-2005


Potential to reduce risk and increase returnFixed-income investors, 1972-2005


Investment Performance with Global Real Estate

http://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/GlobalRealEstateWhitePaper.pdf


Market Capitalization (billions;

as of June 6, 2007) % of Total % of CategoryNorth American REITs $342.72 47.6%

US $317.70 92.70%Canada $25.02 7.30%

Asia $226.08 31.4%Japan $82.75 36.60%Austrailia $73.93 32.70%Hong Kong $56.52 25.00%Other (Sing. & NZ) $12.89 5.70%

Europe $151.20 21.0%UK $71.22 47.10%France $17.24 11.40%Netherlands $17.09 11.30%Other $45.66 30.20%

Total $720.00 100.0%

Source: http://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/GlobalRealEstateWhitePaper.pdf

Other Europe includes Sweden, Spain, Austria, Switzerland, Germany, Belgium, Italy, Fineland, Denmark, Poland and Greece


http://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/GlobalRealEstateWhitePaper.pdf

Pension Funds

For the 12 months ending September 30, 2006

Top 1,000 plan assets grew 8.4% to about $6.5 trillion o Doubled since 1996 o Defined contribution plans grew 9.5% o Defined benefit plans grew 8%

Allocations for top 1000 plans o 43.7% in domestic equity, down 1.6 percentage points o 25.4% in domestic fixed income, up 0.5 percentage points o 16.8% in international equity, unchanged o 1.2% in international fixed income, unchanged o 3.9% in real estate equity, up 0.2% o 0.3% in mortgages, down 0.3% o 3.5% ‘other’

http://www.pionline.com/apps/pbcs.dll/article?AID=/20070122/PRINTSUB/701220730/-1/PENSIONFUNDDIRECTORY

Pension Funds

2006 2005Percent Change

Top 1,000 funds $6,487.70 $5,986.10 8.38%Defined benefit $4,776.50 $4,423.50 7.98%Defined contribution $1,711.20 $1,562.60 9.51%

Top 200 funds $4,911.00 $4,522.40 8.59%Defined benefit $3,869.40 $3,569.70 8.40%Defined contribution $1,041.60 $952.70 9.33%

http://www.pionline.com/apps/pbcs.dll/article?AID=/20070122/CHART/101011785/-1/PENSIONFUNDDIRECTORY

Pension Funds and Real Estate

Pension Fund Historical Asset Allocation

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Stocks

Bonds

Cash

Real Estate Equity


“Hike continues in real estate” For the 12 months ending Sept. 30, 2006

Top 200 defined benefit plans increased real estate equity investments 29.8%, to $150.1 billion

o 17.6% increase in NCREIF index o 10.4% incremental investment

Investments in REITs increased 28.2% to $29.1 billion

o 24.0% increase in FTSE NAREIT o 4.2% incremental investment

Allocation o 90% domestic real estate equity o 5% international real estate equity o 5% timber

Source: http://www.pionline.com/apps/pbcs.dll/article?AID=/20070122/PRINTSUB/701220710/-1/PENSIONFUNDDIRECTORY


“Hike continues in real estate”

CalPERS (CA Public Retirement System), a $228.4b fund, grew real estate equity 80%

o Plans to sell core domestic real estate, go non-core and global real estate.

CalSTRS (CA State Teachers Retirement System), a $156.1b fund, grew its $11.6b real estate equity portfolio 50% from a year earlier

o Plans to increase real estate share from 6% to 11%.

MassPRIM (MA Pension Reserves Investment Management), a $45.5b fund, increased real estate equities 62% to $4.9b.

Source: http://www.pionline.com/apps/pbcs.dll/article?AID=/20070122/PRINTSUB/701220710/-1/PENSIONFUNDDIRECTORY


The Future

total pension fund assets are forecast to increase to $17.6 trillion in 2020.

Holding real estate allocation constant, pension funds

o will hold about $623.6B in 2020

o 8.2% annual rate of increase in funds demand for RE equities

If pension funds gradually increase their allocation to real estate equities to 6%

o pension funds’ real estate holdings will total $1.0 trillion in 2020 o 11.75% annual rate of increase in pension funds real estate holdings

real estate investment performance introduction. real estate investment performance

Documents

global real estate slide

pension funds slide

performance indexes

reits stocks

return stock

return fixedincome investors

bond investors

efficient frontier