REITs and Portfolio
Diversification
Capital Asset Pricing Models (CAPM)
A. Risk compensation
1. unique vs. systematic risk
2. idiosyncratic vs. nondiversifiable
B. Appropriate market portfolio
1. stock and/or bond markets typically used
2. real estate estimated to comprise 50% of US stock
of wealth vs 20% for stocks
stock market risk may be diversifiable
C. market risk and beta
1. Rf = risk-free return
2. Rm = market return
3. Rre = real estate return
Rre  R f  Rm  R f 
Definitions
• Expected Portfolio Return (2 stocks):
– Weighted average of each stock’s expected
return.
 
 
 
~
~
~
E RP  x1 E R1  x 2 E R2
Definitions
• Portfolio Variance:
– sum of share-weighted averages of the
variances of stock returns plus the covariances
among stock returns.
  x   x   2 x1 x2 COV R1 , R2 
2
P
2
1
2
1
2
2
2
2
Definitions
• Covariance:
– absolute measure of the extent to which 2
stocks move together over time.
• Positive Covariance - 2 assets move together
• Negative Covariance - 2 assets move apart
• Gives contribution of stock to overall portfolio risk



~
~
COV R1 , R2   E R1  E R1  R2  E R2    12
Definitions
• Correlation:
– relative measure of the extent to which 2 stocks
move together.
• Perfectly Positive = +1
• Perfectly Negative = -1

COV R1 , R2 
 1 2
Definitions
• Portfolio Variance – reprise
 P2  x12 12  x22 22  2 x1 x2 COV R1 , R2 
  x   x   2 x1 x2  1 2
2
P
2
1
2
1
2
2
2
2
Portfolio Diversification
• Now consider the “market” portfolio.
– How many stocks are in the market?
• Assume market composed of “N” stocks.
N
~
Rm  xi E ( Ri )
i 1
Portfolio Diversification
• Out of the “N” stocks in the market, let’s
assume that #2 represents the return on
REITs.
• How do you measure the REIT contribution
to the overall portfolio risk?
– Answer: Covariance
Portfolio Diversification
• Let’s look at the “N” stock market
variance/covariance matrix
– Gives contribution of each stock to portfolio
risk.
1
1
x12 12
2
x 2 x1 21

N

x N x1 N 1

2
N
x1 x 2 12  x1 x N  1N
x
2
2

2
2
 x 2 x N  1N



x N2  N2
N
  x 2 xi  2 i
i 1
Portfolio Diversification
• The Marginal Risk of REITs =
– Covariance of REIT and market divided by
overall market risk.
N



N


x2 xi 2i x2  xi 2i  x2  cov  R2 ,  xi Ri  

i 1


 
i 1
  i 1
N
 m2
 m2
 m2
Portfolio Diversification
• Note that:
Rm 
n
 xi Ri
i 1
Portfolio Diversification
• Thus:
 cov R2 , Rm  
 2m 2 m 

2 
x2 
  x2 
  x 2  2 m

2
2
m
m 


 m 

Note:

2 
 2m

m 

Portfolio Diversification
• So what’s the point?
– Compound Annual Returns (1981-2001):
•
•
•
•
REITs

S&P 500

Russell 2000
NASDAQ 
10.79%
11.59%
11.44%
11.18%
Portfolio Diversification
• So what’s the point?
– 20-year Standard Deviation of Annual Returns
(1981-2001)
• REITs
• S&P
• NASDAQ



16.5%
19%
29%
Portfolio Diversification
• So, what’s the point?
– Correlation:
• REIT & S&P500
• REIT & NASDAQ
• REIT & Russell 2000



0.25
0.13
0.40
Portfolio Diversification
• So, what’s the point?
1.  REIT   m
2.  REIT , M  1.0
3.   REIT  1.0
• REITs provide diversification benefits to
portfolios.