The American Real Estate Society (ARES) Meeting, April 11-14, 2007
Risk Premium Puzzle in Real Estate:
Are real estate investors overly risk averse?
James D. Shilling
DePaul University
Tien Foo Sing
National University of Singapore
Risk Premium Puzzle in Real Estate:
Are real estate investors overly risk averse?
James D. Shilling
DePaul University
Tien Foo Sing
National University of Singapore
Outline of Presentation
•
•
•
•
Introduction
Motivation of study
Data sources and analysis
Empirical methodology:
– Generating conditional ex-ante returns using VAR framework
– Testing of relationship between ex-post and ex-ante returns
– Variance tests on the ex-post and ex-ante returns
• Empirical Results
• Conclusion
Risk premium puzzle
• Mehra and Prescott (1985) first raised the puzzle on stock market
• The long term excess return of stock of 6.9% from 1889-2000 was
too large to be explained by economic model (Mehra 2003)
• Based on the standard asset pricing model estimation
E[h]  r f
 (h)
   (c)corr(c, h)
• The risk aversion coefficient is more than 98, which is much higher
than many empirical evidence has suggested (  10).
• If   10 and   0.99 are assumed, the risk premium should be
around 1.4% < 6.18% (observed) (Mehra, 2003)
• This irregularity is dubbed the “Risk Premium Puzzle” by Mehra and
Puzzle in stock market.
Long-term Excess Stock Returns in
the US Market
Input Parameters (1889-1978):
Std deviation of Consumption Growth Rate
0.036
Correlation (consumption x real estate)
0.070
Standard deviation of S&P 500 Return
0.165
Period
Mean
Real
Return
Relatively
Riskless
Security
Risk
Premium
Sharpe
Ratio
Risk Aversion
Computation:
C) Stock Market Data: S&P 500 (source: Mehra & Prescott, 1985)
1889-1978
6.98%
0.8%
6.2%
0.374
148.270
1802-1998
7.0%
2.9%
4.1%
0.248
98.367
1889-2000
7.9%
1.0%
6.9%
0.417
165.544
1926-2000
8.7%
0.7%
8.0%
0.484
191.935
1947-2000
8.4%
0.6%
7.8%
0.472
187.137
Is there a real estate risk premium
puzzle?
• Shilling (2003) raised the above question and challenged the real
estate researchers to explain the large ex-ante premiums in real
estate
• He found ex-ante risk premiums of 6 to 6.75%, which were
excessive to be explained by the standard asset pricing models
• The large risk premiums were translated into risk aversion
coefficients of more than 878 in real term!
• Why is there such a large risk premium in real estate?
• Are real estate investors overly risk averse?
• This puzzle has yet to receive as wide attention in real estate
research community compared to the comparable study in equity
risk premium puzzle!
Real estate investors are overly
risk averse?
Property Type
Excess Return
Sharpe
Ratio
Nominal
Excess
Return
Sharpe
Ratio
Real
Risk Aversion
Computation:
Nominal
Real
A) Korpacz Data
Apartment
0.597
7.458
0.031
2.800
2959.399
1111.111
Industry
0.598
9.714
0.030
2.742
3854.917
1088.219
Office
0.597
6.113
0.034
2.723
2425.847
1080.746
Retail
0.595
8.359
0.029
2.213
3317.189
878.367
Apartment
0.054
1.052
0.018
0.330
417.336
131.039
Industry
0.043
0.602
0.007
0.095
239.036
37.877
Office
0.023
0.231
-0.013
-0.133
91.638
-52.623
Retail
0.046
0.638
0.010
0.139
253.217
55.313
B) NCREIF Data
Further examination of the
historical return data
• Ex-ante return series are rather flat
• Investors’ expectation is rather uniform
• Shilling (2003) found the results to be consistent with the “normal
range” hypothesis (Malkei, 1964)
• No variation across different property type
• When compared with ex-post (NCREIF) returns, he found
unexpected capital losses of 2.2% to 5.7% (1Q88 to 3Q02)
• The losses narrow to 1.2% to 4.3% over the full sample period
(1Q88 to 3Q06)
• What drive the unexpected losses?
– Increase in expected future real interest rate (rejected by evidence)
– Increase in future excess returns (rejected by evidence)
– Lower than expected cash flow growth (difference in ex-ante and expost rent growth)
19
88
Q
19 1
89
Q
19 1
90
Q
19 1
91
Q
19 1
92
Q
19 1
93
Q
19 1
94
Q
19 1
95
Q
19 1
96
Q
19 1
97
Q
19 1
98
Q
19 1
99
Q
20 1
00
Q
20 1
01
Q
20 1
02
Q
20 1
03
Q
20 1
04
Q
20 1
05
Q
20 1
06
Q
1
Expected Return (Nominal)
Are investors overly risk averse?
Historical return (nominal) expectation is flat
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Office
Apartment
Retail
Industry
19
88
Q
19 1
89
Q
19 1
90
Q
19 1
91
Q
19 1
92
Q
19 1
93
Q
19 1
94
Q
19 1
95
Q
19 1
96
Q
19 1
97
Q
19 1
98
Q
19 1
99
Q
20 1
00
Q
20 1
01
Q
20 1
02
Q
20 1
03
Q
20 1
04
Q
20 1
05
Q
20 1
06
Q
1
Ex-ante and Ex-post Returns
Ex-ante vs Ex-post return (Retail)
0.40
0.30
0.20
0.10
0.00
-0.10
-0.20
KRRRet
NRRRet
Motivations of this study
• This paper seek to test the puzzle that the unexpected losses in real
estate are too large to be explained by economic models.
• Study of long-term expectation of investors in real estate investments
• Puzzles:
– Why are investors’ expected return uniform and flat?
– Are the expected returns excessive given the risk-return characteristics
of the markets?
– Investors’ expected returns do not seem to vary much across sectors
• Story: investors’ expectations drive long-term investment decision in
real estate, and they do not adjust the return to reflect short-term
volatility in the market. Portfolio rebalancing is highly expensive for
real estate investors. The long-term return expectations remain
rather stable.
• Hypothesis: real estate investors expect higher risk premiums to
compensate for market uncertainty in long term. Ex-ante return
information is decoupled from the actual returns
Data Source & Analysis
• Korpacz real estate investor survey data first published by Korpacz,
then by Pricewaterhouse Cooper after 1993Q3 are used as proxy for
ex-ante variables
• Quarterly survey of institutional investors, and contain information on
rent growth, capitalization rate (Overall cap rate, IRR and residual
IRR), expense change
• National Council of Real Estate Investment Fiduciaries (NCREIF)
data are used to represent ex-post returns
• Inflation rates – ex-ante (Livingston survey data by Philadelphia
FED) and ex-post (computed from CPI)
• Commercial paper rate as a proxy of short-term interest rate
• Returns data are collected for four market sectors: Apartment (A),
Industry (I), Office (O), Retail (R)
• Descriptive Statistics (Table 2) & PP-Unit Root tests (Table 3)
Dynamic Dividend Ratio Model by
Campbell-Shiller (1989)
• Log-return equations:
t  k   pt 1  (1   )dt  pt
 t  k   t   t 1  d t
• Where   1 /(1  exp( )) and k   log( )  (1   ) .
• Taking the log-return in multi-period forward, and setting
limt    t i  0
i
 j
 r k
 t   Et   d t  j  
 j 0
 1 
• Constant excess return, [Etht =Etrt + c],
 i
 ck
 t  Et   (rt  j  d t  j ) 
 j 0
 1 
Generating conditional ex-ante
returns using VAR
• For one period lagged VAR model,zt  A zt 1  t
• The VAR system can be written in matrix form
  ki,t 1   a11
d  r   
 ki,t t  a 21
 ki,t
a12  
  u1t 1 


a 22  d ki,t 1  rt 1  u 2t 1 
• Let vector e1 = [1 0 0]’ and e2 = [0 1 0]’
e1' ( I  A)  e2' A  0
• Restrictions on VAR systems:
• The discounting factor, i = exp (hit - it)
Apartment
Industry
Office
Retail
0.9210
0.9207
0.9162
0.9251
• Estimating forward ex-ante returns:
t  k   pt 1  (1   )dt  pt
Conditional ex-ante returns
0.45
Predicted Ex-ante Returns
0.40
0.35
Mean: 15.96%
Std dev: 8.54%
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
Q1 9Q1 0Q1 1Q1 2Q1 3Q1 4Q1 5Q1 6Q1 7Q1 8Q1 9Q1 0Q1 1Q1 2Q1 3Q1 4Q1 5Q1 6Q1
8
8
8 9
9
9 9
9 9
9 9
0 0
0 0
9 9
0
0 0
19 19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20
M2KARARet
M2KARIRet
M2KARORet
M2KARRRet
Predictability of Ex-post returns
• Do investors’ expected returns explain variation in ex-post return?
• If investors are risk averse, they would expect higher premiums to
compensate for the investment risks
• If their expectations are aligned with market fundamental, we should
expect the ex-ante returns to explain variations in ex-post returns
• To test the hypothesis, the following regression specifications are
tested:
hni ,t  ai  b1i hni ,t 1  b2i hni ,t 4  b3i hki' ,t  b4i hki' ,t 1  b5i hki' ,t 4   i
• The results summarized in Table 5
Variance Tests using GARCH-M
• The GARCH-M (1,1) proposed by Engle, Lilien and Robins (1987):
hni , t  a0  b1hni , t 1  b2 i2,t   i. t
 i2,t   0  1 i2, t 1   2 i2, t 1    ki2, t
•
•
•
•
•
Results are summarized in Table 6
Persistence in ex-post returns
Hypothesis testing: H0: = 0
If rejected, conditional variance in the ex-ante returns do contain
incremental information on variance in ex-post returns
Conclusion
• Historical evidence suggest that real estate investors are risk averse
• There were unexpected losses in ex-post real estate returns
• Income changes drive the deviations between ex-ante and ex-post
returns
• In the tests of the first and second moments of return relationships,
ex-ante returns were found to have significant effects on ex-post
returns in industry market.
• Investors in apartment, office and retail markets seem to have
expectations that are not in line with market fundamental
• In other words, the expected risk premiums may not be realizable in
the actual market
• The hypothesis that they are risk averse can not be rejected.
• Implications: higher expected returns do not commensurate with the
fundamental of the market, and they may be priced out of the market
• The higher returns may reflect investors’ long term investment
returns
• Thank you