Investment Policy for Securitized and Direct Real Estate *
Barry Feldman
Ibbotson Associates
225 North Michigan Avenue
Chicago, IL 60601
[email protected]
May 22, 2003
ABSTRACT
I examine the constant and variable liquidity direct real estate price indexes of
Fisher, Galtzaff, Geltner, and Haurin [2003] and use them in asset allocation
exercises. Review of these indexes suggests they provide improved measures of
direct real estate performance that do much to remedy problems resulting from the
appraisal-induced smoothing of the NCREIF property index. Optimization results
based on the period from 1987 to 2001 indicate that significant overweighting of
both direct and securitized real estate was appropriate and that direct and
securitized real estate were complementary investments. These results and related
considerations suggest that real estate should receive at least neutral weighting in
contemporary institutional portfolios.
*
Thanks to NAREIT, the National Association of Real Estate Investment Trusts, for support of
this work. Thanks also to Chandra Goda analytical support; Michael Grupe and Jack McAllister
for facilitating this work; Jeffrey Fisher and David Geltner for extensive discussion about their
work and access to NCREIF income data; Gary Antonocci, Peng Chen, Jaques Gordon, Jon
Fosheim, Youguo Liang, and Edwin Ryu for helpful comments; and Tom Carlson and Bill Cowen
for making things happen. Errors and interpretations are solely the responsibility of the author.
1
Investment Policy for Securitized and Direct Real
Estate
Investable commercial real estate equity investments of $1.7 billion constituted
more than 10% of a total of the perhaps $16 billion U.S. investable equity
universe at the end of 2002. 1 Most investors, however, held much lower levels of
commercial real estate in their portfolios. Institutional investors in the Greenwich
Associates survey held an average of 3.4% of their assets in equity real estate at
the end of 2002. This figure corresponds to 4.7% of the aggregate institutional
equity portfolio. Commercial real estate ownership by typical individual
investors is much lower. 2
Institutional investors’ relative holdings of commercial real estate equity
in their equity portfolios might be expected to be roughly equal to the sector’s
share of total equity capitalization, assuming efficient markets. The considerable
divergence between actual and expected efficient market holdings could be
considered something of a puzzle from a policy perspective. The fact that the bulk
of institutional real estate investments are direct, as opposed to securitized,
1
Real estate equity data from J.P. Morgan/Flemming. Year-end 2002 public equity $9.87 trillion
based on CRSP 1-10 New York/American/Nasdaq market value. Total private equity for year-end
1998 estatimed at $5.74 trillion by Moskowitz and Vissing-Jorgenson [2002] by using Survey of
Current Finance data to estimate the market value of all proprietorships, partnerships, and S- and
C-corporations. This is a high estimate of the value investable private equity since if only because
the capitalization of the CRSP public equity index declined 19.6% between 1998 and 2002. Many
private equity assets will not be investment grade.
2
investments constitutes an important piece of this puzzle. Low risk adjusted
returns for direct real estate might be inferred from the Moskowitz and VessingJorgenson [2002] study of private equity performance. The primary measure of
direct real estate performance is the NCREIF property index. 3 Mean variance
optimal direct real estate allocations based on using the NCREIF index as a proxy
for direct real estate performance are extremely high. The NCREIF index,
however, is appraisal based and is widely acknowledged to be a poor proxy for
quantitative optimization purposes because of a resulting downward volatility
bias.
In recent years a variety of statistical techniques have been developed to
provide better measures of direct real estate performance. These techniques tend
to indicate high levels of optimal direct real estate investment; however are
relatively ad hoc in nature. 4 This paper studies and considers the implications of
two new indexes developed by Fisher, Galtzaff, Geltner, and Haurin [2003] -FGGH hereafter.
My primary goals in this paper are to see if the FGGH indexes can help
identify prudent levels of real estate investment and clarify the relationship
2
NAREIT estimates that 60% of REIT equity is institutionally owned. Individual investors must
then hold a maximum of $72 billion in REIT equity.
3
NCREIF is the National Council of Real Estate Investment Fiduciaries.
4
Two notable methods are Giliberto’s [1993] hedged REIT index and the Geltner [1993] and
Fisher, Galtner, and Webb [1994] unsmoothing or reverse filter approach. Unsmoothing methods
require an estimate of direct real estate volatility. Geltner, Rodriguez, and O’Connor [1995]
derive allocations.
3
between direct and securitized real estate investment. Many real estate
investment professionals believe direct real estate has unique investment
properties not shared by securitized real estate products such as real estate
investment trusts (REITs). Direct real estate unquestionably offers some unique
advantages; among them the ability to invest in individual properties and, for
taxable investors, significant tax savings. However, for example, many think that
direct real estate should be preferred to securitized investment because it is more
insulated from other equity markets and is thus inherently a better diversifier.
VARIABLE AND CONSTANT LIQUIDITY INDEXES
Hedonic pricing models use real estate characteristics as independent variables in
a regression that estimates the price at which a property sells. Judd and Seaks
[1994] and Galtzaff and Haurin [1994, 1997, 1998], in studies of residential
housing prices, show that such pricing models may have statistically significant
levels of selection bias and produce selection corrected price indexes. Selection
bias in a real estate price index implies a distortion resulting from properties
transacting on at least one point in time not being representative of all the
properties covered by the index.
Selection bias correction (Heckman [1979]) is a two step procedure. In
the first step a probit model of the transaction process is constructed. The probit
4
model is of the event that a seller and buyer meet and make a deal. Buyers and
sellers are assumed to have reservation prices for all properties. If a buyer and
seller meet and that the buyer’s reservation price is above the seller’s reservation
price, a transaction is assumed to take place. The reservation price model may be
related to the standard supply and demand framework by interpreting the error
term in the estimation process as the unobserved heterogeneity of the buyer and
seller populations. Supply and demand schedules can, in principle, can be
recovered by integrating the cumulative values of these distributions.
FGGH model buyer and seller log reservation prices as a linear
combination of values for real estate characteristics, a vector of annual timespecific terms, and random error. These time-specific terms are used to construct
the index. Using the FGGH notation, let the b superscript correspond to buyers
and the s superscript correspond to sellers. Then buyer and seller reservation
prices RPitb and RPits for asset i at time t can be represented as a sum over
characteristics of valuations α bj or α sj for characteristic j which has magnitude
X ijtP for asset i at time t, time-specific valuations β tb or β ts , and normally
distributed asset-specific buyer and seller error terms ε itb or ε its :
RPitb = ∑ α bj X ijtP + ∑ β tb Z t + ε itb
(1)
RPits = ∑ α sj X ijtP + ∑ β ts Z t + ε its
(2)
5
Examples of characteristics include property size, location, and type.
Characteristic values are assumed to be constant over time. Each Z t is a dummy
variable with value one at time t and zero otherwise. The variation of preferences
among different buyers and sellers is represented by ε itb and ε its .
A transaction is observed, then, if and only if RPitb ≥ RPits . Let
ω j = α bj − α sj and γ t = β tb − β ts . The probit model can be represented as
[
]
Pr[RPitb ≥ RPits ] = Φ ∑ ω j X ijtP + ∑ γ t Z t ,
where Φ[
(3)
] is the cumulative normal distribution with variance σ 2 = var( ε itb -
ε its ). 5 The probit results are used to estimate the inverse Mills ratio λit , for asset i
at time t.
FGGH then construct their variable liquidity index by including the
inverse Mills ratio in a hedonic price regression, the standard method for selection
bias correction. Let Pit be the observed (log) transaction price for asset i at time t,
let α j and β t be equilibrium characteristic and time valuation coefficients, and
let σ εη be the covariance between errors in the probit model (3) and the errors in a
simple hedonic model without the selection term. Then Pit can be estimated
using OLS:
Pit = ∑ α j X ijtP + ∑ β t Z t + σ εη λit + υ it .
(4)
6
The results reported in FGGH’s Table 3 show that the coefficient for λ is
statistically significant (p=.01), implying that a simple hedonic model produces
biased results. The logarithmic variable liquidity price return for time t is then β t
- β t −1 .
The constant liquidity index
The constant liquidity index is FGGH’s innovation. They claim that the
cyclical nature of real estate markets, combined with the relative resistance of
sellers to lowering their prices, generates a systematic bias not addressed by the
selection correction procedure. This bias is not in estimated transaction prices,
but in the imputed underlying values. The large variation in transaction volume
over the real estate cycle and large positive correlation of transaction volume with
prices are identified as the visible result of this process. For example, in a cyclic
downturn buyers’ reservation prices decline while sellers’ are relatively
unchanged, leading to a reduction in transaction volume as it becomes less likely
that randomly matched buyers and sellers will make a deal.
FGGH propose that a better representation of underlying values would
result from estimating the prices that would result from a constant level of
transaction volume. They further propose, that, in the context of real estate
markets, the most logical way to do this is to assume that sellers’ reservation
5
Maddala [1983] provides a comprehensive treatment of the probit model.
7
prices are downward flexible and maintain a constant percentage relationship with
buyers’ reservation prices. Thus the constant liquidity index is based on estimates
of the changes in buyers’ reservation prices. In order to identify these changes
econometrically, buyers and sellers are assumed to “split the difference”
(logarithmically) in bargaining. If a transaction takes place, then
Pit =
(
)
1
RPitb + RPits .
2
(5)
This assumption enables FGGH to identify the β tb coefficients that are used to
construct the constant liquidity index.
Index Availability and Date Alignments
FGGH use characteristics and transactions data from the NCREIF data
base to estimate these equations. The availability of characteristics data limits the
indexes to the dates 1985-2001. FGGH interpret the results of the estimation
procedure, based on annual calendar data, as implying returns for the lagging June
30 to June 30 annual period.
Construction of Income Returns
The FGGH indexes cannot be used directly in portfolio construction
because they only measure price appreciation. NCREIF income returns are taken
as a proxy for the true returns in this paper. This is clearly only an approximation
of the FGGH-based income return. The volatility of income is likely understated
8
because simple percentages are used instead of magnitudes that are then
renormalized to an FGGH price denominator and NCREIF price volatility is
lower than that of the FGGH price indexes. 6 Also, income returns are somewhat
overstated because NCREIF subtracts capital expenditures from capital
appreciation instead of income.
CONSIDERATION OF THE INDEXES
A standard set of asset classes was selected for portfolio construction. These are
large cap, small cap, and international equities, long-term government bonds, and
cash equivalents. The performance of these asset classes is represented by the
S&P 500, the Ibbotson Small Stock Index, the MSCI EAFE index, the Ibbotson
U.S. Long Term Government Bond Index, and the Ibbotson U.S. 30 day T-Bill.
Securitized equity real estate performance is represented by the NAREIT equity
index. Direct real estate performance is represented by either the NCREIF
property index or a total return indexed based on the FGGH variable and constant
liquidity price indexes.
Insert Exhibit 1 about here.
6
Jeffrey Fisher and David Geltner tried to help me construct more appropriate income returns
9
Exhibit 1 shows mean arithmetic returns over the periods June 1987 to
June 2001 and June 1985 to June 2001 for the direct and securitized equity real
estate as well as for asset classes to be included in portfolio construction. REIT
and S&P 500 returns can be inferred to have been exceptionally high over 19851986. The REIT performance advantage relative to measures of direct real estate
performance was also exceptionally high. Overall, the 1987 to 2001 appears to
have more representative relationships between returns of other asset classes as
well. Accordingly, data years 1985 and 1986 are dropped.
Insert Exhibit 2 about here.
Exhibit 2 presents mean arithmetic returns and standard deviations over
the June 1987 to June 2001 period. Of the three direct real estate indexes the
constant liquidity index risk-return profile appears to most closely match that of
the NAREIT equity index. This appearance is confirmed by the results of the
significance tests presented in Exhibit 3. NAREIT performance is statistically
indistinguishable from both the variable and the constant liquidity total return
indexes at conventional significance levels.
from NCREIF property-level data, but this turned out to be more difficult than anticipated.
10
Insert Exhibit 3 about here.
The correlations presented in Exhibit 3 are very consistent with the FGGH
contention that that the variable liquidity index provides an improved
representation of direct real estate market value and that this representation is
usefully enhanced by taking the additional step of constructing constant liquidity
prices. First, observe that correlations with REIT equity rise from -.24 using the
NCREIF index to .08 using the variable liquidity index to .31 with the constant
liquidity index. Direct and securitized real estate should have a substantial
positive correlation. This type of progression is observed in correlations with
other asset classes. The correlation with small stocks rises from -.09 to .24 to .34,
the later being very close to the REIT correlation of .37. Similarly, correlation
with cash drops from .23 to -.18 to -.33, the later being very close to the REIT
correlation of -.29. Correlations with the S&P 500 are all weak and very similar.
The consistency of this pattern is particularly striking because selection correction
and constant liquidity construction do not utilize other asset class indexes in any
way. Correlations with long term bonds, however, constitute a notable exception
to this pattern.
11
Insert Exhibit 4 about here.
OPTIMAL PORTFOLIOS
The optimization inputs, shown in Exhibits 2 and 4, are based on historical
performance. The implications are thus retrospective in nature. Consistency
requires that performance for all asset classes be measured over the same time
period. Optimization is performed over the June 1987 to June 2001 period
already examined. 7
Insert Exhibit 5 about here.
The results of mean variance optimization without real estate assets are
shown in Exhibit 5. An approximate 60/40 portfolio allocation obtains between
6% and 8% standard deviation. Optimization results based on using the NCREIF
12
index to represent direct real estate and the NAREIT equity index to represent
securitized real estate are shown for reference in Exhibit 6. The maximum real
estate allocation is at 6.9% standard deviation. At this risk level, the direct
allocation is 30% and the securitized allocation in 15%.
Insert Exhibit 6 about here.
Optimization results based on using the variable liquidity total return
index to represent direct real estate are shown in Exhibit 7. The maximum real
estate allocation is at 6.6% standard deviation, where the direct allocation is 18%
and the REIT allocation is 12%.
Insert Exhibit 7 about here.
Optimization results based on the constant liquidity total return index are
shown in Exhibit 8. Allocations to direct real estate again decline considerably.
The maximum real estate allocation is at 7.7% standard deviation, where the
direct real estate allocation is 8% and the REIT allocation is 13%. Optimization
7
Optimization using other time periods, including 1985-2001, and, using only NAREIT to
represent real estate, 1992-2001 and 1972-2001 all show larger real estate allocations than the
13
with the constant liquidity index but without NAREIT was performed (detailed
results not shown), with a maximum direct real estate is 12%. Optimization was
also done with NAREIT and without any proxy for direct real estate (diailed
results not shown). The maximum allocation is 17%.
Insert Exhibit 8 about here.
The improvement in portfolio performance from the addition of direct and
or securitized real estate to the portfolio is shown in Exhibit 9. When the variable
liquidity index is used to proxy for direct real estate, maximum performance gain
using both types of real estate is about 27 basis points in the 6% to 8% portfolio
risk range, the approximate risk range of the 60/40 portfolio. When the constant
liquidity index is used, the gain is reduced to 16 to 20 basis points. The
diversification benefit of using both direct and securitized real estate is evident in
this table as well.
Insert Exhibit 9 about here.
1987-2001 period.
14
REVIEW OF THE FGGH METHODOLOGY
Both the NCREIF NPI and NAREIT equity index are value weighted.
The FGGH indexes are equal weighted. This may be necessary. NCREIF
members averaged 164 transactions per year (see FGGH’s Table 1). There is
probably considerable skew in property values, with only a very small number of
the largest properties transacting. Therefore, a value weighted index might have
unacceptable estimation error leading to higher estimated volatilities.
Considering that equal weighted indexes tend to have lower volatility than value
weighted indexes, equal weighting may impart some downward volatility bias.
FGGH do not discuss in detail their assessment that the β t represent
average returns over a calendar year and are “more contemporaneous” with
lagging June to June returns for other asset classes. This may be true on average.
However, if there were a large economic shock in the second half of a calendar
year, it would be reflected in the direct real estate indexes a year earlier than other
indexes. As a practical matter, correlations seem to change very little when
calendar year periods are used for other asset classes. Correlation with NAREIT
rises from .31 to .32 for the constant liquidity total return index and falls from .08
to .06 for the variable liquidity total return index.
Random matching of buyers and sellers may seem less realistic than the
assumption that pricing errors are negatively correlated, that buyers with positive
15
errors and sellers with negative errors are more likely to transact. This would
imply greater distance between mean buyer and seller reservation prices.
However, if it were further assumed that this negative correlation is constant over
time, there should be no net effect so long as the estimation of β tb takes account
of this correlation as well.
The assumption that (log) transaction price is midway between buyer and
seller reservation prices is very important. The bargaining power of buyers and
sellers might reasonably shift over the real estate cycle: up markets are
commonly considered “sellers’ markets” while down markets are “buyers’
markets.” Let π tb and π ts be the bargaining power of buyers and sellers at time t,
and normalize so that π tb + π ts =1. Then equation (5) implies π tb = π ts =1/2. Even
with a simple model of variable bargaining power, estimation of equation (4) is
greatly complicated. Under the equal bargaining power assumption
αj =
(
)
1 b
α j − α sj . If bargaining power varied over time the α j coefficients would
2
have to as well even if the α bj and α sj coefficients did not because now
α jt = π tbα bj − π tsα sj . In principle, however,
β tb = β t − π tsσγ t ,
(6)
where γ t and σ are from equation (3) and γ t is estimated by FGGH to be
consistently positive. Since π ts is positive and β t and γ t should be strongly
16
positively correlated, it is evident that modeling of variable bargaining power
would reduce the volatility of the constant liquidity index. It seems likely then
that the constant liquidity index probably has some upward bias in direct real
estate volatility. 8
Finally, the FGGH approach may be questioned because direct real estate
volatility is implied to be higher than that of securitized real estate by the constant
liquidity index. This result may seem particularly questionable because the
NCREIF and FGGH indexes are computed on an unleveraged basis and REITs
employ considerable leverage. 9 REITs, however, constitute a considerably larger
and more diversified property universe. Additionally, empirical research has
failed to identify the theoretically expected effects of leverage on security
volatility. Figleweski and Wang [2000], in a well-received working paper, find at
best weak leverage effects in the returns of S&P 100 securities.
In sum, there may be some room for further development of the FGGH
methodology and some net upward bias in reported volatility, but the constant
8
David Geltner, in personal communication, reports constructing a variable bargaining power
index. He assumes a strong model of bargaining power: transactions at the top of the real estate
cycle are at sellers’ reservation prices ( π t =1) and those at cyclic bottoms are at buyers’
s
reservation prices ( π t =1). Geltner judges the resulting supply index of seller’s reservation prices
b
to have too much cyclic variation. However, the volatility of Geltner’s variable bargaining power
constant liquidity model is midway between that of the equal bargaining power constant liquidity
index and the variable liquidity index. This suggests that aggregate bargaining power does not
shift dramatically, and, therefore, that only modest declines in volatility should be expected from a
model that could estimate the variation in bargaining power implied by the data.
17
liquidity index appears to be a credible and useful measure of direct real estate
performance.
DISCUSSION
This retrospective analysis implies that real estate allocations have been far below
optimal levels. In the case of direct real estate, allocations based on the constant
liquidity total return index, which arguably overestimates expected direct real
estate volatility still reach 8%, even when REITs are included as an investment
option.
In the case of REITs the difference between optimal and actual allocations
is more dramatic. Considering that 2002 institutional holdings are more than $5
trillion (Greenwich Associates), a 3% institutional allocation to REITs would
about equal the total 2002 REIT capitalization of $160 billion. As a practical
matter, REIT investment is supply-constrained in the short-term. The level of
REIT investment indicated here as optimal clearly cannot today be achieved by
institutional investors as a whole. It is possible that supply constraint is a positive
component of the “REIT premium” that will not completely dissipate until REIT
9
Pagliari, Scherer, and Monopoli [2003] construct deleveraged NAREIT returns. Volatility is
reduced by about 40%. This result is questionable as it implies REIT volatilities are lower than
variable liquidity direct real estate volatilities.
18
capitalization reaches long-term equilibrium levels. Continued growth in REIT
capitalization should then be expected for some time.
Institutional Real Estate Allocation Policy
Treating real estate equity as simply another part of the equity portfolio, neutral
weighting in a 60/40 portfolio would be 7% if commercial real estate constitutes
12% of equity market capitalization. Going forward it is hard to imagine that the
relative performance advantage of real estate will be much lower as the study
period compares general equity performance in the longest expansion in U.S.
history to a complete real estate cycle. The implication structural factors such as
real estate market relative illiquidity generate excess returns for both direct and
securitized real estate. It is difficult to see why these structural factors would
change in the foreseeable future. Thus, is seems that today’s neutral policy
allocations should reflect this structural performance advantage and weight real
estate above its market capitalization.
The Choice Between Direct and Securitized Real Estate
The quantitative results overwhelmingly indicate that securitized real estate
investment is increasingly favored as expected risk and targeted return increase.
These results are driven by securitized real estate’s higher expected returns. Are
structural reasons why this differential might persist? REITs must compete for
investor dollars and face the scrutiny of independent analysts, important aspects
19
of the exposure to market discipline. This exposure has likely led to better
performance, if only from a greater alignment of interests, particularly regarding
the roles of consultants and external advisors. It seems likely that such benefits
will persist.
A further structural element that may be related this performance
differential that REITs are exempt from federal taxation if they distribute 90% of
their net operating income as dividends. Both Lamont [1998] and Arnott and
Asness [2003] find that high dividend payout ratios are strongly predictive of
superior future performance. Arnott and Asness hypothesize that high dividend
payouts and greater dependence on market-financing may force managers to give
up on less productive investment options.
These advantages must be balanced against the loss of effective control
resulting form REIT investment. Securitized real estate investment may not make
sense if you can do a better job of selecting or managing properties than public
REIT managers, or have use for the considerable tax benefits of direct real estate
holdings.
The proposition that direct real estate is more insulated from the
conventional markets finds limited support in this paper. When viewed through
the lens of constant liquidity prices correlations, only the negative correlation
between constant liquidity direct real estate and long term bonds supports this
idea. Otherwise, it appears that the relationship between conventional assets and
20
either direct or securitized real estate is remarkably symmetric. This, the positive
but relatively low correlation between NARIET and constant liquidity direct real
estate, and the optimization results, all support the conclusion that direct and
securitized real estate are complementary investments.
REIT investment appears to provide an effective vehicle for small and
medium-size institutional investors to develop a significant real estate allocation
and a means for larger investors to better diversify their real estate portfolios.
Other Applications for Selection Corrected and Constant
Liquidity Price Indexes
Real estate is not the only asset not traded on public exchanges. The appreciation
of specialized types of real property not in the NCREIF and NAREIT universes
such as timerberland, farmland, and oil and gas properties seem well suited to
study with the methods described here. Better measurement of the performance
of other types of private equity that have sufficient price and characteristics data
might also be possible. Conceivably, these index correction techniques might
also be usefully applied to exchange traded assets. Liquidity variation in small
stock, OTC, and fixed income markets might be sufficient to make selection
corrected and constant liquidity prices of interest.
21
REFERENCES
Arnott, Robert D. and Clifford S. Asness. “Surprise! Higher Dividens = Higher
Earnings Growth.” Financial Analysts Journal, v. 59, n. 1, Jan./Feb. 2003, pp. 7087.
Figleweski, Stephen and Xiaozu Wang Is the “Leverage Effect” a Leverage
Effect? Working paper, NYU Stern School of Business, 2000.
Fisher, Jeffrey, Dean Gatzlaff, David Geltner, and Donald Haurin. “Controlling
for the Impact of Variable Liquidity in Commercial Real Estate Price
Indices,” Real Estate Economics, v. 31, 2003, pp. 269-303.
Fisher, Jeff, David Geltner, and R.B. Webb. “Value Indices of Commercial Real
Estate: A Comparison of Index Construction Methods.” Journal of Real
Estate Finance and Economics, v. 9, 1994, pp.137-164.
Gatzlaff, Dean H. and Donald R, Haurin. Selection Bias and Real Estate Index
Construction. Working paper, Florida State University, 1994.
____. "Sample Selection Bias and Repeat Sales Index Estimates." Journal of Real
Estate Finance and Economics, v. 14 n. 1-2, Jan.-March 1997, pp. 33-50.
____. "Sample Selection and Biases in Local House Value Indices." Journal of
Urban Economics, v. 43 n. 2, March 1998, pp. 199-222.
Geltner, David. “Estimating Market Values from Appraised Values Without
Assuming and Efficient Market.” Journal of Real Estate Research, v. 8 n. 3,
Summer 1993, pp. 325-346.
22
Geltner, David, Joe Rodriguez, and Daniel O'Connor. "The Similar Genetics of
Public & Private Real Estate and the Optimal Long-Horizon Portfolio Mix.”
Real Estate Finance, vol. 12 no. 3, 1995, pp. 71-81.
Giliberto, S. Michael. “Measuring Real Estate Returns: The Hedged REIT Index.”
Journal of Portfolio Management, v. 19 n. 3, 1993, 94-99.
Heckman, James. “Sample selection bias as a specification error.” Econometrica,
v. 47, 1979, pp. 153-161.
Jud, G. Donald and Terry G. Seaks. “Sample Selection Bias in Estimating
Housing Sales Prices.” Journal of Real Estate Research, v. 9, n. 3, Summer
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Lamont, Owen. “Earnings and Expected Returns.” Journal of Finance, v. 53,
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Moskowitz, Tobias J., and Annette Vissing-Jorgennsen. “The Returns to
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Private Real Estate Equities: A More Refined Comparison. Working paper.
[email protected].
23
EXHIBIT 1: MEAN RETURNS AND DIFFERENCES
JUNE 1985 – JUNE 2001 AND JUNE 1987 – JUNE 2001
Real Estate
Average
1987-2001
Average
1985-2001
Difference
10.44
8.49
9.41
14.87
12.41
9.33
9.35
5.37
12.48
8.65
9.81
17.06
13.62
14.90
12.78
5.69
-2.04
-0.16
-0.40
-2.19
-1.21
-5.57
-3.44
-0.32
NAREIT
VL Direct Real Estate
CL Direct Real Estate
S&P 500
U.S. Small Stk
MSCI EAFE
U.S. LT Gvt
U.S. 30 Day Tbill
EXHIBIT 2: MEANS AND STANDARD DEVIATIONS ANNUAL DATA
JUNE 1987 – JUNE 2001
Asset Class
Arithmetic
Mean
Return
NAREIT
NCREIF
VL Direct Real Estate
CL Direct Real Estate
S&P 500
U.S. Small Stk
Standard
Deviation
10.44
7.09
8.49
9.41
14.87
12.41
12.12
6.32
10.28
14.45
13.97
12.08
MSCI EAFE
9.33
17.80
U.S. LT Gvt
9.35
8.25
U.S. 30 Day Tbill
5.37
1.40
24
EXHIBIT 3: TESTS OF DIFFERENCES IN SAMPLE MEANS AND
VARIANCES: DATA JUNE 1987 – JUNE 2001
p-Value
Difference
in Means
0.112
0.299
0.425
0.290
0.290
0.325
Comparison
NAREIT v. NCREIF
NAREIT v. VL Direct
NAREIT v. CL Direct
NCREIF v. VL Direct
NCREIF v. CL Direct
VL Direct v. CL Direct
p-Value
Difference
in Variances
0.009
0.259
0.241
0.235
0.001
0.101
Mean difference significance tests are one-tailed.
EXHIBIT 4: CORRELATIONS JUNE 1987 – JUNE 2001
NAREIT
NAREIT
1.00
NCREIF
NCREIF
VL
CL
S&P
Small
MSCI
U.S. LT
30 Day
Direct
Direct
500
Stock
EAFE
Bonds
T-Bill
-0.24
1.00
VL Direct
0.08
0.42
1.00
CL Direct
0.31
0.32
0.85
S&P 500
0.08
0.19
0.10
0.10
1.00
Small Stock
0.37
-0.09
0.24
0.34
0.29
1.00
MSCI EAFE
0.04
0.01
-0.08
0.00
0.44
0.22
1.00
U.S. LT Bonds
0.32
-0.14
-0.19
-0.16
0.21
0.40
-0.29
1.00
-0.29
0.23
-0.18
-0.33
0.08
-0.44
-0.22
0.04
30 Day T-Bill
1.00
25
1.00
EXHIBIT 5: OPTIMAL ALLOCATIONS WITHOUT REAL ESTATE
Std.
Dev.
Equity
S&P
Sm all
MSCI
US LT
30 Day
Total
500
Stock
EAFE
Bonds
T-Bill
Return
2
4
6
8
10
12
6.9
8.7
10.4
11.9
13.4
14.3
17.4
34.7
50.9
64.9
90.8
100.0
5.5
17.5
28.1
37.2
53.3
77.3
10.5
17.2
22.8
27.7
37.5
22.7
1.3
0.0
0.0
0.0
0.0
0.0
5.0
11.9
19.8
26.5
9.2
0.0
77.6
53.4
29.3
8.6
0.0
0.0
EXHIBIT 6: OPTIMAL ALLOCATIONS USING THE NCREIF NPI TO
REPRESENT DIRECT REAL ESTATE
Total
Std.
Dev.
2
4
6
8
10
12
Real Estate
Real
Return
7.0
9.0
10.8
12.2
13.5
14.4
Estate
15.1
31.4
42.0
26.2
12.7
0.0
REITs
NCREIF
S&P
Sm all
MSCI
US LT
30 Day
500
Stock
EAFE
Bonds
T-Bill
5.9
10.9
15.1
16.2
12.7
0.0
9.2
20.5
26.8
10.0
0.0
0.0
4.3
14.6
25.1
38.9
55.8
80.5
8.0
12.2
16.6
23.6
31.5
19.5
1.4
0.4
0.0
0.0
0.0
0.0
4.2
11.1
16.3
11.3
0.0
0.0
66.9
30.4
0.0
0.0
0.0
0.0
14.9
29.6
22.9
15.5
0.0
17.1
0.0
Maxim um Real Estate Portfolio
5.9
10.6
44.5
26
EXHIBIT 7: OPTIMAL ALLOCATIONS USING A VARIABLE LIQUIDITY
TOTAL RETURN INDEX TO REPRESENT DIRECT REAL ESTATE
Risk
Return
Total
Real
Estate
2
4
6
8
10
12
7.0
8.9
10.7
12.2
13.5
14.3
11.2
20.0
28.3
25.0
12.8
0.0
VL Direct
Real
REITs Estate
S&P
500
Small
Stock
MSCI
EAFE
U.S. LT 30 Day
Bonds T-Bill
4.5
8.1
11.4
14.6
12.8
0.0
6.8
12.0
16.9
10.5
0.0
0.0
4.3
15.1
25.3
39.0
55.7
77.2
5.6
8.2
10.8
20.1
31.5
22.8
2.6
2.4
2.1
0.0
0.0
0.0
7.8
16.6
24.9
15.9
0.0
0.0
68.5
37.7
8.6
0.0
0.0
0.0
12.3
18.1
27.9
11.4
2.0
27.0
1.4
Maximum Real Estate Portfolio
6.6
11.2
30.4
EXHIBIT 8: OPTIMAL ALLOCATIONS USING A CONSTANT LIQUIDITY
TOTAL RETURN INDEX TO REPRESENT DIRECT REAL ESTATE
Std.
Dev.
Return
Total
Real
Estate
2
4
6
8
10
12
7.0
8.8
10.6
12.1
13.5
14.3
7.4
12.5
17.3
20.8
12.8
0.0
Real Estate
CL
REITs
Direct
S&P
500
Sm all
Stock
MSCI
EAFE
U.S. LT
Bonds
30 day
T-Bill
3.8
7.5
10.8
13.7
12.8
0.0
3.6
5.0
6.5
7.0
0.0
0.0
4.9
16.6
27.5
37.1
55.7
77.2
6.5
10.7
14.5
18.4
31.5
22.8
2.0
0.8
0.0
0.0
0.0
0.0
6.6
13.0
19.6
23.7
0.0
0.0
72.7
46.4
21.1
0.0
0.0
0.0
7.8
35.2
17.0
0.0
25.3
1.5
Maxim um Real Estate Portfolio
7.7
11.9
21.0
13.2
27
EXHIBIT 9: BASIS POINT IMPROVEMENT FROM ADDING
OPTIMAL LEVELS OF REAL ESTATE TO A PORTFOLIO
Variable Liquidity Index
Risk in
Percent
REIT plus
Direct
Com bined
Direct
Alone
2
4
6
8
10
12
13
20
27
27
9
0
10
14
18
17
0
0
Constant Liquidity Index
REIT Alone
REIT plus
Direct
Com bined
Direct
Alone
REIT Alone
6
10
13
17
9
0
8
11
16
20
9
0
5
6
8
11
0
0
6
10
13
17
9
0
28