James D. Shilling and Charles H. Wurtzebach April 22, 2018 ... · REAL ESTATE: THE CASE FOR...
Transcript of James D. Shilling and Charles H. Wurtzebach April 22, 2018 ... · REAL ESTATE: THE CASE FOR...
REAL ESTATE:
THE CASE FOR INVESTMENT IN PRIVATE AND LISTED REAL ESTATE
James D. Shilling† and Charles H. Wurtzebach‡
April 22, 2018
Abstract
Our analysis of long-term trends points to the outperformance of listed REIT stocks and private
equity real estate opportunistic funds compared with more traditional asset classes – marketable
equities (the S&P500 stock index) and bonds. With these findings, making the practical case for
greater investment in private and listed real estate in relation to stocks and bonds is relatively
straightforward, at least historically, that is. Whether these same results will continue in the
foreseeable future is difficult to predict. However, there is every indication (at least in theory)
that real estate prices will continue to rise relative to bonds, with a contemporaneous increase in
the return of listed REIT stocks and private equity real estate opportunistic funds relative to
bonds, as long as the economy remains in secular stagnation. The study also compares the
outcomes of ex ante and ex post portfolios consisting of marketable equities (stocks), bonds, and
real estate. The former are calculated very simplistically. It seems to be commonly accepted
that optimal ex ante portfolios should be computed from normal returns, and so that is what we
did. A conclusion to be drawn from the comparison is that an optimal ex ante portfolio should
include a combined portfolio weighing on private and listed real estate of between 4 and 20
percent, at least as a minimum, and potentially more if past is prologue.
Key words: Portfolio Choice, Real Estate Investment Decisions, Asset Pricing
JEL Classification: G11; G12
† DePaul University, 1 East Jackson Boulevard, Chicago, IL 60606, Email: [email protected].
‡
DePaul University, 1 East Jackson Boulevard, Chicago, IL 60604, Email: [email protected].
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1 Introduction
How should investors allocate the assets in their funds among broad classes such as stocks, bonds, and
real estate? Most professional advisers would argue for a good deal of conformity. The traditional
advice, which is expounded in most every finance textbook, is to split your investment between a
money-market fund and a broad-based, (passively managed) stock, bond, and real estate fund. The
broad-based, (passively managed) stock, bond, and real estate portfolio should concentrate on
minimizing fees and transactions costs. The portfolio advisor should avoid the temptation of actively
managing its assets, and trying to chase the latest hot stock or real estate deal. Instead, the broad-based,
(passively managed) stock, bond, and real estate portfolio should approximate the “market portfolio”
that passively holds a bit of every asset.
Figure 1 summarizes the economic intuition behind this advice. The figure shows us that we
always have two choices available. We can move along the mean-variance opportunity set by changing
our portfolio of risky assets or we can move along the capital market line (the solid upward sloping line
shown in Figure 1) by holding various combinations of two funds: the market portfolio (where the
market portfolio contains an amount of every asset that is proportional to the total amount outstanding
of that asset) and the risk-free asset. If we have the opportunity to move along the capital market line,
we can be better off than moving along the opportunity set. Therefore, every investor need only hold
different proportions of the risk-free asset and the market portfolio.
However, anyone who took this advice and did not overweight direct real estate investments and
listed REIT stocks in particular over the past twenty-four years missed out on a dramatic surge in both
the private equity real estate and the listed REIT market. Since 1989, listed REIT stocks and private
equity opportunistic real estate funds significantly outperformed the S&P500 stock index (the core of
most portfolios) on the basis of total (gross of fees) returns. The relevance we attach to this longer-
term outperformance is significant. First, listed REIT stocks and private equity opportunistic real estate
funds are not supposed to outperform marketable equities, at least not in the longer-term. Most would
say that since real estate is inherently less risky than marketable equities, listed REIT stocks and private
equity opportunistic real estate funds should invariably have lower returns than marketable equities.
Second, evidence to the contrary leads to the question: What can explain the behavior of listed REIT
stocks and private equity opportunistic real estate funds relative to marketable equities and can this
explanation suggest a better way to invest? In the standard textbook portfolio model, there is no
forecasting of demand shifts. Investors confidently believe that there is no better way to invest than to
put part or all of ones’ money into a “market portfolio” mixed with borrowing or lending. But,
interestingly enough, if an investor is aware that there is indeed a major demand shift taking place, with
the shift causing investors to (say) look for high yielding real estate assets, then the optimal (or
“tangency”) portfolio that reflects this knowledge will be more heavily weighted toward private equity
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opportunistic real estate funds and listed REIT stocks than will the market portfolio held by the average
investor.
Before we worry about the reasons for and the implications of this shift, though, we need to
document that a shift really did occur, and that listed REIT stocks and private equity opportunistic real
estate funds did in fact outperform the S&P500 stock index. The rest of this paper takes a retrospective
look at whether listed REIT stocks and private equity opportunistic real estate funds outperformed
marketable equities and bonds over the past twenty-four years. Once we do so, we then document what
an investor would had earned over this time period on an optimal portfolio more heavily weighted in
real estate than the “market portfolio.” We then compare this return to the return earned on the market
portfolio over this period. The return difference is significant. We dub this premium a “real estate
premium puzzle.” The challenge that these results pose is twofold: to explain the difference in the
behavior of listed REIT stocks and private equity opportunistic real estate funds over the past twenty-
four years and before that, and to examine the related question, Why should the return on listed REIT
stocks and private equity opportunistic real estate funds over this time period outperform both
marketable equities and bonds? We conclude this research by examining whether this real estate
premium will prevail in the future? It is our conviction that the answer to this last question is yes and
in the following we will explain why.
2 Estimates of the Return on Private and Listed Real Estate
2.1 The Sub-Period 1989-2012
We find that annual returns to private equity value-add and opportunistic real estate funds are not
particularly available before 1989 or after 2012. To the best of our knowledge, the private equity
value-add and opportunistic real estate returns used by most research are the National Council of Real
Estate Investment Fiduciaries (NCREIF)/Townsend Fund Indices (which was discontinued in
September 2013). The NCREIF/Townsend Fund Indices provides returns for closed-end value-add
(comprised of moderate risk) and opportunistic (comprised of higher risk) funds. The funds are
classified into value-add and opportunistic based on various criteria in terms of portfolio and
investment level risks, performance history and level of returns achieved, and the style classification
that the fund manager uses when marketing the fund to prospective investors. The total returns
represent average fund performance (gross of fees) by strategy.
The Financial Times Stock Exchange/National Association of Real Estate Investment Trusts
(FTSE/NAREIT) is the most definitive source for listed REIT stock returns. The index is designed to
measure the performance of all listed equity REITs. The companies included in the FTSE/NAREIT All
Equity Index must have 1) a minimum combined sector level weight greater than 3 percent of the
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FTSE/NAREIT All Equity Index by investable market capitalization, and 2) more than 50 percent of
total assets in qualifying real estate assets other than mortgages secured by real property.
To measure the return on marketable equities, we use the Standard & Poor’s 500 (S&P500) index
return. The S&P500 index focuses on the large-cap sector of the market. However, since the S&P500
index includes a significant portion of the total value of the market, it also represents the market. The
companies included in the S&P500 index are considered leading companies in leading industries,
including thirty-two large-cap REITs.
These data provide us with evidence that returns on listed REIT stocks and private equity
opportunistic real estate funds have been considerably higher than those for the S&P500 index. This
result is illustrated in Figure 2, which graphs the capital appreciation of $1 invested (with dividends and
cash flows reinvested) in the three different asset classes from 1989 to 2012. As Figure 2 indicates, $1
invested in listed REIT stocks yields an ending wealth of $11.7 versus a value of $8.7 for $1 invested in
the S&P500 index for the period 1989-2012. The corresponding value for $1 invested in private equity
opportunistic real estate funds is $11.4. In contrast, $1 invested in private equity value-add real estate
funds yields an ending wealth only of $5.5. In these calculations, we assume that all payments to the
underlying asset, including dividend payments to stockholders, are reinvested and that there are no
taxes paid.
These results underscore a remarkable finding, namely, that listed REIT stocks and private equity
opportunistic real estate funds have significantly outperformed the S&P500 stock index on the basis of
total (gross of fees) returns for the period 1989-2012. The results immediately raise the question: Why,
precisely, are the returns on listed REIT stocks and private equity opportunistic real estate funds so
high, and why are they higher than the returns on marketable equities? These are questions that need to
be pondered over.1
2.2 The Sub-Period 1989-2017
Since the NCREIF/Townsend Fund Indices were discontinued in September 2013, we have to work
with different private equity real estate returns data for the sub-period 1989-2017 than we worked with
for the sub-period 1989-2012. In doing so, we switched to using the levered NCREIF Property Index
1 In a 1976 article in the Journal of Portfolio Management, Steven Roulac had asked the same question of real
estate returns we are asking. He suggested in that paper that real estate appears to provide returns similar to
common stocks, but with less variability and more predictability. Of course, Roulac’s sample period was restricted
to the period of the 1960s and 1970s. During this time period, we know that stock prices fluctuated wildly. We
also know (retrospectively) that common stocks failed to provide the attractive returns investors had come to
expect over the twenty years preceding 1966. Following these disappointing stock price returns, many investors
reshuffled their portfolios and shifted away from common stocks and into real estate in search of higher returns.
Under these conditions, the increase in demand leads to rising relative prices for real estate. Holding rents
constant, rising prices imply an increase in the contemporaneous return on real estate. Given this, it is not difficult
to see how Steven Roulac in the mid-1970s arrived at the conclusion that real estate and common stock provide
similar returns. Yet Steven Roulac’s time period is much different from that described here.
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(NPI) for the entire 1989-2017 period. The levered NPI is comprised exclusively of operating
properties acquired primarily on behalf of institutions and held in a fiduciary environment. The levered
NPI index is a value-weighted index and includes property investments in apartment, hotel, industrial,
office, and retail properties. The index is a composite index of core, value-add, and opportunistic
investments.
These results add to the findings above that listed REIT stocks have provided higher returns than
the S&P500 index over long periods. As Figure 3 indicates, $1 invested in listed REIT stocks yields an
ending wealth of $42.7 versus a value of $36.3 for $1 invested in the S&P500 index for the period
1989-2016. However, an interesting fact is that the results do not generalize to a $1 invested in the
levered NPI index for the 28-year period, 1989-2016. This result should not surprise. For example,
while we found that private equity opportunistic real estate funds provided higher returns than the
S&P500 index for the 24-year period, 1989-2012, we did not find similar results for private equity
value-add real estate funds. A possible conclusion could be that investors have been attracted by the
higher yields on private equity opportunistic real estate funds as interest rates stay low as well as by the
marketability that listed REIT stocks provide compared with other fixed-income products. These
features may have led to an increased demand for listed REIT stocks and private equity opportunistic
real estate funds, causing prices to increase, with contemporaneously higher returns.
3 The Economic Implications for Portfolio Selection
The above findings have important economic implications for portfolio selection. If one believes the
above results, and, more importantly, believes that the high returns on private equity opportunistic real
estate funds and listed REIT stocks are likely to prevail in the future, then one ought to change his or
her portfolio strategy dramatically. Standard theory tells us (as mentioned above) that in most
circumstance investors should hold a mixture of the market portfolio with borrowing or lending. The
exception to this rule occurs when the investor has different information or beliefs. In the latter case, as
the investor has knowledge about certain asset return patterns, and as the investor believes that these
return patterns are exploitable anomalies, then the optimal investment portfolio that reflects this
knowledge should (as the theory goes) be more heavily weighted toward these assets than the market
portfolio held by the average investor.
It is not easy (in theory), starting from here, to get an idea of what this portfolio should like. First
of all, identifying the individual asset weightings for this portfolio can only really be done using ex post
data. Second, often the optimal portfolio weightings will shift over time, reflecting structural changes
in expected returns, risk and correlation. Hence, any findings may be sample-specific. Other sample
periods might differ with respect to expected returns, risk and correlation. Differences in the level of
interest rates would also be likely to make a difference.
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These considerations raise some question about whether the portfolio-selection results for the 1978-
2012 period can be generalized beyond the sample. Before worrying about this issue, we use the
historical statistics presented above (plus data on non-US stock returns and data on US and non-US
bond returns) to estimate (ex post) the optimal portfolio mix for a portfolio consisting of stocks, bond,
and real estate, assuming the investor had known, in 1989, the return and risk performances of private
equity opportunistic real estate funds and listed REIT stocks over the 1978-2012 period. We allow no
short selling for the underlying assets. The outcome of this process are portfolio weights that entail
“concentrated” positions in some assets and “less concentrated” positions in other assets, positions that
might be considered imprudent were it not for the high expected returns on private equity opportunistic
real estate funds and listed REIT stocks. We compare these portfolio weights to the portfolio weights
for the “market portfolio” of stock, bond, and real estate, which, as mentioned above, is the optimal
reference portfolio. We also compare the subsequent annual (in-sample) returns for both portfolios.
The questions of interest are how different are the weights in these two portfolios, and how different are
the subsequent annual returns for both portfolios.
3.1 Optimum Portfolio Weights
In this section, portfolios are developed that are ex post efficient using the portfolio selection model
developed by Markowitz (1959). Ordinarily, the Markowitz model uses expectational data as input,
and using these data creates minimum variance portfolios at requested return levels. However, we will
form efficient stock, bond, and real estate portfolios within the Markowitz framework using ex post
(historical) data, and thereafter compare the rate of returns from selected portfolios on this efficient
frontier with the returns to the market portfolio. Importantly, by applying the Markowitz model to ex
post (historical) data, the model solves for how the portfolios on the efficient frontier should have been
structured to take advantage of the high ex post returns on private equity opportunistic real estate funds
and listed REIT stocks documented above. But this implies that the portfolios would be ex ante
efficient to investors who had perfect foresight regarding the future path of returns.
In the Markowitz model, investors choose investment weights so as to minimize the portfolio’s
overall risk, defined as variance, for a given level of return. Hence, when some assets are not highly
correlated with other assets, their risk to a diversified portfolio (the covariance of their returns with
portfolio returns) is much less their return variance, and vice versa. This risk reduction enhances the
contribution of the asset to compound return on the portfolio, causing the portfolio compound return to
be greater than the weighted average of the compound returns on the assets in the portfolio.
Table 1 reports the average annual total returns, volatilities (as measured by the standard deviation
of returns) and correlations for the following seven asset classes over the 1978-2012 period:
* US stocks, as measured by the S&P500 index;
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* US bonds, as measured by the Salomon Brothers US corporate bond index;
* private equity value-add real estate funds, as measured by the NCREIF/Townsend closed-end
value-add real estate fund index;
* private equity opportunistic real estate funds, as measured by the NCREIF/Townsend closed-end
opportunistic real estate fund index;
* international stocks, as measured by the Morgan Stanley Capital International EAFE (Europe,
Australia, Far East) index (in US dollars).
* international bonds, as measured by the Salomon Brothers world bond index (in US dollars); and
* listed REIT stocks, as measured by the FTSE/NAREIT all equity index NCREIF/Townsend
closed-end opportunistic fund index;
The top performance asset class (as measured by average annual total returns) over the 1978-2012
period is listed REIT stocks, followed by private equity opportunistic real estate funds, US stocks,
private equity value-add real estate funds, US bonds, international bonds, and international stocks.
US bonds have a low return and low volatility, but a high return-risk ratio (1.50). Similar to their
US counterpart, international bonds have a low return and low volatility, and a high return-risk ratio
(1.03). Listed REIT stocks and private equity opportunistic real estate funds also have higher returns
and higher volatility than US stocks. In contrast, private equity value-add real estate funds have lower
returns and lower volatility than US stocks. Despite these return and risk differences, listed REIT
stocks, private equity opportunistic real estate funds, the S&P500, and private equity value-add real
estate funds do not differ significantly in terms of their return-risk ratios (the mean return-risk ratio is
0.62). International stocks have low returns but the highest volatility of the seven asset classes.
International stocks have the lowest return-risk ratio (0.31).
In these comparisons, the volatilities for private equity value-add and opportunistic real estate funds
are quite high, despite the fact that these two series are appraisal-based indexes. Ordinarily, given the
nature of the data, researchers would use an upward adjustment in the volatilities of these two indexes
in constructing an efficient frontier so as to avoid any possible under emphasis of risk. Without
showing the details, we can report that the results of the analysis are not qualitatively different when an
upward adjustment to the volatilities of private equity value-add and opportunistic real estate funds is
used. Instead, in our case, what one takes as the mean returns for private equity opportunistic real
estate funds and listed REIT stocks has a bigger effect.
The correlation coefficients shown in Table 1 are normalized measures of how two asset classes
move together. These correlation coefficients are measured as the covariance of the two asset classes
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divided by the product of the standard deviations of the two assets. The correlation coefficients can
range from +1, when the two asset classes move together perfectly, to -1, when the returns on two
assets move in perfectly opposite directions.
From a portfolio perspective, private equity value-add and opportunistic real estate funds are highly
correlated with US bond returns. The two indexes are also highly correlated with each other, and both
are positively correlated with US stocks. International stocks with a 0.96 correlation with the S&P500
and listed REIT stocks with a 0.90 correlation with the S&P500 actually look very much like a US
stock index. Listed REIT stocks are positively correlated with private equity value-add and
opportunistic real estate funds as well.
Using the return and the risk and correlation data from Table 1, we created the efficient frontier of
stocks, bonds, and real estate displayed in Figure 4 and tabulated in Table 2. The efficient portfolios in
Table 2 display some unique characteristics. For low-risk and low-return levels, the efficient portfolios
are dominated by bonds. In the middle ranges of return and risk, there is a clear shift out of bonds and
into private real estate and listed REIT stocks. These results are as expected, with low interest rates on
bonds, investors have been attracted by the higher yields on private equity opportunistic real estate
funds.
At high-risk and high-return levels, the efficient portfolios are dominated by listed REIT stocks.
Here the results differ strikingly from expectations. As mentioned earlier, a possible explanation for
this finding concerns the importance of high dividend yields in today’s low interest rate environment.
Other things equal, as investors have increased their demand for listed REIT stocks relative to bonds in
search of higher yields, the shift in demand leads to rising prices for listed REIT stocks. Holding
dividends constant, rising prices imply an increase in the contemporaneous return on listed REIT
stocks. Thus, during the sample period, listed REIT stocks would have enjoyed a higher realized
premium than they would have without the price effect. We also see that none of the portfolios
(including the corner portfolios) includes stocks (which is another puzzling result).
To examine this matter further, we constructed portfolios of stocks, bonds, and private equity real
estate and listed REITs using the historical data over the sub-period 1989-2016. The portfolios that
maximized return for each level of risk, based upon on the historical data, are shown in Table 3. The
portfolios in Table 3 have a standard deviation of 2.5% or less at low-risk and low-return levels and
5.2% or higher at high-risk and high-return levels. At low-risk and low-return levels, these standard
deviations are higher than those in Table 2. However, at high-risk and high-return levels the standard
deviations in Table 3 are lower than those in Table 2. Yet those portfolios in Table 3 produce higher
returns than in Table 2. Portfolio number 23 in Table 3, for example, produces a return of 12.9% and a
risk of 7.5%. In contrast, portfolio number 19 in Table 2 produces a return of 11.9% and a risk of
16.3%.
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In contrast to the case in Table 2, it is interesting that stocks do enter into the optimal portfolios in
Table 3, low at first and more and more at higher risk levels. Noticeably absent from moderate- and
high-risk and return levels in the optimal portfolios in Table 3 (as well as from the optimal portfolios in
Table 2) are investments in international stocks and bonds. Another interesting aspect of the optimal
portfolios in Table 3 is the dominance of private equity real estate and listed REIT stocks in the high-
risk and high-return portfolios. The optimal portfolios at the high-risk and high-return levels consist of
70% or more of private equity real estate and listed REIT stocks in total.
When we compare the portfolio weightings in Tables 2 to those of the market portfolio (reported in
Table 4), we see that the optimal portfolios are highly concentrated in certain assets, especially in
private equity opportunistic real estate funds and listed REIT stocks. In Table 4, we show measures of
total investable wealth for 1989 and 2012. The financial wealth data are constructed from the Federal
Reserve Board, Flow of Funds Accounts of the United States: Flows and Outstandings, various quarters
(Release Z.1). For 1989, the aggregate value of commercial real estate is taken from the US
Department of Commerce, Bureau of Economic Analysis, Estimates of Fixed Reproducible Tangible
Wealth series. For 2012, the aggregate value of commercial real estate is from the Flows of Funds
Accounts. To obtain an estimate of the private sector commercial real estate market (excluding
commercial real estate held by corporations), we subtracted the value of commercial real estate held by
nonfarm, nonfinancial corporate businesses in 1989 and 2012, as reported by the Flow of Funds
Accounts, from the respective aggregate values of all commercial real estate. We estimate the size of
the private equity value-add and opportunistic real estate market from the Preqin database. We
estimate the size of the public market for real estate from data published by NARIET. All values are in
billions of dollars.
The data in Table 5 for portfolio weights constructed using the historical data over the sub-period
1989-2016 show much of the same effects as those portfolio weights in Table 4. For commercial real
estate, the variance differential is between 495 and 601 percent. For listed REIT stocks, the variance
differential is between 1544 and 8329 percent. The variance differentials are exceedingly large because
the denominator is small and only to a lesser extent because the numerator is high.
3.2 Realized Returns
The analysis now turns to comparing the rate of returns from the optimum portfolios constructed above
with the returns to the market portfolio. Using the assets and their weights created by the Markowitz
model estimated above, these weights were applied to the actual asset returns for the 1989-2012 time
period to determine optimum portfolio realized returns. Realized returns were calculated for the market
portfolio in a similar fashion. Table 6 presents the mean realized (holding period) returns and their
standard deviations for these two investment strategies matched on level of volatility. Of the two
investment strategies, Table 6 reveals, not accidentally by the way, that the optimum portfolio produces
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a higher annualized average realized return (with a lower standard deviation) than the market portfolio
over the1989-2012 time period.
The returns summarized in Table 6 are shown graphically in Figure 5. This figure depicts the value
of a $1 portfolio hypothetically invested in the optimum portfolio and market portfolio during the 1989-
2012 time period. It is evident from Figure 5 that, with respect to terminal wealth level, the optimum
portfolio outperformed the market portfolio by a significant margin. For example, $1 invested in the
optimum portfolio in 1989 yields an ending wealth of $7.5 versus a value of $6.5 for $1 invested in the
market portfolio for the period 1989-2012.
For comparison purposes, we have repeated the same set of exercise for the 1989-2017 sub-period.
Not surprisingly, the realized annual returns and the terminal value of $1 invested are overwhelmingly
higher for the optimal portfolio than for the market portfolio. See Table 7 and Figure 6. We find that
$1 invested in the optimal portfolio yields an ending wealth of $11.0 versus a value of $8.2 for $1
invested in the market portfolio for the sub-period 1989-2017. This long-term perspective underscores
the remarkable wealth building potential of private equity real estate and listed REIT stocks over the
past 28 years.
4 What May Very Well be the Case Going Forward?
Now here is the $64,000 question: Are the high returns to private equity opportunistic real estate funds
and listed REIT stocks that we saw in Figures 1 and 2 likely to continue in the future, and should
investors continue to overweight their portfolios (for all the reasons discussed above) in private equity
opportunistic real estate funds and listed REIT stocks? The answer to this question is very plausibly
“yes.” In the following we will explain why.
To begin with, we must recognize that low interest rates in the US and elsewhere are not just a
response to the Great Recession of 2007-2009, but instead are a culmination of a 25-year trend across
major industrial economies. As is shown in Figure 7, since the mid-1990s Japan has had zero (short-
term) interest rates and interest rates remain near zero today. In the US, (short-term) interest rates were
8.5% in 1989. Since then, however, the short-term interest rate has been on a decrease, precipitously
falling toward zero over the time period 2009-2015. In contrast to this, since 2015 the short-term
interest rate has picked up slightly, but still remains under 1.4%. Short-term interest rates in the UK
have fall from 12.5% in 1989 to near zero today. In Germany, (short-term) interest rates have also
decreased significantly over the 1989-2017 time period. Short-term interest rates in Germany were
below the US level between 1994 and 2001 and from 2004 to 2007, and above the US level between
1995 and 2003. German interest rates turned negative in mid-2016 and remain near zero today. In
Europe, (long-term) interest rates have fallen from above 10% in 1999 to around 2 to 3% in 2013.
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The key to understanding this situation lies in what has been recently dubbed by Summers (2013) as
the secular stagnation hypothesis. The secular stagnation hypothesis holds that real interest rates have
declined due to an increase in desired saving and a lack of investment opportunities. The secular
stagnation hypothesis also asserts that real interest rates are likely to remain low into the future. The
main drivers of low interest rates are aging population, low fertility, and sluggish productivity.
Reductions in mortality and fertility play the largest role. The reduction in mortality leads to an
economy in which individuals need to save more for retirement, increasing the supply of savings and
lowering the interest rate. As interest rates decline, individuals need to save even more for retirement,
which explains the reduction in observed interest rates over arbitrarily long periods.
A reduction in fertility has the same effect on the interest rate. The evidence implies that, as the
baby-boom generation entered the labor market in the 1970s, loan demand increased. With the
assumptions of upward-sloping supply curves and downward-sloping demand curves, an increase in
demand, other things being equal, led to an increased interest rate. Following the baby boom
generation comes the Gen Xers (or the baby bust generation), who were born during a period when
Americans were having fewer children. As the Gen Xers entered the labor market in the 2000s, loan
demand fell, as the number of young decreased relative to the middle aged. As loan demand fell,
interest rates began to fall and continued to fall between 2000 and 2017.
With continuing low interest rates, private equity opportunistic real estate funds and listed REIT
stocks became attractive alternative to low-yielding bonds (consistent with the shift we saw above in
the middle ranges of return and risk, where private real estate and listed REIT stocks are generally
substituted for bonds) to earn a high source of income for retirement. Under these conditions, the shift
in demand led to rising prices for private equity opportunistic real estate funds and listed REIT stocks.
In turn, rising prices implied an increase in the contemporaneous return and a higher realized return, as
we saw above, on portfolios that entailed “concentrated” positions in private equity opportunistic real
estate funds and listed REIT stocks and “less concentrated” positions in bonds.
In a world characterized by a “new normal,” in which the interest rate is low for arbitrarily long
periods of time, then, private equity opportunistic real estate funds and listed REIT stocks should enjoy
a higher return than they would have without a shift in demand. Eventually, these higher returns should
come to an end as the shift in demand slows down. However, it is most unlikely that the trends in
mortality, fertility, and productivity will be halted or reversed, and, thus, it is most unlikely that the
future will be characterized by higher interest rates and a lower expected premia on private equity
opportunistic real estate funds and listed REIT stocks.
While the trends in mortality, fertility, and productivity would predict that private equity
opportunistic real estate funds and listed REIT stocks will outperform marketable equities in the future,
it is equally likely that tax reform will have a significant impact on private equity opportunistic real
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estate funds and listed REIT stocks. The new tax code makes a big change to way in which private
equity opportunistic real estate funds and listed REIT stocks are taxed. Under the new law, investors
who invest in private equity real estate funds and listed REIT stocks will have the opportunity for a
20% deduction of the income generated through those real estate investments.2 These pass-through
rules benefit investors in private equity real estate funds and listed REIT stocks by dropping the top
marginal tax rate of 37% to 29.6%, which ought to cause a further shift out of bonds and into private
equity opportunistic real estate funds and listed REIT stocks.
There are two important caveats to the above argument. First, it is possible that monetary policy
could shift, say, from the policy that began about ten years ago, and largely continued today, to, say, the
policy of the previous two decades. However, there is no guarantee that the shift would address the
dual problem of low interest rates and low economic growth raised by secular stagnation. To wit,
consider the case of Japan. Second, it is also possible for fiscal policy to become, say, aggressive
enough to address the problems raised by secular stagnation. However, this shift would require (in
theory) a considerable fiscal expansion that would increase future disposable income through tax
decreases, thereby reducing the oversupply of savings and raising the natural rate of interest.
Occasionally, we see changes in the tax regime drastic enough to increase future disposable income and
reduce the oversupply of savings. Whether the Tax Cuts and Jobs Act (TCJA) of 2017 is indeed
aggressive enough to increase future disposable income and reduce the oversupply of savings remains
to be seen. What we do know is that the tax code gives investors in private equity opportunistic real
estate funds and listed REIT stocks a significant advantage over investors in bonds, which in itself is
likely to result in a greater demand for private equity opportunistic real estate funds and listed REIT
stocks. If supply and demand curves for private equity opportunistic real estate funds and listed REIT
stocks are not perfectly elastic, then this demand shift ought to affect prices and returns in the future.
5 Turning from Ex Post to Ex Ante
The above results suggest that investors should overweight their portfolios in private equity
opportunistic real estate funds and listed REIT stocks going forward. Interestingly enough, this
prescription is consistent with empirical evidence in Ivkovic, Sialm, and Weisbenner (2008). Ivkovic,
Sialm, and Weisbenner (2008) analyze data from a large US discount brokerage house. Their sample
includes individual investors. Ivkovic, Sialm, and Weisbenner (2008) report that concentrated
2 Limitations on the 20% deduction are imposed as the full amount taxable income a taxpayer files increases from
$315,000 to $415,000 for joint-filers, and from $157,000 to $207,500 for single filers.
12
investors outperform diversified ones by as much as 3 percent per year. Ivkovic, Sialm, and
Weisbenner (2008) also find that out-performance is even higher for investment in local stocks, where
natural information asymmetries are most likely to be present. However, the validity of this
comparison to the case at hand is somewhat questionable, since important factors, like low interest rates
and the oversupply of capital, and subpar economic growth, could, in fact, be different in the future.
In the absence of clear evidence or analysis one way or another, it is perhaps best not to assume that
interest rates will remain low and investors will continue to shift out of low-yielding bonds and into
private and listed real estate in search of yield. That is as true about return forecasting for portfolio
management as it is about return forecasting for private and listed real estate. Taking the risk-free rate,
proxied by the current yield on the 10-year US Treasury bond, to be 3 percent, and the equity premium
to be about 6 percent (see Mehra and Prescott (1985)), we forecast the return on marketable equities
(stocks) to be 9 percent going forward. We then define private equity opportunistic real estate
investments to be those investments underwritten on an a priori basis to achieve 9 percent returns. We
define private equity value-added real estate investments to be those investments underwritten to
produce 8 percent returns, and private equity core real estate investments to be those investments
underwritten to produce 6 percent returns. Once one accounts for the development and re-development
activities undertaken by REITs and the financial leverage used by REITs, one would expect the returns
on REITs to be commensurate with the returns on private equity value-added real estate investments.
With bonds, the yield-to-maturity is the total return anticipated if the bond is held until maturity and if
all payments are made as scheduled. We set the total return anticipated on bonds to be equal to a yield-
to-maturity (or coupon yield) of 4 percent. For international bonds, since interest rates outside the US
are generally around 100 basis points lower than inside the US, we set the total return anticipated on
international bonds to be equal to 3 percent. For international stocks, taking the risk-free rate to be
equal to 2 percent, and the equity premium to be 6 percent, we forecast the return on international
stocks to be about 8 percent.
Next, to forecast the standard deviations on these assets, we assume that historical Sharpe ratios for
these assets will remain fixed in the foreseeable future. Under these conditions, the standard deviation
of each return is directly proportional to the expected returns (in excess of the risk-free rate) on each
asset. Hence, varying the expected return on each asset, holding the Sharpe ratio constant, will directly
lower or raise the standard deviation of return. We also need to specify the correlation matrix of
returns. In this paper, for simplicity, we hypothesize that the historical correlation matrix contains
information about the future mean correlation, and we use historical correlation coefficients over the
sample period as the best estimates of their future values.
Given these input values, we then find the minimum variance portfolios at requested return levels
that minimize the variation (risk) at each given level of return within a feasible range. The portfolios
that maximized return for each level of risk are shown in Table 8, when the efficient mix of assets
13
include private equity value-add and opportunistic real estate funds and listed REIT stocks, and in
Table 9, when the efficient mix of assets just includes private equity real estate and listed REIT stocks.
The combined portfolio weights on private and listed real estate are constrained to be nonnegative and
not larger than 20 percent.
The results in Table 8 and 9 are not surprising. First, since we no longer assume that the expected
returns on private and listed real estate are such that private equity opportunistic real estate funds and
listed REIT stocks will outperform marketable equities, one should expect that private and listed real
estate should matter less in the case of unconstrained portfolios. Indeed, this is exactly what the data
show (results not reported). Second, note that, by construction, because we have kept the historical
Sharpe ratios and the historical correlation matrix intact in these simulations, there still ought to be
some gains to real estate diversification. What we had not expected, however, was the degree to these
diversification benefits still remain.
In order to solve this problem, we imposed constraints on the portfolio weights on private and listed
real estate. Without imposing constraints on the portfolio weights on private and listed real estate, one
runs the risk of holding an overly concentrated portfolio of private and listed real estate that has a
chance of underperforming a broader-based portfolio should the relative investment shift out of bonds
and into real estate slow down or cease. In this latter scenario, one would then be led to expect a much
lower expected premia in the future, as the price effect would come to end and the higher relative prices
for private and listed real estate would imply lower expected premia in the future.
These important insights explain why the results in Tables 8 and 9 are estimated with constraints on
the combined portfolio weights on private and listed real estate. We make five additional observations
regarding the results in Tables 8 and 9. First, and foremost, theory tells us that most investors will take
the relatively high returns and reduced risk on a constrained portfolio (e.g., portfolios 5 through 19 in
Table 8 and portfolios 4 through 19 in Table 9) than invest in a strategy that has a chance of an
extremely high return as well as an extremely low return. Second, for relatively high levels of risk, the
sets of portfolios in Tables 8 and 9 are so constructed as to have the same (constrained) allocation to
private and listed real estate. As we move to lower risk levels, the portfolio weights on private and
listed real estate vary from 4 to 19 percent. Third, for the portfolio with the highest Sharpe ratio (i.e.,
the highest “excess return to variability” ratio) in Table 8, the overall allocation to private equity
opportunistic real estate funds and REIT stocks is 9.2 percent. Within this portfolio, bonds constitute
90.8 percent of the mix and the optimal stock allocation is zero percent. At the lowest risk levels, the
incremental returns due to diversification (the difference between the contribution of private and listed
real estate to the compound return on the portfolio and the compound return on private and listed real
estate) are greater for private and listed real estate than for other assets. The latter occurs because
private and listed real estate are not highly correlated with bonds and, hence, their risk in a portfolio
that consists largely of fixed income securities is much less than their return variance. This
14
diversification benefit substantially increases the contribution of private and listed real estate to the
compound returns on the portfolios at the lowest risk levels. These benefits decrease considerably,
however, for portfolios that include more and more marketable equities (stocks).
Fourth, for the portfolio with the highest Sharpe ratio in Table 9, the overall allocation to private
equity real estate and REIT stocks is 18.2 percent. Another interesting result is that there is a
significant allocation to bonds within this portfolio and a very slight allocation to stocks. The stock-
bond mix is 80.5/1.2. Neither international bonds nor international equities enter into this portfolio.
The return contribution for international bonds is lower than the return contribution for domestic bonds,
and the return due to diversification is quite low. The story for the omission of international stocks is
quite different. Its standard deviation is much higher than the standard deviations of the other assets
and its return is considerably lower than the return for the S&P500.
This brings us to our fifth, and final, observation. To earn a high single digit portfolio return in a
world of low returns, the typical investor will need to move into riskier and riskier assets, and since
private and listed real estate are riskier than bonds, this means taking on more and more private and
listed real estate and less and less bonds, holding all else constant. For example, in Table 8 compare
portfolios 1 through 4, which have expected returns in the 4 to 5 percent range, with portfolios 17
through 19, which have expected returns in the 8.2 to 8.7 percent range. Alternatively, in Table 9,
compare portfolios 1 through 3, which have expected returns in the 4 to 4.6 percent range, with
portfolios 17 through 19, which have expected returns in the 8 to 8.6 percent range. Under these
conditions, the shift in demand should lead to a continual rise in relative prices for private and listed
real estate and to an increase in the contemporaneous return on private and listed real estate. Here the
implication is clear. The shifting asset weights should benefit those investors who maintain a fairly
large (fixed) asset weight on private and listed real estate.
6 Conclusion
In this paper, we provided a strong case for investment in private and listed real estate. To repeat the
argument, since the late 1980s, interest rates on assets of all maturities have declined worldwide, and
they have dropped to near zero during this period in the United States, Japan, and many European
Union member nations, and they have stayed surprisingly low since mid-2016, and in some cases have
even turned negative.
The origin of these low interest rates appears to be a case of secular stagnation. According to the
secular stagnation arguments, real interest rates have declined because the world is richer and healthier.
As the baby boomer generation has approached retirement (and as the first of the boomers have already
reached normal retirement age), and as people have become healthier, individuals have had to save
15
more for retirement, increasing the supply of savings and lowering the interest rate. Further, as interest
rates have declined, baby boomers have been induced to save even more.
Fertility rates have also dropped significantly over this period. Other things being equal, lower
fertility rates imply a decrease in loan demand, as fewer young adults relative to the middle aged enter
the labor market. Furthermore, assuming that the demand curve for mortgage debt is downward-
sloping, a shift in loan demand will lead to lower interest rates.
A slowdown in productivity has also played an important role. First, lower productivity growth
shifts out the supply of savings since lower expected future income induces individuals approaching
retirement to save more. Second, lower productivity growth reduces the demand for loans, as younger
borrowers become constrained from borrowing. Together, these forces alter the relative supply of
savings and investment, causing interest rates to decline.
Ultimately, with lower interest rates private equity opportunistic real estate funds and listed REIT
stocks became attractive alternatives to low-yielding bonds. Under these conditions, the shift in
demand will lead to rising relative prices for private equity opportunistic real estate funds and listed
REIT stocks and an increase in the contemporaneous return. We therefore would expect private equity
opportunistic real estate funds and listed REIT stocks to outperform marketable equities (stocks) and
bonds – which would be a result quite aside from conventional wisdom that stocks are riskier than
private equity opportunistic real estate funds and listed REIT stocks, and that stocks have historically
produced higher returns than private equity opportunistic real estate funds and listed REIT stocks.
To pursue this question, we performed a simple exercise. We compared historical stock, bond, and
real estate return data for two subperiods: 1989 to 2012 and 1989 to 2017. These data suggested that
private equity opportunistic real estate funds and listed REIT stocks outperformed marketable equities
(stocks) and bonds by a wide margin over the twenty-four years from 1989 to 2012 (i.e., an ending
terminal value of $1 invested of $11.7 for listed REIT stocks, $11.4 for private equity opportunistic real
estate funds, and $8.7 for the S&P500 index for the period 1989-2012). The data also suggested that
listed REIT stocks continued to outperform marketable equities (stocks) and bonds over the period
1989 to 2017 (i.e., an ending terminal value of $1 invested of $42.7 for listed REIT stocks versus a
value of $36.3 for the S&P500 index for the period 1989-2016).
We conjecture that this effect has come from unyielding demand shifts that have continued, more or
less permanently over the past twenty years, and have brought about high prices and high
contemporaneous returns on private and listed real estate. These forces explain why private equity
opportunistic real estate funds and listed REIT stocks outperformed marketable equities (stocks) and
bonds over such a long passage of time. But they also help to explain why private and listed real estate
is likely to outperform marketable equities (stocks) and bonds in the future.
16
As demand continues to shift away from bonds and toward private and listed real estate, we would
expect the shift in demand to lead to rising relative prices for private and listed real estate. In turn,
rising prices imply an increase in the contemporaneous return. The analysis discussed above would
then give us a picture of how to invest one’s savings so as to achieve the highest ending wealth. With
perfect hindsight, the portfolio should be committed to virtually 20 to 80 percent real estate investment
to take advantage of the high contemporaneous returns to investment.
Of course, we think it is a bold statement to say that portfolios should be committed to virtually 20
to 80 percent real estate investment because of the achieved excess returns on private equity
opportunistic real estate funds and listed REIT stocks over marketable equities (stocks) and bonds since
the late 1980s. For this reason, we also took an entirely forward-looking approach to the problem. In
such a setting, rather than to look back at historic mean returns, and equate those with what the
expected returns were in the past, we lowered the mean returns that were observed on bonds, stocks,
and real estate for the whole period 1989-2017 from 5.4 to 13.2 percent to 3 to 9 percent. We then
defined these mean returns (which are essentially what investors are looking to earn on investments
now) as the expected returns. To keep things simple, we then used the historical Sharpe performance
ratios to compute a standard deviation for each of these mean (expected) returns (calculating the
standard deviation for these returns as the average excess return over the risk-free rate divided by the
asset’s Sharpe ratio). With one exception, the standard deviations computed from these numbers
generally range from 1.5 to 15.4; the exception being international stocks, which has standard deviation
of 79.1. To obtain the correlations of these returns, we simply used the historical correlation
coefficients. We imposed an upper bound of 20 percent on the portfolio weight on private and listed
real estate, so as to mitigate the effects of forecast error. In addition, by constraining the portfolio
weight on private and listed real estate not larger than 20 percent, one ends up holding a much more
diversified portfolio, and is therefore more likely to own assets that could potentially end up, say,
doubling or tripling in price.
Given this forward-looking approach to the problem, we found that the optimum mixed portfolios
of stocks, bonds, and real estate are comprised of between 4 to 20 percent real estate investment. We
further showed that to earn a high single digit portfolio return in the market now, the typical investor
needs to move into riskier and riskier assets, and since private and listed real estate are riskier than
bonds, this means taking on more and more private and listed real estate and less and less bonds,
holding all else constant.
These calculations bring to the forefront an important lesson. As there is a real prospect that
interest rates are likely to remain low for a number of years, there are substantial reasons to believe that
investors will continue to shift out of low-yielding bonds and into private and listed real estate in search
of yield, and that this shifting will raise prices and increase contemporaneous returns. This shifting
from low-yielding bonds to higher yielding real estate gives an additional reason for choosing to invest
17
in private and listed real estate. Other studies find that real estate can be used as a valuable vehicle for
achieving diversification for a stock and bond portfolio. Our study adds an intertemporal hedging
motive for investing in private and listed real estate. Although we have not taken into account the
changes in the distribution of returns over time that are the essence of the intertemporal asset allocation
model, our results would nevertheless hold over many periods if the unyielding demand shifts from
bonds and toward private and listed real estate are constant over time.
18
References
Steven Roulac. 1976. “Can Real Estate Returns Outperform Common Stocks?” Journal of Portfolio
Management. 2(2) 26-43.
Zoran Ivkovic, Clemens Sialm, and Scott Weisbenner. 2008. “Portfolio Concentration and the
Performance of Individual Investors.” Journal of Financial and Quantitative Analysis 43, 613-656.
Mehra, Rajnish, and Edward C.Prescott. 1985. “The Equity Premium: A Puzzle.” Journal of Monetary
Economics 15, 145–61.
Lawrence Summers. 2013. “Why Stagnation Might Prove to be the New Normal.” The Financial
Times.
19
S&P500 Bonds VA Opp Int'l Stks Int'l Bonds REITs
S&P500 1 0.08 0.14 0.45 0.96 0.24 0.90
Bonds 0.08 1 0.41 0.39 -0.05 0.52 0.04
VA 0.14 0.41 1 0.90 0.02 0.11 0.09
Opp 0.45 0.39 0.90 1 0.39 0.41 0.26
Int'l Stks 0.96 -0.05 0.02 0.39 1 0.37 0.78
Int'l Bonds 0.24 0.52 0.11 0.41 0.37 1 -0.13
REITs
0.90
0.04
0.09
0.26
0.78
-0.13
1
Table 1. Correlation coefficients over the seven return indices. This table shows the correlation matrix for the
(time series of the) following seven return indices: the S&P500 return index (S&P500), the Salomon Brothers US
corporate bond index (Bonds), the NCREIF/Townsend closed-end value-add real estate fund index (VA), the
NCREIF/Townsend closed-end opportunistic real estate fund index (Opp), the Morgan Stanley Capital
International EAFE (Europe, Australia, Far East) stock return index expressed in US dollars (Int’l Stks), the
Salomon Brothers world bond index expressed in US dollars (Int’l Bonds), and the FTSE/NAREIT all equity
index of listed REIT stocks. The correlation coefficients can range from -1 to +1; the higher the number (either
positive or negative), the stronger the relationship between the two variables.
20
S&P500 Bonds VA Opp
Int'l
Stks
Int'l
Bonds REITs
Total
Invested
VA + Opp
+ REITs
Mean Return (%) 11.1 7.3 8.4 12.5 6.4 6.5 12.7
Std Dev (%) 20.2 1.2 21 22.9 24.1 1.7 24.1
Portfolio Mean Return (%) Std Dev (%) Portfolio Weights (%)
1 7.43 1.16 0 87.7 0 0 0 12.1 0.2 100 0.2
2 7.68 1.86 0 93.2 0 2.4 0 0 4.3 100 6.8
3 7.93 2.62 0 88.5 0 5.0 0 0 6.5 100 11.5
4 8.18 3.43 0 83.8 0 7.5 0 0 8.7 100 16.2
5 8.43 4.26 0 79.0 0 10.0 0 0 10.9 100 21.0
6 8.68 5.10 0 74.3 0 12.6 0 0 13.1 100 25.7
7 8.93 5.45 0 69.5 0 15.1 0 0 15.4 100 30.5
8 9.18 6.81 0 64.8 0 17.6 0 0 17.6 100 35.2
9 9.43 7.67 0 60.1 0 20.2 0 0 19.8 100 39.9
10 9.68 8.54 0 55.3 0 22.7 0 0 22.0 100 44.7
11 9.93 9.40 0 50.6 0 25.3 0 0 24.2 100 49.4
12 10.18 10.26 0 45.8 0 27.8 0 0 26.4 100 54.2
13 10.43 11.13 0 41.1 0 30.3 0 0 28.6 100 58.9
14 10.68 11.99 0 36.4 0 32.9 0 0 30.8 100 63.6
15 10.93 12.86 0 31.6 0 35.4 0 0 33.0 100 68.4
16 11.18 13.73 0 26.9 0 37.9 0 0 35.2 100 73.1
17 11.43 14.60 0 22.1 0 40.5 0 0 37.4 100 77.9
18 11.68 12.58 0 17.4 0 43.0 0 0 39.6 100 82.6
19
11.93
16.33
0
12.6
0
45.6
0
0
41.8
100
87.4
Table 2. Efficient portfolios (using annual data for 1989-2012). The figures in the body of the table are the
investment proportions, in percentages adding up to 100 percent for each portfolio. The far right column shows
the total investment in private equity value-add and opportunistic real estate funds and listed REIT stocks.
21
S&P500 Bonds RE Int’l Stks Int’l Bonds REITs Total Invested RE + REITs
Mean Return (%) 12.5 7.5 11.4 11.2 5.4 13.2
Std Dev (%) 16.4 5.6 14.3 22.7 6.3 17.2
Portfolio Mean Return (%) Std Dev (%) Portfolio Weights (%)
1 7.52 4.58 1.2 47.8 15.4 0 34.1 1.5 100 16.9
2 7.77 4.60 2.1 50.5 16.3 0 28.6 2.4 100 18.7
3 8.02 4.66 3.1 53.3 17.3 0 23.1 3.3 100 20.6
4 8.27 4.75 4.0 56.0 18.2 0 17.6 4.2 100 22.4
5 8.52 4.88 4.9 58.7 19.2 0 12.1 5.1 100 24.3
6 8.77 5.05 5.8 61.4 20.2 0 6.6 6.0 100 26.1
7 9.02 5.24 6.8 64.1 21.1 0 1.1 6.9 100 28.0
8 9.27 5.47 8.2 60.7 22.6 0 0 8.5 100 31.1
9 9.52 5.75 9.8 55.6 24.3 0 0 10.4 100 34.6
10 9.77 6.08 11.4 50.5 25.9 0 0 12.2 100 38.1
11 10.02 6.44 13.0 45.4 27.6 0 0 14.1 100 41.6
12 10.27 6.84 14.6 40.3 29.2 0 0 15.9 100 45.1
13 10.52 7.26 16.2 35.2 30.8 0 0 17.8 100 48.6
14 10.77 7.70 17.7 30.1 32.5 0 0 19.6 100 52.1
15 11.02 8.17 19.3 25.1 34.1 0 0 21.5 100 55.6
16 11.27 8.65 20.9 20.0 35.8 0 0 23.3 100 59.1
17 11.52 9.14 22.5 14.9 37.4 0 0 25.2 100 62.6
18 11.77 9.64 24.1 9.8 39.1 0 0 27.0 100 66.1
19 12.02 10.16 25.7 4.7 40.7 0 0 28.9 100 69.6
20 12.27 10.68 27.1 0 41.2 0 0 31.7 100 72.9
21 12.52 11.68 26.1 0 27.2 0 0 46.7 100 73.9
22 12.77 13.34 25.1 0 13.1 0 0 61.7 100 74.9
23 13.02 15.45 21.8 0 0 0 0 78.2 100 78.2
Table 3. Efficient portfolios (using annual data for 1989-2016). The figures in the body of the table are the investment
proportions, in percentages adding up to 100 percent for each portfolio. The far right column shows the total investment in private
equity real estate funds and listed REIT stocks.
22
Weights in Market Portfolio Variance
(1) (2) (3) (4) (5) (6) (7)
Assets (in billions)
Weights in Optimum
Portfolio 1989
2012
(6)=(1)/(3)-1 (7)=(1)/(5)-1
US corporate equities 0.0% $3,813 26% $26,444 33% -100.0% -100.0%
Commercial real estate
Value Add 0.0% $0 0.0% $291 0.4% 0% -100.0%
Opportunistic 15.1% $0 0.0% $292 0.4% inf 4086.6%
Listed REIT stocks 15.4% $26 0.2% $715 0.9% 8671.2% 1636.0%
US debt securities 69.5% $11,008 74% $53,094 66% -6.2% 5.9%
Total
$14,847
100%
$80,835
100%
Table 4. Composition of the optimum portfolio versus the market portfolio (using data for 1989-2012). This table shows the
composition of the optimum and market portfolios. Of the optimal portfolios given in Table 2, the one whose estimated volatility
was closest to that of the market portfolio was selected for the analysis. Here we measure total investable wealth as the value of
private sector commercial real estate assets plus market equities and bonds. The financial wealth data are constructed from the
Federal Reserve Board, Flow of Funds Accounts of the United States: Flows and Outstandings, various quarters (Release Z.1).
The real estate data in 1989 are taken from the US Department of Commerce, Bureau of Economic Analysis, Estimates of Fixed
Reproducible Tangible Wealth series. In 2012, we estimate the size of the commercial real estate market from the Flow of Funds
Account data. We estimate the size of the private equity value-add and opportunistic real estate market from the Preqin database.
We estimate the size of the public market for real estate from data published by NARIET. Variance is calculated as one minus the
ratio of the weights in the optimum portfolio and in the market portfolio; that is, column (6) = (column (1)/column (3))-1, and
column (7) = (column (1)/column (5))-1.
23
Weights in Market Portfolio Variance
(1) (2) (3) (4) (5) (6) (7)
Assets (in billions)
Weights in Optimum
Portfolio 1989
2012
(6)=(1)/(3)-1 (7)=(1)/(5)-1
US corporate equities 12.98% $3,813 24.5% $26,444 32% -47.0% -59.0%
Commercial real estate 27.6% $746 4.6% $3,283 4% 495.6% 601.2%
Listed REIT stocks 14.1% $26 0.2% $715 0.9% 8329.0% 1544.3%
US debt securities 45.40% $11,008 70.7% $53,094 64% -35.8% -28.6%
Total
$15,567
100%
100%
Table 5. Composition of the optimum portfolio versus the market portfolio (using data for 1989-2016). This table shows the
composition of the optimum and market portfolios. Of the optimal portfolios given in Table 3, the one whose estimated volatility
was closest to that of the market portfolio was selected for the analysis. Here we measure total investable wealth as the value of
private sector commercial real estate assets plus market equities and bonds. The financial wealth data are constructed from the
Federal Reserve Board, Flow of Funds Accounts of the United States: Flows and Outstandings, various quarters (Release Z.1).
The real estate data in 1989 are taken from the US Department of Commerce, Bureau of Economic Analysis, Estimates of Fixed
Reproducible Tangible Wealth series. In 2012, we estimate the size of the commercial real estate market from the Flow of Funds
Account data. We estimate the size of the public market for real estate from data published by NARIET. Variance is calculated
as one minus the ratio of the weights in the optimum portfolio and in the market portfolio; that is, column (6) = (column
(1)/column (3))-1, and column (7) = (column (1)/column (5))-1.
24
Market Portfolio
Optimum 1989 2012
Mean Return (%) 8.9 8.4 8.7
Std Dev (%)
5.6
6.8
7.6
Table 6. Realized rates of return and standard deviation for the optimum and market portfolio (using data for 1989-2012). This
table shows the realized annual rate of return and standard deviation for the optimum and market portfolios. Of the optimal
portfolios given in Table 2, the one whose estimated volatility was closest to that of the market portfolio was selected for the
analysis.
25
Market Portfolio
Optimum 1989 2012
Mean Return (%) 10.0 8.9 9.3
Std Dev (%)
6.5
6.3
7.1
Table 7. Realized rates of return and standard deviation for the optimum and market portfolio (using data for 1989-2016). This
table shows the realized annual rate of return and standard deviation for the optimum and market portfolios. Of the optimal
portfolios given in Table 3, the one whose estimated volatility was closest to that of the market portfolio was selected for the
analysis.
26
S&P500 Bonds VA Opp
Int'l
Stks
Int'l
Bonds REITs
Total
Invested
VA + Opp
+ REITs
Mean Return (%) 9.0 4.0 8.0 9.0 8.0 3.0 8.0
Std Dev (%) 15.4 1.5 13.3 12.7 79.1 2.8 10.7
Portfolio Mean Return (%) Std Dev (%) Portfolio Weights (%)
1 4.19 1.45 0 95.0 0 3.8 0 1.2 0 100 3.8
2 4.44 1.57 0 90.8 0 7.3 0 0 1.8 100 9.2
3 4.69 1.86 0 85.2 0 9.8 0 0 4.9 100 14.8
4 4.94 2.23 0.8 79.7 0 12.1 0 0 7.4 100 19.5
5 5.19 2.68 5.0 75.0 0 13.8 0 0 6.2 100 20.0
6 5.44 3.23 9.7 70.3 0 15.4 0 0 4.6 100 20.0
7 5.69 3.84 14.4 65.6 0 17.0 0 0 3.0 100 20.0
8 5.94 4.48 19.1 60.9 0 18.6 0 0 1.4 100 20.0
9 6.19 5.14 23.8 56.2 0 20.0 0 0 0 100 20.0
10 6.44 5.82 28.8 51.2 0 20.0 0 0 0 100 20.0
11 6.69 6.51 33.8 46.2 0 20.0 0 0 0 100 20.0
12 6.94 7.22 38.8 41.2 0 20.0 0 0 0 100 20.0
13 7.19 7.93 43.8 36.2 0 20.0 0 0 0 100 20.0
14 7.44 8.66 48.8 31.2 0 20.0 0 0 0 100 20.0
15 7.69 9.38 53.8 26.2 0 20.0 0 0 0 100 20.0
16 7.94 10.12 58.8 21.2 0 20.0 0 0 0 100 20.0
17 8.19 10.85 63.8 16.2 0 20.0 0 0 0 100 20.0
18 8.44 11.59 68.8 11.2 0 20.0 0 0 0 100 20.0
19
8.69
12.33
73.8
6.2
0
20.0
0
0
0
100
20.0
Table 8. Efficient portfolios (using ex ante annual data). The figures in the body of the table are the investment
proportions, in percentages adding up to 100 percent for each portfolio. The far right column shows the total
investment in private equity value-add and opportunistic real estate funds and listed REIT stocks.
27
S&P500 Bonds RE Int’l Stks Int’l Bonds REITs Total Invested RE + REITs
Mean Return (%) 9.0 4.0 6.0 8.0 3.0 8.0
Std Dev (%) 15.4 1.5 8.5 79.1 2.8 10.7
Portfolio Mean Return (%) Std Dev (%) Portfolio Weights (%)
1 4.08 1.48 0 93.7 4.7 0 1.6 0.0 100 4.7
2 4.33 1.60 0 87.9 7.9 0 0 4.2 100 12.1
3 4.58 1.89 1.2 80.5 10.7 0 0 7.6 100 18.2
4 4.83 2.31 5.0 75.0 11.1 0 0 8.9 100 20.0
5 5.08 2.86 9.7 70.3 10.4 0 0 9.6 100 20.0
6 5.33 3.49 14.4 65.6 9.7 0 0 10.3 100 20.0
7 5.58 4.16 19.2 60.8 9.1 0 0 10.9 100 20.0
8 5.83 4.85 23.9 56.1 8.4 0 0 11.6 100 20.0
9 6.08 5.55 28.6 51.4 7.8 0 0 12.2 100 20.0
10 6.33 6.27 33.4 46.6 7.1 0 0 12.9 100 20.0
11 6.58 7.00 38.1 41.9 6.4 0 0 13.6 100 20.0
12 6.83 7.72 42.9 37.1 5.8 0 0 14.2 100 20.0
13 7.08 8.46 47.6 32.4 5.1 0 0 14.9 100 20.0
14 7.33 9.19 52.3 27.7 4.5 0 0 15.5 100 20.0
15 7.58 9.93 57.1 22.9 3.8 0 0 16.2 100 20.0
16 7.83 10.67 61.8 18.2 3.1 0 0 16.9 100 20.0
17 8.08 11.41 66.5 13.5 2.5 0 0 17.5 100 20.0
18 8.33 12.15 71.3 8.7 1.8 0 0 18.2 100 20.0 19
8.58
12.89
76.0
4.0
1.2
0
0
18.8
100
20.0
Table 9. Efficient portfolios (using ex ante annual data). The figures in the body of the table are the investment proportions, in
percentages adding up to 100 percent for each portfolio. The far right column shows the total investment in private equity real
estate funds and listed REIT stocks.
28
29
Figure 2. Terminal value of $1 invested in private equity value-add and
opportunistic real estate funds, listed REIT stocks and marketable equities.
Vertical axis: Terminal value of $1 invested. Horizontal axis: Year. S&P500 =
Standard & Poor’s index is a market-value-weighted index and one of the most
widely used benchmarks for measuring the performance of larg-capitalization
US-based stocks. REIT = FTSE/NAREIT all equity index of listed REIT stocks.
VA = NCREIF/Townsend closed-end value-add real estate fund index. OPP =
NCREIF/Townsend closed-end opportunistic real estate fund index.
0
2
4
6
8
10
12
14
19
88
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89
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90
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91
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92
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93
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94
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Term
inal
Val
e o
f $
1 in
vest
ed
in S
tock
s an
d R
eal
Es
tate
S&P500 REITs VA OPP
30
Figure 3. Terminal value of $1 invested in private equity value-add and
opportunistic real estate funds, listed REIT stocks and marketable equities.
Vertical axis: Terminal value of $1 invested. Horizontal axis: Year. S&P500 =
Standard & Poor’s index is a market-value-weighted index and one of the most
widely used benchmarks for measuring the performance of larg-capitalization
US-based stocks. REIT = FTSE/NAREIT all equity index of listed REIT stocks.
Private Equity Real Estate = levered NCREIF property index.
0.0
5.0
10.0
15.0
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25.0
30.0
35.0
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45.0
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Term
inal
Val
e o
f $
1 in
vest
ed
in S
tock
s an
d R
eal
Es
tate
S&P500 REITs Private Equity Real Estate
31
32
Figure 5. Differences in realized rate of returns for the optimum and market portfolios for the sub-
period 1989-2012. Vertical axis: Terminal value of $1 invested. Horizontal axis: Year. This figure
compares the realized returns on the optimum and market portfolios. Of the optimal portfolios given in
Table 2, the one whose estimated volatility was closest to that of the market portfolio was selected for
the analysis.
0
1
2
3
4
5
6
7
8
9
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88
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Term
inal
Val
ue
of
$1
Inve
ste
d in
Sto
cks
and
Re
al
Esta
te
Optimum Portfolio Market Portfolio
33
Figure 6. Differences in realized rate of returns for the optimum and market portfolios for the sub-
period 1989-2017. Vertical axis: Terminal value of $1 invested. Horizontal axis: Year. This figure
compares the realized returns on the optimum and market portfolios. Of the optimal portfolios given in
Table 3, the one whose estimated volatility was closest to that of the market portfolio was selected for
the analysis.
0
2
4
6
8
10
12
19
88
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90
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92
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96
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Term
inal
Val
ue
of
$1
Inve
ste
d in
Sto
cks
and
Re
al
Esta
te
Optimum Portfolio Market Portfolio
34
Short term Long term
Figure 7. Short and long term interest rates. Vertical axis: Interest rate in percent. Horizontal axis:
Year-month. The countries shown include the US, the UK, Japan, Germany, and the Eurozone.
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
19
00
-01
-01
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Inte
rest
rat
e, %
US UK Japan Germany
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-01
Inte
rest
rat
e, %
US UK Japan
Germany Eurozone
35
Appendix
This appendix shows the property composition of the FTSE/NAREIT data. The data are broken
down into four property types: apartments, industrial, office, and retail. As evidenced in Figure A1, the
FTSE/NAREIT index is comprised of approximately a “30 percent, 30 percent, and 30 percent” share
in apartments, office, and retail, respectively, and a 10 percent share in industrial.
Figure A1. Property composition of the FTSE/NAREIT index. The pie chart shows the
proportions of the results for each property type. The pie chart has been automatically scaled
so that the shares sum to 100 percent. The proportions reported are the mean shares over the
period 1989-2016 plus or minus the standard error.
One can think of these shares as the optimal portfolio weights that would have yielded the high
returns on listed REIT stocks shown in Figure 2 or better yet in Figure 3. These commercial real estate
allocations have relatively small standard errors reflecting the fact that the allocations are relatively
stable over time. Of course, passive investments in the same proportions as those shown in Figure A1
may not exactly replicate the FTSE/NAREIT index shown in Figures 2 or 3. On a conceptual basis,
REIT managers may differentially invest in value-added real estate assets. Further, REIT managers
may have better knowledge about historical return patterns than individual investors, making their
selections of properties non-replicable by a similarly constructed buy-and-hold portfolio with weights
mirroring those shown in Figure A1.
We also show in this appendix the property composition of the NPI index. See Figure A2. The
data confirm that there are differences in weightings between the FTSE/NAREIT and NPI portfolios,
some fairly obvious, some subtle, and probably some yet to be discovered. First, based on a t-test of
the differences in the property weight on apartments in the FTSE/NAREIT index and NPI index, the
[VALUE] ± 8%
[VALUE] ± 4% [VALUE] ± 14%
[VALUE] ± 8%
Apartments Industrial Office Retail
36
corresponding property weight on apartments in the FTSE/NAREIT index is statistically larger than the
weight in the NPI index. Second, the property weights on industrial and office in the FTSE/NAREIT
index are statistically smaller than the corresponding weights in the NPI index. Third, a t-test on the
differences in the property weight on retail in the FTSE/NAREIT index and the NPI index does not
result in any statistically significant differences. However, this result does not in any way mean that no
differences exist in the two series. Among other things, for example, it has often been highlighted that
most regional malls in the US, including those with the highest productivity, are generally owned by
listed REITs, not institutional investors. One is also challenged by regional differences in investment
focus, degrees of customer interchange across the store types within a center, and the differing tenant
types across these two series. Still, while the NPI property weightings may not exactly replicate the
property weightings in the FTSE/NAREIT index, and while some subtle differences may exist in the
two indices, the results do, indeed, suggest that the FTSE/NAREIT index and the NPI index are
comprised of a fairly broad-based “basket of properties.” In both indices, we also see that there is a
“less than equal” weighting on industrial. Industrial receives only a property weighting of 10 percent ±
4 percent in the FTSE/NAREIT index and a weighting of 15 percent ± 2 percent in the NPI index.
Including a “less than equal” weighting on industrial in the FTSE/NAREIT index and the NPI index
leads to a higher than average property weighting on either apartment, office, and retail, or some
combination thereof (which is what the pie charts in Figures A1 and A2 show). This latter effect comes
purely from an accounting identify.
Figure A2. Property composition of the NPI index. The pie chart shows the proportions of
the results for each property type. . The pie chart has been automatically scaled so that the
shares sum to 100 percent. The proportions reported are the mean shares over the period
1989-2016 plus or minus the standard error.
[VALUE] ± 6%
[VALUE] ± 2%
[VALUE] ± 4%
[VALUE] ± 7%
Apartments Industrial Office Retail