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: shilling@depaul.edu.

‡

DePaul University, 1 East Jackson Boulevard, Chicago, IL 60604, Email: cwurtzeb@depaul.edu.

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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

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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

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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

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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

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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

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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