Electronic copy of this paper is available at: http://ssrn.com/abstract=564904

Expected Returns and the Expected Growth in Rents

of Commercial Real Estate∗

Alberto Plazzi † Walter Torous ‡ Rossen Valkanov §

∗We thank Andrea Berardi, Christopher Downing, Harrison Hong, Andrey Pavlov, Antonio Rubia,Stephen Schaefer and seminar participants at the following conferences for useful comments: the AREUEA,the XXXVI EWGFM, the FMA European meeting, the SAET meetings in Vigo, and the SAFE center atthe University of Verona. We are especially grateful to an anonymous referee for many suggestions that havegreatly improved the paper. All remaining errors are our own.

†The Anderson School at UCLA and University of Verona, 110 Westwood Plaza, Los Angeles, CA 90095-1481, phone: (310) 825-8160, fax: (310) 206-5455, e-mail: alberto.plazzi.2010@anderson.ucla.edu.

‡The Anderson School at UCLA, 110 Westwood Plaza, Los Angeles, CA 90095-1481, phone: (310) 825-4059, fax: (310) 206-5455, e-mail: walter.n.torous@anderson.ucla.edu.

§Corresponding author. Rady School at UCSD, Pepper Canyon Hall, 9500 Gilman Drive, MC 0093, LaJolla, CA 92093, phone: (858) 534-0898, fax: (858) 534-0745, e-mail: rvalkanov@ucsd.edu.

Electronic copy of this paper is available at: http://ssrn.com/abstract=564904

Abstract

We investigate whether the cap rate, that is, the rent-price ratio in commercialreal estate incorporates information about future expected real estate returnsand future growth in rents. Relying on transactions data spanning severalyears across fifty-three metropolitan areas in the U.S., we find that the caprate captures fluctuations in expected returns for apartments, retail, as well asindustrial properties. For offices, by contrast, the cap rate does not forecastreturns even though additional evidence reveals that expected returns on officesare also time-varying. We link these differences in the ability of the cap rate toforecast commercial property returns to differences in the stochastic properties oftheir rental growth rates with the growth in office rents having a higher correlationwith expected returns and being more volatile than for other property types.Taken together, our evidence suggests that variation in commercial real estateprices is largely due to movements in discount rates as opposed to cash flows.

JEL classification: G12, R31

Keywords : Cap rate, real estate, return predictability, rent growth.

2

1 Introduction

U.S. commercial real estate prices fluctuate considerably, both cross-sectionally as well as

over time. For example, the returns to apartments during the last quarter of 1994 ranged

from 21.4 percent in Dallas, Texas to −8.5 percent in Portland, Oregon. Eight years later,

during the last quarter of 2002, the returns to apartments in Dallas and Portland were 1.2

and 4.4 percent, respectively. Other types of commercial real estate, such as retail, industrial,

and office properties, have experienced even larger return fluctuations. Understanding what

drives these fluctuations is an important research question since commercial real estate

represents a substantial fraction of total U.S. wealth. In particular, the value of U.S.

commercial real estate as of the end of 1999 was estimated to be approximately six trillion

dollars, which at the time represented almost half of the U.S. stock market’s value (Case

(2000)).

From an asset pricing perspective, the price of a commercial property, be it an office

building, apartment, retail or industrial space, equals the present value of its future net rents,

that is, rents minus any operating expenses adjusted for vacancies. This fundamental present

value relation implies that the observed fluctuations in commercial real estate prices should

reflect variations in future rents or in future discount rates, or both. In valuing commercial

real estate, it is particularly important to consider the possibility that discount rates and

rental growth rates are time-varying as it is often conjectured that both fluctuate with the

prevailing state of the economy. For example, Case (2000) points out “the vulnerability

of commercial real estate values to changes in economic conditions” by describing recent

boom-and-bust cycles in that market. He provides a simple example of cyclical fluctuations

in expected returns and rental growth rates that give rise to sizable variation in commercial

real estate prices. Case, Goetzmann, and Rouwenhorst (2000) make a similar point using

international data and conclude that commercial real estate is “a bet on fundamental

economic variables.” Despite these and other studies, however, little is known about the

dynamics of commercial real estate prices.

In this paper, we investigate whether expected returns and the expected growth in rents

of commercial real estate are time-varying by relying on a version of Campbell and Shiller’s

(1988) “dynamic Gordon” model. A direct implication of this model is that the cap rate,

defined as the ratio between a property’s net rent and its price, should reflect fluctuations in

expected returns or in rental growth rates, or both. The cap rate is a standard measure of

1

commercial real estate valuation and corresponds to a common stock’s dividend-price ratio

where the property’s net rent plays the role of the dividend. As an illustration, suppose that

the cap rate for apartments in Portland is higher than the cap rate of similar apartments in

Dallas. The dynamic Gordon model suggests that either future discount rates in Portland

will be higher than those expected in Dallas or that future rents in Portland will grow at a

slower rate than in Dallas, or both. Whether or not cap rates can forecast future returns or

future rent growth is ultimately an empirical issue and depends on the variability of these

processes, their persistence, and their mutual correlation.

To investigate whether cap rates do capture future variation in returns or rental growth

rates, we use a novel dataset of commercial real estate transactions across fifty-three U.S.

metropolitan areas reported at a quarterly frequency over the sample period 1994 to 2003.

For a subset of twenty-one of these regions, we also have bi-annual observations beginning

in the last quarter of 1985. These data are available on a variety of property types including

offices, apartments, as well as retail and industrial properties. The transactions nature of

our commercial real estate data differentiates it from the appraisal data typically relied upon

in other real estate studies. For example, unlike the serially correlated returns and rental

growth rates found in appraisal data (Case and Shiller (1989, 1990)), we verify that returns

and rental growth rates in our data are not serially correlated beyond a yearly horizon.

Relying on these data, we document that higher cap rates do indeed predict higher

future returns on apartment buildings as well as retail and industrial properties. Cap

rates, however, do not predict future returns of office buildings. For apartments, retail,

and industrial properties, the predictability of returns is robust to controlling for cross-

sectional differences using fixed effects as well as variables that capture regional differences

reflecting demographic, geographic, and various economic factors. In terms of the economic

significance of this predictability, we find that a one percent increase in cap rates leads to

an increase of up to four percent in the prices of these properties. This large effect is due

to the persistence of the fluctuations in expected returns and is similar in magnitude to

that documented for common stock (Cochrane (2001)). By contrast, we do not find reliable

evidence that cap rates predict future movements in rental growth rates. Only for offices do

we find limited evidence of lower cap rates predicting higher future rental growth rates and

then only at long horizons. This, however, does not imply that the rental growth rates of

commercial real estate do not vary over time. On the contrary, their variability is similar to,

and, in the case of offices, even larger than that of the growth documented in dividends.

2

Our results point to a fundamental difference between apartments, retail and industrial

properties, where cap rates do forecast returns, and office buildings, where they do not.

This difference provides us with a unique opportunity to investigate under what conditions

valuation ratios can or cannot predict future returns. In the context of the dynamic Gordon

model, it is well known that the dividend-price ratio predicts time-varying expected returns

under two conditions. First, expected returns and expected dividend growth rates must be

uncorrelated. If they are correlated, then fluctuations in one series will offset, on average,

fluctuations in the other and, as a result, the dividend-price ratio will remain unchanged.

Secondly, the presence of extreme movements in dividend growth rates that are orthogonal

to the time variation in expected returns will make it difficult to detect a statistically

reliable forecasting relation. These conditions have been discussed by Campbell and Shiller

(1988b), Campbell, Lo, and MacKinlay (1997), and more recently by Lettau and Ludvigson

(2004) and Menzly, Santos, and Veronesi (2004) but only in the context of common stock.

Following the logic in these papers, there are a number of possible interpretations of the

documented lack of forecastability by office cap rates. For example, it may be the case that

the expected returns of office buildings exhibit much less time-variation than the expected

returns of other commercial property types. Alternatively, cap rates may fail to forecast the

variation in future office returns because office rental growth rates are more correlated with

expected returns or are more volatile than the rental growth rates of other properties. These

alternatives have very different implications for asset pricing and portfolio allocation.

We find that the future returns of all four commercial property types exhibit similar

correlations with macroeconomic variables, for example, the term spread, the default spread,

the rate of inflation, and the short interest rate. These variables are known to capture

fluctuations in business cycle conditions and have been widely used in the finance literature

to track the time-varying behavior of stock market returns (Campbell and Shiller (1988a),

Campbell (1991), Fama and French (1989), Lettau and Ludvigson (2004), Torous, Valkanov,

and Yan (2005) and, for a good review, Campbell, Lo, and MacKinlay (1997)). However,

while we find that the rental growth rates of all four commercial property types are correlated

with these macroeconomic variables, the correlations are significantly higher for offices. We

also show that the volatility in rental growth that is orthogonal to the macroeconomic

variables is much higher for offices than for the other property types and is even higher than

the volatility of the stock market’s dividend growth rate over our sample period. Hence, we

conclude that while the expected returns of offices are time-varying, the failure to forecast

their future variation reflects the fact that when compared to the other property types the

3

growth in office rents is more correlated with the state of the economy and its orthogonal

remainder is much more volatile.

The view of commercial real estate that emerges from our research is that of an asset

class characterized by fluctuations in expected returns not unlike that of common stock.

All property types including offices exhibit time-varying returns that are forecastable using

precisely the same business cycle proxies found to forecast common stock returns. This being

the case, our results suggest that institutional investors and others attempting to hedge the

cyclical variation of common stocks should carefully consider the inclusion of commercial

real estate into their portfolios. In fact, among the commercial real estate alternatives, office

properties would appear to provide the least effective hedge as their rental growth rates also

vary with the state of the economy.

Commercial real estate, however, differs from common stock in several important

ways. For example, it is often argued that common stock dividends do not accurately

reflect changing investment opportunities confronting a firm. Dividends are paid at the

discretion of the firm’s management and there is ample evidence that they are either actively

smoothed, the product of managers catering to investors’ demand for dividends, or the result

of managers’ reaction to perceived mispricings (Shefrin and Statman (1984), Stein (1996),

and Baker and Wurgler (2004)). Dividends are also subject to long term trends such as

the recent decrease in the propensity of firms to pay dividends (Fama and French (2001)).

By contrast, rents on commercial properties are not discretionary and are paid by tenants

as opposed to property managers. Furthermore, rents, especially office rents, are more

sensitive to prevailing business conditions. Because commercial real estate is not publicly

traded and is characterized by higher transactions costs, our analysis focuses on long horizon

predictability where these particular factors are expected to be less important. Finally, the

prices of commercial properties are likely to be more sensitive than stocks to geographic,

demographic, and local economic factors. To capture these sensitivities, following Abraham

and Hendershott (1996), Capozza, Hendershott, Mack, and Mayer (2002), and Glaeser,

Gyourko, and Saks (2004), we use population growth, per capita income growth, employment

growth, the growth in construction costs, coastal region dummies, as well as several other

urbanization proxies in an attempt to control for these cross-sectional differences.

The plan of this paper is as follows. In Section 2, we present our valuation framework

and discuss its application to commercial real estate taking special care to account for

locational differences as well as differences across property types. In Section 3, we discuss

4

our commercial real estate data. The main predictive results are presented in Section 4

along with various robustness checks. The economic significance of the predictability and

its implication for the volatility of commercial real estate prices is discussed in Section

5. In Section 6 we provide further evidence on the time-variability of expected returns to

commercial real estate. We link the differences in predictability results across property types

to differences in forecastability as well as to differences in variability of their rental growth

rates. We offer concluding remarks in Section 7.

2 Real Estate Returns, Rents, and Growth in Rents

2.1 The Rent-Price Ratio Model

We denote by Pt the price of, say, an apartment building at the end of period t and by Ht+1

its net rent, that is, rent minus any operating expenses adjusted for vacancies, from period

t to t + 1. The gross return from holding the apartment building from t to t + 1 is:

1 + Rt+1 ≡ Pt+1 + Ht+1

Pt

. (1)

The above definition of the return to commercial real estate is similar to that of common

stock. The only difference is that a commercial property provides real estate services at a

market value Ht+1 instead of paying dividends.

If we define the log return as rt+1 ≡ log(1 + Rt+1) and the log net rent as

ht+1 ≡ log(Ht+1), we can follow Campbell and Shiller (1988) and express rt+1 using a

first-order Taylor approximation as rt+1 ≈ κ + ρpt+1 + (1 − ρ)ht+1 − pt, where κ and ρ

are parameters derived from the linearization1. Solving this relation forward, imposing the

transversality condition limk→∞ ρkpt+k = 0 to avoid the presence of rational bubbles, and

taking expectations at time t, gives the following present value relation for the log price

1In particular, ρ ≡ 1/(1+exp(h− p)), being h− p the average log rent - price ratio. Note that for the UScommercial real estate market, the average log rent - price ratio in the period 1994 - 2003 has been about8.5% annually, implying a value for ρ of 0.92 in annual terms, which is slightly lower than the 0.97 in theequity market for the same period.

5

pt ≡ log(Pt) of a commercial real estate property:

pt =κ

1− ρ+ Et

[ ∞∑

k=0

ρk [(1− ρ)ht+1+k − rt+1+k]

]. (2)

Expression (2) states that a high property price today reflects the expectation of high future

rents or of lower future expected returns or both. If commercial real estate markets are

efficient, then information about future cash flows or future discount rates should be reflected

in current property prices. Expression (2) has been previously used in the asset pricing

literature to analyze the fluctuations of equity returns (see Campbell and Shiller (1988b)

and Campbell (2003) for a review).

If expected returns and rental growth rates are both stationary, expression (2) implies a

log-linear approximation of the rent-price ratio which will facilitate our subsequent empirical

analyses. In the commercial real estate literature, the rent-price ratio Ht/Pt is referred to

as the cap rate (Geltner and Miller (2000)). Therefore, if we define capt ≡ ht − pt, from

expression (2) we can write:

capt = − κ

1− ρ+ Et

[ ∞∑

k=0

ρkrt+1+k

]− Et

[ ∞∑

k=0

ρk∆ht+1+k

]. (3)

The above equation is best understood as a consistency relation. It states that if a

commercial property’s cap rate is high, then either the property’s expected return is high, or

the growth of its rents is expected to be low, or both. This log-linearization framework was

proposed by Campbell and Shiller (1988b) as a generalization of Gordon (1962)’s constant-

growth model and explicitly allows both expected returns and dividend growth rates to be

time-varying. Like any other financial asset, there are good reasons to believe that expected

returns to commercial real estate and rental growth rates are both time-varying. We will

use expression (3) as the starting point for our analysis of fluctuations in commercial real

estate prices.

To proceed, we must make additional assumptions about the dynamics of expected

returns, Etrt+1, as well as expected rental growth rates, Et∆ht+1. We will assume that

expected returns follow a stationary autoregressive process of order one (AR(1)) with

6

autoregressive coefficient φ satisfying |φ| < 1:

Etrt+1 = r + xt = r + φxt−1 + ξt (4)

where r is the unconditional expected return and r+xt is the conditional expected return at

time t. The vector xt contains conditioning information such as the term spread, the default

spread, inflation, and the short interest rate that have been previously shown to capture time-

varying economic conditions2, while ξt is a white noise disturbance. This AR(1) specification

provides a parsimonious representation of slowly evolving macroeconomic conditions.

We further assume that the expected growth of rents is also time-varying,

Et∆ht+1 = g + τxt + yt

= g + τxt + ψyt−1 + ζt (5)

where g is the unconditional expected rental growth rate and ζt is a white noise disturbance.

Here a non-zero value of the coefficient τ implies that rental growth and expected returns

are correlated. For example, if τ = 1 then both rental growth and expected returns respond

equivalently to changing economic conditions. The yt term represents the variation in rental

growth that is orthogonal to the variation in expected returns. We allow yt to also be serially

correlated.3

Using expressions (4) and (5) and ignoring the κ terms, the cap rate, expression (3),

can be written as:

capt =r − g

1− ρ+

[xt(1− τ)

1− ρφ− yt

1− ρψ

]. (6)

The first term in expression (6) reflects the difference between the unconditional expected

return and the unconditional rental growth rate. The second term in expression (6) captures

the influence of time-varying fluctuations in expected returns and rental growth rates on cap

rates. In particular, large deviations from unconditional expected returns (large xt) or more

persistent deviations (large φ) imply high cap rates. Also, fluctuations in expected rental

growth that are orthogonal to expected returns (yt) are negatively correlated with cap rates.

2See Campbell (1991), Campbell and Shiller (1988a), Chen, Roll, and Ross (1986), Fama (1990), Famaand French (1988, 1989), Ferson and Harvey (1991), and Keim and Stambaugh (1986), among others.

3Lettau and Ludvigson (2004) use a similar specification to model the correlation between expectedreturns and expected dividend growth in common stocks.

7

We can immediately see that if expected returns and expected rental growth rates

are correlated, that is, τ lies between zero and one, then it will be difficult for the cap

rate to forecast expected returns. In the extreme case where expected rental growth rates

move one for one with expected returns, τ = 1, the cap rate will be unable to detect any

fluctuations in expected returns because the variation in expected returns will be exactly

offset by corresponding fluctuations in expected rental growth rates. Detecting a forecasting

relation between cap rates and expected returns is also made difficult if the variation in the

portion of rental growth rate orthogonal to the variation in expected returns, yt, is large.

Expressions (3) and (6) impose testable restrictions on the time series behavior of

asset prices including commercial real estate. The extant literature (see, e.g., Campbell and

Shiller (1988b), Fama and French (1988), Campbell, Lo, and MacKinlay (1997), Lettau and

Ludvigson (2004)) tests this relation using data from the US stock market and the main

findings can be summarized as follows: (i) the dividend-price ratio is somewhat successful

at capturing movements in future expected stock returns; (ii) the dividend-price ratio is a

“smooth” variable and, as a result, is most successful at capturing movements in expected

returns at longer horizons; and (iii) the dividend-price ratio does not seem to capture

fluctuations in dividend growth rates which appear to be close to i.i.d.4 These stock market

time series regressions require a lengthly series of data owing to well known small-sample

biases induced by the persistence of the dividend-price ratio (Stambaugh (1999)).

2.2 Real Estate Expected Returns, Rents, and Cap Rates Across

Metropolitan Areas in the US

The dynamic Gordon model outlined in the previous section specifies the time series

properties and resultant forecasting relations expected to prevail between cap rates and

expected commercial real estate returns as well as expected rental growth rates. In principle,

these relations are applicable to any category of commercial real estate located in any

metropolitan area. In this paper, we consider four broad categories of commercial real estate:

apartments, office buildings, industrial and retail properties, denoted by the superscripts A,

O, I, and R, respectively.5 By their very nature, these property types differ in their rent

4Although ongoing research is revisiting these results (Lettau and Ludvigson (2004)).5Hotel properties represent another major category of commercial real estate. Unfortunately, we do not

have data on hotels and so they are excluded from our subsequent analysis. However, hotels represent lessthan four percent of the total value of U.S. commercial real estate. See Case (2000).

8

and risk characteristics while their sensitivities to economic conditions are also expected to

vary.

To fix matters, we concentrate on a particular type of commercial real estate property

(denoted by a “l” superscript and where l = A, O, I, and R) located in two distinct

metropolitan areas, say, Portland (denoted by an “i” subscript) and Dallas (denoted by a

“j” subscript) whose cap rates are each given by expression (3). The difference in their cap

rates at time t can be written as

(capl

i,t − caplj,t

)= kl + Et

[ ∞∑

k=0

ρk(rli,t+1+k − rl

j,t+1+k

)]+ Et

[ ∞∑

k=0

ρk(∆hl

j,t+1+k −∆hli,t+1+k

)]

(7)

where kl ≡ kli − kl

j, and capli,t denotes the cap rate for property type l in area i at time

t.6 Expression (7) decomposes the difference in these cap rates into differences in expected

returns and in expected rent growth rates. For example, suppose that the cap rate of the

average apartment in Portland, area i, is higher than that of the average apartment in Dallas,

area j. This implies that either expected returns of apartments in Portland are higher than

those in Dallas, or that the future growth rate in apartment rents in Portland is lower than

in Dallas, or both. Similar conclusions hold for the other commercial property types.

Differences in cap rates for a particular commercial property type across metropolitan

areas in expression (7) depend on the cross-sectional and time series variations in their

expected returns and expected rental growth rates. To see this, suppose that expected

returns to a particular property type l in each metropolitan area respond differentially to

the same underlying fluctuations in xt

Etrli,t+1 = rl

i + δlixt (8)

where rli is the unconditional return to property type l in area i while δl

i captures, in a

reduced-form fashion, the effects of time variation in underlying economic conditions xt on

expected returns to property type l in area i.

In addition, we allow the growth in rents for a particular property type to differ across

6The same convention applies to the remaining terms. This equation is obtained under the assumptionthat the linearization constant ρ is the same across both markets, which is a realistic assumption in ourdataset where its values range from 0.911 to 0.925.

9

areas. For example, the rental growth rate of property type l in region i is

Et∆hli,t+1 = gl

i + τ lixt + yl

i,t. (9)

It follows that the cap rates of a particular commercial property type l in area i can

be expressed as

capli,t =

(rli − gl

i

1− ρ

)+

[δli(1− τ l

i )xt

1− ρφ− yl

i,t

1− ρψ

]. (10)

In expression (10), the first term captures the difference in the unconditional moments

which is simply a log-linearization of the standard Gordon constant-growth model. Clearly,

the unconditional difference in cap rates for a particular property type across any two

metropolitan areas must be due either to differences in their expected returns or in their

expected rental growth rates. The second term in expression (10) captures time-varying

expected returns and expected rental growth rates.

Metropolitan areas with more variable expected returns (higher δli) will have higher cap

rates even if the unconditional expected returns and growth rates in the two areas are equal.

Similarly, the cap rate will be a better proxy for time-varying expected returns in areas

where the growth in rents is less influenced by economic conditions (lower τ li ). The expected

returns of property types whose growth in rents are more sensitive to the time-varying

economic conditions, τi close to one, will not covary with the cap rate. Also, the variability

of the growth in rents that is orthogonal to expected returns, yli,t, plays an important role in

our ability to detect a relation between cap rates and future returns. Since this variability

is orthogonal to the cap rate as well as to expected returns, it has the effect of noise in

a predictive regression. To the extent that the variability in this component differs across

property types, we should expect to see a stronger forecasting relation between cap rates

and expected returns for precisely those properties with lower variability in yli,t and a lower

total volatility in their rental growth process.

Notice that even small fluctuations in expected return can have a large effect on prices

so long as these fluctuations are persistent, which as we will see below is an empirically

reasonable assumption. This amplifying effect is captured by the denominator in expression

(10). Hence, the introduction of time-varying expected returns is particularly important for

commercial real estate where economic variations have sizeable effects on prices. See, for

10

example, Case (2000) who provides an example illustrating “the vulnerability of commercial

real estate values to changes in economic conditions” along with a review of recent boom-

and-bust cycles in that market.7 Similarly, using international data, Case, Goetzmann, and

Rouwenhorst (2000) find that commercial real estate is “a bet on fundamental economic

variables”. One of the empirical issues that we will subsequently investigate is how large

this particular effect is likely to be.

3 The Commercial Real Estate Data

Our data consists of prices and annualized cap rates of class A offices, apartments, retail and

industrial properties for fifty-three U.S. metropolitan areas. The fifty-three sampled areas

include more than 60% of the U.S. population (2000 data). A listing of these metropolitan

areas is given in Table A1 of the Appendix. The data are provided by Global Real Analytics

(GRA) and are available on a quarterly basis beginning with the second quarter of 1994

(1994:2) and ending with the first quarter of 2003 (2003:1). The prices and cap rates for

each property category are averages of transactions data in a given quarter. Taken together,

we have panel data with 1908 observations (36 quarters × 53 metropolitan areas). We also

have a subset of these data for twenty-one of the areas going back to 1985:4 and ending at

2002:4 but only at a bi-annual frequency.8

Given annual cap rates, CAPt, and prices, Pt, of a particular property type in a given

area, we construct quarter t’s net rents from expression (1) as Ht = (CAPt × Pt−1)/4.9 The

gross returns 1+Rt in quarter t are then obtained from expression (1) while Ht/Ht−1 gives one

plus the growth in rents. For consistency with the previously derived expressions, we work

with log cap rates, capt = ln(CAPt), and log rental growth rates, ∆ht = ln(Ht/Ht−1). Also,

we rely on log excess returns, rt = ln(1 + Rt)− ln(1 + RTblt ), where RTbl

t is the three month

Treasury bill yield. Table A1 in the Appendix also reports time-series averages of excess

7In his example, Case (2000) assumes that expected returns increase and the expected rent growthdecreases with economic conditions.

8While not scientifically rigorous, perhaps a good indication of the data’s accuracy is the fact thatit is used by many real estate, financial, and government institutions. A partial list of the subscribersincludes Citigroup, GE Capital, J.P. Morgan/Chase, Merrill Lynch, Lehman Brothers, Morgan StanleyDean Witter, NAREIT, Pricewaterhouse-Coopers, Standard & Poors, Trammell Crow, Prudential RREEFFunds Capital/Real Estate Investors, Washington Mutual, FDIC, CalPERS, and GMAC.

9We obtain very similar results by modifying the timing convention and relying on the expressionHt = (CAPt × Pt)/4.

11

returns, rental growth rates, and cap rates for all property types across all metropolitan

areas.

We compute autocorrelations of the excess returns for each property type in each

metropolitan area. In Table 1, Panel A, we summarize the autocorrelation structure of the

excess returns at different quarterly lags (k). In particular, at each lag we display the 25th,

50th, and 75th percentiles of the autocorrelations of excess returns for a particular property

type using data from across all areas. We also display at each lag the number of areas

whose autocorrelations are significantly different from zero at the 5% level (denoted by N )

and specify the number that are significantly positive (denoted by +) and negative (denoted

by -). For apartments, the median autocorrelation at a one-quarter lag is −0.007 and the

corresponding inter-quartile range is from −0.101 to 0.170. The number of areas exhibiting

significant autocorrelation in apartment excess returns at a one-quarter lag is five, with four

of these being positive. In the case of industrial, retail, and offices buildings, the median first-

order autocorrelations in the corresponding excess returns are higher than for apartments at

0.043, 0.168, and 0.287, respectively. For retail properties, all eight of the significant first-

order autocorrelations are positive. Similarly, out of the twenty-five significant first-order

autocorrelations for offices, twenty-four are positive. The autocorrelations of excess returns

for all property types decrease rapidly with lag length, even for office buildings which display

the highest degree of serial dependence.10 In general, after three quarters (k = 3) to one year

(k = 4) the median autocorrelations as well as the number of significant autocorrelations are

both small.

These results suggest that while the excess returns of commercial real estate exhibit

some degree of positive serial dependence at a one-quarter lag (k = 1), they are essentially

uncorrelated at lags of one year or longer (k ≥ 4). Since these particular properties are likely

to be held by large institutional investors, it is not surprising to see less serial dependence

in their returns than in single-family home data (Case and Shiller (1989)) where market

inefficiencies and frictions undoubtedly play a larger role. It is also possible that the lack

of significant serial dependence in Panel A of Table 1 is due to our brief sample period as

well as the greater volatility of commercial real estate returns. To illustrate this point, in

Table A2 of the Appendix, we report estimates of the volatilities of quarterly commercial

property returns, rental growth rates, and cap rates for all metropolitan areas as well as

their mean, median, minimum and maximum across metropolitan areas. For example, the

10For offices, almost half of the series exhibit significantly positive serial correlation at a one-quarter lag.

12

average volatility of apartment excess returns is 6.1% per year which, though lower than the

stock market return volatility of 16.7%, is still an order of magnitude larger than the 0.5%

time-series standard deviation of apartment cap rates. Because of this extreme variability,

tests for serial dependence in returns will have low statistical power to reject the null of no

predictability, especially in small samples. Since this issue is especially of concern for short-

horizon predictive regressions, we follow the approach taken in the stock market predictability

literature11 and focus primarily on long-horizon forecasting relations.

We summarize the serial dependence of rental growth rates and cap rates in Panels

B and C of Table 1, respectively. Using data across all sampled metropolitan areas, the

median first-order autocorrelations for rental growth rates are 0.078 for apartments, 0.049

for industrial properties, 0.041 for retail properties, and 0.119 for offices. When areas

exhibit significant first-order autocorrelations in rental growth rates, they tend to be positive

more often than negative. Interestingly, retail properties and office buildings show less

persistence at a one-quarter lag in rental growth rates than in excess returns. At lags of

three quarters to one year (k = 3, 4), the rental growth series exhibit no serial correlation

for any of the property types. By contrast, regardless of the property type, cap rates are

extremely persistent with median one-quarter autocorrelations of 0.815 for apartments, 0.744

for industrial properties, 0.834 for retail properties, and 0.817 for offices. Almost all fifty-

three individual cap rate series exhibit significant positive serial correlation at a one-quarter

lag across all property types which tends to persist for the first two years (k ≤ 8).

4 Predictive Regressions

4.1 Methodology

We are interested in whether the cap rate for a particular property type in a given

metropolitan area reflects investors’ expectations of future returns or rental growth or both.

The framework in Section 2 suggests the following two regressions

ri,t+1→t+k = αk + βk (capi,t) + εi,t+k (11)

∆hi,t+1→t+k = µk + λk (capi,t) + υi,t+k (12)

11Campbell and Shiller (1988a), Campbell (1991), Lettau and Ludvigson (2004), among others.

13

where expected returns and rent growth rates are proxied by rt+1→t+k ≡∑k

l=0 rt+1+l and

∆ht+1→t+k ≡∑k

l=0 ∆ht+1+l, respectively. We run these regressions for various quarterly

horizons k using the pooled sample of fifty-three metropolitan areas over the 1994 to 2003

sample period for each of the four property types. The pooled data are first stacked for all

areas in a given quarter and then for all quarters.

It is important to emphasize that our pooled regressions differ from the time-series

regressions used in the stock return predictability literature. Given the limited time period

spanned by our data, the pooled approach has two main advantages. First, because we are

primarily interested in long-horizon relations but unfortunately do not have a long enough

dataset to run time-series regressions, the only reasonable way of exploring these relations is

to rely on pooled data. Secondly, as shown in Tables A1 and A2 in the Appendix, there is

considerable heterogeneity in returns, rental growth rates, and cap rates across metropolitan

areas at a particular point in time. Therefore, tests based on the pooled regressions are

likely to have higher power than tests based on time-series regressions in which the predictive

variable has only a modest variance (Torous and Valkanov (2001)).

Before presenting our results, a number of statistical issues surrounding our pooled

predictive regression framework must be addressed.12 First, the overlap in long-horizon

returns and rental growth rates must be explicitly taken into account. In our case, this

overlap is particularly large relative to the sample size. In addition to inducing serial

correlation in the residuals, this overlap also changes the stochastic properties of the

regressors by inducing persistence. While this particular problem has been investigated

by many authors in the context of time-series regressions, it is also likely to affect the

small-sample properties of the estimates in our pooled regressions. Secondly, the predictors

themselves are highly cross-sectionally correlated. For instance, the median cross-sectional

correlation of apartment cap rates in our sample is 0.522 and is as high as 0.938 (between

Washington, DC and Philadelphia, PA). As a result, because we effectively have fewer than

fifty-three independent cap rate observations at any particular point in time, a failure to

account for this cross-sectional dependence will lead to inflated t statistics. Finally, the

cap rates are themselves persistent and their innovations are correlated with the return

innovations. Under such conditions, it is well known that, at least in small-samples, the least

squares estimate of the slope coefficient will be biased in time-series predictive regressions

12We thank the referee for suggesting that we conduct inference in our pooled regression framework byusing resampling methods that carefully take into account the small-sample features of the data.

14

(Stambaugh (1999)). In pooled predictive regressions, the slope estimates will also exhibit

this bias because they are effectively weighted averages of the biased estimates of the time-

series predictive regressions for each metropolitan area.

Because of these issues, traditional asymptotic methods are unlikely to provide accurate

inference in our pooled predictive regressions. That being the case, we rely on a two-step

resampling approach. In the first step, as is customary in any predictive regression exercise,

we run a pair of time-series regressions for each of the fifty-three metropolitan areas: one-

period returns regressed on lagged cap rates and cap rates regressed on lagged cap rates.

The coefficients and residuals from these regressions are subsequently stored. For each area

we then resample the return residuals and cap rate residuals jointly across time (without

replacement, as in Nelson and Kim (1993)). The randomized return residuals are used to

create one-period returns under the null of no predictability. To generate cap rates, we

use coefficient estimates from the original regression together with the resampled residuals

from the cap rate autoregression. We then form overlapping multi-period returns from the

resampled single-period returns and, as we do with the original data, we pool the newly

generated data for all fifty-three areas. For each resampling i we then obtain a pooled

estimate β̂ik at each k-quarter horizon, where k ranges from 1 to 20 quarters. Because the data

are generated under the null, the average β̂k across resamplings, denoted by βk = 1I

∑Ii=1 β̂i

k,

is an estimate of the bias in the pooled predictive regression at horizon k. The bias-adjusted

estimate of βk is obtained as β̂adjk = β̂k − βk, where β̂k is the biased estimate of βk from the

pooled predictive regression. This procedure is in essence that suggested by Nelson and Kim

(1993) but applied to a pooled regression. It corrects for the small-sample bias in the slope

coefficient because the contemporaneous correlations between the return residuals and cap

rate residuals in a given metropolitan area as well as across areas is preserved. However,

while this procedure captures the overlap in the multi-period returns, it does not address

the issue of cross-sectional dependence in cap rates. This then necessitates our second step.

To account for the possibility that our predictability results are driven by cross-sectional

correlation in cap rates, we resample the cap rates across metropolitan areas at each point

in time for each return horizon k.13 Then, in a cross-sectional regression, we estimate the

predictive regression at each point in time and so obtain T estimates β̂k, where T is the

sample size. We repeat the entire resampling procedure 1,000 times which produces 1,000 ×13The bootstrap is carried out with replacement. We also tried resampling without replacement and

obtained very similar results.

15

T estimates β̂k. We use these 1,000 × T estimates to compute standard errors, denoted by

se(βk). This second step is very similar to a standard Fama and MacBeth (1973) regression

with the exception that we are running the regressions with 1,000 replications of bootstrapped

data rather than the original sample.

The standard errors from the double resampling account for both time-series and

cross-sectional dependence in the data because in the first resampling step the overlapping

nature of the returns is explicitly taken into account while in the subsequent resampling

step the cap rates are drawn at each point in time from the empirical distribution of cap

rates. The bias-adjusted double resampling t statistic, denoted by tDR, is computed as

tDR = β̂adjk /se(βk) = (β̂k − βk)/se(βk). We use the tDR statistics in all predictive regressions

in this paper involving the cap rate. The 95th and 99th percentiles of the bootstrapped

distributions of the tDR statistic are the critical values in our tests. For the sake of clarity

and conciseness, we report levels of significance next to the estimates (5% and 1%) rather

than small-sample critical values because the latter are a function of the overlap as well as

the cross-sectional cap rate correlation of a particular property type. We also display the

bias-corrected β̂adjk and, in some instances, the biased estimate β̂k for comparison. The same

methods are used in estimating and making inference regarding the slope coefficient λk in

equation (12).14

4.2 Results

Table 2 presents the results of forecasting commercial real estate returns using cap rates

(expression (11)) for apartments, industrial properties, retail properties, and office buildings.

For each property type, we report the least squares non-adjusted as well as the bias-adjusted

estimates, β̂k and β̂adjk , the tDR statistic, and the adjusted R2. Statistical significance of β̂adj

k

at the 5% and 1% level are denoted by superscripts “a” and “b”, respectively.

14A few things are worth mentioning about the above sampling procedure. First, the second bootstrap isnecessary in order to take into account the cross-sectional correlation in cap rates. Without it, the standarderrors would not be corrected for the cross-sectional dependence in cap rates. We verified that if we use onlythe Nelson and Kim (1993) randomization, we obtain t statistics very similar to the Newey and West (1987)results. Second, it is interesting to note that the pooled regression does not produce unbiased estimates.The reason is that given the cross-sectional correlation in cap rates and the fact that cap rate fluctuationsand return shocks are correlated, the pooled regression effectively yields a weighted average of the biasedestimates that would have been obtained in time series regressions for each metropolitan area. Third, thebias correction is large at longer horizons, where the sample is smaller and the overlap is larger.

16

For all property types, we see that at short horizons of less than one year (k < 4),

cap rates are positively correlated with future returns. However, the corresponding bias-

corrected slope coefficients are never statistically significant at the 1% level while the R2s

are uniformly low. The bias-corrected slope coefficients do increase in magnitude as the

horizon k increases and at k = 3 quarters are significant at the 5% level. The general lack

of significance and low R2s at horizons of less than one year are consistent with the large

variability in quarterly commercial property returns documented in the Appendix.15

For longer horizons, k ≥ 4, in the case of apartments the bias-corrected slope estimates

increase from 0.251 at a one-year horizon to 0.778 at a five-year horizon and both of these

estimates are statistically significant at the 1% level. The R2s of the regressions also increase

to 16.6 percent at the five-year horizon. In the case of industrial and retail properties, cap

rates best predict returns at horizons of between two and four years. The largest bias-

corrected slope estimate for industrial properties is 0.758 at k = 16 quarters with a R2 of

12.9 percent. For retail properties, the largest bias-corrected slope estimate is 0.945 at k = 12

quarters with a R2 of 24.6 percent. In both of these cases, the estimates are statistically

significant at the 1% level. Interestingly, in the case of offices there does not appear to be

reliable evidence of predictability at any horizon. The largest bias-corrected slope coefficient

in the case of offices is 0.290 at k = 8 quarters, which is statistically significant at the 5%

level but not at the 1% level. Also, the corresponding R2 is only 3.5 percent. At most other

horizons, the bias-corrected slope coefficients for offices are indistinguishable from zero.16

The results in Table 2 suggest that at least for apartments, industrial and retail

properties, cap rates reliably forecast returns at horizons of between three and five years.17

For office buildings, by contrast, there is little or no evidence of predictability at any horizon.

Recall from expression (3) that the presence of predictability and its magnitude in the context

of the dynamic Gordon model depend critically on the persistence of cap rates and on the

15Also the positive estimates partially reflect the serial correlation in returns at lags of one to three quartersobserved in Table 1.

16As the horizon increases, the number of observations in the predictive regressions decreases even thoughwe compute rt+1→t+k and ∆ht+1→t+k with overlapping data. The last column of each Table shows that,at the one-year horizon, we have 1643 observations, but only 795 observations are available at the five-yearhorizon. The small number of observations reduces the power of our tests and should work against ourdetecting predictability.

17It is interesting to note that we find somewhat similar β estimates to those reported in the stockpredictability literature. For example, Campbell, Lo, and MacKinlay (1997) report coefficients estimates of0.329, 0.601, 0.776, and 0.863 at the one, two, three, and four year horizons, when forecasting stock returns(these numbers refer to the period 1952-1994). These values are very similar to ours reported in Table 2 andsimilar patterns are displayed also for the R2 statistic.

17

forecastability of rental growth. Our results suggest that office buildings may differ from the

other property types either in the persistence of their cap rates or in the properties of their

rent growth.

In Table 3, we present the results from estimating regression (12). It is immediately

evident that for apartments, industrial and retail properties, there is no reliable evidence that

cap rates forecast the future growth in their rents. At horizons up to two years, the bias-

corrected slope coefficients are not significantly different from zero and the corresponding R2s

are small, between 0 and 3.2 percent. At longer horizons, the bias-corrected slope coefficients

for apartments and industrial properties are significant at the 5% level but not at the 1%

level. For retail, we observe significant, at the 1% level, bias-corrected slope coefficients

at k=12 and k=16 quarters only. By contrast, in the case of offices, the bias-corrected

slope coefficients are negative and insignificant up to k=8 quarters. The corresponding R2s

increase with horizon k, reaching a value of 7.7 percent at k = 20 quarters. At this particular

horizon, the slope coefficient is significant at the 1% percent level. In other words, while

for apartments, industrial and retail properties, there is little evidence that cap rates can

forecast the future growth in rents, the evidence is stronger for office buildings and, unlike

the other property types, the estimates have the theoretically correct sign.18

4.3 Robustness

4.3.1 Fixed Effects

Cap rates capture not only time-variation in expected returns but also cross-sectional

differences across metropolitan areas. These cross-sectional differences are related to various

18Expressions (11) and (12) can be thought of as cross-sectional regressions estimated once a quarterwhose coefficients are then averaged over time, similarly to the Fama and MacBeth (1973) procedure. Theestimates from our pooled regressions should be identical to those obtained from the corresponding Famaand MacBeth (1973) regressions if the cap rates do not vary with time (Cochrane (2001)). In fact, theFama-MacBeth approach produces very similar results when applied to our data. For example, in the caseof apartments at the five-year horizon, we obtain a Fama-MacBeth estimate of 0.750 instead of 0.778. Thecorresponding Fama-MacBeth t statistic of 5.714, computed with Newey-West standard errors, is somewhatlarger than the tDR statistic of 4.007 reported in Table 2. For retail properties at the same horizon, weobtain a Fama-MacBeth estimate of 0.660 and a Newey and West (1987) t statistic of 3.830, which are veryclose to the pooled estimate and tDR statistic of 0.699 and 3.309, respectively, reported in Table 2. Whilethe Newey and West (1987) and the tDR statistics are not directly comparable, because one is asymptoticwhile the other one takes into account the small-sample features of the data, they nevertheless illustratethe robustness of our findings. We obtain similar results at all horizons and across property types, whichsuggests that the statistical significance of our small-sample results are quite conservatively stated.

18

demographic, geographic, and economic factors. Since it is quite plausible that rents and

prices adjust quicker to time-series shocks in a given metropolitan area than to variations

across metropolitan areas, we allow for the possibility of unobserved heterogeneity across

areas by incorporating fixed effects into the previous regressions:

ri,t+1→t+k = αk + βk (capi,t) + ϕi + ε̃i,t+k (13)

∆hi,t+1→t+k = µk + λk (capi,t) + ςi + υ̃i,t+k (14)

where the fixed effects coefficients ϕi and ςi capture the heterogeneity across metropolitan

areas. We estimate the regressions by including fifty-three area-specific dummy variables.

Table 4 presents the results of estimating the fixed effects regression (13).19 The

regressions are estimated by first regressing excess returns and rental growth rates on the

cross-sectional dummies and then regressing the residuals on the cap rates. The bias-adjusted

slope estimates and corresponding tDR statistics are computed as described previously.

Notice that neither the slope estimates nor the tDR statistics change dramatically. More

importantly, the predictive power of the cap rates at long-horizons is still evident in the

case of apartments, industrial, and retail properties where we see the bias-adjusted slope

estimates being significant at the 1% level for k ≥ 4 quarters. We conclude that unobserved

heterogeneity across metropolitan areas is unlikely to account for our findings.

4.3.2 Longer Sample Period with Fewer Metropolitan Areas

An obvious question to pose is whether our results will hold over a longer sample period or

are they specific to the 1994 to 2003 period. Indeed, this particular sample period contains

only one full business cycle and coincides with a general upward trend in real estate prices.

To answer this question, we extend the sample back to 1985 by augmenting our data

with the bi-annual observations on all of the property types available for a subset of twenty-

one of the fifty-three metropolitan areas. These data are available from the second half of

1985 to the first half of 1994 and to this we add the post-1994 data for these particular twenty-

one areas sampled at a bi-annual frequency. This gives a sample spanning the 1985 to 2002

time period containing thirty-five semi-annual observations for the twenty-one metropolitan

19We do not report the results of estimating the fixed effects regression (14). Recall that in the absenceof fixed effects, the coefficients are largely insignificant. Adding these fixed effects reduces their significanceeven further.

19

areas giving a total of 735 observations for each property type. We rely on this dataset to

investigate the stability of our predictability findings but at a cost of fewer cross-sectional

observations.

We re-estimate regression (13) with the 1985 to 2002 dataset now using twenty-one

area-specific dummy variables and present the results in Table 5. For all property types,

cap rates can still be seen to forecast future returns and the predictability increases with

the forecasting horizon. The bias-adjusted slope estimates are similar to those previously

reported in Tables 2 and 4 and, in fact, are slightly larger. For example, for apartments, the

slope estimate at the five-year horizon is 1.297 while the corresponding estimate in Table

2 is only 0.778. Similar comparisons hold for the other property types. More importantly,

the bias-adjusted slope estimates remain statistically significant at the 1% level at long

horizons. The predictability results obtain even though we have bi-annual rather than

quarterly data over the 1985 to 2002 sample period and only on twenty-one rather than

fifty-three metropolitan areas. It is also worth noting that future office returns, while still

the least predictable of all four property types, are now more forecastable than in the 1994

to 2003 sample.20 We conclude that the ability of cap rates to capture future fluctuations in

commercial real estate returns does not appear to be driven by the 1994 to 2003 sample.

4.3.3 Other Robustness Checks

In this section, we describe several other robustness checks used to ensure the reliability of

our empirical results. We will discuss these results without detailing them in Tables as they

are in general agreement with our previous findings.

First, we run the forecasting regressions using only non-overlapping returns. The

predictive power of the cap rates remains. In particular, we obtain bias-adjusted slope

estimates that are similar to those previously reported and, in fact, the estimates and

corresponding tDR statistics at longer horizons are larger than those obtained when using

overlapping returns. These results, however, should be interpreted with some caution as the

number of observations at longer horizons is rather small.

In the pooled regressions, all observations are weighted equally. This estimation

approach is efficient under the assumption that the variances of the residuals are equal

20The results from forecasting rental growth are statistically insignificant and are omitted. They areavailable upon request.

20

across metropolitan areas. The homoscedasticity assumption may not be appealing as more

populous metropolitan areas are generally more diverse giving rise to more heterogeneity

in the quality of a given property type. For example, it is unlikely that the variance of

residuals for Los Angeles will be the same as that of, say, Norfolk, Virginia. To address this

concern, we use weighted least squares under the assumption that the heteroscedasticity in

the residuals is proportional to the population in a given area. In particular, the weight given

to a particular metropolitan area is given by its population divided by the total population

of all metropolitan areas in the previous year. We then divide the left- and right-hand side

variables of our predictive regressions (11) and (12) by the square root of these computed

weights. Interestingly, the bias-adjusted slope estimates now increase in magnitude but the

corresponding tDR statistics are very similar. The results for rental growth are once again

insignificant.

As a final remark, note that there are no efficiency gains to be had from estimating

regressions (11) and (12) jointly. In fact, given that the right-hand side variables are the

same, the joint seemingly unrelated equations (SUR) estimator is identical to our equation

by equation estimator.

5 Economic Significance of the Predictability

From an economic perspective, it is easier to interpret the response of future commercial

real estate returns to changes in cap rates rather than to log cap rates. To do so, we divide

the estimated slope coefficients by the average cap rate where the cap rate is expressed in

the same units as the returns (see, e.g., Cochrane (2001)). We compute these transformed

coefficients for apartments, industrial properties, retail properties, and office buildings using

the corresponding β̂adjk estimates from Table 2 and their average cap rates of 8.7%, 9.1%,

9.2%, and 8.7%, respectively.21 For apartments, a small increase in the cap rate implies

that expected returns should increase between 1.789, if we take the five-year estimates

(0.778/(5 × 0.087)), and 2.885, if we take the one-year estimates (0.251/0.087). Similarly,

for industrial properties, retail properties, and office buildings, the sensitivities to a small

increase in the respective cap rate are 3.736, 3.554, 1.793, respectively, if we rely on the

one-year estimates, and 1.486, 1.520, −0.145, respectively, if we use the five-year estimates.

21From the Table A1 in the Appendix.

21

Based on these calculations, as expected, there appears to be a difference between

the predictability of apartments, industrial properties, and retail properties versus office

buildings. For the first three property types, the sensitivities are between 1.5 and 3.7 whereas

for offices they are in the range of between −0.1 and 1.7. Based on this, it is tempting to

conclude that expected returns of office buildings are much less time-varying. However,

such a comparison assumes that the rental growth of all property types are not only equally

unforecastable but that they are also equally volatile. In the next section, we show that

while the rental growth rate of offices is unforecastable, it is much more volatile than the

rental growth rates of the other property types.

To further appreciate the effect of time-varying expected returns on commercial real

estate, it is useful to compare our results to those in the stock market literature. For

the aggregate stock market, a one percentage point increase in expected returns results in

about a 4 to 6 percent increase in prices (see, e.g., Cochrane (2001) for a summary of the

evidence).22 Hence, the sensitivity of commercial real estate prices to changing expected

returns is not very different than that of common stock. To the extent that the fluctuations

in expected returns of the stock market and commercial real estate are both driven by

changing economic conditions23, our findings suggest that an investment in commercial real

estate is not necessarily an effective hedge against stock market risk.

6 Understanding the Results

Thus far we have documented that for apartments as well as industrial and retail properties,

cap rates are significantly correlated, both statistically and economically, with their future

returns but not with the future growth in rents. For offices, cap rates forecast neither future

returns nor future growth in rents. Two immediate questions arise as a result. First, do

cap rates proxy for demographic, geographic, economic or other cross-sectional differences in

commercial real estate prices, or do they capture time variation in expected returns? Second,

why are the results for office buildings so different from the other property types?

22The difference in magnitudes is due mainly to the fact that the dividend yield of the market is about 4percent, which is half of the cap rate of commercial properties.

23Which is something we verify later in the paper.

22

6.1 Is Predictability Due to Time-Varying Expected Returns?

The predictability we have documented is due either to cross-sectional differences in

unconditional returns or to time series variation in conditional returns. To understand this

point, suppose that for a given property type, the cap rate at time t in area i, Portland, is

higher than that in area j, Dallas. From expression (10), the relatively lower price in Portland

can either be due to a lower unconditional expected return or to a higher unconditional

expected growth in rents in Dallas. These cross-sectional pricing differences are not a function

of time.

Cross-Sectional Controls

The pricing of commercial and residential real estate across metropolitan areas and its

relation to demographic, geographic, and economic variables has been widely investigated.

For example, Capozza, Hendershott, Mack, and Mayer (2002) find that house price dynamics

vary with city size, income growth, population growth, and construction costs. Abraham

and Hendershott (1996) document a significant difference in the time-series properties of

house prices in coastal versus inland cities. Lamont and Stein (1999) show that house prices

react more to city-specific shocks, such as shocks to per-capita income, in regions where

homeowners are more leveraged.24 In light of this evidence, we now investigate whether cap

rates are not merely proxying for these cross-sectional effects as opposed to capturing time

variation in economic conditions.

To test this “proxy” hypothesis, we use demographic, geographic, and economic

variables to capture differences across metropolitan areas. More specifically, for each

metropolitan area, we use the following variables: population growth (gpopt), the growth

of income per capita (ginct), and the growth of employment (gempt), all of which are

provided by the Bureau of Economic Analysis at an annual frequency. We also use the

annual growth in construction costs (gcct) compiled by R.S. Means. The construction cost

indices include material costs, installation costs, and a weighted average for total in place

costs.25 In addition, after lagging by two years, we include log population (popt−2), log

24While most of the cited papers focus strictly on the residential market, similar mechanisms are likely atplay in commercial real estate.

25There are missing data for some metropolitan areas in our construction costs database. For these series,we assigned the values of the closest area for which data is available. In detail, we assigned to Oakland andSan Jose the value of San Francisco, to Nassau-Suffolk the values of New York City and to West Palm Beachthe values of Miami. For the areas where merged data is present in the real estate database, a unique indexis constructed as weighted average of the single areas’ construction costs, based on their population.

23

per capita income (inct−2), log employment (empt−2), and log construction costs (cct−2), to

proxy for the level of urbanization (Glaeser, Gyourko, and Saks (2004)). We lag these level

variables by two years to prevent a mechanical correlation with corresponding growth rates.

We also include a dummy variable (coastt) which equals one when the metropolitan area is

in a coastal region.26

We account for these cross-sectional differences by augmenting the regressions (11) and

(12) as follows:

ri,t+1→t+k = αk + βk (capi,t) + θ′kZi,t + εi,t+k (15)

∆hi,t+1→t+k = µk + λk (capi,t) + θ′kZi,t + υi,t+k (16)

where Zi,t is the set of pre-determined characteristics. If cap rates are proxying for differences

across metropolitan areas and not capturing time variation in expected returns, then the

inclusion of these cross-sectional proxies will lower the significance of the estimated cap rate

coefficients while increasing the regression’s R2. Similarly, under the proxy hypothesis, the

exclusion of the cap rate from these regressions should not significantly alter the regression’s

R2.27

The results of estimating regressions (15) and (16) at a four-year horizon (k = 16

quarters) are presented in Tables 6 and 7, respectively. For each property type, we run three

specifications. The first includes the cap rate as well as the growth rates of the economic

variables (gpop, gemp, ginc, and gcc). In the second specification, we add the levels of these

variables as well as the coastal dummy (pop, emp, inc, cc, and coast). The third specification

includes the growth rates and the levels but excludes the cap rate.

Table 6 present the results of forecasting expected returns. Several results emerge.

First, the growth rate variables are not found to be significant for any of the property types

26We also collected data on financing costs in various metropolitan areas, but there was very little variationacross metropolitan areas. Time series variation in interest rates is already captured as we compute all returnsin excess of the Tbill rate. We also tried including the rent-to-income variable, which can be motivated fromthe results in Menzly, Santos, and Veronesi (2004). However, this variable was highly correlated with someof the other controls and we decided against including it in the regressions.

27The fixed effect regressions previously discussed can also be interpreted as tests of the proxy hypothesis.The fixed effects capture the cross-sectional differences of unconditional expected returns and unconditionalgrowth in rents without specifying their origin. Recalling the results from Table 4, we observe that accountingfor cross-sectional differences does not significantly decrease the forecasting power of the cap rate. Thedrawback of this approach is that the dummy variables are simply too coarse to capture variation that canbe better explained if we specify the correct source of heterogeneity.

24

nor does their inclusion affect the R2s. Secondly, the inclusion of the levels of the control

variables increases the regression R2s, but their coefficients are only significant in the case of

office buildings. This result may be due to a strong correlation between the control variables.

For offices, the control variables are significant indicating heterogeneity across metropolitan

areas. Thirdly, the exclusion of the cap rate leads to a dramatic drop in the regression R2s for

apartments, as well as industrial and retail properties. In other words, after accounting for

cross-sectional differences in these metropolitan areas, cap rates do appear able to capture

additional time variation. In the case of offices, however, the exclusion of the cap rate does

not result in a significant drop in the regression R2. Fourthly, the bias-corrected cap rate

estimates are larger than those in Table 2. This difference might be partially due to the

fact that we use annual rather than quarterly data in the regressions, because the additional

economic and demographic controls are only available at that frequency. The results are

similar at other return horizons. Taken together, the evidence in Table 6 suggests that cap

rates are proxying for more than simply differences in expected returns across metropolitan

areas.

Table 7 presents the results for forecasting rental growth rates at a four-year

horizon. The addition of the cross-sectional controls does not markedly alter the cap rate’s

significance. However, the regression R2s can now be seen to increase from a range of 3 to

4 percent (Table 3) to between 16 and 27 percent, depending on the property type with

retail having the highest R2. Several control variable coefficients are significant, depending

on the property type and the particular specification. The office building regressions have

the highest number of significant control variable coefficients, suggesting that cross-sectional

differences in economic conditions play a significant role in determining the future growth

in office rents. Interestingly, the exclusion of the cap rate from these regressions does not

result in a dramatic drop in R2s as was the case for expected returns. Hence, it seems that

the expected growth in rents for all commercial property types is primarily determined by

area-specific characteristics.

The regressions presented in Table 6 and 7 exhibit relatively high R2s while the

control variables have low t statistics and are rarely found to be significant, all of which are

symptoms of multicollinearity in the regression specifications. The high correlation between

the regressors in the vector Zi,t is not surprising as these variables all attempt to capture

similar facets of the underlying economic and demographic conditions in a metropolitan area

at a particular point in time. To reduce the number of correlated variables while at the same

25

time succinctly summarizing their information content, we perform a principal component

analysis (PCA) of the control variables28. Our PCA reveals that three out of eight principal

components account for more than 70% of the overall volatility in Zi,t. The three extracted

principal components (which, by construction, are orthogonal) are particularly correlated

with the level and growth in population and income as well as with the level of construction

costs.

Tables 8 and 9 present the results of regressing future returns and future rental growth,

respectively, on the cap rate, the three principal components and the coastal dummy variable.

We can see that in both regressions the three principal components and the coastal dummy

are statistically significant for most of the property types. In particular, either the first,

the second or both principal components are significant at the 1% level while the cap rate

is still significant when the principal components are added. Moreover, for all property

types but offices, the R2s of the future returns regressions decreases substantially when we

omit the cap rate while for all property types the R2s of the future rental growth regression

are slightly lower. Hence, we conclude that the economic variables are indeed capturing

significant cross-sectional variation in returns and rental growth, but this does not limit the

predictive content of cap rates.

Time-Variation in Expected Returns

Our empirical evidence is consistent with cap rates for apartments, industrial, and retail

properties being able to capture fluctuations in time-varying expected returns. Expected

rental growth rates, by contrast, appear to be determined by cross-sectional determinants and

do not seem to fluctuate over time. To more directly verify this conclusion, we regress future

one-year returns and future yearly rental growth rates on regional dummies and variables

that have previously been documented to capture time-varying economic conditions. The

conditioning information here includes the term spread, the default spread, the CPI inflation

rate, and the three month Treasury bill rate.29 These variables have been widely used in the

stock predictability literature to capture time-varying behavior in aggregate stock market

expected returns (Campbell and Shiller (1988a), Campbell (1991), Fama and French (1989),

28Another possibility is to select the variables according to their ability to improve the R2. However,the set of variables so chosen is likely to vary across property type and the method increases the risk ofoverfitting.

29We also tried using the consumption-wealth variable “cay,” which Lettau and Ludvigson (2001) showforecasts future aggregate stock market returns. In the specification with the term spread, default spread,inflation, and the short rate, the cay variable was not significant. However, it was significant if any one ofthe other variables was dropped.

26

Torous, Valkanov, and Yan (2005) and, for a good review, Campbell, Lo, and MacKinlay

(1997)). The term spread is calculated as the difference between the yield on 10-year and

1-year Treasuries. The default spread is calculated as the difference between the yield on

BAA- and AAA-rated corporate bonds while the CPI inflation rate is the quarterly growth in

the CPI index.30 Under the hypothesis that expected returns are time-varying, they should

be forecasted by the macroeconomic variables. Similarly, we expect these variables to have

only modest power in forecasting future rental growth. In estimating these regressions, we

use the longer 1985 to 2003 sample period with fewer metropolitan areas in order to obtain

more precise parameter estimates as the regressors vary across time but are the same across

metropolitan areas.

We present the results from these regressions in Table 10. Focusing on panel A, we

see that the future returns of apartments, industrial and retail properties are explained by

time variation in the term spread, default spread, inflation, and the short interest rate. For

these property types, the macroeconomic variables explain between 10 and 24 percent of the

time series fluctuations in cap rates. The coefficients of inflation (CPIRET), the short rate

(TB3M), and the default spread (DSPR) are statistically significant for all property types at

the 1% or 5% level. It is interesting to note that for office buildings approximately 23 percent

of the time series fluctuations in future returns is explained by the macroeconomic variables

and is comparable to that for apartments and retail properties. Industrial properties have

the lowest R2. These results suggest that expected returns of offices are time-varying.31

Notice that the coefficients on inflation and the short rate are significantly negative.

This result is consistent with the evidence on predicting stock returns (Campbell (1987),

Fama and Schwert (1977), Fama and French (1989), Fama (1981), and Keim and Stambaugh

(1986), Fama and French (1993), and Lettau and Ludvigson (2001)). The coefficient on the

default spread is also significantly negative. While earlier studies found that the default

spread forecasted future stock returns with a positive coefficient (Fama and French (1989),

Campbell (1991), and Fama and French (1993)), more recently Lettau and Ludvigson (2001),

using a larger and more recent sample that includes most of our 1985 to2003 sample period,

also find the coefficient to be negative. As such, our commercial real estate findings are in

30All these data, except the three month Treasury bill rate, are from the FRED database. The threemonth Treasury bill rate is obtained from Ibbotson Associates. The statistical properties of these variablesare well known and are not provided here.(see, e.g., Torous, Valkanov, and Yan (2005)).

31The results from the shorter 1994-2003 sample are very similar, albeit less significant, with R2s in therange of between ten and fifteen percent.

27

line with those in the stock market predictability literature.32 Our findings are not only

consistent with cap rates capturing time variation in the expected returns of these property

types, but also with the expected returns of stocks and commercial real estate responding in

the same direction to changes in underlying economic conditions.

Panel B of Table 10 presents the results of forecasting the yearly growth in rents

with the macroeconomic variables. In contrast to the results of Panel A, the economic

variables have much less ability to predict the future growth in rents of apartments, industrial

properties, and retail properties. The goodness of fit in these regressions is in the range of

between 4 and 7 percent. For office buildings, we observe a much stronger forecastability

of rental growth. The corresponding R2 of 13.5 percent is about twice as large as that of

other property types with most of the forecastability being driven by the default spread and

inflation. As we discuss in the next section, this difference is important in understanding

the lack of expected return forecastability observed for offices.

6.2 Why are Offices so Different?

A recurring theme thus far has been the differences documented between office buildings

versus the other commercial property types. Only for office buildings do we fail to detect

an economically and statistically significant relation between cap rates and future returns.

Based solely on this evidence, to conclude that the expected returns of offices are less

susceptible to economic fluctuations than the other property types would be correct only

if expected growth in rents for all property types are: (i) equally correlated with expected

returns; and (ii) equally volatile. To see the necessity of assumption (i), consider expression

(10) and suppose that expected returns of offices and, say, apartments are equally exposed

to economic variation (δA = δO). In addition, we assume that the growth in rents of offices is

much more correlated with expected returns than is the growth of apartment rents (τO = 1

while τA ≈ 0), and that the variation in rental growth orthogonal to economic conditions

is the same for offices and apartments (V (yOt ) = V (yA

t )). Under these assumptions, the

cap rate will better predict the expected returns of apartments despite the fact that the

expected returns of both property types are time-varying. This result obtains because the

variability in expected returns for offices is offset by the variability in rental growth and

32We replicated the Lettau and Ludvigson (2001) results and found that, for the 1985-2003 sample, thedefault spread has a negative coefficient in predicting excess stock market returns.

28

the net effect, captured by the term xt(1 − τO), results in an absence of variability in their

cap rates. This argument has been made for the aggregate stock market by Campbell and

Shiller (1988b) and more explicitly by Lettau and Ludvigson (2004) and Menzly, Santos,

and Veronesi (2004).

Assumption (ii) must also hold if different property types are to comparably predict

future returns. Using a similar logic, suppose that the variability in office rent growth that is

orthogonal to economic conditions is greater than that of, say, apartments (V (yOt ) > V (yA

t )),

while their expected returns are equally exposed to economic variables (δA = δO). From

expression (10), it follows that the apartment cap rate will better predict expected returns.

The additional variability in office rent growth that is orthogonal to the variation in expected

returns only adds noise to the predictive regression for offices and so will decrease its power.

Table 10 provides evidence against assumption (i). Panel B of the Table shows that

office rental growth is more forecastable by macroeconomic variables than is the rental growth

of the other three property types. Moreover, it is interesting to note that the same variables

that forecast office rent growth also forecast future office returns. In particular, the default

spread and inflation rate are both negatively correlated with future office rent growth as well

as future office returns. This evidence suggests that office rent growth is time-varying and is

also correlated with office expected returns. As noted earlier, this correlation would make it

difficult to detect predictability using office cap rates even if the expected returns of offices

are time-varying.

The second assumption is also not supported by the data as the growth of office rents

is more volatile than for the other property types. To document this fact, we estimate the

volatility of rental growth that is orthogonal to economic fluctuations for each property type

in each metropolitan area using the time series data from the 1985 to 2003 sample period.

We do so by first regressing the one year rental growth rates on the macroeconomic variables

as in Table 10. Using the residuals from these regressions, we estimate GARCH(1,1) models,

which yield twenty-one time series estimates of volatilities for each property type. We then

compute the median and the mean filtered volatility across metropolitan areas for each

property type.

The results are plotted in Figure 1. It is immediately evident that the median and mean

standard deviations for office buildings (solid line) are almost invariably greater than that for

the other property types. Moreover, office buildings exhibit more conditional autoregressive

29

heteroscedasticity than the other series. Notice that the volatilities of office rent growth

are particularly high during the 1991 to 1993 and the 1997 to 1999 time periods. The first

period coincided with a declining market and decreasing rents while the second period was

one of increasing rents (Case (2000)). The mean values of these volatilities across time

are 7.0 percent, 7.1 percent, and 5.6 percent annually for apartments, retail, and industrial

properties, respectively. For offices, the volatility is significantly higher at 8.5 percent. As a

comparison, we also computed the dividend growth rate of the CRSP value-weighted index,

a proxy for the aggregate stock market. The volatility of the stock market’s dividend growth

rate that is orthogonal to the macroeconomic variables over that period is only 8.1 percent.

In summary, the exposure of expected returns of offices to macroeconomic variables

appears comparable to that of the other property types. Given that the growth in office

rents is more correlated with expected returns and that this growth rate is generally more

volatile, it is not surprising that office cap rates are unable to forecast future returns.

7 Conclusions

This paper empirically analyzes the fluctuations in returns and rental growth rates for

apartments, office buildings, retail properties, and industrial properties. We find that for

apartments as well as retail and industrial properties, the cap rate forecasts time variation

in expected returns but does not forecast expected rental growth rates. For these property

types, the time variation in expected returns generates economically significant movements

in corresponding property prices. For offices, by contrast, the cap rate neither forecasts

expected returns nor rent growth rates.

Commercial real estate markets offer a natural setting in which to demonstrate that the

predictability of expected returns by the dividend-price ratio, that is, the cap rate, is sensitive

to the assumption that the growth rate of cash flows, in our case rents, is unforecastable

as suggested earlier by Campbell and Shiller (1988b) and more recently argued by Lettau

and Ludvigson (2004) and Menzly, Santos, and Veronesi (2004). We demonstrate that

while the expected returns of the four commercial property types have similar exposures

to macroeconomic variables, their rental growth rates differ in terms of their correlations

with expected returns as well as in their volatilities. As a result, the cap rate for offices,

whose rental growth rate is the most highly correlated with expected returns as well as also

30

being the most volatile, does not forecast expected returns even though these returns are

themselves time-varying. Investigating the economic sources underlying the cyclical variation

of office rental growth rates is an interesting issue for future research. Since under certain

circumstances cap rates cannot capture the variation in expected returns, it is natural to ask

whether there is a variable better suited for this task. To answer this question, an extension

of the Menzly, Santos, and Veronesi (2004) model to the case of commercial real estate would

be an interesting problem to pursue in future work.

We also find that the expected returns of commercial real estate and common stock have

similar correlations with macroeconomic variables. In addition to the evidence that expected

returns of commercial real estate are time-varying, this finding suggests that commercial

real estate may not provide an effective hedge against fluctuation in the stock market and

underlying economic conditions. While this paper deals exclusively with the implications of

our findings on the pricing of commercial real estate properties, the portfolio choice problem

involving commercial real estate is also very interesting and is left for future research. Some

work incorporating real estate already exists in this area (Piazzesi, Schneider, and Tuzel

(2003) and Lustig and Van Nieuwerburgh (2004)), but its focus is residential real estate.

Future research in this area should further explore the role of commercial real estate and its

stochastic properties in a portfolio setting.

31

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34

Table 1: Autocorrelation Coefficients of Excess Returns, Rent Growth, and LogCap Rates

The table reports the autocorrelation coefficients of excess returns (Panel A), rent growth (Panel B) and logcap rates (Panel C) for apartments, industrial, retail, and office properties. Excess returns are computed bysubtracting the log total real estate return from the log three-month Treasury bill rate. We first computethe autocorrelation coefficients for each time series of metropolitan area, then consider the cross-sectionalcoefficients for each lag k (in quarters), and evaluate the 25th, 50th and 75th percentile (in the table 25%,50% and 75% respectively). For every k we also report the number N of significant coefficients at the5% level (if they exceed 2/

√T in absolute value) amongst the 53, and the number of significantly positive

(indicated by +) and negative (indicated by -) coefficients. In the table, statistical significance at the 5%level is denoted by superscript a. The sample is quarterly observation of 53 areas from 1994:2 to 2003:1.

Panel A: Excess Returns

Apartments Industrial

k 25% 50% 75% N + - 25% 50% 75% N + -1 -0.101 -0.007 0.170 5 4 1 -0.093 0.043 0.162 7 4 32 -0.171 -0.083 0.038 8 3 4 -0.186 -0.072 0.073 7 2 53 -0.121 -0.019 0.090 4 1 3 -0.109 -0.032 0.069 1 1 04 -0.063 0.029 0.149 1 1 0 -0.104 0.016 0.105 1 0 18 -0.128 0.032 0.150 1 1 0 -0.061 0.017 0.117 2 1 112 -0.117 -0.023 0.101 5 2 3 -0.078 -0.030 0.111 6 3 316 -0.100 -0.016 0.121 4 3 1 -0.107 -0.040 0.044 3 2 120 -0.172 -0.053 0.068 6 3 3 -0.057 0.057 0.146 9 5 4

Retail Offices

k 25% 50% 75% N + - 25% 50% 75% N + -1 0.058 0.168 0.283 8 8 0 0.101 0.287 0.380* 25 24 12 -0.042 0.092 0.216 8 7 1 0.008 0.099 0.212 8 8 03 -0.058 0.054 0.196 2 1 1 -0.082 0.074 0.216 1 1 04 -0.086 -0.011 0.106 2 1 1 -0.102 -0.003 0.141 0 0 08 -0.267 -0.129 -0.050 4 0 4 -0.176 -0.072 0.021 5 0 512 -0.165 -0.104 0.015 5 2 3 -0.200 -0.018 0.070 6 0 616 -0.214 -0.109 0.052 3 1 2 -0.209 -0.110 -0.019 10 2 820 -0.064 0.142 0.361a 18 16 2 -0.056 0.078 0.197 12 9 3

35

Table 1 (Cont’d): Autocorrelation Coefficients of Excess Returns, Rent Growth,and Log Cap Rates

Panel B: Rent Growth

Apartments Industrial

k 25% 50% 75% N + - 25% 50% 75% N + -1 -0.069 0.078 0.168 8 7 1 -0.090 0.049 0.204 10 6 42 -0.070 0.077 0.241 6 6 0 -0.099 0.049 0.173 4 3 13 -0.003 0.075 0.235 7 7 0 -0.016 0.081 0.187 6 6 04 0.016 0.128 0.228 6 5 1 -0.012 0.067 0.150 1 1 08 -0.117 0.028 0.135 3 0 3 -0.096 -0.004 0.132 3 1 212 -0.120 -0.020 0.167 9 8 1 -0.158 -0.055 0.121 5 1 416 -0.168 -0.048 0.064 5 1 4 -0.163 -0.078 0.029 4 1 320 -0.198 -0.008 0.115 5 0 5 -0.172 -0.053 0.096 5 0 5

Retail Offices

k 25% 50% 75% N + - 25% 50% 75% N + -1 -0.042 0.041 0.124 6 3 3 0.018 0.119 0.374a 17 14 32 -0.098 0.039 0.188 6 6 0 0.032 0.122 0.264 9 9 03 -0.082 0.042 0.192 4 3 1 -0.017 0.070 0.168 7 7 04 -0.069 0.013 0.173 1 1 0 -0.044 0.041 0.134 5 5 08 -0.130 -0.049 0.052 2 0 2 -0.099 -0.013 0.077 2 1 112 -0.130 -0.033 0.058 5 2 3 -0.136 -0.011 0.079 6 1 516 -0.108 -0.043 0.043 2 2 0 -0.217 -0.052 0.048 6 1 520 -0.090 -0.024 0.090 7 3 4 -0.210 -0.076 0.016 9 1 8

Table continued from previous page.

36

Table 1 (Cont’d): Autocorrelation Coefficients of Excess Returns, Rent Growth,and Log Cap Rates

Panel C: Log Cap Rates

Apartments Industrial

k 25% 50% 75% N + - 25% 50% 75% N + -1 0.723a 0.815a 0.861a 53 53 0 0.635a 0.744a 0.818a 52 52 02 0.469a 0.660a 0.740a 46 46 0 0.403a 0.517a 0.658a 43 43 03 0.363a 0.532a 0.652a 42 42 0 0.198 0.357a 0.495a 31 31 04 0.281 0.405a 0.545a 38 38 0 0.103 0.259 0.393a 21 21 08 -0.091 0.121 0.232 6 3 3 -0.111 0.008 0.129 4 1 312 -0.142 -0.029 0.048 1 0 1 -0.187 -0.110 0.004 2 0 216 -0.252 -0.138 -0.011 4 0 4 -0.278 -0.155 -0.054 4 0 420 -0.318 -0.226 -0.097 8 0 8 -0.277 -0.087 -0.037 9 0 9

Retail Offices

k 25% 50% 75% N + - 25% 50% 75% N + -1 0.729a 0.834a 0.879a 52 52 0 0.782a 0.817a 0.880a 53 53 02 0.524a 0.657a 0.757a 50 50 0 0.535a 0.640a 0.759a 50 50 03 0.305 0.496a 0.646a 36 36 0 0.339 0.479a 0.636a 40 40 04 0.166 0.381a 0.533a 32 32 0 0.243 0.365a 0.500a 33 33 08 -0.118 0.029 0.142 5 3 2 -0.140 0.010 0.156 7 4 312 -0.265 -0.158 -0.039 7 0 7 -0.302 -0.190 -0.049 10 0 1016 -0.333a -0.223 -0.141 13 0 13 -0.348a -0.234 -0.118 15 0 1520 -0.280 -0.173 -0.070 6 0 6 -0.319 -0.184 -0.025 10 0 10

Table continued from previous page.

37

Table 2: Forecasting Regressions of Excess Returns on Log Cap Rate

The table reports the results from the pooled OLS overlapping regressions of excess returns between t + 1and t + k on the log cap rate at time t for apartments, industrial, retail, and office properties as it appearsin equation (11). Excess returns over k periods are evaluated as sum of quarterly excess returns, includingrents (total returns). In the table, k is the horizon of the forecasting regression (in quarters), β̂k is the OLScoefficient of the log cap rate, β̂adj

k and tDR are, respectively, the bias-adjusted coefficient on the cap rateand its t-ratio obtained using the double-resampling procedure described in Section 4.1, R2 is the associatedR2 statistic and N is the number of observations involved in the pooled regression. Statistical significanceat the 5% and 1% level, evaluated using the empirical distribution from the double-resampling procedure, isdenoted by superscripts a and b, respectively. The sample is quarterly observation of 53 areas from 1994:2to 2003:1.

Apartments Industrial

k β̂k β̂adjk tDR R2 β̂k β̂adj

k tDR R2 N1 0.078 0.072 1.461 0.032 0.118 0.098 1.218 0.038 18022 0.138 0.132 1.936 0.044 0.205 0.201 1.775 0.055 17493 0.201 0.198a 2.119 0.061 0.286 0.275a 2.011 0.073 16964 0.275 0.251b 2.375 0.084 0.371 0.340b 2.148 0.093 16438 0.532 0.460b 3.024 0.137 0.640 0.548b 2.604 0.124 143112 0.654 0.566b 3.353 0.134 0.788 0.641b 2.688 0.120 127216 0.800 0.637b 3.287 0.146 0.946 0.758b 2.919 0.129 100720 0.961 0.778b 4.007 0.166 0.853 0.676b 2.543 0.083 795

Retail Offices

k β̂k β̂adjk tDR R2 β̂k β̂adj

k tDR R2 N1 0.090 0.062 0.940 0.039 0.052 0.025 0.491 0.014 18022 0.199 0.139 1.565 0.076 0.105 0.068 0.915 0.022 17493 0.307 0.237a 2.217 0.104 0.156 0.112 1.235 0.027 16964 0.415 0.327b 2.650 0.129 0.203 0.156 1.550 0.030 16438 0.833 0.689b 4.234 0.219 0.346 0.290a 2.174 0.035 143112 1.098 0.945b 4.928 0.246 0.339 0.270a 1.746 0.021 127216 1.074 0.932b 4.608 0.201 0.191 0.145 0.850 0.005 100720 0.857 0.699b 3.309 0.120 0.020 -0.063 -0.369 0.000 795

38

Table 3: Forecasting Regressions of Rent Growth on Log Cap Rate

The table reports the results from the pooled OLS overlapping regressions of rent growth between t + 1 andt + k on the log cap rate at time t for apartments, industrial, retail, and office properties as it appears inequation (12). In the table, k is the horizon of the forecasting regression, λ̂k is the OLS coefficient of the logcap rate, λ̂adj

k and tDR are, respectively, the bias-adjusted coefficient on the cap rate and its t-ratio obtainedusing the double-resampling procedure described in Section 4.1, R2 is the associated R2 statistic and N isthe number of observations involved in the pooled regression. Statistical significance at the 5% and 1% level,evaluated using the empirical distribution from the double-resampling procedure, is denoted by superscriptsa and b, respectively. The sample is quarterly observation of 53 areas from 1994:2 to 2003:1.

Apartments Industrial

k λ̂k λ̂adjk tDR R2 λ̂k λ̂adj

k tDR R2 N1 0.024 0.024 0.558 0.005 0.013 -0.018 -0.255 0.001 18022 0.051 0.045 0.751 0.010 0.023 -0.007 -0.069 0.001 17493 0.078 0.065 0.932 0.014 0.046 0.006 0.048 0.003 16964 0.107 0.091 1.082 0.018 0.074 0.031 0.238 0.006 16438 0.207 0.187 1.653 0.026 0.218 0.168 0.948 0.020 143112 0.242 0.252a 1.893 0.024 0.279 0.226 1.115 0.020 127216 0.285 0.272a 1.907 0.024 0.425 0.386a 1.764 0.033 100720 0.380 0.352b 2.326 0.035 0.381 0.405a 1.807 0.020 795

Retail Offices

k λ̂k λ̂adjk tDR R2 λ̂k λ̂adj

k tDR R2 N1 0.010 -0.009 -0.154 0.001 -0.013 -0.029 -0.532 0.001 18022 0.011 0.005 0.063 0.000 -0.021 -0.041 -0.548 0.001 17493 0.043 0.012 0.120 0.003 -0.030 -0.048 -0.543 0.001 16964 0.075 0.050 0.436 0.006 -0.033 -0.054 -0.528 0.001 16438 0.263 0.259a 1.718 0.032 -0.108 -0.094 -0.669 0.004 143112 0.385 0.436b 2.411 0.043 -0.292 -0.262a -1.643 0.019 127216 0.369 0.459b 2.419 0.031 -0.509 -0.441b -2.500 0.043 100720 0.184 0.337a 1.743 0.007 -0.728 -0.655b -3.749 0.077 795

39

Table 4: Forecasting Regressions of Excess Returns on Log Cap Rate with FixedEffect

The table reports the results from the pooled OLS overlapping regressions of excess returns between t+1 andt + k on the log cap rate at time t and on 53 cross-sectional dummies for apartments, industrial, retail, andoffice properties. Excess returns over k periods are evaluated as sum of quarterly excess returns, includingrents (total returns). The regression is performed by first regressing excess returns on 53 cross-sectionaldummies, and then regressing the errors from this regression on the log cap rate. In the table, k is thehorizon of the forecasting regression (in quarters), β̂k is the OLS coefficient of the log cap rate, β̂adj

k andtDR are, respectively, the bias-adjusted coefficient on the cap rate and its t-ratio obtained using the double-resampling procedure described in Section 4.1, R2 is the associated R2 statistic and N is the number ofobservations involved in the pooled regression. Statistical significance at the 5% and 1% level, evaluatedusing the empirical distribution from the double-resampling procedure, is denoted by superscripts a and b,respectively. The sample is quarterly observation of 53 areas from 1994:2 to 2003:1. The coefficients on thedummies are omitted.

Apartments Industrial

k β̂k β̂adjk tDR R2 β̂k β̂adj

k tDR R2 N1 0.085 0.089 1.665 0.039 0.129 0.111 1.386 0.046 18022 0.151 0.163a 2.156 0.055 0.223 0.225 1.960 0.068 17493 0.214 0.217b 2.346 0.075 0.309 0.304a 2.169 0.091 16964 0.287 0.270b 2.565 0.103 0.399 0.373b 2.393 0.116 16438 0.535 0.477b 3.355 0.176 0.684 0.606b 2.852 0.170 143112 0.616 0.561b 3.286 0.181 0.827 0.696b 3.011 0.184 127216 0.633 0.556b 3.281 0.169 0.925 0.803b 3.348 0.213 100720 0.588 0.528b 3.311 0.154 0.725 0.674b 3.052 0.156 795

Retail Offices

k β̂k β̂adjk tDR R2 β̂k β̂adj

k tDR R2 N1 0.088 0.062 0.969 0.038 0.067 0.042 0.819 0.024 18022 0.188 0.137 1.552 0.073 0.134 0.100 1.382 0.038 17493 0.286 0.225a 2.098 0.100 0.200 0.158 1.746 0.049 16964 0.383 0.307b 2.556 0.126 0.264 0.217a 2.157 0.058 16438 0.724 0.598b 3.665 0.214 0.457 0.406b 3.095 0.078 143112 0.891 0.757b 4.128 0.237 0.479 0.425b 2.831 0.072 127216 0.759 0.672b 3.748 0.182 0.294 0.303a 2.038 0.030 100720 0.365 0.306b 1.773 0.069 0.089 0.051 0.364 0.005 795

40

Table 5: Forecasting Regressions of Excess Returns on Log Cap Rate with FixedEffect from 1985

The table reports the results from the pooled OLS overlapping regressions of excess returns between t + 1and t + k on the log cap rate at time t and on 21 cross-sectional dummies for apartments, industrial, retail,and office properties from 1985 to 2002. The regression is performed by first regressing excess returns on21 cross-sectional dummies, and then regressing the errors from this regression on the log cap rate. Excessreturns over k periods are evaluated as sum of quarterly excess returns, including rents (total returns). In thetable, k is the horizon of the forecasting regression (in quarters), β̂k is the OLS coefficient of the log cap rate,β̂adj

k and tDR are, respectively, the bias-adjusted coefficient on the cap rate and its t-ratio obtained using thedouble-resampling procedure described in Section 4.1, R2 is the associated R2 statistic and N is the numberof observations involved in the pooled regression. Statistical significance at the 5% and 1% level, evaluatedusing the empirical distribution from the double-resampling procedure, is denoted by superscripts a and b,respectively. The sample is biannual observation of 21 areas between 1985:4 and 2002:4. The coefficients onthe dummies are omitted.

Apartments Industrial

k β̂k β̂adjk tDR R2 β̂k β̂adj

k tDR R2 N4 0.261 0.136 0.561 0.057 0.438 0.293 0.938 0.099 6728 0.606 0.362 1.086 0.128 0.865 0.556 1.264 0.162 63012 1.023 0.644a 1.527 0.217 1.374 0.888a 1.696 0.240 58816 1.470 0.995b 2.122 0.310 1.888 1.328b 2.295 0.318 54620 1.768 1.297b 2.545 0.357 2.230 1.701b 2.674 0.359 504

Retail Offices

k β̂k β̂adjk tDR R2 β̂k β̂adj

k tDR R2 N4 0.376 0.212 0.819 0.126 0.278 0.176 0.922 0.105 6728 0.793 0.534a 1.541 0.213 0.593 0.426a 1.603 0.171 63012 1.175 0.859b 2.086 0.272 0.908 0.683b 2.214 0.226 58816 1.469 1.110b 2.488 0.305 1.159 0.919b 2.664 0.253 54620 1.649 1.288b 2.694 0.315 1.326 1.045b 2.920 0.262 504

41

Table

6:

Fore

cast

ing

Regre

ssio

ns

ofExce

ssR

etu

rns

on

Log

Cap

Rate

and

Eco

nom

icV

ari

able

s

The

tabl

ere

port

sth

ere

sult

sfr

omth

epo

oled

OLS

over

lapp

ing

regr

essi

ons

ofex

cess

retu

rns

betw

een

t+

1an

dt+

kon

the

log

cap

rate

and

econ

omic

vari

able

sat

tim

et

for

apar

tmen

ts,in

dust

rial

,re

tail

and

office

s.T

here

sult

sre

fer

toa

4-ye

arho

rizo

n.T

heta

ble

show

sth

ree

spec

ifica

tion

sfo

rea

chre

ales

tate

prop

erty

type

:(1

)in

clud

esth

elo

gca

pra

tean

dth

edi

ffere

nce

inlo

gof

the

econ

omic

vari

able

s,(2

)in

clud

esth

elo

gca

pra

te,th

edi

ffere

nce

inlo

gof

the

econ

omic

vari

able

s,th

ele

velof

the

econ

omic

vari

able

sla

gged

twic

ean

dth

eco

asta

ldu

mm

y,(3

)in

clud

esth

edi

ffere

nce

inlo

gof

the

econ

omic

vari

able

s,th

ele

velo

fthe

econ

omic

vari

able

stw

ice

lagg

edan

dth

eco

asta

ldum

my.

The

vari

able

sar

ede

fined

asfo

llow

s:ca

pis

the

log

cap

rate

atti

me

t,gpop

,gem

p,g

inc

and

gcc

are

grow

thin

popu

lati

on,em

ploy

men

t,pe

rca

pita

inco

me

and

cons

truc

tion

cost

sat

tim

et

resp

ecti

vely

,pop

,em

p,i

nc

and

ccar

eth

ele

vels

ofth

eva

riab

les

atti

me

t−

2an

dco

ast

isth

eco

asta

ldum

my.

The

t-ra

tios

,in

pare

nthe

ses,

are

eval

uate

dus

ing

the

doub

le-r

esam

plin

gpr

oced

ure

desc

ribe

din

Sect

ion

4.1.

The

coeffi

cien

ton

the

cap

rate

isbi

as-a

djus

ted

usin

gth

esa

me

proc

edur

e.St

atis

tica

lsi

gnifi

canc

eat

the

5%an

d1%

leve

l,ev

alua

ted

usin

gth

eem

piri

caldi

stri

buti

onfr

omth

edo

uble

-res

ampl

ing

proc

edur

e,is

deno

ted

bysu

pers

crip

tsa

and

b,re

spec

tive

ly.

The

sam

ple

isan

nual

obse

rvat

ions

of53

area

sbe

twee

n19

94an

d20

01.

Apa

rtm

ents

Indu

stri

alR

etai

lO

ffice

s(1

)(2

)(3

)(1

)(2

)(3

)(1

)(2

)(3

)(1

)(2

)(3

)

cap

0.93

5b1.

028b

-0.

803b

0.98

3b-

1.05

3b1.

112b

-0.

081

0.57

4-

(4.4

28)

(4.6

00)

(2.9

82)

(3.4

79)

(3.9

86)

(3.9

08)

(0.3

23)

(1.8

25)

gpop

1.75

83.

348

0.93

70.

136

1.48

80.

385

3.39

0b4.

122b

2.37

2-0

.896

1.11

20.

521

(0.9

70)

(1.5

94)

(0.2

80)

(0.0

95)

(0.8

33)

(0.1

16)

(2.6

89)

(2.8

77)

(1.6

90)

(-0.

446)

(0.2

79)

(0.0

95)

gem

p-1

.422

-0.8

16-0

.768

0.73

81.

104

0.83

50.

220

-0.0

340.

431

0.67

81.

055

1.01

3(-

0.88

0)(-

0.33

1)(-

0.23

2)(0

.602

)(0

.834

)(0

.712

)(0

.192

)(0

.101

)(0

.462

)(0

.373

)(0

.652

)(0

.593

)gi

nc-0

.248

-0.8

45-1

.897

-1.1

07-1

.093

-1.9

71a

-0.4

54-0

.029

-0.6

730.

009

-1.3

50-1

.074

(-0.

183)

(-0.

713)

(-1.

663)

(-1.

241)

(-1.

194)

(-2.

176)

(-0.

601)

(-0.

183)

(-0.

923)

(0.0

06)

(-0.

978)

(-0.

785)

gcc

-0.0

950.

209

0.93

70.

366

0.53

20.

807

0.62

70.

720

1.03

0-1

.026

-0.1

01-0

.236

(-0.

083)

(0.1

92)

(0.7

90)

(0.3

65)

(0.5

95)

(0.8

67)

(0.7

07)

(0.8

13)

(1.1

72)

(-0.

768)

(-0.

114)

(-0.

189)

pop

--0

.039

-0.0

03-

0.11

00.

125

0.07

40.

102

--0

.443

b-0

.315

(-0.

270)

(-0.

141)

(0.8

03)

(0.8

20)

(0.5

32)

(1.2

57)

(-2.

780)

(-1.

778)

emp

-0.

105

0.06

1-

-0.0

57-0

.079

--0

.039

-0.0

77-

0.49

0b0.

340

(0.6

18)

(0.4

43)

(-0.

417)

(-0.

495)

(-0.

201)

(-1.

008)

(3.0

92)

(1.9

44)

pcin

c-

-0.0

45-0

.062

-0.

014

-0.0

01-

-0.0

16-0

.053

--0

.192

b-0

.172

b

(-0.

519)

(-0.

667)

(0.5

61)

(-0.

202)

(-0.

270)

(-1.

368)

(-3.

161)

(-2.

872)

cc-

0.19

80.

160

-0.

078

0.06

7-

-0.0

87-0

.134

-0.

358

0.30

6(1

.596

)(1

.291

)(1

.240

)(1

.100

)(-

0.96

4)(-

1.89

3)(1

.973

)(1

.646

)co

ast

-0.

055a

0.06

4b-

0.04

3a0.

033

-0.

032

0.01

7-

0.11

2b0.

106b

(2.0

51)

(2.4

69)

(2.1

40)

(1.6

89)

(1.6

83)

(0.9

00)

(3.6

33)

(3.5

69)

R2 adj

0.19

00.

352

0.18

80.

159

0.30

90.

156

0.38

30.

421

0.18

9-0

.009

0.18

30.

140

42

Table

7:

Fore

cast

ing

Regre

ssio

ns

ofR

ent

Gro

wth

on

Log

Cap

Rate

and

Eco

nom

icV

ari

able

s

The

tabl

ere

port

sth

ere

sult

sfr

omth

epo

oled

OLS

over

lapp

ing

regr

essi

ons

ofre

ntgr

owth

betw

een

t+

1an

dt+

kon

the

log

cap

rate

and

econ

omic

vari

able

sat

tim

et

for

apar

tmen

ts,in

dust

rial

,re

tail,

and

office

prop

erti

es.

The

resu

lts

refe

rto

a4-

year

hori

zon.

The

tabl

esh

ows

thre

esp

ecifi

cati

ons

for

each

real

esta

tepr

oper

tyty

pe:

(1)

incl

udes

the

log

cap

rate

and

the

diffe

renc

ein

log

ofth

eec

onom

icva

riab

les,

(2)

incl

udes

the

log

cap

rate

,th

edi

ffere

nce

inlo

gof

the

econ

omic

vari

able

s,th

ele

vel

ofth

eec

onom

icva

riab

les

lagg

edtw

ice

and

the

coas

tal

dum

my,

(3)

incl

udes

the

diffe

renc

ein

log

ofth

eec

onom

icva

riab

les,

the

leve

lof

the

econ

omic

vari

able

stw

ice

lagg

edan

dth

eco

asta

ldu

mm

y.T

heva

riab

les

are

defin

edas

follo

ws:

cap

isth

elo

gca

pra

teat

tim

et,

gpop

,gem

p,g

inc

and

gcc

are

grow

thin

popu

lati

on,em

ploy

men

t,pe

rca

pita

inco

me

and

cons

truc

tion

cost

sat

tim

et

resp

ecti

vely

,pop

,em

p,i

nc

and

ccar

eth

ele

vels

ofth

eva

riab

les

atti

me

t−

2an

dco

ast

isth

eco

asta

ldu

mm

y.T

het-

rati

os,in

pare

nthe

ses,

are

eval

uate

dus

ing

the

doub

le-r

esam

plin

gpr

oced

ure

desc

ribe

din

Sect

ion

4.1.

The

coeffi

cien

ton

the

cap

rate

isbi

as-a

djus

ted

usin

gth

esa

me

proc

edur

e.St

atis

tica

lsi

gnifi

canc

eat

the

5%an

d1%

leve

l,ev

alua

ted

usin

gth

eem

piri

cal

dist

ribu

tion

from

the

doub

le-r

esam

plin

gpr

oced

ure,

isde

note

dby

supe

rscr

ipts

aan

db,

resp

ecti

vely

.T

hesa

mpl

eis

annu

alob

serv

atio

nsof

53ar

eas

betw

een

1994

and

2001

.

Apa

rtm

ents

Indu

stri

alR

etai

lO

ffice

s(1

)(2

)(3

)(1

)(2

)(3

)(1

)(2

)(3

)(1

)(2

)(3

)

cap

0.28

70.

373a

-0.

328

0.48

1a-

0.49

5a0.

543a

--0

.576

b-0

.175

-(1

.558

)(1

.929

)(1

.513

)(2

.110

)(2

.251

)(2

.292

)(-

2.41

9)(-

0.70

0)gp

op0.

150

1.35

40.

654

-0.7

180.

293

-0.1

833.

111b

3.78

0b3.

140a

-1.3

55-0

.050

0.16

9(0

.097

)(0

.639

)(0

.195

)(-

0.59

0)(0

.130

)(-

0.24

8)(2

.698

)(2

.818

)(2

.350

)(-

0.68

9)(-

0.26

0)(-

0.21

4)ge

mp

-0.1

530.

111

0.12

51.

116

1.40

51.

289

-0.0

03-0

.335

-0.1

650.

968

1.24

91.

264

(-0.

113)

(0.2

65)

(0.3

09)

(1.0

95)

(1.2

85)

(1.2

29)

(-0.

003)

(-0.

169)

(-0.

006)

(0.5

49)

(0.7

49)

(0.7

80)

ginc

-1.8

58-2

.102

a-2

.408

b-1

.679

b-1

.610

a-1

.988

b-1

.203

-0.8

30-1

.066

-0.9

54-1

.962

-2.0

64(-

1.68

3)(-

2.02

5)(-

2.36

7)(-

2.34

1)(-

2.09

2)(-

2.63

5)(-

1.84

6)(-

1.15

9)(-

1.48

1)(-

0.63

4)(-

1.43

7)(-

1.51

8)gc

c0.

238

0.41

90.

630

0.27

70.

385

0.50

40.

356

0.49

30.

606

-0.5

200.

187

0.23

7(0

.228

)(0

.387

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.584

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.345

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.522

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.673

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.460

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.624

)(0

.770

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0.46

4)(0

.073

)(0

.096

)po

p-

0.03

60.

046

-0.

089

0.09

6-

0.02

20.

033

--0

.377

b-0

.425

b

(0.1

54)

(0.2

02)

(0.7

63)

(0.7

78)

(0.2

62)

(0.6

14)

(-2.

847)

(-3.

188)

emp

-0.

008

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05-

-0.0

42-0

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-0.

013

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01-

0.40

8b0.

464b

(0.1

16)

(-0.

056)

(-0.

351)

(-0.

393)

(0.1

52)

(-0.

230)

(3.0

69)

(3.4

68)

pcin

c-

-0.0

24-0

.030

-0.

012

0.00

6-

-0.0

48-0

.062

--0

.147

b-0

.155

b

(-0.

096)

(-0.

061)

(0.4

59)

(0.3

33)

(-1.

382)

(-1.

939)

(-3.

518)

(-3.

827)

cc-

0.13

70.

126

-0.

025

0.02

0-

-0.0

83-0

.100

-0.

225

0.24

5(1

.217

)(1

.119

)(0

.690

)(0

.619

)(-

1.37

5)(-

1.80

8)(1

.347

)(1

.450

)co

ast

-0.

030

0.03

2-

0.03

5a0.

031

-0.

033a

0.02

7-

0.09

2b0.

094b

(1.2

42)

(1.3

91)

(1.9

98)

(1.7

86)

(2.0

76)

(1.7

50)

(3.3

31)

(3.3

71)

R2 adj

0.07

50.

164

0.14

90.

078

0.19

00.

157

0.22

50.

275

0.23

70.

040

0.16

20.

158

43

Table

8:

Fore

cast

ing

Regre

ssio

ns

ofExce

ssR

etu

rns

on

Log

Cap

Rate

and

Pri

nci

palC

om

ponents

The

tabl

ere

port

sth

ere

sult

sfr

omth

epo

oled

OLS

over

lapp

ing

regr

essi

ons

ofex

cess

retu

rns

betw

een

t+

1an

dt+

kon

the

log

cap

rate

and

the

thre

em

ain

prin

cipa

lco

mpo

nent

sex

trac

ted

from

the

econ

omic

vari

able

sat

tim

et

for

apar

tmen

ts,in

dust

rial

,re

tail

and

office

s.T

here

sult

sre

fer

toa

4-ye

arho

rizo

n.T

heta

ble

show

stw

osp

ecifi

cati

ons

for

each

real

esta

tepr

oper

tyty

pe:

(1)

incl

udes

the

cap

rate

and

the

thre

epr

inci

palc

ompo

nent

san

dth

eco

asta

ldum

my,

(2)in

clud

esju

stth

epr

inci

palc

ompo

nent

san

dth

eco

asta

ldum

my.

The

t-ra

tios

,in

pare

nthe

ses,

are

eval

uate

dus

ing

the

doub

le-r

esam

plin

gpr

oced

ure

desc

ribe

din

Sect

ion

4.1.

The

coeffi

cien

ton

the

cap

rate

isbi

as-a

djus

ted

usin

gth

esa

me

proc

edur

e.St

atis

tica

lsi

gnifi

canc

eat

the

5%an

d1%

leve

l,ev

alua

ted

usin

gth

eem

piri

caldi

stri

buti

onfr

omth

edo

uble

-res

ampl

ing

proc

edur

e,is

deno

ted

bysu

pers

crip

tsa

and

b,re

spec

tive

ly.

The

sam

ple

isan

nual

obse

rvat

ions

of53

area

sbe

twee

n19

94an

d20

01.

Apa

rtm

ents

Indu

stri

alR

etai

lO

ffice

s

(1)

(2)

(1)

(2)

(1)

(2)

(1)

(2)

cap

0.96

4b-

1.01

2b-

1.04

9b-

0.28

1-

(4.4

10)

(3.7

67)

(3.9

71)

(1.1

54)

pc 1

-0.0

17b

-0.0

25b

-0.0

06-0

.011

b0.

015b

0.01

5b-0

.006

-0.0

03(-

3.16

8)(-

4.85

4)(-

1.04

4)(-

2.74

7)(2

.663

)(2

.681

)(-

0.68

8)(-

0.41

3)pc 2

-0.0

33b

-0.0

18a

-0.0

23b

-0.0

13-0

.024

b-0

.016

b-0

.038

b-0

.033

b

(-3.

943)

(-2.

156)

(-3.

213)

(-1.

801)

(-3.

607)

(-2.

488)

(-3.

675)

(-3.

274)

pc 3

-0.0

05-0

.005

-0.0

05-0

.005

0.00

20.

004

-0.0

16-0

.017

(-0.

491)

(-0.

457)

(-0.

596)

(-0.

569)

(0.2

33)

(0.5

87)

(-1.

123)

(-1.

203)

coas

t0.

049a

0.05

6a0.

042a

0.03

20.

019

0.00

20.

096b

0.09

6b

(2.0

95)

(2.3

91)

(2.2

12)

(1.6

99)

(1.0

26)

(0.1

34)

(3.3

30)

(3.3

49)

R2 adj

0.36

60.

191

0.24

90.

074

0.32

60.

084

0.15

90.

142

44

Table

9:

Fore

cast

ing

Regre

ssio

ns

ofR

ent

Gro

wth

on

Log

Cap

Rate

and

Pri

nci

palC

om

ponents

The

tabl

ere

port

sth

ere

sult

sfr

omth

epo

oled

OLS

over

lapp

ing

regr

essi

ons

ofre

ntgr

owth

betw

een

t+

1an

dt+

kon

the

log

cap

rate

and

the

thre

em

ain

prin

cipa

lco

mpo

nent

sex

trac

ted

from

the

econ

omic

vari

able

sat

tim

et

for

apar

tmen

ts,in

dust

rial

,re

tail

and

office

s.T

here

sult

sre

fer

toa

4-ye

arho

rizo

n.T

heta

ble

show

stw

osp

ecifi

cati

ons

for

each

real

esta

tepr

oper

tyty

pe:

(1)

incl

udes

the

thre

epr

inci

palco

mpo

nent

san

dth

eco

asta

ldu

mm

y,(2

)in

clud

esju

stth

epr

inci

pal

com

pone

nts

and

the

coas

tal

dum

my.

The

t-ra

tios

,in

pare

nthe

ses,

are

eval

uate

dus

ing

the

doub

le-r

esam

plin

gpr

oced

ure

desc

ribe

din

Sect

ion

4.1.

The

coeffi

cien

ton

the

cap

rate

isbi

as-a

djus

ted

usin

gth

esa

me

proc

edur

e.St

atis

tica

lsi

gnifi

canc

eat

the

5%an

d1%

leve

l,ev

alua

ted

usin

gth

eem

piri

caldi

stri

buti

onfr

omth

edo

uble

-res

ampl

ing

proc

edur

e,is

deno

ted

bysu

pers

crip

tsa

and

b,re

spec

tive

ly.

The

sam

ple

isan

nual

obse

rvat

ions

of53

area

sbe

twee

n19

94an

d20

01.

Apa

rtm

ents

Indu

stri

alR

etai

lO

ffice

s

(1)

(2)

(1)

(2)

(1)

(2)

(1)

(2)

cap

0.47

1b-

0.57

2b-

0.53

7b-

-0.4

03a

-(2

.566

)(2

.670

)(2

.382

)(-

2.02

1)pc 1

-0.0

13b

-0.0

17b

-0.0

06-0

.009

a0.

012b

0.01

2b-0

.003

-0.0

06(-

2.59

1)(-

3.33

5)(-

1.29

1)(-

1.90

0)(2

.882

)(2

.927

)(-

0.51

9)(-

0.89

0)pc 2

-0.0

24b

-0.0

18a

-0.0

16b

-0.0

11b

-0.0

19b

-0.0

16b

-0.0

24b

-0.0

29b

(-2.

988)

(-2.

208)

(-2.

847)

(-2.

546)

(-3.

444)

(-2.

914)

(-2.

559)

(-3.

094)

pc 3

-0.0

08-0

.008

-0.0

04-0

.004

0.00

40.

005

-0.0

14-0

.013

(-0.

813)

(-0.

803)

(-0.

555)

(-0.

537)

(0.6

18)

(0.7

97)

(-1.

184)

(-1.

109)

coas

t0.

027

0.03

0.03

4a0.

029

0.01

90.

013

0.07

7b0.

077b

(1.2

59)

(1.3

97)

(1.9

74)

(1.6

88)

(1.2

61)

(0.8

53)

(2.7

77)

(2.7

84)

R2 adj

0.16

00.

121

0.11

60.

063

0.13

60.

088

0.14

30.

120

45

Table 10: Regressions of Future Excess Returns and Rent Growth on EconomicVariables from 1985

The table reports the results of the pooled OLS regression of 1-year ahead excess returns and rent growth oneconomic variables. TSPR is the difference between the yield on 10-year and 1-year Treasuries, DSPR is thedifference between the yield on BAA and AAA rated corporate bonds, CPIRET is inflation computed as thegrowth of the CPI index, and TB3M is the three-months Treasury bill rate. The t-ratios, in parentheses, areevaluated as t/

√k as suggested in Torous, Valkanov, and Yan (2005) to correct for the overlap. Statistical

significance at the 5% and 1% level is denoted by superscripts a and b, respectively. The sample is biannualobservations from 1985:4 to 2002:4.

Panel A: Future Excess Returns

Apartments Industrial Retail Offices

TSPR 0.545 0.083 -0.321 -0.454(0.875) (0.145) (-0.807) (-0.727)

DSPR -10.645b -4.241a -3.031a -8.413b

(-4.182) (-1.807) (-1.864) (-3.300)CPIRET -0.736a -0.946b -0.958b -1.479b

(-1.703) (-2.374) (-3.471) (-3.417)TB3M -1.150a -0.737 -1.315b -1.417b

(-2.012) (-1.398) (-3.599) (-2.474)

R2 0.200 0.101 0.243 0.234

Panel B: Future Rent Growth

Apartments Industrial Retail Offices

TSPR 0.894b 0.475 0.467 0.354(2.046) (1.121) (1.421) (0.668)

DSPR -6.739b -4.084b -4.116b -9.236b

(-3.772) (-2.360) (-3.068) (-4.271)CPIRET -0.498 -0.704b -0.530b -1.235b

(-1.642) (-2.395) (-2.325) (-3.363)TB3M 0.401 0.397 0.215 0.327

(1.000) (1.021) (0.714) (0.674)

R2 0.069 0.042 0.066 0.135

46

Figure 1: Volatilities of Rent Growth

The figure reports the median (top panel) and mean (bottom panel) cross-sectional yearly volatilities of theportion of rent growth that is orthogonal to economic fluctuations, fitted from a GARCH(1,1) model. Toconstruct these series, we first regress the rent growth rates of each property type and each metropolitanarea on the term spread, default, spread, inflation, and the 3-months Treasury bill rate as in Table (10).Using the residuals from these regressions, we estimate a GARCH(1,1) model for each of the twenty-onetime series of rent growth for every property type. We then compute for a given property type the medianand mean fitted volatilities across the metropolitan areas in each period. Results from offices are marked bya solid line. The sample is biannual observations from 1985 : 4 to 2002 : 4.

1986 1988 1990 1992 1994 1996 1998 2000 20020.05

0.06

0.07

0.08

0.09

0.1

Median of GARCH(1,1) Fitted Volatilities

Date

Sta

ndar

d D

evia

tion

(Yea

rly) Apartments

IndustrialRetailOffices

1986 1988 1990 1992 1994 1996 1998 2000 2002

0.06

0.08

0.1

0.12

Mean of GARCH(1,1) Fitted Volatilities

Date

Sta

ndar

d D

evia

tion

(Yea

rly) Apartments

IndustrialRetailOffices

47

Table

A1:

Avera

ge

Retu

rns,

Rent

Gro

wth

Rate

s,and

CA

PR

ate

sfo

rA

llM

etr

opolita

nA

reas

Thi

sta

ble

cont

ains

ade

scri

ptio

nan

dsu

mm

ary

stat

isti

csof

the

data

used

inth

eem

piri

cals

ecti

on.

The

tabl

ere

port

sth

est

ate,

met

ropo

litan

area

asw

ella

sav

erag

esof

quar

terl

yex

cess

retu

rns

(den

oted

byr)

,ren

tgr

owth

(den

oted

byg),

and

cap

rate

s(d

enot

edby

cap),

forap

artm

ents

(sup

ersc

ript

apt)

,ind

ustr

ial(

supe

rscr

ipt

ind),

reta

il(s

uper

scri

ptrt

l)an

doffi

ces

(sup

ersc

ript

off).

All

stat

isti

csar

ean

nual

ized

.T

heda

tais

avai

labl

efo

rth

e19

94:2

and

2003

:1pe

riod

for

53ar

eas.

The

aver

age

annu

alth

ree-

mon

thTre

asur

ybi

llra

tedu

ring

the

peri

odis

0.04

5.

Sta

teM

etro

pol

itan

area

rapt

rin

drr

tlro

ff

gapt

gin

dg

rtl

gof

fca

papt

cap

ind

cap

rtl

cap

of

f

Ala

bam

a1

.B

irm

ingh

am-

MSA

0.07

20.

063

0.07

70.

067

0.02

20.

010

0.01

80.

020

0.08

90.

093

0.09

70.

094

Ari

zona

2.

Pho

enix

-M

SA0.

107

0.08

90.

120

0.08

00.

054

0.03

40.

056

0.03

00.

084

0.08

50.

092

0.09

2C

alifo

rnia

3.

Ora

nge

Cou

nty

-P

MSA

0.11

60.

079

0.07

50.

089

0.05

30.

023

0.01

80.

033

0.08

70.

087

0.09

10.

084

4.

Sacr

amen

to-

CM

SA0.

104

0.08

40.

071

0.07

70.

046

0.02

40.

023

0.03

20.

091

0.09

30.

092

0.08

35

.Los

Ang

eles

-P

MSA

0.13

90.

120

0.08

30.

064

0.06

60.

046

0.01

90.

009

0.08

40.

089

0.09

40.

083

6.

Oak

land

-Eas

tB

ay-

PM

SA0.

101

0.08

40.

076

0.05

80.

037

0.03

20.

021

0.01

00.

087

0.09

20.

091

0.09

07

.Sa

nD

iego

-M

SA0.

129

0.08

40.

080

0.11

40.

058

0.03

40.

020

0.04

60.

082

0.09

30.

092

0.08

58

.R

iver

side

-S.B

erna

rdin

o-

PM

SA0.

129

0.11

50.

078

0.08

40.

072

0.03

80.

016

0.02

40.

089

0.09

00.

090

0.09

69

.Sa

nJo

se-

PM

SA0.

104

0.09

60.

064

0.12

10.

033

0.04

30.

011

0.06

20.

082

0.08

90.

095

0.09

210

.Sa

nFr

anci

sco

-P

MSA

0.10

30.

082

0.05

40.

134

0.04

00.

024

0.00

80.

085

0.08

50.

091

0.08

90.

085

Col

orad

o11

.D

enve

r-

CM

SA0.

115

0.09

90.

108

0.09

90.

042

0.04

00.

055

0.04

50.

085

0.09

00.

092

0.08

4C

onne

ctic

ut12

.H

artf

ord

-M

SA0.

080

0.04

30.

063

0.06

20.

029

-0.0

120.

006

0.00

80.

091

0.09

60.

096

0.09

8D

.C.

13.

Was

hing

ton

-M

SA0.

109

0.09

70.

081

0.10

30.

033

0.03

60.

027

0.04

90.

089

0.09

30.

090

0.08

1Flo

rida

14.

Fort

Lau

derd

ale

-P

MSA

0.09

00.

082

0.09

80.

072

0.03

40.

033

0.03

30.

020

0.08

70.

093

0.09

20.

093

15.

Jack

sonv

ille

-M

SA0.

092

0.07

60.

087

0.07

80.

053

0.01

50.

033

0.01

60.

089

0.09

00.

094

0.09

916

.M

iam

i-

PM

SA0.

075

0.08

40.

066

0.06

40.

023

0.03

70.

014

0.04

40.

087

0.08

90.

090

0.08

817

.O

rlan

do-

MSA

0.08

00.

086

0.09

40.

070

0.02

30.

039

0.03

00.

028

0.08

90.

094

0.09

10.

089

18.

Wes

tPal

mB

each

-M

SA0.

089

0.09

00.

079

0.07

80.

035

0.03

40.

035

0.03

20.

086

0.09

00.

090

0.09

119

.Tam

pa-S

t.Pet

ersb

urg

-M

SA0.

090

0.08

40.

091

0.07

90.

030

0.02

80.

034

0.02

80.

090

0.09

40.

094

0.09

3G

eorg

ia20

.A

tlan

ta-

MSA

0.08

50.

082

0.06

50.

056

0.03

10.

017

0.02

20.

026

0.08

20.

090

0.09

00.

090

48

Table

A1:

Avera

ge

Retu

rns,

Rent

Gro

wth

Rate

s,and

CA

PR

ate

sfo

rA

llM

etr

opolita

nA

reas

(Cont’

d)

Sta

teM

etro

pol

itan

area

rapt

rin

drr

tlro

ff

gapt

gin

dg

rtl

gof

fca

papt

cap

ind

cap

rtl

cap

of

f

Illin

ois

21.

Chi

cago

-P

MSA

0.08

20.

071

0.07

40.

098

0.02

50.

013

0.02

60.

026

0.08

70.

091

0.09

10.

087

Indi

ana

22.

Indi

anap

olis

-M

SA0.

083

0.05

20.

056

0.05

30.

035

0.00

40.

003

0.00

80.

090

0.09

30.

095

0.09

1Lou

isia

na23

.N

ewO

rlea

ns-

MSA

0.11

10.

054

0.07

30.

098

0.04

10.

002

0.01

60.

034

0.09

70.

094

0.09

60.

100

Mar

ylan

d24

.B

alti

mor

e-

PM

SA0.

093

0.07

10.

066

0.08

70.

029

0.01

90.

019

0.04

70.

090

0.09

20.

094

0.09

1M

assa

chus

etts

25.

Bos

ton

-P

MSA

0.13

10.

091

0.05

10.

100

0.07

80.

034

0.01

10.

061

0.09

20.

092

0.09

00.

082

Mic

higa

n26

.D

etro

it-

PM

SA0.

081

0.08

10.

060

0.03

70.

026

0.03

00.

009

0.00

00.

089

0.09

50.

094

0.09

1M

inne

sota

27.

Min

neap

olis

-St.

Pau

l-

MSA

0.10

10.

083

0.06

20.

084

0.05

00.

029

0.00

90.

037

0.08

60.

095

0.09

40.

092

Mis

sour

i28

.K

ansa

sC

ity

-M

SA0.

083

0.06

40.

085

0.05

50.

039

0.01

30.

034

0.01

20.

086

0.09

40.

095

0.08

929

.St

.Lou

is-

MSA

0.09

20.

089

0.08

10.

038

0.03

20.

037

0.02

8-0

.002

0.08

90.

091

0.09

50.

091

Nev

ada

30.

Las

Veg

as-

MSA

0.06

40.

084

0.08

90.

056

0.02

70.

019

0.04

10.

008

0.08

60.

088

0.09

20.

093

New

Jers

ey31

.C

entr

alN

ewJe

rsey

-PM

SAs

0.10

20.

081

0.06

60.

111

0.04

20.

028

0.01

30.

050

0.08

90.

092

0.08

90.

090

32.

Nor

ther

nN

ewJe

rsey

-PM

SAs

0.11

30.

086

0.06

40.

056

0.05

20.

030

0.01

3-0

.005

0.09

30.

092

0.08

90.

096

New

Yor

k33

.N

assa

u-Su

ffolk

-P

MSA

0.11

60.

080

0.06

60.

078

0.05

80.

025

0.01

00.

014

0.09

30.

090

0.09

20.

088

Nor

thC

arol

ina

34.

Cha

rlot

te-

MSA

0.08

50.

058

0.06

30.

055

0.03

50.

003

0.00

90.

008

0.08

80.

091

0.09

30.

088

35.

Ral

eigh

-Dur

ham

-M

SA0.

064

0.06

40.

074

0.06

40.

011

0.01

10.

018

0.01

40.

083

0.09

10.

090

0.08

636

.G

reen

sbor

o-W

inst

on-S

alem

-0.

061

0.05

40.

072

0.05

50.

020

0.00

80.

021

0.00

60.

091

0.09

40.

096

0.09

5H

igh

Poi

nt-

MSA

Ohi

o37

.C

inci

nnat

i-

CM

SA0.

086

0.07

00.

055

0.04

70.

040

0.02

80.

004

0.00

50.

094

0.09

00.

093

0.09

038

.C

leve

land

-C

MSA

0.07

40.

085

0.06

60.

062

0.00

70.

025

0.01

60.

007

0.09

50.

096

0.09

50.

092

39.

Col

umbu

s-

MSA

0.07

30.

061

0.04

70.

025

0.02

30.

006

-0.0

02-0

.012

0.09

00.

092

0.09

10.

092

Okl

ahom

a40

.O

klah

oma

City

-M

SA0.

111

0.08

60.

108

0.08

60.

044

0.03

60.

042

0.02

10.

097

0.09

50.

094

0.09

7O

rego

n41

.Por

tlan

d-

PM

SA0.

089

0.09

10.

097

0.08

80.

024

0.03

60.

034

0.03

30.

088

0.09

20.

093

0.08

5Pen

nsyl

vani

a42

.P

hila

delp

hia

-P

MSA

0.09

50.

065

0.06

30.

060

0.03

60.

014

0.00

30.

009

0.09

10.

093

0.09

40.

094

43.

Pit

tsbu

rgh

-M

SA0.

062

0.06

90.

049

0.04

80.

005

0.01

5-0

.005

0.00

20.

096

0.09

60.

098

0.09

4

49

Table

A1:

Avera

ge

Retu

rns,

Rent

Gro

wth

Rate

s,and

CA

PR

ate

sfo

rA

llM

etr

opolita

nA

reas

(Cont’

d)

Sta

teM

etro

pol

itan

area

rapt

rin

drr

tlro

ff

gapt

gin

dg

rtl

gof

fca

papt

cap

ind

cap

rtl

cap

of

f

Ten

ness

ee44

.M

emph

is-

MSA

0.09

30.

054

0.06

70.

054

0.03

70.

011

0.01

50.

008

0.08

50.

088

0.09

50.

092

45.

Nas

hvill

e-

MSA

0.11

00.

073

0.08

00.

043

0.02

70.

026

0.02

50.

006

0.08

90.

091

0.09

40.

092

Tex

as46

.A

usti

n-

MSA

0.10

70.

059

0.10

00.

080

0.03

70.

011

0.05

00.

028

0.08

40.

092

0.09

10.

090

47.

Dal

las-

Ft.

Wor

th-

CM

SA0.

105

0.07

90.

095

0.07

30.

052

0.02

40.

032

0.02

00.

085

0.09

00.

090

0.08

948

.H

oust

on-

PM

SA0.

120

0.09

30.

115

0.10

30.

049

0.04

90.

045

0.04

60.

087

0.08

90.

095

0.09

649

.Sa

nA

nton

io-

MSA

0.11

20.

090

0.07

50.

064

0.03

60.

041

0.02

30.

020

0.09

00.

093

0.09

30.

093

Uta

h50

.Sa

ltLak

eC

ity

-M

SA0.

065

0.05

50.

081

0.06

90.

025

0.00

50.

024

0.02

40.

091

0.09

30.

089

0.08

8V

irgi

nia

51.

Nor

folk

-M

SA0.

093

0.05

50.

062

0.07

20.

041

0.00

10.

009

0.02

20.

089

0.09

60.

091

0.09

6W

ashi

ngto

n52

.Se

attl

e-

PM

SA0.

121

0.06

40.

069

0.08

60.

038

0.01

80.

026

0.04

50.

084

0.08

60.

090

0.08

5W

isco

nsin

53.

Milw

auke

e-

PM

SA0.

068

0.09

00.

056

0.05

40.

012

0.03

70.

007

0.00

00.

095

0.09

30.

094

0.09

1

Nat

iona

lA

vera

ge0.

104

0.08

20.

072

0.09

10.

039

0.02

30.

017

0.02

70.

087

0.09

10.

092

0.08

7

50

Table

A2:

Sta

ndard

Devia

tions

ofR

etu

rns,

Rent

Gro

wth

Rate

s,and

CA

PR

ate

sfo

rA

llM

etr

opolita

nA

reas

Thi

sta

ble

repo

rts

tim

e-se

ries

stan

dard

devi

atio

nsfo

rea

chm

etro

polit

anar

eaof

quar

terl

yex

cess

retu

rns

(den

oted

byr)

,ren

tgr

owth

(den

oted

byg)

and

cap

rate

s(d

enot

edby

cap),

for

apar

tmen

ts(s

uper

scri

ptapt)

,in

dust

rial

(sup

ersc

ript

ind),

reta

il(s

uper

scri

ptrt

l)an

doffi

ces

(sup

ersc

ript

off).

We

also

incl

ude

the

aver

age,

med

ian,

max

imum

and

min

imum

valu

esfo

rth

eov

eral

lsam

ple.

All

stat

isti

csar

ean

nual

ized

.T

heda

tais

avai

labl

efo

rth

e19

94:2

and

2003

:1pe

riod

for

53ar

eas.

Sta

teM

etro

pol

itan

area

rapt

rin

drr

tlro

ff

gapt

gin

dg

rtl

gof

fca

papt

cap

ind

cap

rtl

cap

of

f

Ala

bam

a1

.B

irm

ingh

am-

MSA

0.06

10.

020

0.02

10.

035

0.04

20.

013

0.02

60.

041

0.00

30.

002

0.00

20.

002

Ari

zona

2.

Pho

enix

-M

SA0.

066

0.07

70.

074

0.04

70.

036

0.04

30.

053

0.05

00.

005

0.00

50.

006

0.00

3C

alifo

rnia

3.

Ora

nge

Cou

nty

-P

MSA

0.04

40.

112

0.04

10.

049

0.04

00.

109

0.02

40.

066

0.00

40.

005

0.00

40.

005

4.

Sacr

amen

to-

CM

SA0.

040

0.04

20.

027

0.03

50.

043

0.02

90.

026

0.02

90.

004

0.00

40.

002

0.00

35

.Los

Ang

eles

-P

MSA

0.07

70.

073

0.04

80.

071

0.04

30.

042

0.03

90.

054

0.00

90.

006

0.00

40.

007

6.

Oak

land

-Eas

tB

ay-

PM

SA0.

074

0.07

10.

037

0.11

30.

068

0.05

30.

035

0.11

00.

005

0.00

30.

004

0.00

47

.Sa

nD

iego

-M

SA0.

063

0.10

90.

050

0.04

80.

039

0.05

30.

055

0.04

10.

009

0.00

40.

005

0.00

68

.R

iver

side

-S.B

erna

rdin

o-

PM

SA0.

080

0.08

40.

032

0.04

00.

055

0.03

30.

019

0.02

50.

005

0.00

70.

004

0.00

49

.Sa

nJo

se-

PM

SA0.

099

0.07

00.

041

0.08

80.

081

0.05

80.

028

0.09

70.

010

0.00

50.

002

0.00

410

.Sa

nFr

anci

sco

-P

MSA

0.07

80.

057

0.02

40.

115

0.07

30.

044

0.02

10.

107

0.00

70.

004

0.00

30.

006

Col

orad

o11

.D

enve

r-

CM

SA0.

062

0.06

90.

059

0.07

20.

039

0.06

20.

089

0.05

80.

008

0.00

40.

003

0.00

6C

onne

ctic

ut12

.H

artf

ord

-M

SA0.

028

0.04

20.

023

0.03

00.

023

0.04

30.

023

0.03

50.

002

0.00

20.

004

0.00

2D

.C.

13.

Was

hing

ton

-M

SA0.

086

0.07

80.

050

0.10

30.

043

0.06

20.

033

0.04

80.

009

0.00

30.

004

0.00

5Flo

rida

14.

Fort

Lau

derd

ale

-P

MSA

0.06

90.

062

0.04

60.

033

0.04

10.

034

0.03

60.

031

0.00

40.

002

0.00

30.

002

15.

Jack

sonv

ille

-M

SA0.

090

0.06

50.

040

0.03

00.

042

0.04

90.

035

0.02

40.

004

0.00

30.

005

0.00

516

.M

iam

i-

PM

SA0.

045

0.03

70.

039

0.05

80.

033

0.04

00.

025

0.06

40.

003

0.00

30.

003

0.00

617

.O

rlan

do-

MSA

0.06

20.

051

0.04

90.

049

0.04

00.

038

0.04

10.

050

0.00

30.

002

0.00

50.

002

18.

Wes

tPal

mB

each

-M

SA0.

049

0.04

30.

047

0.03

00.

035

0.05

60.

040

0.04

80.

004

0.00

40.

003

0.00

319

.Tam

pa-S

t.Pet

ersb

urg

-M

SA0.

083

0.03

80.

039

0.03

40.

041

0.03

20.

032

0.05

40.

006

0.00

20.

004

0.00

3G

eorg

ia20

.A

tlan

ta-

MSA

0.10

30.

104

0.05

20.

037

0.05

10.

053

0.03

20.

035

0.00

50.

004

0.00

40.

005

51

Table

A2:

Sta

ndard

Devia

tions

ofR

etu

rns,

Rent

Gro

wth

Rate

s,and

CA

PR

ate

sfo

rA

llM

etr

opolita

nA

reas

(Cont’

d)

Sta

teM

etro

pol

itan

area

rapt

rin

drr

tlro

ff

gapt

gin

dg

rtl

gof

fca

papt

cap

ind

cap

rtl

cap

of

f

Illin

ois

21.

Chi

cago

-P

MSA

0.03

70.

057

0.05

50.

063

0.03

90.

040

0.03

60.

060

0.00

40.

004

0.00

30.

005

Indi

ana

22.

Indi

anap

olis

-M

SA0.

044

0.02

70.

019

0.04

80.

041

0.02

40.

012

0.04

80.

003

0.00

10.

001

0.00

2Lou

isia

na23

.N

ewO

rlea

ns-

MSA

0.05

10.

037

0.04

30.

075

0.03

90.

023

0.02

70.

089

0.00

60.

002

0.00

40.

007

Mar

ylan

d24

.B

alti

mor

e-

PM

SA0.

037

0.07

10.

036

0.08

20.

030

0.04

00.

035

0.06

30.

007

0.00

50.

003

0.00

3M

assa

chus

etts

25.

Bos

ton

-P

MSA

0.05

00.

057

0.02

60.

071

0.04

90.

064

0.02

40.

059

0.00

30.

003

0.00

20.

004

Mic

higa

n26

.D

etro

it-

PM

SA0.

035

0.05

80.

028

0.03

90.

040

0.05

70.

013

0.02

10.

003

0.00

20.

001

0.00

3M

inne

sota

27.

Min

neap

olis

-St.

Pau

l-

MSA

0.04

00.

035

0.02

60.

059

0.03

20.

036

0.01

60.

052

0.00

30.

003

0.00

10.

002

Mis

sour

i28

.K

ansa

sC

ity

-M

SA0.

039

0.02

40.

031

0.02

30.

037

0.02

10.

034

0.01

80.

002

0.00

20.

002

0.00

129

.St

.Lou

is-

MSA

0.06

00.

064

0.03

70.

040

0.04

70.

041

0.04

40.

023

0.00

40.

003

0.00

10.

004

Nev

ada

30.

Las

Veg

as-

MSA

0.07

50.

043

0.03

70.

028

0.03

20.

035

0.04

20.

026

0.00

50.

005

0.00

30.

002

New

Jers

ey31

.C

entr

alN

ewJe

rsey

-PM

SAs

0.03

30.

032

0.03

40.

074

0.02

90.

025

0.04

10.

040

0.00

40.

002

0.00

30.

006

32.

Nor

ther

nN

ewJe

rsey

-PM

SAs

0.03

50.

049

0.02

50.

047

0.04

40.

036

0.01

70.

021

0.00

20.

003

0.00

30.

004

New

Yor

k33

.N

assa

u-Su

ffolk

-P

MSA

0.02

90.

030

0.03

40.

026

0.03

00.

018

0.01

90.

020

0.00

30.

003

0.00

30.

005

Nor

thC

arol

ina

34.

Cha

rlot

te-

MSA

0.11

40.

039

0.03

50.

155

0.07

80.

022

0.03

80.

156

0.00

50.

004

0.00

30.

003

35.

Ral

eigh

-Dur

ham

-M

SA0.

069

0.04

20.

031

0.07

10.

053

0.01

60.

029

0.02

40.

004

0.00

30.

003

0.00

636

.G

reen

sbor

o-W

inst

on-S

alem

-0.

047

0.04

20.

020

0.02

50.

036

0.03

10.

025

0.04

50.

002

0.00

30.

002

0.00

3H

igh

Poi

nt-

MSA

Ohi

o37

.C

inci

nnat

i-

CM

SA0.

047

0.08

20.

024

0.01

90.

047

0.04

20.

032

0.05

40.

002

0.00

40.

002

0.00

238

.C

leve

land

-C

MSA

0.05

20.

047

0.02

30.

028

0.04

90.

040

0.02

70.

023

0.00

40.

003

0.00

20.

003

39.

Col

umbu

s-

MSA

0.03

80.

064

0.05

50.

023

0.03

20.

036

0.01

80.

016

0.00

20.

003

0.00

50.

004

Okl

ahom

a40

.O

klah

oma

City

-M

SA0.

062

0.02

30.

051

0.01

80.

067

0.03

30.

041

0.03

30.

005

0.00

10.

005

0.00

3O

rego

n41

.Por

tlan

d-

PM

SA0.

073

0.05

60.

053

0.04

50.

036

0.03

60.

055

0.06

90.

007

0.00

20.

004

0.00

3Pen

nsyl

vani

a42

.P

hila

delp

hia

-P

MSA

0.03

90.

053

0.02

70.

031

0.03

70.

036

0.02

00.

017

0.00

40.

003

0.00

30.

002

43.

Pit

tsbu

rgh

-M

SA0.

029

0.01

70.

025

0.02

10.

038

0.02

00.

018

0.01

80.

003

0.00

10.

002

0.00

3

52

Table

A2:

Sta

ndard

Devia

tions

ofR

etu

rns,

Rent

Gro

wth

Rate

s,and

CA

PR

ate

sfo

rA

llM

etr

opolita

nA

reas

(Cont’

d)

Sta

teM

etro

pol

itan

area

rapt

rin

drr

tlro

ff

gapt

gin

dg

rtl

gof

fca

papt

cap

ind

cap

rtl

cap

of

f

Ten

ness

ee44

.M

emph

is-

MSA

0.07

40.

059

0.02

40.

029

0.03

90.

032

0.01

90.

034

0.00

40.

005

0.00

20.

002

45.

Nas

hvill

e-

MSA

0.10

60.

062

0.03

10.

028

0.04

10.

095

0.03

00.

026

0.00

60.

003

0.00

20.

003

Tex

as46

.A

usti

n-

MSA

0.08

90.

023

0.03

60.

040

0.05

50.

021

0.04

90.

051

0.00

60.

001

0.00

30.

004

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53