1.
A Cross-Sectional Asset-Pricing Analysis of the
U.S. Housing Market with Zip Code Data
Susanne Cannon, Norman G. Miller and Gurupdesh S. Pandher∗
February 19, 2006
Abstract
This paper carries out an asset-pricing analysis of the U.S. metropolitan housing market.
We use zip code level housing data to study the cross-sectional role of volatility, price
level, stock market risk and idiosyncratic volatility in explaining housing returns. While
the related literature tends to focus on the dynamic role of volatility and housing returns
within submarkets over time, our risk-return analysis is cross-sectional and covers the
national U.S. metropolitan housing market.
The study provides a number of important findings on the asset-pricing features
of the U.S. housing market. Specifically, we find i) a positive relation between housing
returns and volatility with returns rising by 2.48% annually for a 10% rise in volatility, ii)
a positive but diminishing price effect on returns, iii) that stock market risk is priced
directionally in the housing market and iv) idiosyncratic volatility is priced in housing
returns. Our results on the return-volatility-price relation are robust to i) MSA
(metropolitan statistical area) clustering effects and ii) differences in socioeconomic
characteristics among submarkets related to income, employment rate, managerial
employment, owner occupied housing, gross rent and population density.
Keywords: housing submarkets, risk and return, asset-pricing, volatility, CAPM, Fama-
French.
*Norm Miller is with the College of Business at the University of Cincinnati and Susanne Cannon and
Gurupdesh Pandher are with the Department of Finance at DePaul University (the corresponding author
may be contacted at gpandher@depaul.edu, 312-362-5915). The authors are thankful to the Co-Editor
Crocker Liu and two anonymous referees for helpful comments and suggestions that greatly improved the
paper. We also thank seminar participants and the discussant at the AREUEA 2006 Annual meeting in
Boston for their comments and discussion.
2.
I. INTRODUCTION
It is well known that investment assets trading in financial markets typically
exhibit a positive relation between risk and return. For example, as an asset class, the
more volatile small-cap stocks exhibit higher returns over the long run than large-cap
stocks. Does such a relation also exist in the U.S. housing market where housing has the
dual role of consumption and investment and where transaction costs and liquidity risk
are high? In other words, do riskier more volatile housing markets also provide higher
returns? Furthermore, what is the impact of the house price-level on this risk-return
relation and how does exposure to the stock market affect housing returns?
“No one owns the median home in the USA or even in a MSA. They own
property in a submarket.”1 When studying housing risk or talking about the possibility of
bubbles, the national market is not very relevant to most home owners. In this paper, we
empirically examine the questions posed above by using disaggregate housing sale price
data at the zip code level. Prices at this level will correspond more closely to an
individual perspective. Here we investigate the role of housing return volatility, price
level, stock market exposure and idiosyncratic volatility in explaining housing returns.
While the related literature tends to focus on the longitudinal role of volatility and
housing returns within metropolitan statistical areas (MSAs), our risk-return analysis is
cross-sectional and covers the national U.S. metropolitan housing market.2 Our study
uses disaggregate zip code level housing data from the International Data Management
Corporation (IDM) and consists of 155 MSAs and 7,234 zip codes. The use of zip codes
as the spatial unit provides a more localized delineation of housing submarkets for
examining the risk-return structure across submarkets.
1 Quote from William C. Wheaton, MIT Professor, April 15th 2005 in a panel presentation at the ARES
meeting in Sante Fe, NM on the topic of housing prices and bubble risks.
2A number of well known studies including Case and Shiller (1989, 1990) and, more recently, Capozza,
Hendershott and Mack (2004) are at the MSA level.
2
3.
We find that MSAs explain only 19.6% of the overall zip-code level variation in
housing returns, implying that cross-sectional analysis at this level would eliminate 80%
of the return variation in our data. This suggests that aggregation to the MSA level blurs
the heterogeneity of hedonic factors that defines neighborhoods more locally and masks
their influence on property values. For example, neighborhoods with higher priced
homes where households tend to be employed in managerial occupations may be more
sensitive to changes in the stock market through an income/wealth effect. Moreover, a
low risk MSA may still contain higher risk submarkets and vice versa.
While there is some arbitrariness in the use of zip codes to define submarkets,
empirical studies show that they provide a reasonable spatial delineation that is correlated
with important factors impacting property values. For example, Goodman and
Thibodeau (1998, GT) propose a hierarchical hedonic model for identifying housing
submarket boundaries based on public school quality which is used to estimate property
value by Goodman and Thibodeau (2003)3. The study finds that the prediction mean
square error for (logged) house prices is 0.04335 when zip codes are used to define
neighborhoods while the same under the GT approach is 0.0420. The authors conclude
(page 19): “Indeed, given the arcane formulation of zip codes, it is surprising how well
they characterize submarkets. Moreover, they are the easiest submarket indicator to use –
everyone knows his or her zip code”.
Goetzmann and Speigel (1997) also estimate zip code level housing returns where
all repeat-sales in a metropolitan areas are weighted using distance functions based on
geographical and socio-economic characteristics. They find that submarket return indices
often deviate dramatically from the city-wide index in San Francisco indicating the need
to further explore and understand these differences in submarket price movements. In
this regard broad metropolitan area indices may be misleading to lenders and investors as
3Others have also used zip code data in hedonic pricing models such as Graddy (1997), or for clustering as
in Goetzman and Speigel (1997) or Goetzman, Speigel and Wachter (1998) and Decker et.al. (2005).
3
4.
a proxy for capital appreciation or risk. Given the well established use of zip codes as a
spatial unit, we believe that the use of zip codes to delineate submarkets is a reasonable
and practical first start to investigating the cross-sectional role of risk and return across
the U.S. housing market.
Our empirical results provide a number of important insights into the asset-pricing
features of the U.S. metropolitan housing market. First, we find that the U.S.
metropolitan real-estate market is in conformance with the general risk-return hypothesis
where higher return volatility is rewarded by higher return. Housing returns increase by
2.48% annually for a 10% rise in volatility. Second, the return on housing investment is
positively affected by the price-level, although the price effect declines as the house price
level increases.
Third, we find that stock market risk is also priced by the housing market and a
more complex effect emerges based on the direction of the stock market. Submarket
sensitivity to the stock market is measured through “housing betas” estimated by
regressing housing returns to S&P500 index returns. We find that submarkets with
higher exposure to the stock market experience higher returns over the period where the
market rises (1996-1999) while returns decline when the market falls (2000-2003).
Regression estimates imply that a submarket with a housing beta of 0.5 yields an
expected 8.21% higher return over 1996-1999 than a zero beta submarket, while it yields
a 7.9% lower return than the zero beta submarket over the 2000-2003 stock market
downturn.
One possible explanation follows from the degree to which household income and
wealth in various submarkets is sensitive to the wider economy, whose leading indicator
is the stock market. Houses in zip codes that are more sensitive to the stock market have
the potential of greater price appreciation in states of the stock market that provide those
households with higher income and wealth (when, for example, higher corporate profits
increase compensation, bonuses, and stock options to managers). Since housing supply is
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5.
relatively fixed in urban submarkets in the short-run, housing demand can rise sharply
with income, leading to higher housing returns in zip codes that are more sensitive to the
stock market. This suggests a positive relation between return and beta in periods of
rising stock market performance.4
The same mechanism leads to a fall in demand when the stock market declines
because household income is affected more negatively in submarkets with greater market
sensitivity. This implies a declining relation between return and beta in falling periods of
the stock market. Due to the dependence of the return-beta relation on the direction of
the stock market, aggregation of returns over the entire 1996-2003 period then lead to a
“U-shaped” pattern of returns with respect to beta (see Figure 6 and 8).
Fourth, the return-volatility-price relation identified in the paper is robust to i)
MSA fixed effects and ii) differences in socioeconomic characteristics among submarkets
related to income, employment rate, managerial employment, owner occupied housing,
gross rent and population density. While differences among the 155 metropolitan
statistical areas (MSAs) explain 20% of the total return variation among zip codes, the
inclusion of volatility and price level explains an additional 40% of the total return
variation. Among the six socioeconomic variables, median household income, gross rent
and population density exert a significant positive effect on returns while percentage
managerial employment have a negative effect (the unemployment rate and percentage
owner-occupied are not significant). Further, while price and income have a positive
impact on housing returns, their interaction is negative, suggesting that housing returns
fall in submarkets where income and price level simultaneously rise. An implication of
this empirical finding is that for any given price level, investment in a relatively lower
income submarket leads to higher housing investment returns than in higher income
submarkets.
4This result is consistent with Miller and Peng (2006) which studies volatility in MSAs using Garch
modeling and finds that volatility is Granger-caused by the home appreciation and GMP growth rates.
5
6.
Fifth, we find that idiosyncratic price risk is also an important determinant of
returns with a 10% increase in idiosyncratic volatility raising returns by 1.88% annually.
Since housing investment is largely undiversified, this result implies that undiversified
risk is compensated with higher returns in the real estate market.
Lastly, we analyze the house price effect as a Fama-French type factor. This
allows us to confirm that house prices impact the return generating process across
submarkets and in not merely a statistical artifact. Fama and French (1992) define the
“Small Minus Big” (SMB) factor as the return between low and high market
capitalization stocks and estimate its impact on stock returns by including it in the CAPM
regression. Using the analogy between house price and a company’s market-capitalization,
we similarly construct the house price FF factor by sorting median-priced houses by zip
code into three price ranked sub-portfolios each year and then taking the difference
between the average return between the lowest and highest priced groups (SMB). The
estimation reveals that the house price FF factor is statistically significant in explaining
housing returns in the cross-section.
There have been a number of studies on housing price dynamics, from Ozanne
and Thibodeau (1983) to Bourassa et al (2005). Some of the empirical literature
examines the efficiency and predictability of the housing market or explains price change
while more recent work examines the dynamic relation between volatility and house
prices within localized metropolitan areas. In comparison, the focus of our paper is on
the cross-sectional asset-pricing relation between risk, price level and housing returns
across the U.S. metropolitan housing market at the submarket level. A discussion of the
related literature is given below.
In addition to Goodman and Thibodeau (2003) and Goetzman and Speigel (1997)
mentioned above, a number of other studies have also used zip codes as the spatial unit of
analysis.5 Dolde and Tirtiroglu (1997) observe time-varying volatility and positive
5For example, Graddy (1997) tests for differences in prices charged by fast-food restaurants that serve
markets with customers of widely divergent incomes and ethnic backgrounds. The study finds significant
6
7.
relations between conditional variance and returns in Connecticut and San Francisco over
the period from 1971 to 1994. Dolde and Tirtiroglu (2002) identified 36 volatility events
in four regional housing markets from 1975 to 1993 and suggest that price volatility
surges are associated with changes in economic conditions. Miller and Peng (2006) use
GARCH models and a panel VAR model to analyze the time variation of home value
appreciation and the interaction between volatility and economic growth. They find
evidence of time varying volatility in about 17% of the MSAs and find that volatility is
Granger-caused by the home appreciation rate and GMP growth rate.
A notable early study on housing market efficiency by Rayburn, Devaney and
Evans (1987) used 15 years of housing price data for 10 submarkets of Memphis, TN,
and estimates an ARIMA time series model of differenced log prices based on the means
of sale price per square foot of single-unit residential properties. After adjusting for
transaction costs, all submarkets were deemed weak-form efficient because of the
inability to exploit the time-series pattern to create an arbitrage profit. High transactions
costs in the housing market make it very difficult to exploit all but the strongest of
disequilibrium’s for those confident enough to be sure that price corrections are due.
Case and Shiller (1989, 1990) found evidence of positive autocorrelation in real
house prices and performed weak and strong form efficiency tests on weighted repeated
sales price data for Atlanta, Chicago, Dallas and San Francisco during the 1970–1986
period. They also analyzed the performance of a trading rule where individuals wishing
to purchase a home buy if the forecasted price change was greater than the average price
change and, otherwise, wait a year. Based on such a system they were able to generate
modest trading profits of 1 to 3 percent for the four cities.
differences in prices charged based on the race and income characteristics of a zip-code region. When
income and cost differences are taken into account, meal prices rise approximately 5 percent for a 50
percent rise in the black population. Decker et. al. (2005) used a cross-sectional hedonic pricing model to
investigate the relationship between the U.S. Environmental Protection Agency's (EPA) Toxics Release
Inventory (TRI) data releases and the prices of single-family residences within postal zip code areas
situated in Omaha, Nebraska's Douglas County. Results improved when controlling for relevant
socioeconomic variables and in this case TRI pollutant releases were significant determinants of residential
housing values.
7
8.
Guntermann and Norrbin (1991) used a market model and a dynamic multiple-
indicator model to forecast mean house price changes using structural and economic
characteristics for 15 census tracts in Lubbock, TX. Their results suggest inefficiency
consistent with an adaptive-expectations of the market. Tirtiroglu (1992) and Clapp and
Tirtiroglu (1994) added a spatial aspect to efficiency tests. Using data from Hartford,
CT, metropolitan area, they regressed excess returns (submarket return less metropolitan
area return) on lagged excess returns of a group of neighboring towns and on a “control
group” of non-neighboring towns. Their results favor a spatial diffusion pattern and are
consistent with a positive feedback hypothesis.
Pollakowski and Ray (1997) performed a spatial and temporal analysis of price
diffusion at a sub-national level between nine U.S. census divisions and between the five
largest PMSAs within the New York–Northern New Jersey–Long Island consolidated
metropolitan statistical area (CMSA) from 1975 through 1994. Their results show that
sub-national housing price changes did not seem to follow a spatial diffusion process
while analysis within census divisions and for New York indicated support for the
positive-feedback hypothesis. Capozza, Hendershott and Mack (2004) explored the
dynamics of housing price mean reversion and responses to various demand and supply
variables for 62 metro areas from 1979 to 1995. They found heterogeneity in terms of
the price trend responses to these economic variables based on the time period and the
specific MSA. Malpezzi and Wachter (2005) examined supply constraints in the natural
or political sense and demonstrate that price elasticity of supply plays a key role in
housing volatility. They conclude that speculation has a great role in price volatility
when supply is less elastic. More recently, Bourassa, Haurin, et al (2005), explored the
causes of price variation within three New Zealand markets and their analysis suggests
that the bargaining power of buyers and sellers differs in strong versus weak markets and
that price changes are affected by changes in total employment. Their work also touches
upon atypical housing attributes as influencing appreciation rates.
8
9.
The remainder of the paper is organized as follows. Section II describes the data
used in our cross-sectional analysis of housing returns. The role of volatility and price
level in explaining housing returns is examined in Section III. Section IV investigates the
effect of socioeconomic variables and Section V relates returns to housing betas and
idiosyncratic volatility, and carries out a Fama-French style analysis for the price effect.
Section V concludes the paper.
II. DATA
Our study uses a panel data set comprised of 7,234 postal zip codes falling in 155
urban metropolitan statistical areas (MSAs) across the U.S.. Annual data on median zip
code house prices are available from the International Data Management Corporation
(IDM) in the post-1995 period and our sample spans the period from 1995 through 2003.
Zip code level socioeconomic data from the 2000 census are obtained from the website
maintained by the University of Missouri.6
Socioeconomic data used in the study include median household income (Inc), the
civilian unemployment rate (Unemp), percentage managerial employment (Prof),
percentage of owner occupied housing (Owner), gross rent (Rent) and population density
defined as persons per square mile (Popsq). The source of fixed rate mortgage data is
Fidelity National Financial and Freddie Mac and the S&P500 index is obtained from
Bloomberg.
Quality adjusted house prices (such as those provided by OFHEO, the Office of
Federal Housing Enterprise Oversight) are not available at the zip code level. Although
the IDM data does not have very extensive time-variation, it does have very rich cross-
sectional depth. This is a particularly attractive feature of the data for the purpose of our
6 See http://mcdc2.missouri.edu/websas/dp3_2kmenus/us
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10.
study which focuses on the cross-sectional risk-return and asset pricing features of the
U.S. urban housing market.7
The cross-sectional depth of the data also overcomes some econometric
limitations due to the shortness of the time series. In evaluating the role of housing return
volatility on housing returns, we regress average housing returns across zip codes on
estimates of their volatility (standard deviation of returns). Although the estimate of
volatility is unbiased, its sampling variance is large due to the shortness of the time
series. This implies that we have stochastic regressors in the cross-sectional regression
(1) of Section III. However, because of the large cross-sectional sample of 7,234 zip code
observations, the regression estimators are asymptotically unbiased8. The same applies to
regression (3) where housing returns are related to the stock market sensitivity (beta) of
the submarket.
Further, as discussed above, the limitation posed by the shorter time series are
ameliorated and counterbalanced by the cross-sectional richness of the sample including
7,234 zip codes. Lastly, while the sample period is not long, it does exhibit substantial
temporal heterogeneity with respect to economic conditions.
[Figure 1 and 2 about here]
7Besides the IDM data, an alternative potential data source is First American which provides home price
indexes from single family residential repeat sales. The First American website states that “repeat sales
i
with less than one year between sale dates are not used and five percent of the data with the highest
monthly increases or decreases are also not used.” Repeat sales data is likely to be very thin in zip codes.
Although, this data goes back further in time than IDM data, it excludes a large portion (80%) of residential
sales data. The median house price data from IDM are robust to such selection and exclusion criteria.
8This critical OLS condition for unbiased regression estimation is E (ε | X ) = 0 where ε is the regression
error and X are the regressors which may be stochastic (see White (1999, p. 7)). In our cross-sectional
regression (1) of Section III, X = (Vol , ln Pr ice) . Although the estimate of Vol is unbiased, it has a large
sampling variance due to the short time series, implying that it is a stochastic regressor. The size of the
variance of X , however, is not relevant to the condition E (ε | X ) = 0 as long as it is finite. Therefore, the
result that regression estimators with stochastic regressors are asymptotically unbiased under E (ε | X ) = 0
(White (1999, p. 20)) allows us to assert that the regression estimators for (1) are also asymptotically
unbiased due to the large cross-sectional sample of 7,234 observations.
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11.
Figure 1 and 2 plot the annual return on the S&P500 index and average housing
returns across zip codes over 1996 to 2003. Fluctuations in returns on the S&P500 index
range from -22% to 33% and the stock market was a mix of a bullish and bearish. The
years 1996, 1997, 1998 and 1999 register strong positive stock market returns while
strongly negative returns are observed over 2000, 2001 and 2002. In 2003, market
returns rise and become positive again.
Summary statistics are reported in Table I. The reported figures are first averaged
over the eight year period and then averaged over zip codes. The average median house
price (Price) over 1995-2003 across the 7,234 metropolitan zip codes is $188,845 while
the average annualized return is 5.70% (Return). The corresponding volatility (Vol) of
median house price returns is 14.8%. While house prices have a significant positive skew
(3.330), the natural logarithm of house prices is relatively symmetric. On average, the
unemployment rate (Unemp) is 5.51%, 35.4% of the households have a member
employed in a managerial occupation (Prof), 69.6% of the units are owner occupied
(Owner) and the gross rent is $706. The average excess return of the S&P500 index is
9.55% over the 1995-2003 period, the average three-month T-Bill rate is 3.92%, and the
annualized monthly mortgage rate is 7.15%.
Beta is the sensitivity of house returns to the stock market and is estimated by
regressing returns for the median-priced house in each zip code on the S&P500 index
(see equation (2)). The average house return betas for the 7,234 zip codes is close to zero
(-0.077) while its range is between -2.075 and 2.235.
[Table I about here]
Figure 3 plots the housing Sharpe ratios (return per unit risk) across zip codes
over the eight years of the sample. For each year, it is calculated as the average housing
return across zip codes divided by the standard deviation of returns. Over 1996-1999, the
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12.
Sharpe ratio is below 0.28; however, it rises dramatically over the next four years and is
close to 0.88 in 2003. This shift parallels the end of the secular stock market rise in 2000
and the start of the bear market from 2000 to 2003. This suggests that the latter part of
the bull period (1995-2000) in the stock market had a positive spillover effect on the real
estate market. The positive effect impact continued well into 2001 and 2002.
[Figure 3 about here]
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13.
III. HOUSING RETURNS, VOLATILITY & PRICE-LEVEL
The analysis of this section uses both ranked two-way portfolios and cross-
sectional regressions to examine and quantify the effect of volatility and the price-level
on housing returns. We also study the role of MSA fixed effects on the asset pricing
relation between housing returns, volatility and price level.
As an initial glimpse into the risk-return relationship across the 7,234 zip codes
falling in the U.S. metropolitan areas, average median house returns by zip code are
plotted against return volatility and price level in Figure 4 and 5. A discernable positive
trend is apparent in both graphs.
[Figures 4 and 5 about here]
A. Ranked Housing Portfolios – by Price & Volatility
For each year, median-priced houses in each U.S. postal zip code are first sorted
into ten ranked price deciles (rows) and, then, within each price decile into ten ranked
volatility groups (columns). The return volatility (Vol) is the standard deviation of annual
returns on the median-priced house in the zip. Average annual housing returns by price-
volatility combinations are reported in Panel A of Table II while the corresponding
average volatility Vol and the house prices (ln(Price)) are reported in Panels B and C,
respectively. “P-1” and “V-1” are the low price and volatility deciles, respectively, while
“P-10” and “V-10” are the high price and volatility deciles.
Table II exhibits the cross-sectional relation between housing return, volatility
and price-level in the US residential housing market. First, we find that housing returns
increase uniformly with volatility: rising from 5.31% to 15.74% over the lowest (V-1) to
the highest volatility (V-10) deciles (top row of Panel A). Meanwhile, average volatility
increases from 4.02% to 45.29% over the same deciles (top row of Panel B). Although
we examine this result further using cross-sectional regressions in Tables III-VI, this is
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preliminary indication that a risk-based asset-pricing pattern exists at the disaggregate zip
code level in the U.S. housing market. Second, the positive relation between housing
return and volatility prevails uniformly at all price levels (rows “P-1” to “P-10”). Third,
returns increase with the price level, from 5.14% to 10.52% (“All” column of Panel A).
[Table II about here]
Fourth, the top row of Panel C suggests that the increase in return of the median-
priced house due to volatility is independent of price-level as the average house price
shows no clear trend with increasing volatility (columns). Lastly, the “ALL” column of
Panel A and B shows that the positive effect of price-level on return is independent of
volatility (which falls between 13.49% and 16.92%).
The ranked two-way results indicate a i) strong positive relation between housing
returns and volatility and the price-level and ii) these effects are independent of each
other.
B. Cross-Sectional Regressions on Volatility & Price-level
Next, median-priced house returns for the 7,234 zip codes covering the U.S.
metropolitan housing market are regressed on return volatility and market price over
1995-2003. The mean return and volatility (Vol) are computed for each zip code over the
eight-year period.
Let ri represent the average annual return for the median-price house in zip code
i = 1,..., n ( n = 7234) . To investigate the role of volatility (Vol) and price-level on
returns to housing investment, returns are decomposed using the cross-sectional
regression
ri = α 0 + α 1Voli + α 2 ln Pr icei + ε i (1)
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15.
where
Vol is the return volatility for the median-priced house in each zip code over the
years 1996-2003,
LnPrice is the average of the natural logarithm of house prices (in $000s), and,
ε is the standard Gaussian error.
Results from the cross-sectional regressions are reported in Table III and reveal
that both volatility and the price-level are positively priced in the U.S. housing market.
The coefficients for both volatility and price-level are highly significant and positive and
the regression’s adjusted R-square is 0.50. An asset pricing implication of the estimated
full model is as follows. The estimated coefficient for Vol predicts that a 10% increase in
return volatility leads to an increase of 2.48% in the median house price. Meanwhile, the
regression estimate for ln(Price) implies that a $500,000 house earns on average an
additional 1.43% return annually than a house priced at $300,000 (calculated as
0.02801[ln(500) – ln(300)]).
[Table III about here]
Table IV further reports the cross-sectional regression by five market segments.
The metropolitan housing market consisting of 7,234 zips is separated into five ranked
quintile portfolios by market price (Qprice = 1, 2, . . ., 5) and model (1) is estimated
separately in each quintile. The volatility coefficient (Vol) remains relatively constant
over the five market segments and is the highest for the middle quintile (Qprice=3). The
coefficient for Vol across the five segments are 0.2330, 0.2573, 0.2897, 0.2438 and
0.2264, respectively. The relationship of housing returns and the price level is more
variable. The largest value for the LnPrice coefficient occurs in the lowest quintile
(3.214) and the middle quintile (4.209), the lowest value occurs in the highest quintile
(1.436).
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The segmented analysis reveals that the positive relation between housing return
and volatility is fairly constant across different price segments of the housing market.
Meanwhile, the price effect, although significant and positive in all five segments,
generally declines with the price level.
[Table IV about here]
C. MSA Fixed Effects & the Return-Volatility-Price Relation
Goetzmann, Spiegel and Wachter (1998) define neighborhoods using zip codes
and show that when two properties are separated in space but perceived by the market as
substitutes for each other, their prices also fluctuate together. We now examine whether
the positive relation between housing returns and volatility and price level is robust to the
clustering effects from the 155 MSAs in which the 7,234 zip-codes fall. This is done by
including fixed effects for the MSAs in the cross-sectional regressions of housing returns
on volatility and price level (Table III). The results of this analysis are reported in Table
V.
The coefficients for volatility and the price level continue to remain highly
significant after the inclusion of the MSA fixed effects. Further, the magnitude of the
volatility effect remains effectively unchanged at 0.2496 (from 0.2474), while the price
level effect diminishes to 0.0180 (from 0.0280). Last, model fit reveal that MSAs alone
explain only 20.8% of the total return variation among zip codes while the inclusion of
volatility and price level explains an additional 40.6% of the price return variation. This
suggests that the asset pricing relation between volatility, price and return is robust to
clustering effects from MSAs.
[Table V about here]
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IV. ROLE OF SOCIOECONOMIC VARIABLES
We now investigate whether the return-volatility-price relation identified in the
previous section continues to hold after accounting for differences in socioeconomic
characteristics among submarkets. The analysis also gives additional insights into the
role of these variables on housing returns.
The literature provides evidence that socio-economic factors (e.g. income,
employment) influence investment returns and volatility in housing submarkets markets.
For example, Ozanne and Thibodeau (1983) find that socio-economic variables are found
to explain metropolitan price variation, and Goetzmann and Speigel (1997) determine
median household income to be the salient variable in explaining the covariance of
neighborhood housing returns. More recently, Bourassa, Haurin, et al (2005) report that
price changes are affected by employment in three New Zealand submarkets and Miller
and Peng (2006) also find evidence that income growth and house price appreciation
Granger-cause volatility changes at the MSA level. It is, therefore, important to check if
the relation between housing returns, volatility and price level identified earlier is robust
to effects of socioeconomic variables.
A. Socioeconomic Variables & Hypothesis
We extend the asset-pricing analysis of Section III by including zip code level
socioeconomic variables in the cross-sectional regressions of house price returns on
return volatility and price level (Table VI). These variables include log-income
(LnIncome), employment rate (Unemp), managerial employment (Prof), percentage
owner occupied housing (Owner), gross rent (Rent) and population density (Popsq).
Our hypotheses regarding the effect of these variables on housing returns is as follows:
(1) LnIncome has a positive effect as shown in previous studies where income changes
and price movements are correlated.
(2) Unemp has a negative effect as greater unemployment should lower home prices.
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18.
(3) Prof may likely have a positive effect as professional employment is positively
correlated with income and education. On the other hand, neighborhoods where a
high proportion of households are employed in managerial occupations may form
more exclusive submarkets that induce a “herding” demand effect. This would lead
to a premium in house prices and this overvaluation may be subsequently reflected in
lower returns in such exclusive localities.
(4) Owner has a positive effect as the greater proportion of owners should imply a
greater vested interest in the neighborhood.
(5) Rent has a positive effect as higher rents reduce affordability and should push home
demand. Although one might argue that the direction is vice versa, the effect is still
the same.
(6) PopSq has a positive effect as greater population density is shown to increase land
values and in turn housing prices.
B. Empirical Results
First note from the volatility coefficient (Vol) across columns A-Fin Table VI
that the basic risk-return relation identified earlier is robust to differences in
socioeconomic characteristics across submarkets. Over the six regressions, the volatility
coefficient is highly significant and falls in the narrow range of 0.2326-0.2387. Second,
the role of price level remains positive and significant although the coefficient value rises
with the inclusion of Unemp, Prof, Owner, Rent and Popsq.
Third, the regressions of columns A-D (Table VI) investigate the role of price and
income separately and jointly. Independently, both price and income have a positive
impact on housing returns and the coefficients are highly significant. Meanwhile, their
interaction term is negative, suggesting that housing returns fall in submarkets where
income and price level rise simultaneously. An implication of this empirical finding is
that if two submarkets have the same median level of income, the one with lower prices
18
19.
experiences higher price appreciation. The implication is that house prices catch up to
household incomes over submarkets.
Fourth, in columns E and F we observe that housing returns are lower in
submarkets with higher rates of employment in managerial occupations after controlling
for price and income (meanwhile, the unemployment rate coefficient is negative but not
statistically significant). The reason for this unexpected outcome is not apparent. One
possible conjecture for this empirical finding is that localities with higher household
incomes form more exclusive submarkets that become relatively overvalued. This
“herding” to exclusive neighborhoods created an ex-ante premium in the acquisition price
that, subsequently, results in lower growth rates relative to less exclusive submarkets.
For example, based on the estimate for the Prof coefficient in column F, the median
priced house in a submarket where 70% of the labor force is employed in managerial
professions is expected to yield a 2.6% lower annual return than an equivalent submarket
with 20% employment in management.
Lastly, the role of other local demand-supply indicators such as gross rents and
population density is positive and significant. The percentage of owner occupied units is,
however, found to be not significant after accounting for the other variables.
[Table VI about here]
The asset-pricing analysis with socioeconomic variables reveals that household
income, rents and population density have a positive effect on housing returns.
Managerial employment has a negative impact while the role of owner occupied housing
is statistically weak. Controlling for the six socioeconomic characteristics among
submarkets does not, however, alter the basic asset-pricing relation between return,
volatility and price level identified earlier in Tables III-IV. Housing returns still rise with
both return volatility and the price level and this result is robust to differences in
socioeconomic characteristics among submarkets.
19
21.
V. STOCK MARKET EXPOSURE
This section further explores the relation between housing returns and submarket
exposure to the stock market and idiosyncratic volatility. We also carry out a Fama and
French (1992) style analysis to investigate if the price effect is primarily a statistical
artifact or whether it is an asset-pricing factor that impacts the return generating process
across submarkets. Since housing supply is relatively fixed in urban submarkets in the
short-run, housing demand can rise sharply with increases in wealth, leading to higher
housing returns in zip codes that are more sensitive to the stock market. This suggests a
positive relation between return and beta in periods of rising stock market performance.
A. Measuring Submarket Sensitivity to the Stock Market
To estimate the sensitivity of housing submarkets to the stock market, we regress
the median housing return in each zip code on returns of the S&P500 index. The
estimation is analogous to the estimation of stock betas in the capital asset pricing model
(CAPM) which captures the sensitivity of a given stock to market performance. The
difference in our situation is that we relate housing returns in each zip code (“our stock”)
to the S&P500 index return (a common proxy for stock market performance).
Let Rit = rit − rt represent the annual excess return on the median-price house in
f
zip code i = 1,..., n ( n = 7234) where the risk-free rate rt is the average annualized
f
return on three-month T-Bills in year t . The house-return beta is estimated for each zip
code using a CAPM regression for housing investment returns
Rit = α 0 + β i RSP500 t + ε t (2)
where
RSP500 is the excess annual return on the S&P500 index over the risk-free return in
years t = 1996,...,2003 ,
ε is the standard Gaussian error.
21
22.
We use the “housing CAPM” (2) to specifically measure housing submarket
sensitivity to the stock market. In our application, we depart from the strict theoretical
interpretation of the market portfolio as capturing the return of all assets in the economy.
Standard applications of the CAPM proxy the market portfolio with the S&P500 index
and we do the same in measuring housing exposure to the stock market. More
specifically, we do not combine the returns of a diversified real-estate portfolio with the
S&P500 portfolio to construct a combined market portfolio in estimating (2). Instead, we
use only the S&P500 index because our purpose is to specifically estimate housing
submarket sensitivities only to the stock market.
B. Ranked Housing Portfolios – by Price & Housing Betas
For each year, median-priced houses in each zip code are first sorted into ten
ranked price deciles (rows) and, then, ten ranked beta β groups (columns). The betas are
the slopes from the regression of median-priced house returns in zip codes on the returns
of the S&P500 index.
The average annual return for the median-priced house in each ranked price-beta
combination is reported in Panel A of Table VII. The corresponding average values for
β and house price (lnPrice) are reported in Panels B and C, respectively. “P-1” and “ β
-1” are the low price and beta deciles, respectively, while “P-10” and “ β -10” are the
high price and β deciles.
Table VII illustrates how returns on housing investment vary with stock market
exposure and the price level. First, we note from the top rows of Panel A and B that
median housing returns have a quadratic (“U-shaped”) relation to beta with returns
increasing over both negative and positive betas. Note that the lowest return of 6.44% for
the mid-beta group ( β -6) rises in both directions towards the low and high beta groups
22
23.
(9.30% for β -1 and 13.21% for β -10). The average value of beta in the low-beta group
( β -1) is -0.56 and increases to 0.51 for the high-beta groups ( β -10).
Second, the quadratic relation between stock market sensitivity and housing
return prevails uniformly at all price levels (“P-1” to “P-10”), although the returns
increase with the price level.
Third, the top row of Panel C suggests that the relation between housing returns
and beta is independent of the price level as the average lnPrice remains relatively
constant over price deciles (columns). Fourth, we note from the “ALL” column of Panel
A and B that i) house returns increase with the price-level (from 5.14% to 10.52%) and ii)
the price effect is independent of beta as it does not exhibit any clear pattern over the
price deciles ( β falls between -0.13 and -0.03).
[Table VII about here]
C. Regressions with Housing Beta & Price-level
Next, the average return for median-priced houses in the 7,234 zip codes of the
U.S. metropolitan housing market (over 1995-2003) are regressed on their sensitivity to
the stock market (housing beta), price level and non-systematic volatility. Housing return
betas are the slopes of a CAPM regression of zip code housing returns on excess return
on the S&P500 index as described by (2).
The hypothesis that systematic stock market risk and idiosyncratic risk are priced
in the U.S. housing market is examined using cross-sectional regressions of the form
Ri = α 0 + α 1 β i + α 2 β i2 + α 3 ln Pr icei + α 4 Sigmai + ε t (3)
where the new covariate Sigma is the root mean-square error (RMSE) of the residuals in
the housing CAPM model (2) and LnPrice is the natural logarithm of median house
prices (in $000s). Sigma is an estimate of the idiosyncratic volatility in housing returns
23
24.
as it is the residual return variation not explained by the submarket’s systematic exposure
to the stock market.
The quadratic relationship between return and beta that was noted earlier in the
ranked estimates of Table VII and the “U-shaped” pattern is also clearly visible in the
plot of Figure 4. The squared-beta term β i2 is included to capture this non-linear
functional relationship. Significant coefficients for beta, as well as the price and
idiosyncratic risk variables, in (3) provide evidence that these effects are priced in the
housing returns across the U.S. residential real-estate market.
[Figure 6 about here]
The estimation of (3) is reported in Table VIII. First, note that inclusion of the
squared beta term (Beta2) in Panel B dramatically increases the regression fit with the
adjusted R-square rising to 0.2266 (from 0.0323) ; coefficients for both the Beta and
Beta2 terms are highly statistically significant (p-value < 0.0001). The quadratic
relationship between housing returns is also visible in the return-beta graph of Figure 6.
The estimates imply that median house prices rise by 3.84% annually when the housing
beta increases to 0.5 from zero ( as calculated 0.02763(0.5) + 0.09844(0.25)).
Next, the price-level effect is included in the cross-sectional regression of housing
returns in Panel C. The coefficient of lnPrice is highly significant and the R-square
further rises to 0.3384. The corresponding regression estimate implies that a $500,000
house earns on average an additional 1.39% return annually compared to a median-priced
house priced at $300,000 (0.02721[ln(500) – ln(300)]).
Idiosyncratic housing return volatility is introduced in Panel E. This raises the
adjusted R-square to .5047 and the coefficient for Sigma is highly significant. The
estimated regression implies that a 10% increase in non-systematic risk leads to a 1.88%
24
25.
higher annual return for the median price house; the same increase in total volatility leads
to a 2.48% increase in return (Table VIII and Figure 7).
[Table VIII about here]
[Figure 7 about here]
Overall, the cross-sectional regressions reveal that both stock market exposure
and idiosyncratic volatility are priced in the U.S. metropolitan housing market. We next
examine if the quadratic relation between return and stock market exposure is explained
by changes in the stock market. A dummy variable (BD) for the post-1999 period is
included in the full model (Panel D) of Table IX. BD=0 for average returns over
1996-1999 and BD=1 for the 2000-2003 period9. The estimation of the coefficients in (3)
is carried out as before and the regression estimates are reported in Table IX.
The linear and quadratic coefficients are both highly statistically significant along
with the same effects crossed with the dummy variable (BD*Beta and BD*Beta2). The
linear coefficient changes from 0.1642 over 1996-1999 to -0.1565 in the 2000-2003
period; similarly, the quadratic coefficient changes from 0.01918 to 0.00418. While the
response of average returns to beta is positive over the 1996-1999 period, it is negative
over 2000-2003 (beta would have to exceed 0.1565/0.00418=37 .4 to give positive
returns).
[Table IX about here]
[Figure 7 about here]
Hence, a complex story emerges from our period-specific analysis of the relation
between housing returns and stock market exposure. Over 1996 to 2003, we find that
9The authors are thankful to an anonymous referee for suggesting this analysis.
25
26.
submarkets with high exposure to the stock market experience higher returns when the
market rises (1996-1999). Meanwhile, returns in submarkets with greater exposure to the
market fall when the market declines (2000-2003). This leads to the “U-shaped” pattern
of returns vs. beta seen in Figures 6 and 8 where returns rise as beta becomes more
positive and negative. One can observe those markets which reveal higher betas, positive
or negative, in Figure 9. California, Florida and several East Coast markets where
population densities are higher and land supply is less elastic are apparent in the simple
shaded map. Additional explanation for the result is provided in Section VI below.
[Figure 8 about here]
[Figure 9 about here]
D. House Price-level as a Fama-French Factor
Is the price effect identified above as influencing housing returns an asset-pricing
factor across submarkets? In other words, is it primarily a statistical artifact or does it
impact the return generating process across submarkets?
In this section, we address this issue by investigating the role of the house price
level as a Fama-French (FF) asset-pricing factor. This is in the spirit of Fama and
French’s(1992) definition of their “Small Minus Big” (SMB) factor for low vs. high
market capitalization stocks (meanwhile, the second FF-factor “High Minus Low”
(HML) captures the return difference between value and growth stocks, where stocks are
sorted by their market to book ratio). FF investigate the role of the market-cap factor in
explaining stock performance by regressing excess returns on excess market returns and
the difference between returns to portfolios of small and large market cap stocks. If the
return difference between small and large stocks is zero or stock returns do not exhibit
any sensitivity to return differences in the small and large market-cap portfolios, then the
SMB factor would not be an asset-pricing factor for stock returns.
26
27.
Using the analogy of house price to stock market-capitalization (market price by
shares outstanding), we construct the house price FF factor using median-priced houses
in zip code. The FF house price factor is based on sorting zip codes every year into three
portfolios ranked using housing prices at the start of year and then taking the difference
between the average return in the highest and lowest priced groups (SMB). Starting year
prices are used to avoid the correlation between price and return from influencing the
formation of the FF-price factor. Factor loading for the FF house price factor are
estimated from the regression of house returns onto SMB. This is done by augmenting
the submarket CAPM regression (2) as
Rit = α 0 + β i RSP500 t + γ i SMBt + ε t . (4)
Next, the role of the FF-price factor as a determinant of housing returns across the
U.S. metropolitan housing market is tested using the cross-sectional regression
Ri = α 0 + α 1 β i + α 2 β i2 + α 1γ i + α 2γ i2 + α 3 ln Pr icei + α 3 ( βγ ) i + ε t . (5)
Similar to the quadratic effect of beta on housing returns, the FF-price effect is also non-
linear (see Figure 5), therefore, squared term γ i2 is included to capture the correct
functional relationship. The ( βγ ) i term represents the interaction between the beta and
SML. Only significant interactions are included in the reported model.
The results in Table X show that the FF-price factor represented by SMB is priced
in housing returns and, once again the relationship is quadratic in nature. Panel A shows
that both the linear and squared factor loadings for SMB are highly significant, yielding a
R-square of 0.21. Inclusion of the beta loadings (Panel B) increases the fit to 0.27 and all
linear and quadratic terms for beta and SMB are statistically significant (at the 0.0001
significance level). Further, including the interaction between beta and SMB loadings
and lnPrice raises the R-square to 0.41 and both terms are highly significant.
[Table X about here]
27
28.
Lastly, we repeat the FF analysis above by defining the SMB factor more locally
using the first two digits of the zip code10. For example, New York City and environs are
represented by “10xxx”. In the high-priced zip codes, the least expensive houses have a
tendency to appreciate by the greatest amount because there is a relative shortage of
“affordable” houses. In such areas, the lowest-priced homes are likely to be “tear-
downs” purchased solely for the location. Conversely, the more expensive homes in the
lower-priced zip codes will be mixed with the lower priced houses in the higher-priced
zip codes.
SMB portfolios are now formed by sorting median-priced houses in zip codes into
three ranked portfolios within the two-digit zip codes each year and then taking the
difference between the average return in the highest and lowest priced groups. Results
from the regression estimation are reported in Table XI. Panels A-D show that the
localized SMB factor is highly significant in explaining housing returns across
submarkets. Further, its impact on returns remains robust to the inclusion of beta and the
price level. There is, however, some reduction in fit over the “global SMB” factor as the
R-square of the complete regression in Panel D falls to 0.175 from 0.412.
[Table XI about here]
The results based on the global and more local formulation of the SMB Fama-
French Factor show that differences in returns between higher and lower priced houses
(top third minus bottom third) is a systematic factor in explaining housing returns across
submarkets. Our earlier estimation found that the price-level significantly influences
returns across zip codes. The FF analysis allows us to determine that the price-level
effect is not merely a statistical artifact, but an asset-pricing factor.
10We are thankful to one of the referees for suggesting this analysis.
28
29.
VI. CONCLUSION
This paper carries out a cross-sectional analysis of risk and return across the U.S.
residential housing market. We use zip code level housing data as a proxy for
submarkets to investigate the role of volatility, price level, stock market exposure and
idiosyncratic volatility on housing returns. The study provides a number of important
empirical insights into various asset-pricing features of the U.S. metropolitan housing
market.
First, we find that median-priced houses across the 7,234 zip codes in the U.S.
metropolitan real-estate market are in conformance with the risk-return hypothesis that
higher return volatility is rewarded by higher housing return. Cross-sectional regression
estimates reveal that annual housing returns increase by 2.48% when volatility rises by
10%. Second, the return on housing investment is positively affected by the price level
although the price effect declines with increasing house prices (for example. a $500,000
house provides a 1.43% annualized return over a $300,000 house). Although rare, when
prices go down, higher priced homes are more likely to fall more quickly than lower
priced homes.
Third, we find that stock market risk is also priced in the housing market and an
interesting directional asset pricing story emerges. We measure submarket sensitivity to
the stock market through “housing betas” estimated by regressing housing returns on
S&P500 index returns. Submarkets with higher exposure to the stock market exhibit
higher returns when the market rises (1996-1999) while returns in submarkets with
greater exposure to the market decline when the market falls (2000-2003). These
regression estimates imply that a submarket with a housing beta of 0.5 yields a 8.2%
higher return over 1996-1999 than a zero beta housing submarket. Meanwhile, over the
2000-2003 down turn in the stock market, the 0.5 beta housing submarket yields a 7.9%
lower return than the zero beta submarket.
29
30.
We believe that it will be fruitful to study this empirical finding further from both
a theoretical and empirical perspective. One possible explanation follows from the
degree to which household income and wealth in various submarkets is sensitive to the
wider economy, where the leading indicator is the stock market. Houses in zip codes that
are more sensitive to the stock market, presumably in wealthier neighborhoods, have the
potential of greater price appreciation when the stock market is doing well. When the
stock market is rising more than average some households in these stock-sensitive
markets have more wealth via the stock market, both directly and indirectly from those
factors associated with the professional corporate world: higher corporate profits
increase compensation, bonuses, and stock options to managers. Some of this wealth
may be transferred into housing, especially if the future stock market outlook is less
positive.
Similarly, the same mechanism leads to a fall in demand when the stock market
declines since household income in submarkets with greater market sensitivity is
negatively affected. This leads to a declining relation between return and beta in falling
periods. Due to the dependence of the return-beta relation on the direction of the stock
market, aggregation of returns over the entire 1996-2003 period then lead to the “U-
shaped” pattern of returns with respect to beta (see Figure 6 and 8).
We also find that the return-volatility-price relation identified in the paper is
robust to i) MSA fixed effects and ii) differences in socioeconomic characteristics among
submarkets related to income, employment rate, managerial employment, owner
occupied housing, gross rent and population density. Over the six return-volatility-price
regressions with socioeconomic characteristics, the volatility coefficients are highly
significant, falling in the range of 0.2326-0.2387 while the price level coefficient remains
significantly positive and increases with the inclusion of the socioeconomic variables.
Clustering effects from MSAs explain only 20% of the overall return variation across zip
30
31.
codes while inclusion of volatility and price level explains an additional 40% of the
return variation.
Among the six socioeconomic variables, median household income, gross rent
and population density exert a significant positive effect on returns while percentage
managerial employment has a negative effect (the unemployment rate and percentage
owner-occupied are not significant). Further, while price and income have a positive
impact on housing returns, their interaction is negative, suggesting that housing returns
fall in submarkets where income and price level simultaneously rise. An implication of
this empirical finding is that given the same level of income, investment in relatively
lower priced neighborhoods leads to higher housing investment returns than in
submarkets with higher house prices.
The empirical finding that returns fall with rising managerial occupation is
unexpected. One conjecture for this intriguing result is that it may be induced by
“herding" to exclusive localities by families employed in managerial professions. This
ex-ante build-up of a premium in the acquisition price would then result in lower
subsequent returns (the estimates in Table IX imply that a submarket with 70%
employment in managerial professions is expected to yield a 2.6% lower annual return
than the same with 20% managerial employment).
Lastly, we find that idiosyncratic price risk is also an important determinant of
returns with a 10% increase in risk raising returns by 1.88% annually. By its nature,
housing investment is largely undiversified. This result suggests that undiversified risk is
compensated with higher returns in the real estate market.
31
32.
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34.
Table I. Descriptive Statistics
Summary statistics for the data used in the empirical study are reported. The housing data includes annual
median house prices in zip codes covering the urban U.S. residential housing market and comprises a total
of 155 metropolitan statistics areas (MSAs) and 7,234 zip codes over the period 1995-2003 (disaggregate-
level zip code data is available only in the post-1995 period). Data sources include the International Data
Management Corporation (IDM), Bloomberg for the S&P 500 index, Fidelity National Financial and
Freddie Mac for fixed rate mortgage data and 2000 census socioeconomic data at the zip code level
maintained by the University of Missouri (http://mcdc2.missouri.edu/websas/dp3_2kmenus/us).
The reported figures are means obtained by first averaging over the sample period and then
averaging over zip codes. Price is the median house price in the zip code (in $000s), Return is the annual
return on the median-price house, Income is the median household income at the zip code level, Prof is the
percentage of employed in managerial occupations, Unemp is the employment rate, Owner is the
percentage of owner-occupied housing units, Rent is the gross median rent, Popsq is the number of persons
per square mile. Vol is the return volatility across zip codes and RSP500 is the annual return on the
S&P500 index. The Risk-Free Rate is the average monthly annualized return for three-month T-Bills and
the same for monthly mortgage rates is given by the Mortgage Rate. Beta is the housing beta based on a
CAPM type regression of zip code housing returns on S&P500 index returns and is calculated according to
equation (2).
Obs Mean Median Std Min Max Kurt Skew
Price ($000s) 7234 188.845 147.462 1.753 34.480 1857.14 18.099 3.330
LnPrice 7234 1.609 1.608 0.00142 1.264 2.018 -0.073 0.076
Income 7173 51,700 48,373 242 7,619 200,001 3.999 1.391
Prof 7171 35.385 33.550 0.156 0 100 -0.134 0.521
Unemp 7171 5.512 4.327 0.049 0 76.1561 24.979 3.343
Owner 7173 69.624 73.376 0.212 1.4091 100 0.546 -0.928
Rent 7155 706 663 2.777 193 2001 4.316 1.552
Popsq 7173 2885 1425 50.900 0.630 69013 34.553 4.360
Return (%) 7234 5.695 4.595 2.878 -4.284 20.849 0.452 0.785
RSP500 (%) 8 9.552 17.473 7.429 -23.367 33.303 -1.480 -0.558
Risk-Free Rate (%) 8 3.919 4.700 0.610 1.117 5.814 -0.738 -0.896
Mortgage Rate (%) 8 7.146 7.201 0.259 5.819 8.063 0.069 -0.678
Beta 7234 -0.077 -0.093 0.003 -2.075 2.235 7.248 0.741
Volatility (%) 7234 14.845 10.188 0.158 1.386 101.440 8.044 2.551
34
35.
Table II. Housing Returns by Volatility and Price Deciles
The housing data includes a total of 7,234 zip codes covering the U.S. metropolitan housing market over
1996-2003 (disaggregate-level zip code data is available only in the post-1995 period). Each year, median-
priced houses in zip code are first sorted into ten ranked price deciles (rows) and, then, within each price
decile into ten ranked volatility groups (columns). The return volatility (Vol) is the standard deviation of
annual housing returns. The reported figures are yearly averages over the sample period. The yearly return
in Panel A is the average of the return for median priced house in the price-volatility group, the average Vol
is reported in Panel C, and the mean logarithm of median house prices in Panel C. “P-1” and “V-1” are the
lowest house price and volatility deciles, respectively, while “P-10” and “V-10” are the highest price and
volatility deciles. The first row and column of each panel report overall averages by the level of price and
volatility, respectively.
All V-1 V-2 V-3 V -4 V-5 V-6 V-7 V-8 V-9 V-10
Panel A: Average Yearly House Price Return (%)
All 5.31 5.81 6.13 6.46 6.59 6.97 7.26 7.83 8.75 15.74
P-1 5.14 3.49 3.63 3.86 3.74 4.18 4.58 4.52 5.66 5.64 12.19
P-2 6.16 4.07 4.14 4.17 4.66 4.61 5.25 4.96 6.35 7.41 16.07
P-3 6.59 4.58 4.67 4.76 5.30 4.87 4.84 5.89 7.16 7.99 15.92
P-4 6.63 4.36 4.67 4.90 5.00 5.22 6.48 6.49 6.69 8.32 14.21
P-5 7.35 4.40 5.13 6.04 6.39 6.80 6.61 7.16 7.38 8.37 15.31
P-6 7.84 4.45 5.17 6.43 6.74 6.47 7.36 7.52 7.93 9.17 17.20
P-7 8.31 5.33 6.34 6.94 7.12 7.25 7.95 8.12 8.37 9.51 16.20
P-8 9.09 6.14 7.25 7.47 8.19 8.43 8.37 8.39 9.56 10.39 16.77
P-9 9.15 7.72 7.95 7.60 8.12 8.57 8.58 9.23 8.87 9.57 15.30
P-10 10.52 8.56 9.11 9.13 9.27 9.53 9.67 10.27 10.31 11.17 18.26
Panel B: Average Standard Deviation of Returns (%)
All 4.02 5.70 6.99 8.15 9.45 11.03 13.37 16.97 23.79 45.29
P-1 16.92 4.17 6.39 8.38 10.14 12.08 14.29 17.46 21.62 28.39 46.53
P-2 16.42 3.83 5.74 7.18 8.71 10.56 12.77 16.08 20.59 28.81 50.25
P-3 15.08 3.64 5.44 6.84 8.19 9.62 11.25 13.81 18.22 25.61 48.51
P-4 13.66 3.30 4.95 6.01 7.25 8.69 10.46 13.24 16.65 23.43 42.86
P-5 13.55 3.39 5.00 6.43 7.46 8.79 10.51 12.77 16.51 22.66 42.18
P-6 13.49 3.43 4.97 6.36 7.31 8.36 9.58 11.76 14.99 22.37 46.03
P-7 13.49 4.06 5.72 6.78 7.79 8.85 10.14 11.90 15.30 21.85 42.73
P-8 14.00 4.28 5.88 7.00 7.96 8.79 9.98 11.84 15.07 21.79 47.69
P-9 13.29 4.56 6.05 6.97 7.86 8.83 9.95 11.61 14.53 20.71 42.05
P-10 14.61 5.51 6.82 7.94 8.85 9.98 11.36 13.25 16.20 22.28 44.11
Panel C: Average Price (lnPrice)
All 5.03 5.03 5.03 5.04 5.03 5.02 5.04 5.04 5.04 5.05
P-1 4.06 4.11 4.07 4.08 4.04 4.06 4.01 4.05 4.03 4.03 4.06
P-2 4.41 4.41 4.40 4.40 4.41 4.42 4.40 4.41 4.41 4.40 4.41
P-3 4.61 4.61 4.61 4.60 4.61 4.60 4.60 4.60 4.62 4.61 4.60
P-4 4.77 4.77 4.77 4.77 4.76 4.77 4.77 4.77 4.77 4.77 4.77
P-5 4.92 4.92 4.91 4.93 4.93 4.92 4.92 4.92 4.92 4.91 4.92
P-6 5.07 5.07 5.07 5.08 5.07 5.06 5.06 5.07 5.07 5.07 5.06
P-7 5.23 5.23 5.24 5.22 5.22 5.24 5.23 5.23 5.24 5.23 5.23
P-8 5.42 5.43 5.43 5.42 5.43 5.42 5.41 5.42 5.42 5.43 5.41
P-9 5.67 5.66 5.65 5.67 5.66 5.67 5.66 5.69 5.67 5.67 5.67
P-10 6.21 6.09 6.12 6.17 6.24 6.18 6.16 6.22 6.28 6.27 6.36
35
36.
Table III. Cross-sectional Regressions of Housing Returns on Volatility and Price
Level
Median-price house returns for 7,234 zip codes in the U.S. metropolitan housing market over 1996-2003
are regressed on volatility and market price as in (1). The mean return and volatility (Vol) are computed for
each zip code over this eight-year period. LnPrice is the mean of the natural logarithm of median house
prices (in $000s). “SE” represents the standard error of the estimated regression coefficient.
Intercept Vol lnPrice R-Square RMSE
Estimate -10.0071* 0.24790* 0.02801* 0.4987 0.03533
SE 0.34973 0.00326 0.006787
Estimate 4.19183* 0.24126* 0.3807 0.03927
SE 0.06975 0.00362
The significance level denoted by * is 0.0001.
Table IV. Cross-Sectional Regression of Housing Returns on Volatility and Price by
Market Segment
Cross-sectional regressions of house price returns on return volatility and price level are reported by market
segment. The average annual return and volatility (Vol) are computed for 7,234 metropolitan zip codes
over the 1996-2003 period. LnPrice is the mean of the natural logarithm of median house prices (in
$000s). For estimation, zip codes are sorted within each year by price level and constructed into five
portfolios ranked by market price (Qprice = 1, 2, . . ., 5). “SE” represents the standard error of the
estimated regression coefficient.
Intercept Vol lnPrice R-Square RMSE
Lowest Price Quintile: Qprice=1
Estimate -12.67579* 0.23302* .034139* 0.4613 .034804
SE 1.78398 0.00675 0.004194
Qprice=2
Estimate -3.941 0.25734* 0.014619 0.4891 .03375
SE 4.41112 0.00691 0.009396
Qprice=3
Estimate -17.34341** 0.28965* 0.042092* 0.4955 .03740
SE 5.62683 0.00771 0.00112591
Qprice=4
Estimate -10.58323** 0.24382* 0.029912* 0.4171 .03600
SE 4.59831 0.00762 0.0086315
Highest Price Quintile: Qprice=5
Estimate -1.85041 0.22636* 0.014363* 0.4203 .03306
SE 1.42488 0.00737 0.0024132
The significance levels denoted by *, ** and *** are 0.0001, 0.002 and 0.03, respectively.
36
37.
Table V. Cross-sectional Regressions with MSA Fixed Effects
Fixed effects for Metropolitan Statistical Areas (MSAs) are included in the cross-sectional regressions of
house price returns on return volatility and price level of Table III. There are a total of 154 MSA for the
7,234 metropolitan zip codes in the 1996-2003 sample. “SE” represents the standard error of the estimated
regression coefficient.
Estimate Estimate SE Estimate SE
MSA Fixed Effects Yes NO Yes
Intercept -0.1001* -0.00351 -0.0537* 0.004207
Vol 0.2474* 0.0033 0.2496* 0.003018
LnPrice 0.0280* 0.000681 0.0180* 0.000838
R-Square 0.2079 0.4941 0.6130
RMSE 0.04239 0.0352 0.02963
The significance levels denoted by * is 0.0001.
Table VI. Cross-sectional Regressions with Socioeconomic Variables
Socioeconomic variables for income, managerial employment, employment rate, owner occupied housing,
rent, population density at the zip-code level are included in the cross-sectional regressions of house price
returns on return volatility and price level (Table III). LnIncome is the natural-log of median household
income by zip code, Unemp is the employment rate, Prof is the percentage of employed in managerial
occupations, Owner is the percentage of owner-occupied housing units, Rent is the gross median rent,
Popsq is the number of persons per square mile. The socioeconomic data is from the 2000 census.
Average annual returns and their volatility (Vol) are computed for 7,155 metropolitan zip codes over
1996-2003 (79 of the original 7,234 zip codes could not be matched to the socioeconomic data). LnPrice is
the mean of logged median house prices (in $000s).
Coefficient Estimates
A B C D E F
Intercept -0.09896* -0.18995* 0.06441* -0.47072* -0.40747* -0.44994*
Vol 0.23702* 0.23797* 0.2326* 0.2333* 0.23331* 0.23873*
lnPrice 0.02786* 0.03617* 0.1419* 0.12028* 0.12417*
lnIncome 0.02145* -0.01898* 0.03056* 0.02428* 0.02294**
Price*Income -0.00976* -0.00735* -0.00784*
Unemp -0.01701 -0.02382
Prof -0.04834* -0.05186*
Owner 0.00611
Rent 0.00797*
Popsq 0.00128*
R-Square 0.5015 0.5138 0.5138 0.5045 0.5175 0.5272
RMSE 0.03292 0.03251 0.03251 0.0349 0.03239 0.0321
The significance levels denoted by * and ** are 0.0001 and 0.003, respectively.
37
38.
Table VII. Returns by Housing Beta and Price level
The median-priced house in each of the 7,234 postal zip codes covering the U.S. metropolitan housing
market over 1996-2003 are first assigned to ten ranked price deciles (rows), and, then subdivided into ten
ranked beta groups (columns). House return betas are the CAPM slopes where returns to median-priced
houses by zip code are regressed on the excess return on the S&P500 index:
Rit = α 0 + β i RSP500 t + ε t , t = 1996,...,2003 (2)
where Rit is the annual excess return on the median-price house in zip code i over the average return on
three-month T-Bills in year t . The reported figures are yearly averages over the sample period. Panel A
reports the average annual return for median-priced houses in the price-beta group, the average beta is
reported in Panel C, and the mean logarithm of median house prices in Panel C. “P-1” is the lowest house
price decile while “P-10” is the highest price decile. The first row and column of each panel report overall
averages by the level of price and beta, respectively.
All β -1 β -2 β -3 β -4 β -5 β -6 β -7 β -8 β -9 β -10
Panel A: Average Yearly House Return (%)
All 9.30 7.46 6.94 6.63 6.49 6.44 6.47 6.46 7.40 13.21
P-1 5.14 6.47 3.77 3.79 4.06 3.98 3.93 4.47 5.49 6.62 8.87
P-2 6.16 8.92 5.12 5.05 4.66 5.07 4.70 5.00 4.38 5.48 13.23
P-3 6.59 8.05 6.43 4.71 5.41 5.36 5.65 4.98 5.23 7.33 12.81
P-4 6.63 7.37 6.36 6.25 4.89 5.54 5.35 5.04 5.65 7.21 12.68
P-5 7.35 8.47 7.92 6.81 6.02 5.64 5.85 5.68 6.34 7.23 13.60
P-6 7.84 9.86 7.95 7.39 6.80 6.38 6.17 6.05 6.45 6.57 14.78
P-7 8.31 10.69 8.59 8.52 7.67 6.98 6.51 6.83 6.37 6.91 14.01
P-8 9.09 10.12 9.61 9.05 8.16 8.00 7.91 7.81 7.30 7.85 15.11
P-9 9.15 10.64 8.72 8.45 9.00 8.50 8.85 8.80 8.05 8.11 12.35
P-10 10.52 12.38 10.19 9.38 9.62 9.49 9.52 9.98 9.41 10.66 14.62
Panel B: Average Housing Beta ( β )
All -0.56 -0.30 -0.22 -0.17 -0.12 -0.07 -0.02 0.04 0.14 0.51
P-1 -0.05 -0.63 -0.30 -0.21 -0.14 -0.09 -0.03 0.03 0.10 0.22 0.56
P-2 -0.04 -0.64 -0.29 -0.19 -0.13 -0.08 -0.03 0.03 0.10 0.23 0.66
P-3 -0.03 -0.54 -0.27 -0.19 -0.13 -0.08 -0.04 0.02 0.09 0.20 0.60
P-4 -0.04 -0.52 -0.26 -0.18 -0.13 -0.08 -0.03 0.01 0.07 0.17 0.52
P-5 -0.07 -0.50 -0.31 -0.22 -0.15 -0.10 -0.06 -0.01 0.04 0.13 0.49
P-6 -0.09 -0.54 -0.31 -0.24 -0.18 -0.12 -0.08 -0.03 0.03 0.11 0.51
P-7 -0.11 -0.59 -0.34 -0.27 -0.20 -0.14 -0.09 -0.04 0.02 0.11 0.48
P-8 -0.12 -0.56 -0.34 -0.28 -0.22 -0.17 -0.12 -0.06 0.00 0.10 0.49
P-9 -0.13 -0.53 -0.33 -0.26 -0.22 -0.18 -0.13 -0.09 -0.04 0.05 0.39
P-10 -0.10 -0.57 -0.27 -0.21 -0.17 -0.13 -0.09 -0.05 0.00 0.09 0.44
Panel C: Average Price (lnPrice)
All 5.04 5.03 5.03 5.03 5.04 5.04 5.04 5.03 5.04 5.04
P-1 4.06 4.04 4.04 4.02 4.03 4.10 4.08 4.07 4.08 4.05 4.05
P-2 4.41 4.41 4.42 4.38 4.40 4.42 4.42 4.39 4.40 4.41 4.41
P-3 4.61 4.60 4.61 4.60 4.59 4.61 4.61 4.62 4.61 4.60 4.61
P-4 4.77 4.77 4.76 4.77 4.77 4.77 4.77 4.77 4.77 4.77 4.78
P-5 4.92 4.92 4.91 4.93 4.92 4.92 4.92 4.91 4.92 4.92 4.93
P-6 5.07 5.07 5.07 5.08 5.07 5.08 5.07 5.07 5.06 5.07 5.06
P-7 5.23 5.23 5.24 5.23 5.24 5.23 5.23 5.23 5.23 5.23 5.23
P-8 5.42 5.41 5.40 5.42 5.43 5.42 5.43 5.41 5.41 5.43 5.43
P-9 5.67 5.66 5.67 5.66 5.67 5.67 5.67 5.68 5.66 5.66 5.66
P-10 6.21 6.28 6.19 6.18 6.17 6.16 6.17 6.24 6.15 6.27 6.29
38
39.
Table VIII. Regression of Housing Returns on Beta, Price and Idiosyncratic Risk
Median-priced house returns for 7,234 zip codes in the U.S. metropolitan real-estate market from
1996-2003 are decomposed into beta, market price and idiosyncratic volatility using the cross-sectional
regression
Ri = α 0 + α1 β i + α 2 β i2 + α 3 ln Pr icei + α 4 Sigmai + ε t (3)
where Ri is the average annual excess housing return for zip codes i = 1,...,7,234 . House-return betas are
the slopes of the CAPM regression (2) based on returns to median-priced houses by zip codes and the
excess return on the S&P500 index. Idiosyncratic volatility is the root mean square error (Sigma) of the
residual from the CAPM regression of housing returns. LnPrice is the is the natural logarithm of the
median house price (in $000s). “SE” represents the standard error of the estimated regression coefficient.
Intercept Beta Beta2 lnPrice Sigma R-Square MSE
Panel A: Beta Only
Estimate 0.03911* 0.03256* 0.0323 0.04901
SE 0.000598 0.00209
Panel B: Beta and Beta2
Estimate 0.0307* 0.02763* 0.09844* 0.2266 0.04381
SE 0.00057 0.00188 0.00231
Panel C: Beta, Beta2 and lnPrice
Estimate -0.10612* 0.03075* 0.09899* 0.02721* 0.3384 0.04053
SE 0.00395 0.00174 0.00214 0.000779
Panel D: Beta, Beta2 and Idiosyncratic Volatility
Estimate 0.00681* 0.00475** 0.04157* 0.18029* 0.3795 0.03925
SE 0.000762 0.00177 0.00247 0.00427
Panel E: Beta, Beta2, lnPrice and Idiosyncratic Volatility
Estimate -0.13944* 0.00701* 0.03958* 0.02887* 0.18847* 0.5047 0.03506
SE 0.00348 0.00158 0.00221 0.000674 0.00382
The significance levels denoted by * and ** are 0.0001 and 0.002, respectively.
Table X. Housing Returns and Pre-Post 2000 Housing Betas
The regression in Table VII, Panel D, is repeated with a dummy variable (BD) for the post-1999 period.
BD=0 for average returns over 1996-1999 and BD=1 for the 2000-2003 period. The estimation of the
coefficients in (3) is done as before.
Intercept Beta Beta2 Sigma BD*Beta BD*Beta2 R-Square
Estimate 0.0122 0.16424 0.01918 0.1536 -0.32072 -0.0150 0.5586
SE 0.000589 0.00189 0.000711 0.00276 0.0025 0.00078
The significance level denoted by * is 0.0001.
39
40.
Table X. Housing Price as a SMB Fama-French Factor
The role of the housing price as a Fama-French (FF) type pricing factor is investigated in the cross-section
of 7,234 zip codes in the U.S. metropolitan housing market from 1996-2003. The FF-price factor is based
on sorting median-priced houses by zip code every year into three portfolios ranked using house prices at
the start of the year and, then, taking the difference between the average return in the highest and lowest
priced groups (SMB). Starting year prices are used to avoid the price-return correlation from influencing
the formation of the FF-price factor. Factor loading for SMB are estimated from the regression of excess
housing investment returns on SMB:
Rit = α 0 + βi RSP500t + γ i SMBt + ε t , t = 1996,...,2003 . (4)
where Rit is the annual excess return on the median-price house in zip code i over the average annual
return on three-month T-Bills in year t . Next, average returns are regressed on linear and quadratic terms
involving the beta and SMB factor loadings:
Ri = α 0 + α1β i + α 2 β i2 + α1γ i + α 2γ i2 + α 3 ln Pr icei + α 3 ( βγ ) i + ε t (5)
where Ri is the average annual excess housing return for zip codes i = 1,...,7,234 . Beta-SMB is the
interaction term (only statistically significant interactions are reported) and LnPrice is the natural logarithm
of the median house price (in $000s). “SE” represents the standard error of the estimated regression
coefficient.
Beta
Intercept Beta Beta2 SMB SMB2 lnPrice SMB R-Sq MSE
Panel A: SMB and SMB2 only
Estimate 0.07247* 0.00587* 0.00193* 0.2204 0.0416
SE 0.0005455 0.000364 0.0000645
Panel B: Quadratic SMB and Beta
Estimate 0.072* -0.0084* 0.05342* 0.00499* 0.00194* 0.2221 0.04157
SE 0.000559 0.00225 0.00226 0.000433 0.00006456
Panel C: Price Effect and Quadratic SMB and Beta
0.06674
Estimate -0.0693* -0.00332 * 0.00647* 0.0011* 0.02761* 0.4148 0.03605
SE 0.00353 0.00195 0.0023 0.000377 0.00006235 0.000696
Panel D: Additional SMB & Beta Interaction
0.00534* 0.12374
Estimate -0.07092* * * 0.00814* 0.00299* 0.0276* 0.0277* 0.4715 0.03425
SE 0.00335 0.00188 0.00299 0.000363 0.00009005 0.000661 0.000994
The significance levels denoted by * is 0.0001 and ** is 0.005.
40
41.
Table XI. Housing Price as a Local Fama-French Factor
The analysis of Table VII is repeated by defining the SMB factor more locally using the first two digits of
the zip code. SMB portfolios are now formed by sorting median-priced houses by zip into three ranked
portfolios within each MSA, and then taking the difference between the average return in the highest and
lowest priced groups.
Beta
Intercept Beta Beta2 SMB SMB2 lnPrice SMB R-Sq MSE
Panel A: SMB and SMB2 only
0.00386 0.0471
Estimate 0.0353* 0.00689* * 0.074 8
SE 0.00060 0.00073 0.00017
Panel B: SMB and Beta
0.00423* 0.00431 0.078 0.0470
Estimate 0.03554* * -.00070* 0.00718* * 9 5
SE 0.00061 0.00138 0.00012 0.00076 0.00019
Panel C: Price Effect, SMB and Beta
0.00396 0.02545 0.175 0.0445
Estimate -0.09385* 0.00506* -.00065* 0.00418* * * 6 2
SE 0.00472 0.00131 0.00011 0.00073 0.00018 0.00092
Panel D: With SMB & Beta Interaction
0.00399 0.02546 0.175 0.0445
Estimate -0.09393* 0.00515* -0.00048 0.00423* * * 0.00039 5 2
SE 0.00472 0.00132 0.00033 0.00073 0.00019 0.00092 0.00070
The significance levels denoted by * is 0.0001; ** denotes 0.003.
41
42.
Figure 1. S&P500 Index Returns by Year
Annual returns on the S&P500 index (RSP500) are plotted over the sample period from 1996 to 2003.
42
43.
Figure 2. Average Housing Returns by Year
Return is the average annual return for the median-priced house over the 7,234 zip-codes of the U.S.
metropolitan housing market from 1996-2003.
43
44.
Figure 3. Housing Sharpe Ratios by Year
For each year, housing Sharpe ratios are calculated as the average housing return across zip codes divided
by the standard deviation of returns.
44
45.
Figure 4. Risk & Return in the U. S. Metropolitan Housing Market
Return is the average annual return for the median-priced house across the 7,234 zip-codes of the U.S.
metropolitan housing market from 1996-2003. The return volatility (Vol) is the standard deviation of
returns.
45
46.
Figure 5. Return and Price-level in the U.S. Metropolitan Housing Market
Return is the average annual return over 1995-2003 for median-priced houses in the 7,234 zip codes of the
U.S. metropolitan housing market. LnPrice is the mean of natural logarithm of house prices ($000s) by zip
code.
46
47.
Figure 6. Housing Betas & Returns
House-return betas are the slopes of the CAPM regression where returns on median-priced houses by zip
code are regressed on the returns on the S&P500 index. Return is the average annual return over
1996-2003 for median-priced houses in the 7234 zip codes of the U.S. metropolitan housing market.
47
48.
Figure 7. Idiosyncratic Risk & Housing Returns
Sigma is the root mean square error of residuals from the CAPM regression of median-priced house returns
by zip code on returns to the S&P500 index. Return is the average annual return over 1996-2003 for
median-priced houses in the 7,234 zip codes covering the U.S. metropolitan housing market.
48
49.
Figure 8. Housing Betas & Returns over 1996-1999 and 2000-2003
Average housing returns over 1996-1999 (“+”) and 2000-2003 (“0”) period are plotted against the housing
betas of Figure 6.
49
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