realestate.uc.edu

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 [email protected], 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.

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.

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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).

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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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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.

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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

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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.

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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.

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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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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 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 where is the regression

error and are the regressors which may be stochastic (see White (1999, p. 7)). In our cross-sectional

regression (1) of Section III, . 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 , however, is not relevant to the condition as long as it is finite. Therefore, the

result that regression estimators with stochastic regressors are asymptotically unbiased under (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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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

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return across zip codes divided by the standard deviation of returns. Over 1996-1999, the

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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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 represent the average annual return for the median-price house in zip code

ni ,...,1 ( . To investigate the role of volatility (Vol) and price-level on returns

to housing investment, returns are decomposed using the cross-sectional regression

(1)

where

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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,

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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(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

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

20

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 ftitit rrR represent the annual excess return on the median-price house in

zip code ni ,...,1 ( where the risk-free rate is the average annualized return

on three-month T-Bills in year . The house-return beta is estimated for each zip code

using a CAPM regression for housing investment returns

(2)

where

RSP500 is the excess annual return on the S&P500 index over the risk-free return in

years ,

is the standard Gaussian error.

21

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 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

and house price (lnPrice) are reported in Panels B and C, respectively. “P-1” and “ -

1” are the low price and beta deciles, respectively, while “P-10” and “ -10” are the high

price and 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 ( -6) rises in both directions towards the low and high beta groups

(9.30% for -1 and 13.21% for -10). The average value of beta in the low-beta group (

-1) is -0.56 and increases to 0.51 for the high-beta groups ( -10).

22

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 ( 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

(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

as it is the residual return variation not explained by the submarket’s systematic exposure

to the stock market.

23

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 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%

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).

24

[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

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

9The authors are thankful to an anonymous referee for suggesting this analysis.

25

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.

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

26

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

. (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

. (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 is included to capture the correct

functional relationship. The 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]

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

10We are thankful to one of the referees for suggesting this analysis.

27

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.

28

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

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

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

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33

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 SkewPrice ($000s) 7234 188.845 147.462 1.753 34.480 1857.14 18.099 3.330LnPrice 7234 1.609 1.608 0.00142 1.264 2.018 -0.073 0.076Income 7173 51,700 48,373 242 7,619 200,001 3.999 1.391Prof 7171 35.385 33.550 0.156 0 100 -0.134 0.521Unemp 7171 5.512 4.327 0.049 0 76.1561 24.979 3.343Owner 7173 69.624 73.376 0.212 1.4091 100 0.546 -0.928Rent 7155 706 663 2.777 193 2001 4.316 1.552Popsq 7173 2885 1425 50.900 0.630 69013 34.553 4.360Return (%) 7234 5.695 4.595 2.878 -4.284 20.849 0.452 0.785RSP500 (%) 8 9.552 17.473 7.429 -23.367 33.303 -1.480 -0.558Risk-Free Rate (%) 8 3.919 4.700 0.610 1.117 5.814 -0.738 -0.896Mortgage Rate (%) 8 7.146 7.201 0.259 5.819 8.063 0.069 -0.678Beta 7234 -0.077 -0.093 0.003 -2.075 2.235 7.248 0.741Volatility (%) 7234 14.845 10.188 0.158 1.386 101.440 8.044 2.551

34

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-10Panel 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 15.74P-1 5.14 3.49 3.63 3.86 3.74 4.18 4.58 4.52 5.66 5.64 12.19P-2 6.16 4.07 4.14 4.17 4.66 4.61 5.25 4.96 6.35 7.41 16.07P-3 6.59 4.58 4.67 4.76 5.30 4.87 4.84 5.89 7.16 7.99 15.92P-4 6.63 4.36 4.67 4.90 5.00 5.22 6.48 6.49 6.69 8.32 14.21P-5 7.35 4.40 5.13 6.04 6.39 6.80 6.61 7.16 7.38 8.37 15.31P-6 7.84 4.45 5.17 6.43 6.74 6.47 7.36 7.52 7.93 9.17 17.20P-7 8.31 5.33 6.34 6.94 7.12 7.25 7.95 8.12 8.37 9.51 16.20P-8 9.09 6.14 7.25 7.47 8.19 8.43 8.37 8.39 9.56 10.39 16.77P-9 9.15 7.72 7.95 7.60 8.12 8.57 8.58 9.23 8.87 9.57 15.30P-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 45.29P-1 16.92 4.17 6.39 8.38 10.14 12.08 14.29 17.46 21.62 28.39 46.53P-2 16.42 3.83 5.74 7.18 8.71 10.56 12.77 16.08 20.59 28.81 50.25P-3 15.08 3.64 5.44 6.84 8.19 9.62 11.25 13.81 18.22 25.61 48.51P-4 13.66 3.30 4.95 6.01 7.25 8.69 10.46 13.24 16.65 23.43 42.86P-5 13.55 3.39 5.00 6.43 7.46 8.79 10.51 12.77 16.51 22.66 42.18P-6 13.49 3.43 4.97 6.36 7.31 8.36 9.58 11.76 14.99 22.37 46.03P-7 13.49 4.06 5.72 6.78 7.79 8.85 10.14 11.90 15.30 21.85 42.73P-8 14.00 4.28 5.88 7.00 7.96 8.79 9.98 11.84 15.07 21.79 47.69P-9 13.29 4.56 6.05 6.97 7.86 8.83 9.95 11.61 14.53 20.71 42.05P-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 5.05P-1 4.06 4.11 4.07 4.08 4.04 4.06 4.01 4.05 4.03 4.03 4.06P-2 4.41 4.41 4.40 4.40 4.41 4.42 4.40 4.41 4.41 4.40 4.41P-3 4.61 4.61 4.61 4.60 4.61 4.60 4.60 4.60 4.62 4.61 4.60P-4 4.77 4.77 4.77 4.77 4.76 4.77 4.77 4.77 4.77 4.77 4.77P-5 4.92 4.92 4.91 4.93 4.93 4.92 4.92 4.92 4.92 4.91 4.92P-6 5.07 5.07 5.07 5.08 5.07 5.06 5.06 5.07 5.07 5.07 5.06P-7 5.23 5.23 5.24 5.22 5.22 5.24 5.23 5.23 5.24 5.23 5.23P-8 5.42 5.43 5.43 5.42 5.43 5.42 5.41 5.42 5.42 5.43 5.41P-9 5.67 5.66 5.65 5.67 5.66 5.67 5.66 5.69 5.67 5.67 5.67P-10 6.21 6.09 6.12 6.17 6.24 6.18 6.16 6.22 6.28 6.27 6.36

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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 RMSEEstimate -10.0071* 0.24790* 0.02801* 0.4987 0.03533SE 0.34973 0.00326 0.006787

Estimate 4.19183* 0.24126* 0.3807 0.03927SE 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 RMSELowest Price Quintile: Qprice=1

Estimate -12.67579* 0.23302* .034139* 0.4613 .034804SE 1.78398 0.00675 0.004194    

Qprice=2Estimate -3.941 0.25734* 0.014619 0.4891 .03375SE 4.41112 0.00691 0.009396    

Qprice=3Estimate -17.34341** 0.28965* 0.042092* 0.4955 .03740SE 5.62683 0.00771 0.00112591    

Qprice=4Estimate -10.58323** 0.24382* 0.029912* 0.4171 .03600SE 4.59831 0.00762 0.0086315    

Highest Price Quintile: Qprice=5Estimate -1.85041 0.22636* 0.014363* 0.4203 .03306SE 1.42488 0.00737 0.0024132    

The significance levels denoted by *, ** and *** are 0.0001, 0.002 and 0.03, respectively.

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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 SEMSA Fixed Effects Yes NO YesIntercept -0.1001* -0.00351 -0.0537* 0.004207Vol 0.2474* 0.0033 0.2496* 0.003018LnPrice 0.0280* 0.000681 0.0180* 0.000838R-Square 0.2079 0.4941 0.6130RMSE 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 EstimatesA 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 -0.02382Prof -0.04834* -0.05186*Owner 0.00611Rent 0.00797*Popsq 0.00128*

R-Square 0.5015 0.5138 0.5138 0.5045 0.5175 0.5272RMSE 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.

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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:

(2)where is the annual excess return on the median-price house in zip code over the average return on

three-month T-Bills in year . 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 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10Panel A: Average Yearly House Return (%)

All 9.30 7.46 6.94 6.63 6.49 6.44 6.47 6.46 7.40 13.21P-1 5.14 6.47 3.77 3.79 4.06 3.98 3.93 4.47 5.49 6.62 8.87P-2 6.16 8.92 5.12 5.05 4.66 5.07 4.70 5.00 4.38 5.48 13.23P-3 6.59 8.05 6.43 4.71 5.41 5.36 5.65 4.98 5.23 7.33 12.81P-4 6.63 7.37 6.36 6.25 4.89 5.54 5.35 5.04 5.65 7.21 12.68P-5 7.35 8.47 7.92 6.81 6.02 5.64 5.85 5.68 6.34 7.23 13.60P-6 7.84 9.86 7.95 7.39 6.80 6.38 6.17 6.05 6.45 6.57 14.78P-7 8.31 10.69 8.59 8.52 7.67 6.98 6.51 6.83 6.37 6.91 14.01P-8 9.09 10.12 9.61 9.05 8.16 8.00 7.91 7.81 7.30 7.85 15.11P-9 9.15 10.64 8.72 8.45 9.00 8.50 8.85 8.80 8.05 8.11 12.35P-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 ( )All -0.56 -0.30 -0.22 -0.17 -0.12 -0.07 -0.02 0.04 0.14 0.51P-1 -0.05 -0.63 -0.30 -0.21 -0.14 -0.09 -0.03 0.03 0.10 0.22 0.56P-2 -0.04 -0.64 -0.29 -0.19 -0.13 -0.08 -0.03 0.03 0.10 0.23 0.66P-3 -0.03 -0.54 -0.27 -0.19 -0.13 -0.08 -0.04 0.02 0.09 0.20 0.60P-4 -0.04 -0.52 -0.26 -0.18 -0.13 -0.08 -0.03 0.01 0.07 0.17 0.52P-5 -0.07 -0.50 -0.31 -0.22 -0.15 -0.10 -0.06 -0.01 0.04 0.13 0.49P-6 -0.09 -0.54 -0.31 -0.24 -0.18 -0.12 -0.08 -0.03 0.03 0.11 0.51P-7 -0.11 -0.59 -0.34 -0.27 -0.20 -0.14 -0.09 -0.04 0.02 0.11 0.48P-8 -0.12 -0.56 -0.34 -0.28 -0.22 -0.17 -0.12 -0.06 0.00 0.10 0.49P-9 -0.13 -0.53 -0.33 -0.26 -0.22 -0.18 -0.13 -0.09 -0.04 0.05 0.39P-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 5.04P-1 4.06 4.04 4.04 4.02 4.03 4.10 4.08 4.07 4.08 4.05 4.05P-2 4.41 4.41 4.42 4.38 4.40 4.42 4.42 4.39 4.40 4.41 4.41P-3 4.61 4.60 4.61 4.60 4.59 4.61 4.61 4.62 4.61 4.60 4.61P-4 4.77 4.77 4.76 4.77 4.77 4.77 4.77 4.77 4.77 4.77 4.78P-5 4.92 4.92 4.91 4.93 4.92 4.92 4.92 4.91 4.92 4.92 4.93P-6 5.07 5.07 5.07 5.08 5.07 5.08 5.07 5.07 5.06 5.07 5.06P-7 5.23 5.23 5.24 5.23 5.24 5.23 5.23 5.23 5.23 5.23 5.23P-8 5.42 5.41 5.40 5.42 5.43 5.42 5.43 5.41 5.41 5.43 5.43P-9 5.67 5.66 5.67 5.66 5.67 5.67 5.67 5.68 5.66 5.66 5.66P-10 6.21 6.28 6.19 6.18 6.17 6.16 6.17 6.24 6.15 6.27 6.29

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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

(3)

where is the average annual excess housing return for zip codes . 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 MSEPanel A: Beta Only

Estimate 0.03911* 0.03256* 0.0323 0.04901SE 0.000598 0.00209

Panel B: Beta and Beta2

Estimate 0.0307* 0.02763* 0.09844* 0.2266 0.04381SE 0.00057 0.00188 0.00231

Panel C: Beta, Beta2 and lnPriceEstimate -0.10612* 0.03075* 0.09899* 0.02721* 0.3384 0.04053SE 0.00395 0.00174 0.00214 0.000779

Panel D: Beta, Beta2 and Idiosyncratic VolatilityEstimate 0.00681* 0.00475** 0.04157* 0.18029* 0.3795 0.03925SE 0.000762 0.00177 0.00247 0.00427

Panel E: Beta, Beta2, lnPrice and Idiosyncratic VolatilityEstimate -0.13944* 0.00701* 0.03958* 0.02887* 0.18847* 0.5047 0.03506SE 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-SquareEstimate 0.0122 0.16424 0.01918 0.1536 -0.32072 -0.0150 0.5586SE 0.000589 0.00189 0.000711 0.00276 0.0025 0.00078

The significance level denoted by * is 0.0001.

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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:

. (4)

where is the annual excess return on the median-price house in zip code over the average annual

return on three-month T-Bills in year . Next, average returns are regressed on linear and quadratic terms involving the beta and SMB factor loadings:

(5)

where is the average annual excess housing return for zip codes . 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.

Intercept Beta Beta2 SMB SMB2 lnPriceBetaSMB R-Sq MSE

Panel A: SMB and SMB2 onlyEstimate 0.07247* 0.00587* 0.00193* 0.2204 0.0416SE 0.0005455 0.000364 0.0000645

Panel B: Quadratic SMB and BetaEstimate 0.072* -0.0084* 0.05342* 0.00499* 0.00194* 0.2221 0.04157SE 0.000559 0.00225 0.00226 0.000433 0.00006456

Panel C: Price Effect and Quadratic SMB and Beta Estimate -0.0693* -0.00332 0.06674* 0.00647* 0.0011* 0.02761* 0.4148 0.03605SE 0.00353 0.00195 0.0023 0.000377 0.00006235 0.000696

Panel D: Additional SMB & Beta InteractionEstimate -0.07092* 0.00534** 0.12374* 0.00814* 0.00299* 0.0276* 0.0277* 0.4715 0.03425SE 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.

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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.

Intercept Beta Beta2 SMB SMB2 lnPriceBetaSMB R-Sq MSE

Panel A: SMB and SMB2 onlyEstimate 0.0353* 0.00689* 0.00386* 0.074 0.04718SE 0.00060 0.00073 0.00017

Panel B: SMB and BetaEstimate 0.03554* 0.00423** -.00070* 0.00718* 0.00431* 0.0789 0.04705SE 0.00061 0.00138 0.00012 0.00076 0.00019

Panel C: Price Effect, SMB and BetaEstimate -0.09385* 0.00506* -.00065* 0.00418* 0.00396* 0.02545* 0.1756 0.04452SE 0.00472 0.00131 0.00011 0.00073 0.00018 0.00092

Panel D: With SMB & Beta InteractionEstimate -0.09393* 0.00515* -0.00048 0.00423* 0.00399* 0.02546* 0.00039 0.1755 0.04452SE 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.

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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

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

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

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

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

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

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.

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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

Figure 9. Housing Betas By US Zip Code

50