risk and return in the u.s. housing market: a cross ... · features of the u.s. housing market....

2006 V34 4: pp. 519–552

REAL ESTATE

ECONOMICS

Risk and Return in the U.S. HousingMarket: A Cross-Sectional Asset-PricingApproachSusanne Cannon,∗ Norman G. Miller∗∗ and Gurupdesh S. Pandher∗∗∗

This article carries out an asset-pricing analysis of the U.S. metropolitan housingmarket. We use ZIP code–level housing data to study the cross-sectional role ofvolatility, price level, stock market risk and idiosyncratic volatility in explaininghousing returns. While the related literature tends to focus on the dynamic roleof volatility and housing returns within submarkets over time, our risk–returnanalysis is cross-sectional and covers the national U.S. metropolitan housingmarket. The study provides a number of important findings on the asset-pricingfeatures of the U.S. housing market. Specifically, we find (i) a positive relationbetween housing returns and volatility, with returns rising by 2.48% annuallyfor a 10% rise in volatility, (ii) a positive but diminishing price effect on returnsand (iii) that stock market risk is priced directionally in the housing market.Our results on the return-volatility-price relation are robust to (i) metropolitanstatistical area clustering effects and (ii) differences in socioeconomic charac-teristics among submarkets related to income, employment rate, managerialemployment, owner-occupied housing, gross rent and population density.

It is well known that investment assets trading in financial markets typicallyexhibit a positive relation between risk and return. For example, as an assetclass, the more volatile small-cap stocks exhibit higher returns over the longrun than large-cap stocks. Does such a relation also exist in the U.S. housingmarket where housing has the dual role of consumption and investment andwhere transaction costs and liquidity risk are high? In other words, do riskier,more volatile housing markets also provide higher returns? Furthermore, whatis the impact of the house-price level on this risk–return relation and how doesexposure to the stock market affect housing returns?

∗Department of Finance, DePaul University, Chicago, IL 60604 or [email protected].

∗∗College of Business, University of Cincinnati, Cincinnati, OH 45221-0195 or [email protected].

∗∗∗Department of Finance, DePaul University, Chicago, IL 60604 or [email protected].

C© 2006 American Real Estate and Urban Economics Association

520 Cannon, Miller and Pandher

When studying housing risk or talking about the possibility of bubbles, the na-tional market is not very relevant to most home owners. “No one owns the me-dian home in the USA or even in a MSA. They own property in a submarket.”1

In this article, we empirically examine the questions posed above by usingdisaggregate housing sale price data at the ZIP code level. Prices at this levelwill correspond more closely to an individual perspective. Here we investigatethe role of housing return volatility, price level, stock market exposure and id-iosyncratic volatility in explaining housing returns. While the related literaturetends to focus on the longitudinal role of volatility and housing returns withinmetropolitan statistical areas (MSAs), our risk–return analysis is cross-sectionaland covers the national U.S. metropolitan housing market.2 Our study uses dis-aggregate ZIP code–level housing data from the International Data ManagementCorporation (IDM) and consists of 155 MSAs and 7,234 ZIP codes. The use ofZIP codes as the spatial unit provides a more localized delineation of housingsubmarkets for examining the risk–return structure across submarkets.

We find that MSAs explain only 19.6% of the overall ZIP code–level variationin housing returns, implying that cross-sectional analysis at this level wouldeliminate 80% of the return variation in our data. This suggests that aggrega-tion to the MSA level blurs the heterogeneity of hedonic factors that definesneighborhoods more locally and masks their influence on property values. Forexample, neighborhoods with higher priced homes where households tend tobe employed in managerial occupations may be more sensitive to changes inthe stock market through an income/wealth effect. Moreover, a low-risk MSAmay 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 thatis correlated with important factors impacting property values. For example,Goodman and Thibodeau (1998, referred to as GT) propose a hierarchical hedo-nic model for identifying housing submarket boundaries based on public schoolquality 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

1 Quote from William C. Wheaton, MIT Professor, April 15, 2005, in a panel presenta-tion at the ARES meeting in Sante Fe, New Mexico, on the topic of housing prices andbubble risks.2 A number of well-known studies including Case and Shiller (1989, 1990) and, morerecently, Capozza, Hendershott and Mack (2004) are at the MSA level.3 Others have also used ZIP code data in hedonic pricing models such as Graddy (1997),or for clustering as in Goetzmann and Spiegel (1997) or Goetzmann, Spiegel and Wachter(1998) and Decker, Nielsen and Sindt (2005).

A Cross-Sectional Asset-Pricing Approach 521

while the same under the GT approach is 0.0420. The authors conclude: “In-deed, given the arcane formulation of ZIP codes, it is surprising how well theycharacterize submarkets. Moreover, they are the easiest submarket indicator touse—everyone knows his or her ZIP code” (p. 19).

Goetzmann and Spiegel (1997) also estimate ZIP code–level housing returnswhere all repeat sales in a metropolitan areas are weighted using distance func-tions based on geographical and socioeconomic characteristics. They find thatsubmarket return indices often deviate dramatically from the citywide indexin San Francisco indicating the need to further explore and understand thesedifferences in submarket price movements. In this regard broad metropolitanarea indices may be misleading to lenders and investors as a proxy for capitalappreciation or risk. Given the well established use of ZIP codes as a spatialunit, we believe that the use of ZIP codes to delineate submarkets is a reason-able and practical start to investigating the cross-sectional role of risk and returnacross 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 theU.S. metropolitan real estate market is in conformance with the general risk–return hypothesis where higher volatility is rewarded by higher return. Hous-ing 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, anda 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&P 500 index returns. We find thatsubmarkets with higher exposure to the stock market experience higher returnsover the period where the market rises (1996–1999) while returns decline whenthe market falls (2000–2003). Regression estimates imply that a submarket witha housing beta of 0.5 yields an expected 8.21% higher return over 1996–1999than a zero beta submarket, while it yields a 7.9% lower return than the zerobeta submarket over the 2000–2003 stock market downturn.

One possible explanation follows from the degree to which household incomeand wealth in various submarkets is sensitive to the wider economy, whoseleading indicator is the stock market. Houses in ZIP codes that are more sensitiveto the stock market have the potential of greater price appreciation in statesof the stock market that provide those households with higher income andwealth (when, e.g., higher corporate profits increase compensation, bonusesand stock options to managers). Because housing supply is relatively fixed


in urban submarkets in the short run, housing demand can rise sharply withincome, leading to higher housing returns in ZIP codes that are more sensitiveto the stock market. This suggests a positive relation between return and betain periods of rising stock market performance.4

The same mechanism leads to a fall in demand when the stock market de-clines because household income is affected more negatively in submarketswith greater market sensitivity. This implies a declining relation between returnand beta in falling periods of the stock market. Due to the dependence of thereturn–beta relation on the direction of the stock market, aggregation of returnsover the entire 1996–2003 period then lead to a U-shaped pattern of returnswith respect to beta (see Figures 6 and 8).

Fourth, the return-volatility-price relation identified in the article is robust to (i)MSA fixed effects and (ii) differences in socioeconomic characteristics amongsubmarkets related to income, employment rate, managerial employment,owner-occupied housing, gross rent and population density. While differencesamong the 155 MSAs explain 20% of the total return variation among ZIP codes,the inclusion of volatility and price level explains an additional 40% of the totalreturn variation. Among the six socioeconomic variables, median householdincome, gross rent and population density exert a significant positive effecton 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, theirinteraction is negative, suggesting that housing returns fall in submarkets whereincome and price level simultaneously rise. An implication of this empiricalfinding is that, for any given price level, investment in a relatively lower incomesubmarket leads to higher housing investment returns than in higher incomesubmarkets.

Finally, we analyze the house-price effect as a Fama–French type factor. This al-lows us to confirm that house prices impact the return generating process acrosssubmarkets and in not merely a statistical artifact. Fama and French (1992, re-ferred to as FF) define the “Small Minus Big” (SMB) factor as the return betweenlow and high market capitalization stocks and estimate its impact on stock re-turns by including it in the capital asset pricing model (CAPM) regression.Using the analogy between house price and a company’s market capitaliza-tion, we similarly construct the house price FF factor by sorting median-pricedhouses by ZIP code into three price ranked subportfolios each year and then

4 This result is consistent with Miller and Peng (2006), which studies volatility inMSAs using Garch modeling and finds that volatility is Granger-caused by the homeappreciation and GMP growth rates.


taking the difference between the average return between the lowest and highestpriced groups (SMB). The estimation reveals that the house price FF factor isstatistically significant in explaining housing returns in the cross-section.

There have been a number of studies on housing-price dynamics, from Ozanneand Thibodeau (1983) to Bourassa et al. (2005). Some of the empirical literatureexamines the efficiency and predictability of the housing market or explainsprice change while more recent work examines the dynamic relation betweenvolatility and house prices within localized metropolitan areas. In comparison,the focus of our article is on the cross-sectional asset-pricing relation betweenrisk, price level and housing returns across the U.S. metropolitan housing marketat the submarket level. A discussion of the related literature is given below.

In addition to Goodman and Thibodeau (2003) and Goetzmann and Spiegel(1997) as mentioned above, a number of other studies have also used ZIP codesas the spatial unit of analysis.5 Dolde and Tirtiroglu (1997) observe time-varyingvolatility and positive relations between conditional variance and returns inConnecticut and San Francisco over the period from 1971 to 1994. Dolde andTirtiroglu (2002) identified 36 volatility events in four regional housing marketsfrom 1975 to 1993 and suggest that price volatility surges are associated withchanges in economic conditions. Miller and Peng (2006) use generalizedautoregressive conditional heteroskedasticity (GARCH) models and a panelvector autoregressive (VAR) model to analyze the time variation of home valueappreciation and the interaction between volatility and economic growth. Theyfind evidence of time-varying volatility in about 17% of the MSAs and find thatvolatility is Granger-caused by the home appreciation rate and GMP growthrate.

A notable early study on housing market efficiency by Rayburn, Devaney andEvans (1987) used 15 years of housing-price data for ten submarkets of Mem-phis, Tennessee, and estimates an ARIMA time-series model of differenced logprices based on the means of sale price per square foot of single-unit residentialproperties. After adjusting for transaction costs, all submarkets were deemed

5 For example, Graddy (1997) tests for differences in prices charged by fast-food restau-rants that serve markets with customers of widely divergent incomes and ethnic back-grounds. The study finds significant differences in prices charged based on the race andincome characteristics of a ZIP code region. When income and cost differences are takeninto account, meal prices rise approximately 5% for a 50% rise in the black population.Decker, Nielsen and Sindt (2005) use a cross-sectional hedonic pricing model to in-vestigate the relationship between the U.S. Environmental Protection Agency’s ToxicsRelease Inventory (TRI) data releases and the prices of single-family residences withinpostal ZIP code areas situated in Douglas County in Omaha, Nebraska. Results improvedwhen controlling for relevant socioeconomic variables, and in this case TRI pollutantreleases were significant determinants of residential housing values.


weak-form efficient because of the inability to exploit the time-series pattern tocreate an arbitrage profit. Case and Shiller (1989, 1990) found evidence of pos-itive autocorrelation in real house prices and performed weak and strong formefficiency tests on weighted repeated sales price data for Atlanta, Chicago, Dal-las and San Francisco during the 1970–1986 period. They also analyzed theperformance of a trading rule where individuals wishing to purchase a homebuy if the forecasted price change was greater than the average price changeand, otherwise, wait a year. Based on such a system they were able to generatemodest trading profits of 1–3% for the four cities.

Guntermann and Norrbin (1991) used a market model and a dynamic multiple-indicator model to forecast mean house price changes using structural andeconomic characteristics for 15 census tracts in Lubbock, Texas. Their resultssuggest inefficiency consistent with an adaptive expectation of the market. Tir-tiroglu (1992) and Clapp and Tirtiroglu (1994) added a spatial aspect to effi-ciency tests. Using data from the Hartford, Connecticut, metropolitan area theyregressed excess returns (submarket return less metropolitan area return) onlagged excess returns of a group of neighboring towns and on a control groupof nonneighboring towns. Their results favor a spatial diffusion pattern and areconsistent with a positive feedback hypothesis.

Pollakowski and Ray (1997) performed a spatial and temporal analysis of pricediffusion at a subnational level between nine U.S. census divisions and betweenthe five largest primary metropolitan statistical areas (PMSAs) within the NewYork–Northern New Jersey–Long Island consolidated metropolitan statisticalarea (CMSA) from 1975 through 1994. Their results show that subnationalhousing price changes did not seem to follow a spatial diffusion process, whileanalysis within census divisions and for New York indicated support for thepositive-feedback hypothesis. Capozza, Hendershott and Mack (2004) exploredthe dynamics of housing price mean reversion and responses to various demandand supply variables for 62 metropolitan areas from 1979 to 1995. They foundheterogeneity in terms of the price trend responses to these economic vari-ables based on the time period and the specific MSA. Malpezzi and Wachter(2005) examined supply constraints in the natural or political sense and demon-strate that price elasticity of supply plays a key role in housing volatility. Theyconclude that speculation has a great role in price volatility when supply isless elastic. More recently, Bourassa et al. (2005) explored the causes of pricevariation within three New Zealand markets, and their analysis suggests thatthe bargaining power of buyers and sellers differs in strong versus weak mar-kets and that price changes are affected by changes in total employment. Theirwork also touches upon atypical housing attributes as influencing appreciationrates.


The remainder of the article is organized as follows. The next section describesthe data used in our cross-sectional analysis of housing returns. The role ofvolatility and price level in explaining housing returns is examined in the thirdsection. The fourth section investigates the effect of socioeconomic variablesand the fifth section relates returns to housing betas and idiosyncratic volatilityand also carries out a Fama–French style analysis for the price effect. Thesixth and final section concludes the article.

Data

Our study uses a panel data set comprising 7,234 postal ZIP codes falling in 155urban MSAs across the United States. Annual data on median ZIP code houseprices are available from IDM in the post-1995 period, and our sample spansthe period from 1995 through 2003. ZIP code–level socioeconomic data fromthe 2000 census are obtained from the Web site maintained by the Universityof 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) andpopulation density defined as persons per square mile (Popsq). The source offixed rate mortgage data is Fidelity National Financial and Freddie Mac, andthe S&P500 index is obtained from Bloomberg.

Quality-adjusted house prices (such as those provided by OFHEO, the Office ofFederal Housing Enterprise Oversight) are not available at the ZIP code level.Although the IDM data does not have very extensive time-variation, it doeshave very rich cross-sectional depth. This is a particularly attractive featureof the data for the purpose of our study, which focuses on the cross-sectionalrisk–return and asset-pricing features of the U.S. urban housing market.7

The cross-sectional depth of the data also overcomes some econometric limi-tations due to the shortness of the time series. In evaluating the role of housing

6 See http://mcdc2.missouri.edu/websas/dp3 2kmenus/us.7 Besides the IDM data, an alternative potential data source is First American, whichprovides home-price indexes from single-family residential repeat sales. The First Amer-ican website states that “repeat sales with less than one year between sale dates are notused and five percent of the data with the highest monthly increases or decreases are alsonot used.” Repeat-sales data are likely to be very thin in ZIP codes. Although these datago back further in time than IDM data, it excludes a large portion (80%) of residentialsales data. The median house price data from IDM are robust to such selection andexclusion criteria.


return volatility on housing returns, we regress average housing returns acrossZIP codes on estimates of their volatility (standard deviation of returns). Al-though the estimate of volatility is unbiased, its sampling variance is largely dueto the shortness of the time series. This implies that we have stochastic regres-sors in the cross-sectional regression (1). However, because of the large cross-sectional sample of 7,234 ZIP code observations, the regression estimators areasymptotically unbiased.8 The same applies to regression (3) where housingreturns are related to the stock market sensitivity (beta) of the submarket.

Further, as discussed above, the limitation posed by the shorter time series areameliorated and counterbalanced by the cross-sectional richness of the sampleincluding 7,234 ZIP codes. Finally, while the sample period is not long, it doesexhibit substantial temporal heterogeneity with respect to economic conditions.

Figures 1 and 2 plot the annual return on the S&P 500 index and average housingreturns across ZIP codes over 1996–2003. Fluctuations in returns on the S&P500 index range from −22% to 33%, and the stock market was a bullish andbearish mix. The years 1996, 1997, 1998 and 1999 register strong positive stockmarket returns, while strongly negative returns are observed over 2000, 2001and 2002. In 2003, market returns rise and become positive again.

Summary statistics are reported in Table 1. The reported figures are first av-eraged over the 8-year period and then averaged over ZIP codes. The averagemedian house price (Price) over 1995–2003 across the 7,234 metropolitan ZIPcodes is $188,845, while the average annualized return is 5.70% (Return). Thecorresponding volatility (Vol) of median house price returns is 14.8%. Whilehouse prices have a significant positive skew (3.330), the natural logarithmof house prices is relatively symmetric. On average, the unemployment rate(Unemp) is 5.51%, 35.4% of the households have a member employed in amanagerial occupation (Prof), 69.6% of the units are owner occupied (Owner)and the gross rent is $706. The average excess return of the S&P 500 index is9.55% over the 1995–2003 period, the average 3-month T-Bill rate is 3.92%and the annualized monthly mortgage rate is 7.15%.

8 This critical OLS condition for unbiased regression estimation is E(ε|X ) = 0 where εis the regression error and X are the regressors which may be stochastic (see White 1999,p. 7). In our cross-sectional regression (1), X = (Vol, inPrice). Although the estimate ofVol is unbiased, it has a large sampling variance due to the short time series, implyingthat it is a stochastic regressor. The size of the variance of X , however, is not relevantto the condition E(ε|X ) = 0 as long as it is finite. Therefore, the result that regressionestimators 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 alsoasymptotically unbiased due to the large cross-sectional sample of 7,234 observations.


Figure 1 � S&P 500 index returns by year. Annual returns on the S&P 500 index(RSP500) are plotted over the sample period from 1996 to 2003.

Figure 2 � Average housing returns by year. Return is the average annual return for themedian-priced house over the 7,234 ZIP codes of the U.S. metropolitan housing marketfrom 1996 to 2003.

Beta is the sensitivity of house returns to the stock market and is estimated byregressing 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 7,234ZIP codes are close to zero (−0.077), while its range is between −2.075 and2.235.


Table 1 � Descriptive statistics.

Obs. Mean Median Std. Min. Max. Kurt Skew

Price($000s) 7,234 188.845 147.462 1.753 34.480 1857.14 18.099 3.330LnPrice 7,234 1.609 1.608 0.00142 1.264 2.018 −0.073 0.076Income 7,173 51,700 48,373 242 7,619 200,001 3.999 1.391Prof 7,171 35.385 33.550 0.156 0 100 −0.134 0.521Unemp 7,171 5.512 4.327 0.049 0 76.1561 24.979 3.343Owner 7,173 69.624 73.376 0.212 1.4091 100 0.546 −0.928Rent 7,155 706 663 2.777 193 2,001 4.316 1.552Popsq 7,173 2,885 1,425 50.900 0.630 69,013 34.553 4.360Return (%) 7,234 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 7,234 −0.077 −0.093 0.003 −2.075 2.235 7.248 0.741Volatility (%) 7,234 14.845 10.188 0.158 1.386 101.440 8.044 2.551

Summary statistics for the data used in the empirical study are reported. The housing data includesannual median house prices in ZIP codes covering the urban U.S. residential housing market andcomprises a total of 155 MSAs and 7,234 ZIP codes over the period 1995–2003 (disaggregate-levelZIP code data is available only in the post-1995 period). Data sources include the International DataManagement Corporation, Bloomberg for the S&P 500 index, Fidelity National Financial and FreddieMac for fixed-rate mortgage data as well as 2000 census socioeconomic data at the ZIP code–levelmaintained 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 overZIP codes. Price is the median house price in the ZIP code (in $000s), Return is the annual return on themedian-price house, Income is the median household income at the ZIP code level, Prof is the percentageof employed in managerial occupations, Unemp is the employment rate, Owner is the percentage ofowner-occupied housing units, Rent is the gross median rent, Popsq is the number of persons per squaremile, Vol is the return volatility across ZIP codes and RSP500 is the annual return on the S&P 500 index.The Risk-Free Rate is the average monthly annualized return for 3-month T-Bills, and the same formonthly mortgage rates is given by the Mortgage Rate. Beta is the housing beta based on a CAPM–typeregression of ZIP code housing returns on S&P 500 index returns and is calculated according toEquation (2).

Figure 3 plots the housing Sharpe ratios (return per unit risk) across ZIP codesover the 8 years of the sample. For each year, it is calculated as the averagehousing return across ZIP codes divided by the standard deviation of returns.Over 1996–1999, the Sharpe ratio is below 0.28; however, it rises dramaticallyover the next 4 years and is close to 0.88 in 2003. This shift parallels the endof the secular stock market rise in 2000 and the start of the bear market from2000 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. Thepositive effect impact continued well into 2001 and 2002.

Housing Returns, Volatility and Price Level

The analysis in this section uses both ranked two-way portfolios and cross-sectional regressions to examine and quantify the effect of volatility and the


Figure 3 � Housing Sharpe ratios by year. For each year, housing Sharpe ratios arecalculated as the average housing return across ZIP codes divided by the standarddeviation of returns.

price level on housing returns. We also study the role of MSA fixed effects onthe asset pricing relation between housing returns, volatility and price level.

As an initial glimpse into the risk–return relationship across the 7,234 ZIPcodes falling in the U.S. metropolitan areas, average median house returns byZIP code are plotted against return volatility and price level in Figures 4 and 5.A discernable positive trend is apparent in both graphs.

Ranked Housing Portfolios by Price and Volatility

For each year, median-priced houses in each U.S. postal ZIP code are first sortedinto ten ranked price deciles (rows) and, then, within each price decile into tenranked volatility groups (columns). The return volatility (Vol) is the standarddeviation of annual returns on the median-priced house in the ZIP code. Averageannual housing returns by price–volatility combinations are reported in Panel Aof Table 2, while the corresponding average volatility Vol and the house prices(lnPrice) are reported in Panels B and C, respectively. “P-1” and “V-1” are thelow price and volatility deciles, respectively, while “P-10” and “V-10” are thehigh price and volatility deciles.

Table 2 exhibits the cross-sectional relation between housing return, volatilityand price level in the U.S. residential housing market. First, we find thathousing returns increase uniformly with volatility: rising from 5.31% to


Figure 4 � Risk and return in the U.S. metropolitan housing market. Return is theaverage annual return for the median-priced house across the 7,234 ZIP codes of theU.S. metropolitan housing market from 1996 to 2003. The return volatility (Vol) is thestandard deviation of returns.

Figure 5 � Return and price level in the U.S. metropolitan housing market. Return isthe average annual return over 1995–2003 for median-priced houses in the 7,234 ZIPcodes of the U.S. metropolitan housing market. lnPrice is the mean of natural logarithmof house prices ($000s) by ZIP code.

15.74% over the lowest (V-1) to the highest volatility (V-10) deciles (top row ofPanel A). Meanwhile, average volatility increases from 4.02% to 45.29% overthe same deciles (top row of Panel B). Although we examine this result furtherusing cross-sectional regressions in Tables 3–6, this is a preliminary indicationthat a risk-based asset-pricing pattern exists at the disaggregate ZIP code level in


Table 2 � Housing returns by volatility and price deciles.

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 15.74P-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 18.26Panel 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 44.11Panel 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

The housing data include a total of 7,234 ZIP codes covering the U.S. metropolitanhousing market over 1996–2003 (disaggregate-level ZIP code data is available onlyin the post-1995 period). Each year, median-priced houses in ZIP code are first sortedinto ten ranked price deciles (rows) and, then, within each price decile into ten rankedvolatility groups (columns). The return volatility (Vol) is the standard deviation ofannual housing returns. The reported figures are yearly averages over the sampleperiod. The yearly return in Panel A is the average of the return for median-pricedhouse in the price-volatility group, the average Vol is reported in Panel C and themean logarithm of median house prices in Panel C. P-1 and V-1 are the lowest houseprice and volatility deciles, respectively, while P-10 and V-10 are the highest price andvolatility deciles. The first row and column of each panel report overall averages by thelevel of price and volatility, respectively.


the U.S. housing market. Second, the positive relation between housing returnand volatility prevails uniformly at all price levels (rows P-1–P-10). Third,returns increase with the price level, from 5.14% to 10.52% (“All” column ofPanel A).

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 houseprice shows no clear trend with increasing volatility (columns). Finally, the“All” column of Panel A and B shows that the positive effect of price level onreturn is independent of volatility (which falls between 13.49% and 16.92%).

The ranked two-way results indicate (i) a strong positive relation between hous-ing returns and volatility and the price level and (ii) that these effects are inde-pendent of each other.

Cross-Sectional Regressions on Volatility and 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 priceover 1995–2003. The mean return and volatility (Vol) are computed for eachZIP code over the 8-year period.

Let ri represent the average annual return for the median-price house in ZIPcode I = 1, . . . , n (n = 7,234). To investigate the role of volatility (Vol) andprice-level on returns to housing investment, returns are decomposed using thecross-sectional regression

ri = α0 + α1 Voli + α2 lnPricei + εi (1)

where

� Vol is the return volatility for the median-priced house in each ZIP codeover 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 3 and revealthat both volatility and the price level are positively priced in the U.S. housingmarket. The coefficients for both volatility and price level are highly significantand positive, and the regression’s adjusted R2 is 0.50. An asset-pricing implica-tion of the estimated full model is as follows. The estimated coefficient for Vol


Table 3 � Cross-sectional regressions of housing returns on volatility and price level.

Intercept Vol lnPrice R2 RMSE

Estimate −10.0071∗ 0.24790∗ 0.02801∗ 0.4987 0.03533SE 0.34973 0.00326 0.006787Estimate 4.19183∗ 0.24126∗ 0.3807 0.03927SE 0.06975 0.00362

The significance level denoted by ∗ is 0.0001.Median-price house returns for 7,234 ZIP codes in the U.S. metropolitan housingmarket over 1996–2003 are regressed on volatility and market price as in (1). The meanreturn and volatility (Vol) are computed for each ZIP code over this 8-year period.lnPrice is the mean of the natural logarithm of median house prices (in $000s). SErepresents the standard error of the estimated regression coefficient. RMSE = rootmean square error.

predicts that a 10% increase in return volatility leads to an increase of 2.48% inthe median house price. Meanwhile, the regression estimate for lnPrice impliesthat a $500,000 house earns on average an additional 1.43% return annuallythan a house priced at $300,000 (calculated as 0.02801[ln(500)–ln(300)]).

Table 4 further reports the cross-sectional regression by five market segments.The metropolitan housing market consisting of 7,234 ZIP codes is separatedinto five quintile portfolios ranked by market price (Qprice = 1, 2, . . . , 5), andmodel (1) is estimated separately in each quintile. The volatility coefficient (Vol)remains relatively constant over the five market segments and is the highest forthe middle quintile (Qprice = 3). The coefficient for Vol across the five segmentsis 0.2330, 0.2573, 0.2897, 0.2438 and 0.2264, respectively. The relationship ofhousing returns and the price level is more variable. The largest value for thelnPrice coefficient occurs in the lowest quintile (3.214) and the middle quintile(4.209); the lowest value occurs in the highest quintile (1.436).

The segmented analysis reveals that the positive relation between housing returnand volatility is fairly constant across different price segments of the housingmarket. Meanwhile, the price effect, although significant and positive in all fivesegments, generally declines with the price level.

MSA Fixed Effects and the Return-Volatility-Price Relation

Goetzmann, Spiegel and Wachter (1998) define neighborhoods using ZIP codesand show that when two properties are separated in space but perceived by themarket as substitutes for each other, their prices also fluctuate together. We nowexamine whether the positive relation between housing returns and volatility


Table 4 � Cross-sectional regression of housing returns on volatility and price bymarket segment.

Intercept Vol lnPrice R2 RMSE

Lowest price quintile: Qprice = 1

Estimate −12.67579∗ 0.23302∗ 0.034139∗ 0.4613 0.034804SE 1.78398 0.00675 0.004194

Qprice = 2

Estimate −3.941 0.25734∗ 0.014619 0.4891 0.03375SE 4.41112 0.00691 0.009396

Qprice = 3

Estimate −17.34341∗∗ 0.28965∗ 0.042092∗ 0.4955 0.03740SE 5.62683 0.00771 0.00112591

Qprice = 4

Estimate −10.58323∗∗ 0.24382∗ 0.029912∗ 0.4171 0.03600SE 4.59831 0.00762 0.0086315

Highest Price Auintile: Qprice = 5

Estimate −1.85041 0.22636∗ 0.014363∗ 0.4203 0.03306SE 1.42488 0.00737 0.0024132

The significance levels denoted by ∗,∗∗ and ∗∗∗ are 0.0001, 0.002 and 0.03, respectively.Cross-sectional regressions of house price returns on return volatility and price levelare reported by market segment. The average annual return and volatility (Vol) arecomputed for 7,234 metropolitan ZIP codes over the 1996–2003 period. lnPrice is themean of the natural logarithm of median house prices (in $000s). For estimation, ZIPcodes are sorted within each year by price level and constructed into five portfoliosranked by market price (Qprice = 1, 2, . . . , 5). SE represents the standard error of theestimated regression coefficient. RMSE = root mean square error.

and price level are robust to the clustering effects from the 155 MSAs in whichthe 7,234 ZIP codes fall. This is done by including fixed effects for the MSAs inthe cross-sectional regressions of housing returns on volatility and price level(Table 3). The results of this analysis are reported in Table 5.

The coefficients for volatility and the price level continue to remain highlysignificant after the inclusion of the MSA fixed effects. Further, the magnitudeof 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 fitreveal that MSAs alone explain only 20.8% of the total return variation amongZIP codes, while the inclusion of volatility and price level explains an addi-tional 40.6% of the price return variation. This suggests that the asset-pricingrelation between volatility, price and return is robust to clustering effects fromMSAs.


Table 5 � Cross-sectional regressions with MSA fixed effects.

Estimate Estimate SE Estimate SE

MSA 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∗ 0.000838R2 0.2079 0.4941 0.6130RMSE 0.04239 0.0352 0.02963

The significance level denoted by ∗ is 0.0001.Fixed effects for MSAs are included in the cross-sectional regressions of house pricereturns on return volatility and price level of Table 3. There are a total of 154 MSA forthe 7,234 metropolitan ZIP codes in the 1996–2003 sample. SE represents the standarderror of the estimated regression coefficient. RMSE = root mean square error.

Role of Socioeconomic Variables

We now investigate whether the return-volatility-price relation identified in theprevious section continues to hold after accounting for differences in socioe-conomic characteristics among submarkets. The analysis also gives additionalinsights into the role of these variables on housing returns.

The literature provides evidence that socioeconomic factors (e.g., income, em-ployment) influence investment returns and volatility in housing submarkets.For example, Ozanne and Thibodeau (1983) determine that socioeconomicvariables are found to explain metropolitan price variation, and Goetzmannand Spiegel (1997) find median household income to be the salient variablein explaining the covariance of neighborhood housing returns. More recently,Bourassa et al. (2005) report that price changes are affected by employmentin three New Zealand submarkets, and Miller and Peng (2006) also find evi-dence that income growth and house-price appreciation Granger-caused volatil-ity changes at the MSA level. It is, therefore, important to check if the relationbetween housing returns, volatility and price level identified earlier is robust toeffects of socioeconomic variables.

Socioeconomic Variables and Hypothesis

We extend the asset-pricing analysis of the preceding section by includingZIP code–level socioeconomic variables in the cross-sectional regressions ofhouse-price returns on return volatility and price level (Table 6). These vari-ables include log-income (lnIncome), employment rate (Unemp), managerialemployment (Prof), percentage owner-occupied housing (Owner), gross rent(Rent) and population density (Popsq).


Our hypotheses regarding the effect of these variables on housing returns areas follows:

1. lnIncome has a positive effect as shown in previous studies where in-come changes and price movements are correlated.

2. Unemp has a negative effect as greater unemployment should lowerhome prices.

3. Prof may likely have a positive effect as professional employment ispositively correlated with income and education. On the other hand,neighborhoods where a high proportion of households are employedin managerial occupations may form more exclusive submarkets thatinduce a “herding” demand effect. This would lead to a premium inhouse prices and this overvaluation may be subsequently reflected inlower returns in such exclusive localities.

4. Owner has a positive effect as the greater proportion of owners shouldimply a greater vested interest in the neighborhood.

5. Rent has a positive effect as higher rents reduce affordability and shouldpush home demand. Although one might argue that the direction is viceversa, the effect is still the same.

6. PopSq has a positive effect as greater population density is shown toincrease land values and in turn housing prices.

Empirical Results

First note from the volatility coefficient (Vol) across columns A–F in Table 6that the basic risk–return relation identified earlier is robust to differences insocioeconomic characteristics across submarkets. Over the six regressions, thevolatility 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 althoughthe coefficient value rises with the inclusion of Unemp, Prof, Owner, Rent andPopsq.

Third, the regressions of columns A–D (Table 6) investigate the role of priceand income separately and jointly. Independently, both price and income havea positive impact on housing returns, and the coefficients are highly significant.Meanwhile, their interaction term is negative, suggesting that housing returnsfall in submarkets where income and price level rise simultaneously. An impli-cation of this empirical finding is that, if two submarkets have the same medianlevel of income, the one with lower prices experiences higher price apprecia-tion. The implication is that house prices catch up to household incomes oversubmarkets.


Table 6 � Cross-sectional regressions with socioeconomic variables.

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 −0.02382Prof −0.04834∗ −0.05186∗Owner 0.00611Rent 0.00797∗Popsq 0.00128∗

R2 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.Socioeconomic variables for income, managerial employment, employment rate, owner-occupiedhousing, rent and population density at the ZIP code level are included in the cross-sectionalregressions of house price returns on return volatility and price level (Table 3). lnIncome is thenatural log of median household income by ZIP code, Unemp is the employment rate, Prof is thepercentage of employed in managerial occupations, Owner is the percentage of owner-occupiedhousing units, Rent is the gross median rent and 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 ZIPcodes could not be matched to the socioeconomic data). lnPrice is the mean of logged medianhouse prices (in $000s). RMSE = root mean square error.

Fourth, in columns E and F we observe that housing returns are lower in sub-markets with higher rates of employment in managerial occupations after con-trolling for price and income (meanwhile, the unemployment rate coefficient isnegative but not statistically significant). The reason for this unexpected out-come is not apparent. One possible conjecture for this empirical finding is thatlocalities with higher household incomes form more exclusive submarkets thatbecome relatively overvalued. This herding to exclusive neighborhoods createdan ex ante premium in the acquisition price that, subsequently, results in lowergrowth rates relative to less exclusive submarkets. For example, based on theestimate for the Prof coefficient in column F, the median priced house in asubmarket where 70% of the labor force is employed in managerial professionsis expected to yield a 2.6% lower annual return than an equivalent submarketwith 20% employment in management.

Finally, the role of other local demand–supply indicators such as gross rentsand population density is positive and significant. The percentage of owner-occupied units is, however, found to be not significant after accounting for theother variables.


The asset-pricing analysis with socioeconomic variables reveals that householdincome, rents and population density have a positive effect on housing returns.Managerial employment has a negative impact while the role of owner-occupiedhousing is statistically weak. Controlling for the six socioeconomic characteris-tics among submarkets does not, however, alter the basic asset-pricing relationbetween return, volatility and price level identified earlier in Tables 3–4. Hous-ing returns still rise with both return volatility and the price level, and this resultis robust to differences in socioeconomic characteristics among submarkets.

Stock Market Exposure

This section further explores the relation between housing returns and submar-ket exposure to the stock market and idiosyncratic volatility. We also carry outa Fama and French (1992) style analysis to investigate if the price effect is pri-marily a statistical artifact or whether it is an asset-pricing factor that impactsthe return-generating process across submarkets. Because housing supply isrelatively fixed in urban submarkets in the short run, housing demand can risesharply with increases in wealth, leading to higher housing returns in ZIP codesthat are more sensitive to the stock market. This suggests a positive relationbetween return and beta in periods of rising stock market performance.

Measuring Submarket Sensitivity to the Stock Market

To estimate the sensitivity of housing submarkets to the stock market, we regressthe median housing return in each ZIP code on returns of the S&P 500 index.The estimation is analogous to the estimation of stock betas in the CAPM, whichcaptures the sensitivity of a given stock to market performance. The differencein our situation is that we relate housing returns in each ZIP code (“our stock”)to the S&P 500 index return (a common proxy for stock market performance).

Let Rit = tit − r ft represent the annual excess return on the median-price house

in ZIP code i = 1, . . . , n (n = 7,234), where the risk-free rate r ft is the aver-

age annualized return on 3-month T-Bills in year t . The house-return beta isestimated for each ZIP code using a CAPM regression for housing investmentreturns:

Rit = α0 + βi RSP500t + εt (2)

where

� RSP500 is the excess annual return on the S&P 500 index over therisk-free return in years t = 1996, . . . , 2003 and

� ε is the standard Gaussian error.


We use the housing CAPM (2) to specifically measure housing submarket sensi-tivity to the stock market. In our application, we depart from the strict theoreticalinterpretation of the market portfolio as capturing the return of all assets in theeconomy. Standard applications of the CAPM proxy the market portfolio withthe S&P 500 index, and we do the same in measuring housing exposure to thestock market. More specifically, we do not combine the returns of a diversifiedreal estate portfolio with the S&P 500 portfolio to construct a combined marketportfolio in estimating (2). Instead, we use only the S&P 500 index because ourpurpose is to specifically estimate housing submarket sensitivities only to thestock market.

Ranked Housing Portfolios by Price and Housing Betas

For each year, median-priced houses in each ZIP code are first sorted into tenranked price deciles (rows) and, then, ten ranked beta (β) groups (columns).The betas are the slopes from the regression of median-priced house returns inZIP codes on the returns of the S&P 500 index.

The average annual return for the median-priced house in each ranked price–betacombination is reported in Panel A of Table 7. The corresponding average valuesfor β and house price (lnPrice) are reported in Panels B and C, respectively. P-1and β-1 are the low price and beta deciles, respectively, while P-10 and β-10are the high price and β deciles.

Table 7 illustrates how returns on housing investment vary with stock marketexposure and the price level. First, we note from the top rows of Panels A and Bthat median housing returns have a quadratic (U-shaped) relation to beta withreturns increasing over both negative and positive betas. Note that the lowestreturn of 6.44% for the mid-beta group (β-6) rises in both directions toward thelow and high beta groups (9.30% for β-1 and 13.21% for β-10). The averagevalue of beta in the low-beta group (β-1) is −0.56 and increases to 0.51 for thehigh-beta groups (β-10).

Second, the quadratic relation between stock market sensitivity and housingreturn prevails uniformly at all price levels (P-1 to P-10), although the returnsincrease with the price level.

Third, the top row of Panel C suggests that the relation between housingreturns and beta is independent of the price level as the average lnPrice remainsrelatively 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


Table 7 � Returns by housing beta and price level.

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 13.21P-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 (β)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

The median-priced house in each of the 7,234 postal ZIP codes covering the U.S. metropolitanhousing market over 1996–2003 are first assigned to ten ranked price deciles (rows) and thensubdivided into ten ranked beta groups (columns). House return betas are the CAPM slopes wherereturns to median-priced houses by ZIP code are regressed on the excess return on the S&P 500index:

Rit = α0 + βi RSP500t + εt , t = 1996, . . . , 2003 (2)

where Rit is the annual excess return on the median-price house in ZIP code i over theaverage return on three-month T-Bills in year t . The reported figures are yearly averages overthe sample period. Panel A reports the average annual return for median-priced houses in theprice–beta group. The average beta is reported in Panel C, as is the mean logarithm of medianhouse prices. P-1 is the lowest house price decile, while P-10 is the highest price decile. Thefirst row and column of each panel report overall averages by the level of price and beta, respectively.


does not exhibit any clear pattern over the price deciles (β falls between −0.13and −0.03).

Regressions with Housing Beta and Price Level

Next, the average return for median-priced houses in the 7,234 ZIP codes ofthe U.S. metropolitan housing market (over 1995–2003) are regressed on theirsensitivity to the stock market (housing beta), price level and nonsystematicvolatility. Housing return betas are the slopes of a CAPM regression of ZIPcode housing returns on excess return on the S&P 500 index as described by (2).

The hypothesis that systematic stock market risk and idiosyncratic risk arepriced in the U.S. housing market is examined using cross-sectional regressionsof the form

Ri = α0 + α1βi + α2β2i + α3 lnPricei + α4 Sigmai + εt (3)

where the new covariate Sigma is the root mean-square error (RMSE) of theresiduals in the housing CAPM model (2), and lnPrice is the natural logarithmof median house prices (in $000s). Sigma is an estimate of the idiosyncraticvolatility in housing returns, as it is the residual return variation not explainedby the submarket’s systematic exposure to the stock market.

The quadratic relationship between return and beta that was noted earlier inthe ranked estimates of Table 7 and the U-shaped pattern is also clearly visiblein the plot of Figure 4. The squared-beta term β2

i is included to capture thisnonlinear functional relationship. Significant coefficients for beta, as well as theprice and idiosyncratic risk variables, in (3) provide evidence that these effectsare priced in the housing returns across the U.S. residential real estate market.

The estimation of (3) is reported in Table 8. First, note that inclusion of thesquared beta term (Beta2) in Panel B dramatically increases the regression fitwith the adjusted R2 rising to 0.2266 (from 0.0323); coefficients for both theBeta 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 by3.84% annually when the housing beta increases to 0.5 from zero (as calculated0.02763(0.5) + 0.09844(0.25)).

Next, the price-level effect is included in the cross-sectional regression of hous-ing returns in Panel C. The coefficient of lnPrice is highly significant, andthe R2 further rises to 0.3384. The corresponding regression estimate impliesthat a $500,000 house earns on average an additional 1.39% return annually


Figure 6 � Housing betas and returns. House-return betas are the slopes of the CAPMregression where returns on median-priced houses by ZIP code are regressed on thereturns on the S&P 500 index. Return is the average annual return over 1996–2003 formedian-priced houses in the 7,234 ZIP codes of the U.S. metropolitan housing market.

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 theadjusted R2 to 0.5047, and the coefficient for Sigma is highly significant. Theestimated regression implies that a 10% increase in nonsystematic risk leads toa 1.88% higher annual return for the median price house; the same increase intotal volatility leads to a 2.48% increase in return (Table 8 and Figure 7).

Overall, the cross-sectional regressions reveal that both stock market exposureand idiosyncratic volatility are priced in the U.S. metropolitan housing market.We next examine if the quadratic relation between return and stock marketexposure 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 9.BD = 0 for average returns over 1996–1999 and BD = 1 for the 2000–2003period.9 The estimation of the coefficients in (3) is carried out as before, andthe regression estimates are reported in Table 9.

The linear and quadratic coefficients are both highly statistically significantalong with the same effects crossed with the dummy variable (BD∗Beta andBD∗Beta2). The linear coefficient changes from 0.1642 over 1996–1999 to−0.1565 in the 2000–2003 period; similarly, the quadratic coefficient changes

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


Table 8 � Regression of housing returns on beta, price and idiosyncratic risk.

Intercept Beta Beta2 lnPrice Sigma R2 MSE

Panel A: beta onlyEstimate 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 0.03925Std. Error 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.Median-priced house returns for 7,234 ZIP codes in the U.S. metropolitan real estatemarket from 1996 to 2003 are decomposed into beta, market price and idiosyncraticvolatility using the cross-sectional regression

Ri = α0 + α1βi + α2β2i + α3 lnPricei + α4 Sigmai + εt (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 tomedian-priced houses by ZIP codes and the excess return on the S&P 500 index. Idiosyn-cratic volatility is the root mean square error (Sigma) of the residual from the CAPMregression of housing returns. lnPrice is the natural logarithm of the median houseprice (in $000s). SE represents the standard error of the estimated regression coefficient.

from 0.01918 to 0.00418. While the response of average returns to beta ispositive over the 1996–1999 period, it is negative over 2000–2003 (beta wouldhave to exceed 0.1565/0.00418 = 37.4 to give positive returns).

Hence, a complex story emerges from our period-specific analysis of the rela-tion between housing returns and stock market exposure. Over 1996–2003, wefind that submarkets with high exposure to the stock market experience higherreturns when the market rises (1996–1999). Meanwhile, returns in submarketswith greater exposure to the market fall when the market declines (2000–2003).This leads to the U-shaped pattern of returns versus beta seen in Figures 6 and8 where returns rise as beta becomes more positive and negative. One can ob-serve those markets which reveal higher betas, positive or negative, in Figure 9.California, Florida and several East Coast markets where population densities


Figure 7 � Idiosyncratic risk and housing returns. Sigma is the root mean square errorof residuals from the CAPM regression of median-priced house returns by ZIP code onreturns to the S&P 500 index. Return is the average annual return over 1996–2003 formedian-priced houses in the 7,234 ZIP codes covering the U.S. metropolitan housingmarket.

Table 9 � Housing returns and pre/post-2000 housing betas.

Intercept Beta Beta2 Sigma BD∗Beta BD∗Beta2 R2

Estimate 0.0122 0.16424 0.01918 0.1536 −0.32072 −0.0150 0.5586Standard Error 0.000589 0.00189 0.000711 0.00276 0.0025 0.00078

The significance level denoted by ∗ is 0.0001.The regression in Table 7, Panel D, is repeated with a dummy variable (BD) for thepost-1999 period. BD = 0 for average returns over 1996–1999 and BD = 1 for the2000–2003 period. The estimation of the coefficients in (3) is done as before.

are higher and land supply is less elastic are apparent in the simple shaded map.Additional explanation for the result is provided below in the conclusion.

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 statisticalartifact, or does it impact the return generating process across submarkets?

In this section, we address this issue by investigating the role of the house pricelevel as a FF asset-pricing factor. This is in the spirit of Fama and French’s(1992) definition of their SMB factor for low versus high market capitalization


Figure 8 � Housing betas and returns over 1996–1999 and 2000–2003. Averagehousing returns over the 1996–1999 (+) and 2000–2003 (0) periods are plotted againstthe housing betas of Figure 6.

Figure 9 � Housing betas by U.S. ZIP code.

stocks (meanwhile, the second FF-factor “High Minus Low” captures the returndifference between value and growth stocks, where stocks are sorted by theirmarket to book ratio). FF investigate the role of the market-cap factor in explain-ing stock performance by regressing excess returns on excess market returnsand the difference between returns to portfolios of small and large market-capstocks. If the return difference between small and large stocks is zero or stockreturns 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 factorfor stock returns.

Using the analogy of house price to stock market capitalization (market priceby 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 ZIPcodes every year into three portfolios ranked using housing prices at the startof year and then taking the difference between the average return in the highestand lowest priced groups (SMB). Starting year prices are used to avoid thecorrelation between price and return from influencing the formation of theFF price factor. Factor loading for the FF house-price factor are estimated fromthe regression of house returns onto SMB. This is done by augmenting thesubmarket CAPM regression (2) as

Rit = α0 + βi RSP500t + γi SMBt + εt . (4)

Next, the role of the FF price factor as a determinant of housing returnsacross the U.S. metropolitan housing market is tested using the cross-sectionalregression

Ri = α0 + α1βi + α2β2i + α1γi + α2γ

2i + α3 lnPricei + α3(βγ )i + εt . (5)

Similar to the quadratic effect of beta on housing returns, the FF price effect isalso nonlinear (see Figure 5), therefore, squared term γ 2

i is included to capturethe correct functional relationship. The (βγ )i term represents the interactionbetween the beta and SML. Only significant interactions are included in thereported model.

The results in Table 10 show that the FF price factor represented by SMB ispriced 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 arehighly significant, yielding a R2 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 arestatistically significant (at the 0.0001 significance level). Further, including theinteraction between beta and SMB loadings and lnPrice raises the R2 to 0.41,and both terms are highly significant.

Finally, we repeat the FF analysis above by defining the SMB factor morelocally using the first two digits of the ZIP code.10 For example, New York Cityand environs are represented by “10xxx.” In the high-priced ZIP codes, the leastexpensive houses have a tendency to appreciate by the greatest amount becausethere is a relative shortage of affordable houses. In such areas, the lowest-priced

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

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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 withthe lower-priced houses in the higher-priced ZIP codes.

SMB portfolios are now formed by sorting median-priced houses in ZIP codesinto three ranked portfolios within the two-digit ZIP codes each year and thentaking the difference between the average return in the highest and lowestpriced groups. Results from the regression estimation are reported in Table 11.Panels A–D show that the localized SMB factor is highly significant in explain-ing housing returns across submarkets. Further, its impact on returns remainsrobust to the inclusion of beta and the price level. There is, however, some re-duction in fit over the “global SMB” factor as the R2 of the complete regressionin Panel D falls to 0.175 from 0.412.

The results based on the global and more local formulation of the SMB FFfactor show that differences in returns between higher and lower priced houses(top third minus bottom third) is a systematic factor in explaining housingreturns across submarkets. Our earlier estimation found that the price levelsignificantly influences returns across ZIP codes. The FF analysis allows us todetermine that the price-level effect is not merely a statistical artifact, but anasset-pricing factor.

Conclusions

This article carries out a cross-sectional analysis of risk and return across theU.S. residential housing market. We use ZIP code–level housing data as a proxyfor submarkets to investigate the role of volatility, price level, stock marketexposure and idiosyncratic volatility on housing returns. The study provides anumber of important empirical insights into various asset-pricing features ofthe U.S. metropolitan housing market.

First, we find that median-priced houses across the 7,234 ZIP codes in theU.S. metropolitan real estate market are in conformance with the risk–returnhypothesis that higher return volatility is rewarded by higher housing return.Cross-sectional regression estimates reveal that annual housing returns increaseby 2.48% when volatility rises by 10%. Second, the return on housing invest-ment is positively affected by the price level although the price effect declineswith increasing house prices (e.g., a $500,000 house provides a 1.43% annual-ized return over a $300,000 house).

Third, we find that stock market risk is also priced in the housing market, andan interesting directional asset pricing story emerges. We measure submarketsensitivity to the stock market through housing betas estimated by regressing


housing returns on S&P 500 index returns. Submarkets with higher exposureto the stock market exhibit higher returns when the market rises (1996–1999),while returns in submarkets with greater exposure to the market decline whenthe market falls (2000–2003). These regression estimates imply that a submarketwith a housing beta of 0.5 yields a 8.2% higher return over 1996–1999 than azero beta housing submarket. Meanwhile, over the 2000–2003 downturn in thestock market, the 0.5 beta housing submarket yields a 7.9% lower return thanthe zero beta submarket.

We believe that it will be fruitful to study this empirical finding further fromboth a theoretical and empirical perspective. One possible explanation followsfrom the degree to which household income and wealth in various submarkets issensitive to the wider economy, where the leading indicator is the stock market.Houses in ZIP codes that are more sensitive to the stock market, presumablyin wealthier neighborhoods, have the potential of greater price appreciationwhen the stock market is doing well. When the stock market is rising, somehouseholds in these stock-sensitive markets have more income and wealth due tothe positive impact of the market on professional and managerial compensation(e.g., bonuses, equity and stock options). Some of this wealth may be transferredinto housing, especially if the future stock market outlook is less positive.Similarly, the same mechanism leads to a fall in demand when the stock marketdeclines as household income in submarkets with greater market sensitivity isnegatively affected. This leads to a declining relation between return and betain falling periods. Due to the dependence of the return-beta relation on thedirection of the stock market, aggregation of returns over the entire 1996–2003period then lead to the U-shaped pattern of returns with respect to beta (seeFigures 6 and 8).

We also find that the return-volatility-price relation identified in the article isrobust to (i) MSA fixed effects and (ii) differences in socioeconomic charac-teristics among submarkets related to income, employment rate, managerialemployment, owner-occupied housing, gross rent and population density. Overthe 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 in-creases with the inclusion of the socioeconomic variables. Clustering effectsfrom MSAs explain only 20% of the overall return variation across ZIP codes,while inclusion of volatility and price level explains an additional 40% of thereturn variation.

Among the six socioeconomic variables, median household income, grossrent and population density exert a significant positive effect on returns, whilepercentage managerial employment has a negative effect (the unemploymentrate and percentage owner-occupied are not significant). Further, while price


and income have a positive impact on housing returns, their interaction isnegative, suggesting that housing returns fall in submarkets where incomeand price level simultaneously rise. An implication of this empirical findingis that, given the same level of income, investment in relatively lower pricedneighborhoods leads to higher housing investment returns than in submarketswith higher house prices.

The empirical finding that returns fall with rising managerial occupation isunexpected. One conjecture for this intriguing result is that it may be induced byherding to exclusive localities by families employed in managerial professions.This ex ante buildup of a premium in the acquisition price would then result inlower subsequent returns (the estimates in Table 9 imply that a submarket with70% employment in managerial professions is expected to yield a 2.6% lowerannual return than the same with 20% managerial employment).

Finally, we find that idiosyncratic price risk is also an important determinantof returns, with a 10% increase in risk raising returns by 1.88% annually. Byits nature, housing investment is largely undiversified. This result suggests thatundiversified risk is compensated with higher returns in the real estate market.

We are thankful to the co-editor Crocker Liu and two anonymous referees forhelpful comments and suggestions that greatly improved the article. We alsothank seminar participants and the discussant at the AREUEA 2006 Annualmeeting in Boston for their comments and discussion.

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