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  • A Cross-Sectional Asset-Pricing Analysis of the U.S. Housing Market with Zip Code Data Susanne Cannon, Norman G. Miller and Gurupdesh S. Pandher∗ February 19, 2006 Abstract This paper carries out an asset-pricing analysis of the U.S. metropolitan housing market. We use zip code level housing data to study the cross-sectional role of volatility, price level, stock market risk and idiosyncratic volatility in explaining housing returns. While the related literature tends to focus on the dynamic role of volatility and housing returns within submarkets over time, our risk-return analysis is cross-sectional and covers the national U.S. metropolitan housing market. The study provides a number of important findings on the asset-pricing features of the U.S. housing market. Specifically, we find i) a positive relation between housing returns and volatility with returns rising by 2.48% annually for a 10% rise in volatility, ii) a positive but diminishing price effect on returns, iii) that stock market risk is priced directionally in the housing market and iv) idiosyncratic volatility is priced in housing returns. Our results on the return-volatility-price relation are robust to i) MSA (metropolitan statistical area) clustering effects and ii) differences in socioeconomic characteristics among submarkets related to income, employment rate, managerial employment, owner occupied housing, gross rent and population density. Keywords: housing submarkets, risk and return, asset-pricing, volatility, CAPM, Fama- French. *Norm Miller is with the College of Business at the University of Cincinnati and Susanne Cannon and Gurupdesh Pandher are with the Department of Finance at DePaul University (the corresponding author may be contacted at gpandher@depaul.edu, 312-362-5915). The authors are thankful to the Co-Editor Crocker Liu and two anonymous referees for helpful comments and suggestions that greatly improved the paper. We also thank seminar participants and the discussant at the AREUEA 2006 Annual meeting in Boston for their comments and discussion.
  • I. INTRODUCTION It is well known that investment assets trading in financial markets typically exhibit a positive relation between risk and return. For example, as an asset class, the more volatile small-cap stocks exhibit higher returns over the long run than large-cap stocks. Does such a relation also exist in the U.S. housing market where housing has the dual role of consumption and investment and where transaction costs and liquidity risk are high? In other words, do riskier more volatile housing markets also provide higher returns? Furthermore, what is the impact of the house price-level on this risk-return relation and how does exposure to the stock market affect housing returns? “No one owns the median home in the USA or even in a MSA. They own property in a submarket.”1 When studying housing risk or talking about the possibility of bubbles, the national market is not very relevant to most home owners. In this paper, we empirically examine the questions posed above by using disaggregate housing sale price data at the zip code level. Prices at this level will correspond more closely to an individual perspective. Here we investigate the role of housing return volatility, price level, stock market exposure and idiosyncratic volatility in explaining housing returns. While the related literature tends to focus on the longitudinal role of volatility and housing returns within metropolitan statistical areas (MSAs), our risk-return analysis is cross-sectional and covers the national U.S. metropolitan housing market.2 Our study uses disaggregate zip code level housing data from the International Data Management Corporation (IDM) and consists of 155 MSAs and 7,234 zip codes. The use of zip codes as the spatial unit provides a more localized delineation of housing submarkets for examining the risk-return structure across submarkets. 1 Quote from William C. Wheaton, MIT Professor, April 15th 2005 in a panel presentation at the ARES meeting in Sante Fe, NM on the topic of housing prices and bubble risks. 2A number of well known studies including Case and Shiller (1989, 1990) and, more recently, Capozza, Hendershott and Mack (2004) are at the MSA level. 2
  • We find that MSAs explain only 19.6% of the overall zip-code level variation in housing returns, implying that cross-sectional analysis at this level would eliminate 80% of the return variation in our data. This suggests that aggregation to the MSA level blurs the heterogeneity of hedonic factors that defines neighborhoods more locally and masks their influence on property values. For example, neighborhoods with higher priced homes where households tend to be employed in managerial occupations may be more sensitive to changes in the stock market through an income/wealth effect. Moreover, a low risk MSA may still contain higher risk submarkets and vice versa. While there is some arbitrariness in the use of zip codes to define submarkets, empirical studies show that they provide a reasonable spatial delineation that is correlated with important factors impacting property values. For example, Goodman and Thibodeau (1998, GT) propose a hierarchical hedonic model for identifying housing submarket boundaries based on public school quality which is used to estimate property value by Goodman and Thibodeau (2003)3. The study finds that the prediction mean square error for (logged) house prices is 0.04335 when zip codes are used to define neighborhoods while the same under the GT approach is 0.0420. The authors conclude (page 19): “Indeed, given the arcane formulation of zip codes, it is surprising how well they characterize submarkets. Moreover, they are the easiest submarket indicator to use – everyone knows his or her zip code”. Goetzmann and Speigel (1997) also estimate zip code level housing returns where all repeat-sales in a metropolitan areas are weighted using distance functions based on geographical and socio-economic characteristics. They find that submarket return indices often deviate dramatically from the city-wide index in San Francisco indicating the need to further explore and understand these differences in submarket price movements. In this regard broad metropolitan area indices may be misleading to lenders and investors as 3Others have also used zip code data in hedonic pricing models such as Graddy (1997), or for clustering as in Goetzman and Speigel (1997) or Goetzman, Speigel and Wachter (1998) and Decker et.al. (2005). 3 View slide
  • 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 4 View slide
  • relatively fixed in urban submarkets in the short-run, housing demand can rise sharply with income, leading to higher housing returns in zip codes that are more sensitive to the stock market. This suggests a positive relation between return and beta in periods of rising stock market performance.4 The same mechanism leads to a fall in demand when the stock market declines because household income is affected more negatively in submarkets with greater market sensitivity. This implies a declining relation between return and beta in falling periods of the stock market. Due to the dependence of the return-beta relation on the direction of the stock market, aggregation of returns over the entire 1996-2003 period then lead to a “U-shaped” pattern of returns with respect to beta (see Figure 6 and 8). Fourth, the return-volatility-price relation identified in the paper is robust to i) MSA fixed effects and ii) differences in socioeconomic characteristics among submarkets related to income, employment rate, managerial employment, owner occupied housing, gross rent and population density. While differences among the 155 metropolitan statistical areas (MSAs) explain 20% of the total return variation among zip codes, the inclusion of volatility and price level explains an additional 40% of the total return variation. Among the six socioeconomic variables, median household income, gross rent and population density exert a significant positive effect on returns while percentage managerial employment have a negative effect (the unemployment rate and percentage owner-occupied are not significant). Further, while price and income have a positive impact on housing returns, their interaction is negative, suggesting that housing returns fall in submarkets where income and price level simultaneously rise. An implication of this empirical finding is that for any given price level, investment in a relatively lower income submarket leads to higher housing investment returns than in higher income submarkets. 4This result is consistent with Miller and Peng (2006) which studies volatility in MSAs using Garch modeling and finds that volatility is Granger-caused by the home appreciation and GMP growth rates. 5
  • Fifth, we find that idiosyncratic price risk is also an important determinant of returns with a 10% increase in idiosyncratic volatility raising returns by 1.88% annually. Since housing investment is largely undiversified, this result implies that undiversified risk is compensated with higher returns in the real estate market. Lastly, we analyze the house price effect as a Fama-French type factor. This allows us to confirm that house prices impact the return generating process across submarkets and in not merely a statistical artifact. Fama and French (1992) define the “Small Minus Big” (SMB) factor as the return between low and high market capitalization stocks and estimate its impact on stock returns by including it in the CAPM regression. Using the analogy between house price and a company’s market-capitalization, we similarly construct the house price FF factor by sorting median-priced houses by zip code into three price ranked sub-portfolios each year and then taking the difference between the average return between the lowest and highest priced groups (SMB). The estimation reveals that the house price FF factor is statistically significant in explaining housing returns in the cross-section. There have been a number of studies on housing price dynamics, from Ozanne and Thibodeau (1983) to Bourassa et al (2005). Some of the empirical literature examines the efficiency and predictability of the housing market or explains price change while more recent work examines the dynamic relation between volatility and house prices within localized metropolitan areas. In comparison, the focus of our paper is on the cross-sectional asset-pricing relation between risk, price level and housing returns across the U.S. metropolitan housing market at the submarket level. A discussion of the related literature is given below. In addition to Goodman and Thibodeau (2003) and Goetzman and Speigel (1997) mentioned above, a number of other studies have also used zip codes as the spatial unit of analysis.5 Dolde and Tirtiroglu (1997) observe time-varying volatility and positive 5For example, Graddy (1997) tests for differences in prices charged by fast-food restaurants that serve markets with customers of widely divergent incomes and ethnic backgrounds. The study finds significant 6
  • relations between conditional variance and returns in Connecticut and San Francisco over the period from 1971 to 1994. Dolde and Tirtiroglu (2002) identified 36 volatility events in four regional housing markets from 1975 to 1993 and suggest that price volatility surges are associated with changes in economic conditions. Miller and Peng (2006) use GARCH models and a panel VAR model to analyze the time variation of home value appreciation and the interaction between volatility and economic growth. They find evidence of time varying volatility in about 17% of the MSAs and find that volatility is Granger-caused by the home appreciation rate and GMP growth rate. A notable early study on housing market efficiency by Rayburn, Devaney and Evans (1987) used 15 years of housing price data for 10 submarkets of Memphis, TN, and estimates an ARIMA time series model of differenced log prices based on the means of sale price per square foot of single-unit residential properties. After adjusting for transaction costs, all submarkets were deemed weak-form efficient because of the inability to exploit the time-series pattern to create an arbitrage profit. High transactions costs in the housing market make it very difficult to exploit all but the strongest of disequilibrium’s for those confident enough to be sure that price corrections are due. Case and Shiller (1989, 1990) found evidence of positive autocorrelation in real house prices and performed weak and strong form efficiency tests on weighted repeated sales price data for Atlanta, Chicago, Dallas and San Francisco during the 1970–1986 period. They also analyzed the performance of a trading rule where individuals wishing to purchase a home buy if the forecasted price change was greater than the average price change and, otherwise, wait a year. Based on such a system they were able to generate modest trading profits of 1 to 3 percent for the four cities. differences in prices charged based on the race and income characteristics of a zip-code region. When income and cost differences are taken into account, meal prices rise approximately 5 percent for a 50 percent rise in the black population. Decker et. al. (2005) used a cross-sectional hedonic pricing model to investigate the relationship between the U.S. Environmental Protection Agency's (EPA) Toxics Release Inventory (TRI) data releases and the prices of single-family residences within postal zip code areas situated in Omaha, Nebraska's Douglas County. Results improved when controlling for relevant socioeconomic variables and in this case TRI pollutant releases were significant determinants of residential housing values. 7
  • Guntermann and Norrbin (1991) used a market model and a dynamic multiple- indicator model to forecast mean house price changes using structural and economic characteristics for 15 census tracts in Lubbock, TX. Their results suggest inefficiency consistent with an adaptive-expectations of the market. Tirtiroglu (1992) and Clapp and Tirtiroglu (1994) added a spatial aspect to efficiency tests. Using data from Hartford, CT, metropolitan area, they regressed excess returns (submarket return less metropolitan area return) on lagged excess returns of a group of neighboring towns and on a “control group” of non-neighboring towns. Their results favor a spatial diffusion pattern and are consistent with a positive feedback hypothesis. Pollakowski and Ray (1997) performed a spatial and temporal analysis of price diffusion at a sub-national level between nine U.S. census divisions and between the five largest PMSAs within the New York–Northern New Jersey–Long Island consolidated metropolitan statistical area (CMSA) from 1975 through 1994. Their results show that sub-national housing price changes did not seem to follow a spatial diffusion process while analysis within census divisions and for New York indicated support for the positive-feedback hypothesis. Capozza, Hendershott and Mack (2004) explored the dynamics of housing price mean reversion and responses to various demand and supply variables for 62 metro areas from 1979 to 1995. They found heterogeneity in terms of the price trend responses to these economic variables based on the time period and the specific MSA. Malpezzi and Wachter (2005) examined supply constraints in the natural or political sense and demonstrate that price elasticity of supply plays a key role in housing volatility. They conclude that speculation has a great role in price volatility when supply is less elastic. More recently, Bourassa, Haurin, et al (2005), explored the causes of price variation within three New Zealand markets and their analysis suggests that the bargaining power of buyers and sellers differs in strong versus weak markets and that price changes are affected by changes in total employment. Their work also touches upon atypical housing attributes as influencing appreciation rates. 8
  • 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 9
  • study which focuses on the cross-sectional risk-return and asset pricing features of the U.S. urban housing market.7 The cross-sectional depth of the data also overcomes some econometric limitations due to the shortness of the time series. In evaluating the role of housing return volatility on housing returns, we regress average housing returns across zip codes on estimates of their volatility (standard deviation of returns). Although the estimate of volatility is unbiased, its sampling variance is large due to the shortness of the time series. This implies that we have stochastic regressors in the cross-sectional regression (1) of Section III. However, because of the large cross-sectional sample of 7,234 zip code observations, the regression estimators are asymptotically unbiased8. The same applies to regression (3) where housing returns are related to the stock market sensitivity (beta) of the submarket. Further, as discussed above, the limitation posed by the shorter time series are ameliorated and counterbalanced by the cross-sectional richness of the sample including 7,234 zip codes. Lastly, while the sample period is not long, it does exhibit substantial temporal heterogeneity with respect to economic conditions. [Figure 1 and 2 about here] 7Besides the IDM data, an alternative potential data source is First American which provides home price indexes from single family residential repeat sales. The First American website states that “repeat sales i with less than one year between sale dates are not used and five percent of the data with the highest monthly increases or decreases are also not used.” Repeat sales data is likely to be very thin in zip codes. Although, this data goes back further in time than IDM data, it excludes a large portion (80%) of residential sales data. The median house price data from IDM are robust to such selection and exclusion criteria. 8This critical OLS condition for unbiased regression estimation is E (ε | X ) = 0 where ε is the regression error and X are the regressors which may be stochastic (see White (1999, p. 7)). In our cross-sectional regression (1) of Section III, X = (Vol , ln Pr ice) . Although the estimate of Vol is unbiased, it has a large sampling variance due to the short time series, implying that it is a stochastic regressor. The size of the variance of X , however, is not relevant to the condition E (ε | X ) = 0 as long as it is finite. Therefore, the result that regression estimators with stochastic regressors are asymptotically unbiased under E (ε | X ) = 0 (White (1999, p. 20)) allows us to assert that the regression estimators for (1) are also asymptotically unbiased due to the large cross-sectional sample of 7,234 observations. 10
  • Figure 1 and 2 plot the annual return on the S&P500 index and average housing returns across zip codes over 1996 to 2003. Fluctuations in returns on the S&P500 index range from -22% to 33% and the stock market was a mix of a bullish and bearish. The years 1996, 1997, 1998 and 1999 register strong positive stock market returns while strongly negative returns are observed over 2000, 2001 and 2002. In 2003, market returns rise and become positive again. Summary statistics are reported in Table I. The reported figures are first averaged over the eight year period and then averaged over zip codes. The average median house price (Price) over 1995-2003 across the 7,234 metropolitan zip codes is $188,845 while the average annualized return is 5.70% (Return). The corresponding volatility (Vol) of median house price returns is 14.8%. While house prices have a significant positive skew (3.330), the natural logarithm of house prices is relatively symmetric. On average, the unemployment rate (Unemp) is 5.51%, 35.4% of the households have a member employed in a managerial occupation (Prof), 69.6% of the units are owner occupied (Owner) and the gross rent is $706. The average excess return of the S&P500 index is 9.55% over the 1995-2003 period, the average three-month T-Bill rate is 3.92%, and the annualized monthly mortgage rate is 7.15%. Beta is the sensitivity of house returns to the stock market and is estimated by regressing returns for the median-priced house in each zip code on the S&P500 index (see equation (2)). The average house return betas for the 7,234 zip codes is close to zero (-0.077) while its range is between -2.075 and 2.235. [Table I about here] Figure 3 plots the housing Sharpe ratios (return per unit risk) across zip codes over the eight years of the sample. For each year, it is calculated as the average housing return across zip codes divided by the standard deviation of returns. Over 1996-1999, the 11
  • 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] 12
  • 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 13
  • preliminary indication that a risk-based asset-pricing pattern exists at the disaggregate zip code level in the U.S. housing market. Second, the positive relation between housing return and volatility prevails uniformly at all price levels (rows “P-1” to “P-10”). Third, returns increase with the price level, from 5.14% to 10.52% (“All” column of Panel A). [Table II about here] Fourth, the top row of Panel C suggests that the increase in return of the median- priced house due to volatility is independent of price-level as the average house price shows no clear trend with increasing volatility (columns). Lastly, the “ALL” column of Panel A and B shows that the positive effect of price-level on return is independent of volatility (which falls between 13.49% and 16.92%). The ranked two-way results indicate a i) strong positive relation between housing returns and volatility and the price-level and ii) these effects are independent of each other. B. Cross-Sectional Regressions on Volatility & Price-level Next, median-priced house returns for the 7,234 zip codes covering the U.S. metropolitan housing market are regressed on return volatility and market price over 1995-2003. The mean return and volatility (Vol) are computed for each zip code over the eight-year period. Let ri represent the average annual return for the median-price house in zip code i = 1,..., n ( n = 7234) . To investigate the role of volatility (Vol) and price-level on returns to housing investment, returns are decomposed using the cross-sectional regression ri = α 0 + α 1Voli + α 2 ln Pr icei + ε i (1) 14
  • where  Vol is the return volatility for the median-priced house in each zip code over the years 1996-2003,  LnPrice is the average of the natural logarithm of house prices (in $000s), and,  ε is the standard Gaussian error. Results from the cross-sectional regressions are reported in Table III and reveal that both volatility and the price-level are positively priced in the U.S. housing market. The coefficients for both volatility and price-level are highly significant and positive and the regression’s adjusted R-square is 0.50. An asset pricing implication of the estimated full model is as follows. The estimated coefficient for Vol predicts that a 10% increase in return volatility leads to an increase of 2.48% in the median house price. Meanwhile, the regression estimate for ln(Price) implies that a $500,000 house earns on average an additional 1.43% return annually than a house priced at $300,000 (calculated as 0.02801[ln(500) – ln(300)]). [Table III about here] Table IV further reports the cross-sectional regression by five market segments. The metropolitan housing market consisting of 7,234 zips is separated into five ranked quintile portfolios by market price (Qprice = 1, 2, . . ., 5) and model (1) is estimated separately in each quintile. The volatility coefficient (Vol) remains relatively constant over the five market segments and is the highest for the middle quintile (Qprice=3). The coefficient for Vol across the five segments are 0.2330, 0.2573, 0.2897, 0.2438 and 0.2264, respectively. The relationship of housing returns and the price level is more variable. The largest value for the LnPrice coefficient occurs in the lowest quintile (3.214) and the middle quintile (4.209), the lowest value occurs in the highest quintile (1.436). 15
  • 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] 16
  • 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. 17
  • (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 Rit = rit − rt represent the annual excess return on the median-price house in f zip code i = 1,..., n ( n = 7234) where the risk-free rate rt is the average annualized f return on three-month T-Bills in year t . The house-return beta is estimated for each zip code using a CAPM regression for housing investment returns Rit = α 0 + β i RSP500 t + ε t (2) where  RSP500 is the excess annual return on the S&P500 index over the risk-free return in years t = 1996,...,2003 ,  ε is the standard Gaussian error. 21
  • We use the “housing CAPM” (2) to specifically measure housing submarket sensitivity to the stock market. In our application, we depart from the strict theoretical interpretation of the market portfolio as capturing the return of all assets in the economy. Standard applications of the CAPM proxy the market portfolio with the S&P500 index and we do the same in measuring housing exposure to the stock market. More specifically, we do not combine the returns of a diversified real-estate portfolio with the S&P500 portfolio to construct a combined market portfolio in estimating (2). Instead, we use only the S&P500 index because our purpose is to specifically estimate housing submarket sensitivities only to the stock market. B. Ranked Housing Portfolios – by Price & Housing Betas For each year, median-priced houses in each zip code are first sorted into ten ranked price deciles (rows) and, then, ten ranked beta β groups (columns). The betas are the slopes from the regression of median-priced house returns in zip codes on the returns of the S&P500 index. The average annual return for the median-priced house in each ranked price-beta combination is reported in Panel A of Table VII. The corresponding average values for β and house price (lnPrice) are reported in Panels B and C, respectively. “P-1” and “ β -1” are the low price and beta deciles, respectively, while “P-10” and “ β -10” are the high price and β deciles. Table VII illustrates how returns on housing investment vary with stock market exposure and the price level. First, we note from the top rows of Panel A and B that median housing returns have a quadratic (“U-shaped”) relation to beta with returns increasing over both negative and positive betas. Note that the lowest return of 6.44% for the mid-beta group ( β -6) rises in both directions towards the low and high beta groups 22
  • (9.30% for β -1 and 13.21% for β -10). The average value of beta in the low-beta group ( β -1) is -0.56 and increases to 0.51 for the high-beta groups ( β -10). Second, the quadratic relation between stock market sensitivity and housing return prevails uniformly at all price levels (“P-1” to “P-10”), although the returns increase with the price level. Third, the top row of Panel C suggests that the relation between housing returns and beta is independent of the price level as the average lnPrice remains relatively constant over price deciles (columns). Fourth, we note from the “ALL” column of Panel A and B that i) house returns increase with the price-level (from 5.14% to 10.52%) and ii) the price effect is independent of beta as it does not exhibit any clear pattern over the price deciles ( β falls between -0.13 and -0.03). [Table VII about here] C. Regressions with Housing Beta & Price-level Next, the average return for median-priced houses in the 7,234 zip codes of the U.S. metropolitan housing market (over 1995-2003) are regressed on their sensitivity to the stock market (housing beta), price level and non-systematic volatility. Housing return betas are the slopes of a CAPM regression of zip code housing returns on excess return on the S&P500 index as described by (2). The hypothesis that systematic stock market risk and idiosyncratic risk are priced in the U.S. housing market is examined using cross-sectional regressions of the form Ri = α 0 + α 1 β i + α 2 β i2 + α 3 ln Pr icei + α 4 Sigmai + ε t (3) where the new covariate Sigma is the root mean-square error (RMSE) of the residuals in the housing CAPM model (2) and LnPrice is the natural logarithm of median house prices (in $000s). Sigma is an estimate of the idiosyncratic volatility in housing returns 23
  • as it is the residual return variation not explained by the submarket’s systematic exposure to the stock market. The quadratic relationship between return and beta that was noted earlier in the ranked estimates of Table VII and the “U-shaped” pattern is also clearly visible in the plot of Figure 4. The squared-beta term β i2 is included to capture this non-linear functional relationship. Significant coefficients for beta, as well as the price and idiosyncratic risk variables, in (3) provide evidence that these effects are priced in the housing returns across the U.S. residential real-estate market. [Figure 6 about here] The estimation of (3) is reported in Table VIII. First, note that inclusion of the squared beta term (Beta2) in Panel B dramatically increases the regression fit with the adjusted R-square rising to 0.2266 (from 0.0323) ; coefficients for both the Beta and Beta2 terms are highly statistically significant (p-value < 0.0001). The quadratic relationship between housing returns is also visible in the return-beta graph of Figure 6. The estimates imply that median house prices rise by 3.84% annually when the housing beta increases to 0.5 from zero ( as calculated 0.02763(0.5) + 0.09844(0.25)). Next, the price-level effect is included in the cross-sectional regression of housing returns in Panel C. The coefficient of lnPrice is highly significant and the R-square further rises to 0.3384. The corresponding regression estimate implies that a $500,000 house earns on average an additional 1.39% return annually compared to a median-priced house priced at $300,000 (0.02721[ln(500) – ln(300)]). Idiosyncratic housing return volatility is introduced in Panel E. This raises the adjusted R-square to .5047 and the coefficient for Sigma is highly significant. The estimated regression implies that a 10% increase in non-systematic risk leads to a 1.88% 24
  • higher annual return for the median price house; the same increase in total volatility leads to a 2.48% increase in return (Table VIII and Figure 7). [Table VIII about here] [Figure 7 about here] Overall, the cross-sectional regressions reveal that both stock market exposure and idiosyncratic volatility are priced in the U.S. metropolitan housing market. We next examine if the quadratic relation between return and stock market exposure is explained by changes in the stock market. A dummy variable (BD) for the post-1999 period is included in the full model (Panel D) of Table IX. BD=0 for average returns over 1996-1999 and BD=1 for the 2000-2003 period9. The estimation of the coefficients in (3) is carried out as before and the regression estimates are reported in Table IX. The linear and quadratic coefficients are both highly statistically significant along with the same effects crossed with the dummy variable (BD*Beta and BD*Beta2). The linear coefficient changes from 0.1642 over 1996-1999 to -0.1565 in the 2000-2003 period; similarly, the quadratic coefficient changes from 0.01918 to 0.00418. While the response of average returns to beta is positive over the 1996-1999 period, it is negative over 2000-2003 (beta would have to exceed 0.1565/0.00418=37 .4 to give positive returns). [Table IX about here] [Figure 7 about here] Hence, a complex story emerges from our period-specific analysis of the relation between housing returns and stock market exposure. Over 1996 to 2003, we find that 9The authors are thankful to an anonymous referee for suggesting this analysis. 25
  • submarkets with high exposure to the stock market experience higher returns when the market rises (1996-1999). Meanwhile, returns in submarkets with greater exposure to the market fall when the market declines (2000-2003). This leads to the “U-shaped” pattern of returns vs. beta seen in Figures 6 and 8 where returns rise as beta becomes more positive and negative. One can observe those markets which reveal higher betas, positive or negative, in Figure 9. California, Florida and several East Coast markets where population densities are higher and land supply is less elastic are apparent in the simple shaded map. Additional explanation for the result is provided in Section VI below. [Figure 8 about here] [Figure 9 about here] D. House Price-level as a Fama-French Factor Is the price effect identified above as influencing housing returns an asset-pricing factor across submarkets? In other words, is it primarily a statistical artifact or does it impact the return generating process across submarkets? In this section, we address this issue by investigating the role of the house price level as a Fama-French (FF) asset-pricing factor. This is in the spirit of Fama and French’s(1992) definition of their “Small Minus Big” (SMB) factor for low vs. high market capitalization stocks (meanwhile, the second FF-factor “High Minus Low” (HML) captures the return difference between value and growth stocks, where stocks are sorted by their market to book ratio). FF investigate the role of the market-cap factor in explaining stock performance by regressing excess returns on excess market returns and the difference between returns to portfolios of small and large market cap stocks. If the return difference between small and large stocks is zero or stock returns do not exhibit any sensitivity to return differences in the small and large market-cap portfolios, then the SMB factor would not be an asset-pricing factor for stock returns. 26
  • Using the analogy of house price to stock market-capitalization (market price by shares outstanding), we construct the house price FF factor using median-priced houses in zip code. The FF house price factor is based on sorting zip codes every year into three portfolios ranked using housing prices at the start of year and then taking the difference between the average return in the highest and lowest priced groups (SMB). Starting year prices are used to avoid the correlation between price and return from influencing the formation of the FF-price factor. Factor loading for the FF house price factor are estimated from the regression of house returns onto SMB. This is done by augmenting the submarket CAPM regression (2) as Rit = α 0 + β i RSP500 t + γ i SMBt + ε t . (4) Next, the role of the FF-price factor as a determinant of housing returns across the U.S. metropolitan housing market is tested using the cross-sectional regression Ri = α 0 + α 1 β i + α 2 β i2 + α 1γ i + α 2γ i2 + α 3 ln Pr icei + α 3 ( βγ ) i + ε t . (5) Similar to the quadratic effect of beta on housing returns, the FF-price effect is also non- linear (see Figure 5), therefore, squared term γ i2 is included to capture the correct functional relationship. The ( βγ ) i term represents the interaction between the beta and SML. Only significant interactions are included in the reported model. The results in Table X show that the FF-price factor represented by SMB is priced in housing returns and, once again the relationship is quadratic in nature. Panel A shows that both the linear and squared factor loadings for SMB are highly significant, yielding a R-square of 0.21. Inclusion of the beta loadings (Panel B) increases the fit to 0.27 and all linear and quadratic terms for beta and SMB are statistically significant (at the 0.0001 significance level). Further, including the interaction between beta and SMB loadings and lnPrice raises the R-square to 0.41 and both terms are highly significant. [Table X about here] 27
  • Lastly, we repeat the FF analysis above by defining the SMB factor more locally using the first two digits of the zip code10. For example, New York City and environs are represented by “10xxx”. In the high-priced zip codes, the least expensive houses have a tendency to appreciate by the greatest amount because there is a relative shortage of “affordable” houses. In such areas, the lowest-priced homes are likely to be “tear- downs” purchased solely for the location. Conversely, the more expensive homes in the lower-priced zip codes will be mixed with the lower priced houses in the higher-priced zip codes. SMB portfolios are now formed by sorting median-priced houses in zip codes into three ranked portfolios within the two-digit zip codes each year and then taking the difference between the average return in the highest and lowest priced groups. Results from the regression estimation are reported in Table XI. Panels A-D show that the localized SMB factor is highly significant in explaining housing returns across submarkets. Further, its impact on returns remains robust to the inclusion of beta and the price level. There is, however, some reduction in fit over the “global SMB” factor as the R-square of the complete regression in Panel D falls to 0.175 from 0.412. [Table XI about here] The results based on the global and more local formulation of the SMB Fama- French Factor show that differences in returns between higher and lower priced houses (top third minus bottom third) is a systematic factor in explaining housing returns across submarkets. Our earlier estimation found that the price-level significantly influences returns across zip codes. The FF analysis allows us to determine that the price-level effect is not merely a statistical artifact, but an asset-pricing factor. 10We are thankful to one of the referees for suggesting this analysis. 28
  • 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
  • REFERENCES Bourassa, Steven C., Haurin, Donald R., Haurin, Jessica L., Hoesli, Martin Edward Ralph and Sun, Jian, "House Price Changes and Idiosyncratic Risk: The Impact of Property Characteristics" (November 2005). FAME Research Paper No. 160. Capozza, Dennis R., Patric H. Hendershott and Charlotte Mack, 2004, “An Anatomy of Price Dynamics in Illiquid Markets: Analysis and Evidence from Local Housing Markets”. Real Estate Economics, 32(1), 1-32. Case, Karl E. and Robert Shiller, 1989, “The Efficiency of the Market for Single Family Homes.” American Economic Review, 79(1), 125-37. Case, Karl E. and Robert Shiller, 1990, “Forecasting Prices and Excess Returns in the Housing Market.” AREUEA Journal, 18(3), 253-73. Clapp, John M. and Dogan Tirtiroglu, 1994, “Positive Feedback Trading and Diffusion of Asset Price Changes: Evidence from Housing Transactions.” Journal of Economic Behavior and Organization, 24, 337-55. Decker, Christopher, Donald Nielsen and Roger Sindt, 2005, "Residential Property Values and Community Right-to-Know Laws: Has the Toxics Release Inventory Had an Impact?" Growth and Change, 36 (1), 113-133. Dolde, Walter and Dogan Tirtiroglue, 1997, “Temporal and Spatial Information Diffusion in Real Estate Price Changes and Variances.” Real Estate Economics, 25(4), 539-65. Dolde, Walter and Dogan Tirtiroglue, 2002, “Housing Price Volatility Changes and Their Effects.” Real Estate Economics, 30(1), 41-66. Evenson, Bengte, 2003, “Understanding House Price Volatility: Measuring and Explaining the Supply Side of Metropolitan Area Housing Markets.” Illinois State University Working Paper. Fama, Eugene. F. and Kenneth French, 1992, “The cross-section of expected stock returns”, Journal of Finance, 47, 427-465. Flavin, Marjorie and Takashi Yamashita, 2002, “Owner-Occupied Housing and the Composition of the Household Portfolio.” American Economic Review, 92, 345-62. Gillen, Kevin, Thomas Thibodeau and Susan Wachter, 2001, “Anistrophic Autocorrelation in House Prices.” Journal of Real Estate Finance and Economics, 23(1), 5-30. Goetzmann, William, Matthew Spiegel and Susan Wachter, 1998, “Do Cities and Suburbs Cluster?”, Journal of Policy Development and Research, 3(3), 193-203. 32
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  • Table I. Descriptive Statistics Summary statistics for the data used in the empirical study are reported. The housing data includes annual median house prices in zip codes covering the urban U.S. residential housing market and comprises a total of 155 metropolitan statistics areas (MSAs) and 7,234 zip codes over the period 1995-2003 (disaggregate- level zip code data is available only in the post-1995 period). Data sources include the International Data Management Corporation (IDM), Bloomberg for the S&P 500 index, Fidelity National Financial and Freddie Mac for fixed rate mortgage data and 2000 census socioeconomic data at the zip code level maintained by the University of Missouri (http://mcdc2.missouri.edu/websas/dp3_2kmenus/us). The reported figures are means obtained by first averaging over the sample period and then averaging over zip codes. Price is the median house price in the zip code (in $000s), Return is the annual return on the median-price house, Income is the median household income at the zip code level, Prof is the percentage of employed in managerial occupations, Unemp is the employment rate, Owner is the percentage of owner-occupied housing units, Rent is the gross median rent, Popsq is the number of persons per square mile. Vol is the return volatility across zip codes and RSP500 is the annual return on the S&P500 index. The Risk-Free Rate is the average monthly annualized return for three-month T-Bills and the same for monthly mortgage rates is given by the Mortgage Rate. Beta is the housing beta based on a CAPM type regression of zip code housing returns on S&P500 index returns and is calculated according to equation (2). Obs Mean Median Std Min Max Kurt Skew Price ($000s) 7234 188.845 147.462 1.753 34.480 1857.14 18.099 3.330 LnPrice 7234 1.609 1.608 0.00142 1.264 2.018 -0.073 0.076 Income 7173 51,700 48,373 242 7,619 200,001 3.999 1.391 Prof 7171 35.385 33.550 0.156 0 100 -0.134 0.521 Unemp 7171 5.512 4.327 0.049 0 76.1561 24.979 3.343 Owner 7173 69.624 73.376 0.212 1.4091 100 0.546 -0.928 Rent 7155 706 663 2.777 193 2001 4.316 1.552 Popsq 7173 2885 1425 50.900 0.630 69013 34.553 4.360 Return (%) 7234 5.695 4.595 2.878 -4.284 20.849 0.452 0.785 RSP500 (%) 8 9.552 17.473 7.429 -23.367 33.303 -1.480 -0.558 Risk-Free Rate (%) 8 3.919 4.700 0.610 1.117 5.814 -0.738 -0.896 Mortgage Rate (%) 8 7.146 7.201 0.259 5.819 8.063 0.069 -0.678 Beta 7234 -0.077 -0.093 0.003 -2.075 2.235 7.248 0.741 Volatility (%) 7234 14.845 10.188 0.158 1.386 101.440 8.044 2.551 34
  • Table II. Housing Returns by Volatility and Price Deciles The housing data includes a total of 7,234 zip codes covering the U.S. metropolitan housing market over 1996-2003 (disaggregate-level zip code data is available only in the post-1995 period). Each year, median- priced houses in zip code are first sorted into ten ranked price deciles (rows) and, then, within each price decile into ten ranked volatility groups (columns). The return volatility (Vol) is the standard deviation of annual housing returns. The reported figures are yearly averages over the sample period. The yearly return in Panel A is the average of the return for median priced house in the price-volatility group, the average Vol is reported in Panel C, and the mean logarithm of median house prices in Panel C. “P-1” and “V-1” are the lowest house price and volatility deciles, respectively, while “P-10” and “V-10” are the highest price and volatility deciles. The first row and column of each panel report overall averages by the level of price and volatility, respectively. All V-1 V-2 V-3 V -4 V-5 V-6 V-7 V-8 V-9 V-10 Panel A: Average Yearly House Price Return (%) All 5.31 5.81 6.13 6.46 6.59 6.97 7.26 7.83 8.75 15.74 P-1 5.14 3.49 3.63 3.86 3.74 4.18 4.58 4.52 5.66 5.64 12.19 P-2 6.16 4.07 4.14 4.17 4.66 4.61 5.25 4.96 6.35 7.41 16.07 P-3 6.59 4.58 4.67 4.76 5.30 4.87 4.84 5.89 7.16 7.99 15.92 P-4 6.63 4.36 4.67 4.90 5.00 5.22 6.48 6.49 6.69 8.32 14.21 P-5 7.35 4.40 5.13 6.04 6.39 6.80 6.61 7.16 7.38 8.37 15.31 P-6 7.84 4.45 5.17 6.43 6.74 6.47 7.36 7.52 7.93 9.17 17.20 P-7 8.31 5.33 6.34 6.94 7.12 7.25 7.95 8.12 8.37 9.51 16.20 P-8 9.09 6.14 7.25 7.47 8.19 8.43 8.37 8.39 9.56 10.39 16.77 P-9 9.15 7.72 7.95 7.60 8.12 8.57 8.58 9.23 8.87 9.57 15.30 P-10 10.52 8.56 9.11 9.13 9.27 9.53 9.67 10.27 10.31 11.17 18.26 Panel B: Average Standard Deviation of Returns (%) All 4.02 5.70 6.99 8.15 9.45 11.03 13.37 16.97 23.79 45.29 P-1 16.92 4.17 6.39 8.38 10.14 12.08 14.29 17.46 21.62 28.39 46.53 P-2 16.42 3.83 5.74 7.18 8.71 10.56 12.77 16.08 20.59 28.81 50.25 P-3 15.08 3.64 5.44 6.84 8.19 9.62 11.25 13.81 18.22 25.61 48.51 P-4 13.66 3.30 4.95 6.01 7.25 8.69 10.46 13.24 16.65 23.43 42.86 P-5 13.55 3.39 5.00 6.43 7.46 8.79 10.51 12.77 16.51 22.66 42.18 P-6 13.49 3.43 4.97 6.36 7.31 8.36 9.58 11.76 14.99 22.37 46.03 P-7 13.49 4.06 5.72 6.78 7.79 8.85 10.14 11.90 15.30 21.85 42.73 P-8 14.00 4.28 5.88 7.00 7.96 8.79 9.98 11.84 15.07 21.79 47.69 P-9 13.29 4.56 6.05 6.97 7.86 8.83 9.95 11.61 14.53 20.71 42.05 P-10 14.61 5.51 6.82 7.94 8.85 9.98 11.36 13.25 16.20 22.28 44.11 Panel C: Average Price (lnPrice) All 5.03 5.03 5.03 5.04 5.03 5.02 5.04 5.04 5.04 5.05 P-1 4.06 4.11 4.07 4.08 4.04 4.06 4.01 4.05 4.03 4.03 4.06 P-2 4.41 4.41 4.40 4.40 4.41 4.42 4.40 4.41 4.41 4.40 4.41 P-3 4.61 4.61 4.61 4.60 4.61 4.60 4.60 4.60 4.62 4.61 4.60 P-4 4.77 4.77 4.77 4.77 4.76 4.77 4.77 4.77 4.77 4.77 4.77 P-5 4.92 4.92 4.91 4.93 4.93 4.92 4.92 4.92 4.92 4.91 4.92 P-6 5.07 5.07 5.07 5.08 5.07 5.06 5.06 5.07 5.07 5.07 5.06 P-7 5.23 5.23 5.24 5.22 5.22 5.24 5.23 5.23 5.24 5.23 5.23 P-8 5.42 5.43 5.43 5.42 5.43 5.42 5.41 5.42 5.42 5.43 5.41 P-9 5.67 5.66 5.65 5.67 5.66 5.67 5.66 5.69 5.67 5.67 5.67 P-10 6.21 6.09 6.12 6.17 6.24 6.18 6.16 6.22 6.28 6.27 6.36 35
  • Table III. Cross-sectional Regressions of Housing Returns on Volatility and Price Level Median-price house returns for 7,234 zip codes in the U.S. metropolitan housing market over 1996-2003 are regressed on volatility and market price as in (1). The mean return and volatility (Vol) are computed for each zip code over this eight-year period. LnPrice is the mean of the natural logarithm of median house prices (in $000s). “SE” represents the standard error of the estimated regression coefficient. Intercept Vol lnPrice R-Square RMSE Estimate -10.0071* 0.24790* 0.02801* 0.4987 0.03533 SE 0.34973 0.00326 0.006787 Estimate 4.19183* 0.24126* 0.3807 0.03927 SE 0.06975 0.00362 The significance level denoted by * is 0.0001. Table IV. Cross-Sectional Regression of Housing Returns on Volatility and Price by Market Segment Cross-sectional regressions of house price returns on return volatility and price level are reported by market segment. The average annual return and volatility (Vol) are computed for 7,234 metropolitan zip codes over the 1996-2003 period. LnPrice is the mean of the natural logarithm of median house prices (in $000s). For estimation, zip codes are sorted within each year by price level and constructed into five portfolios ranked by market price (Qprice = 1, 2, . . ., 5). “SE” represents the standard error of the estimated regression coefficient. Intercept Vol lnPrice R-Square RMSE Lowest Price Quintile: Qprice=1 Estimate -12.67579* 0.23302* .034139* 0.4613 .034804 SE 1.78398 0.00675 0.004194 Qprice=2 Estimate -3.941 0.25734* 0.014619 0.4891 .03375 SE 4.41112 0.00691 0.009396 Qprice=3 Estimate -17.34341** 0.28965* 0.042092* 0.4955 .03740 SE 5.62683 0.00771 0.00112591 Qprice=4 Estimate -10.58323** 0.24382* 0.029912* 0.4171 .03600 SE 4.59831 0.00762 0.0086315 Highest Price Quintile: Qprice=5 Estimate -1.85041 0.22636* 0.014363* 0.4203 .03306 SE 1.42488 0.00737 0.0024132 The significance levels denoted by *, ** and *** are 0.0001, 0.002 and 0.03, respectively. 36
  • Table V. Cross-sectional Regressions with MSA Fixed Effects Fixed effects for Metropolitan Statistical Areas (MSAs) are included in the cross-sectional regressions of house price returns on return volatility and price level of Table III. There are a total of 154 MSA for the 7,234 metropolitan zip codes in the 1996-2003 sample. “SE” represents the standard error of the estimated regression coefficient. Estimate Estimate SE Estimate SE MSA Fixed Effects Yes NO Yes Intercept -0.1001* -0.00351 -0.0537* 0.004207 Vol 0.2474* 0.0033 0.2496* 0.003018 LnPrice 0.0280* 0.000681 0.0180* 0.000838 R-Square 0.2079 0.4941 0.6130 RMSE 0.04239 0.0352 0.02963 The significance levels denoted by * is 0.0001. Table VI. Cross-sectional Regressions with Socioeconomic Variables Socioeconomic variables for income, managerial employment, employment rate, owner occupied housing, rent, population density at the zip-code level are included in the cross-sectional regressions of house price returns on return volatility and price level (Table III). LnIncome is the natural-log of median household income by zip code, Unemp is the employment rate, Prof is the percentage of employed in managerial occupations, Owner is the percentage of owner-occupied housing units, Rent is the gross median rent, Popsq is the number of persons per square mile. The socioeconomic data is from the 2000 census. Average annual returns and their volatility (Vol) are computed for 7,155 metropolitan zip codes over 1996-2003 (79 of the original 7,234 zip codes could not be matched to the socioeconomic data). LnPrice is the mean of logged median house prices (in $000s). Coefficient Estimates A B C D E F Intercept -0.09896* -0.18995* 0.06441* -0.47072* -0.40747* -0.44994* Vol 0.23702* 0.23797* 0.2326* 0.2333* 0.23331* 0.23873* lnPrice 0.02786* 0.03617* 0.1419* 0.12028* 0.12417* lnIncome 0.02145* -0.01898* 0.03056* 0.02428* 0.02294** Price*Income -0.00976* -0.00735* -0.00784* Unemp -0.01701 -0.02382 Prof -0.04834* -0.05186* Owner 0.00611 Rent 0.00797* Popsq 0.00128* R-Square 0.5015 0.5138 0.5138 0.5045 0.5175 0.5272 RMSE 0.03292 0.03251 0.03251 0.0349 0.03239 0.0321 The significance levels denoted by * and ** are 0.0001 and 0.003, respectively. 37
  • Table VII. Returns by Housing Beta and Price level The median-priced house in each of the 7,234 postal zip codes covering the U.S. metropolitan housing market over 1996-2003 are first assigned to ten ranked price deciles (rows), and, then subdivided into ten ranked beta groups (columns). House return betas are the CAPM slopes where returns to median-priced houses by zip code are regressed on the excess return on the S&P500 index: Rit = α 0 + β i RSP500 t + ε t , t = 1996,...,2003 (2) where Rit is the annual excess return on the median-price house in zip code i over the average return on three-month T-Bills in year t . The reported figures are yearly averages over the sample period. Panel A reports the average annual return for median-priced houses in the price-beta group, the average beta is reported in Panel C, and the mean logarithm of median house prices in Panel C. “P-1” is the lowest house price decile while “P-10” is the highest price decile. The first row and column of each panel report overall averages by the level of price and beta, respectively. All β -1 β -2 β -3 β -4 β -5 β -6 β -7 β -8 β -9 β -10 Panel A: Average Yearly House Return (%) All 9.30 7.46 6.94 6.63 6.49 6.44 6.47 6.46 7.40 13.21 P-1 5.14 6.47 3.77 3.79 4.06 3.98 3.93 4.47 5.49 6.62 8.87 P-2 6.16 8.92 5.12 5.05 4.66 5.07 4.70 5.00 4.38 5.48 13.23 P-3 6.59 8.05 6.43 4.71 5.41 5.36 5.65 4.98 5.23 7.33 12.81 P-4 6.63 7.37 6.36 6.25 4.89 5.54 5.35 5.04 5.65 7.21 12.68 P-5 7.35 8.47 7.92 6.81 6.02 5.64 5.85 5.68 6.34 7.23 13.60 P-6 7.84 9.86 7.95 7.39 6.80 6.38 6.17 6.05 6.45 6.57 14.78 P-7 8.31 10.69 8.59 8.52 7.67 6.98 6.51 6.83 6.37 6.91 14.01 P-8 9.09 10.12 9.61 9.05 8.16 8.00 7.91 7.81 7.30 7.85 15.11 P-9 9.15 10.64 8.72 8.45 9.00 8.50 8.85 8.80 8.05 8.11 12.35 P-10 10.52 12.38 10.19 9.38 9.62 9.49 9.52 9.98 9.41 10.66 14.62 Panel B: Average Housing Beta ( β ) All -0.56 -0.30 -0.22 -0.17 -0.12 -0.07 -0.02 0.04 0.14 0.51 P-1 -0.05 -0.63 -0.30 -0.21 -0.14 -0.09 -0.03 0.03 0.10 0.22 0.56 P-2 -0.04 -0.64 -0.29 -0.19 -0.13 -0.08 -0.03 0.03 0.10 0.23 0.66 P-3 -0.03 -0.54 -0.27 -0.19 -0.13 -0.08 -0.04 0.02 0.09 0.20 0.60 P-4 -0.04 -0.52 -0.26 -0.18 -0.13 -0.08 -0.03 0.01 0.07 0.17 0.52 P-5 -0.07 -0.50 -0.31 -0.22 -0.15 -0.10 -0.06 -0.01 0.04 0.13 0.49 P-6 -0.09 -0.54 -0.31 -0.24 -0.18 -0.12 -0.08 -0.03 0.03 0.11 0.51 P-7 -0.11 -0.59 -0.34 -0.27 -0.20 -0.14 -0.09 -0.04 0.02 0.11 0.48 P-8 -0.12 -0.56 -0.34 -0.28 -0.22 -0.17 -0.12 -0.06 0.00 0.10 0.49 P-9 -0.13 -0.53 -0.33 -0.26 -0.22 -0.18 -0.13 -0.09 -0.04 0.05 0.39 P-10 -0.10 -0.57 -0.27 -0.21 -0.17 -0.13 -0.09 -0.05 0.00 0.09 0.44 Panel C: Average Price (lnPrice) All 5.04 5.03 5.03 5.03 5.04 5.04 5.04 5.03 5.04 5.04 P-1 4.06 4.04 4.04 4.02 4.03 4.10 4.08 4.07 4.08 4.05 4.05 P-2 4.41 4.41 4.42 4.38 4.40 4.42 4.42 4.39 4.40 4.41 4.41 P-3 4.61 4.60 4.61 4.60 4.59 4.61 4.61 4.62 4.61 4.60 4.61 P-4 4.77 4.77 4.76 4.77 4.77 4.77 4.77 4.77 4.77 4.77 4.78 P-5 4.92 4.92 4.91 4.93 4.92 4.92 4.92 4.91 4.92 4.92 4.93 P-6 5.07 5.07 5.07 5.08 5.07 5.08 5.07 5.07 5.06 5.07 5.06 P-7 5.23 5.23 5.24 5.23 5.24 5.23 5.23 5.23 5.23 5.23 5.23 P-8 5.42 5.41 5.40 5.42 5.43 5.42 5.43 5.41 5.41 5.43 5.43 P-9 5.67 5.66 5.67 5.66 5.67 5.67 5.67 5.68 5.66 5.66 5.66 P-10 6.21 6.28 6.19 6.18 6.17 6.16 6.17 6.24 6.15 6.27 6.29 38
  • Table VIII. Regression of Housing Returns on Beta, Price and Idiosyncratic Risk Median-priced house returns for 7,234 zip codes in the U.S. metropolitan real-estate market from 1996-2003 are decomposed into beta, market price and idiosyncratic volatility using the cross-sectional regression Ri = α 0 + α1 β i + α 2 β i2 + α 3 ln Pr icei + α 4 Sigmai + ε t (3) where Ri is the average annual excess housing return for zip codes i = 1,...,7,234 . House-return betas are the slopes of the CAPM regression (2) based on returns to median-priced houses by zip codes and the excess return on the S&P500 index. Idiosyncratic volatility is the root mean square error (Sigma) of the residual from the CAPM regression of housing returns. LnPrice is the is the natural logarithm of the median house price (in $000s). “SE” represents the standard error of the estimated regression coefficient. Intercept Beta Beta2 lnPrice Sigma R-Square MSE Panel A: Beta Only Estimate 0.03911* 0.03256* 0.0323 0.04901 SE 0.000598 0.00209 Panel B: Beta and Beta2 Estimate 0.0307* 0.02763* 0.09844* 0.2266 0.04381 SE 0.00057 0.00188 0.00231 Panel C: Beta, Beta2 and lnPrice Estimate -0.10612* 0.03075* 0.09899* 0.02721* 0.3384 0.04053 SE 0.00395 0.00174 0.00214 0.000779 Panel D: Beta, Beta2 and Idiosyncratic Volatility Estimate 0.00681* 0.00475** 0.04157* 0.18029* 0.3795 0.03925 SE 0.000762 0.00177 0.00247 0.00427 Panel E: Beta, Beta2, lnPrice and Idiosyncratic Volatility Estimate -0.13944* 0.00701* 0.03958* 0.02887* 0.18847* 0.5047 0.03506 SE 0.00348 0.00158 0.00221 0.000674 0.00382 The significance levels denoted by * and ** are 0.0001 and 0.002, respectively. Table X. Housing Returns and Pre-Post 2000 Housing Betas The regression in Table VII, Panel D, is repeated with a dummy variable (BD) for the post-1999 period. BD=0 for average returns over 1996-1999 and BD=1 for the 2000-2003 period. The estimation of the coefficients in (3) is done as before. Intercept Beta Beta2 Sigma BD*Beta BD*Beta2 R-Square Estimate 0.0122 0.16424 0.01918 0.1536 -0.32072 -0.0150 0.5586 SE 0.000589 0.00189 0.000711 0.00276 0.0025 0.00078 The significance level denoted by * is 0.0001. 39
  • Table X. Housing Price as a SMB Fama-French Factor The role of the housing price as a Fama-French (FF) type pricing factor is investigated in the cross-section of 7,234 zip codes in the U.S. metropolitan housing market from 1996-2003. The FF-price factor is based on sorting median-priced houses by zip code every year into three portfolios ranked using house prices at the start of the year and, then, taking the difference between the average return in the highest and lowest priced groups (SMB). Starting year prices are used to avoid the price-return correlation from influencing the formation of the FF-price factor. Factor loading for SMB are estimated from the regression of excess housing investment returns on SMB: Rit = α 0 + βi RSP500t + γ i SMBt + ε t , t = 1996,...,2003 . (4) where Rit is the annual excess return on the median-price house in zip code i over the average annual return on three-month T-Bills in year t . Next, average returns are regressed on linear and quadratic terms involving the beta and SMB factor loadings: Ri = α 0 + α1β i + α 2 β i2 + α1γ i + α 2γ i2 + α 3 ln Pr icei + α 3 ( βγ ) i + ε t (5) where Ri is the average annual excess housing return for zip codes i = 1,...,7,234 . Beta-SMB is the interaction term (only statistically significant interactions are reported) and LnPrice is the natural logarithm of the median house price (in $000s). “SE” represents the standard error of the estimated regression coefficient. Beta Intercept Beta Beta2 SMB SMB2 lnPrice SMB R-Sq MSE Panel A: SMB and SMB2 only Estimate 0.07247* 0.00587* 0.00193* 0.2204 0.0416 SE 0.0005455 0.000364 0.0000645 Panel B: Quadratic SMB and Beta Estimate 0.072* -0.0084* 0.05342* 0.00499* 0.00194* 0.2221 0.04157 SE 0.000559 0.00225 0.00226 0.000433 0.00006456 Panel C: Price Effect and Quadratic SMB and Beta 0.06674 Estimate -0.0693* -0.00332 * 0.00647* 0.0011* 0.02761* 0.4148 0.03605 SE 0.00353 0.00195 0.0023 0.000377 0.00006235 0.000696 Panel D: Additional SMB & Beta Interaction 0.00534* 0.12374 Estimate -0.07092* * * 0.00814* 0.00299* 0.0276* 0.0277* 0.4715 0.03425 SE 0.00335 0.00188 0.00299 0.000363 0.00009005 0.000661 0.000994 The significance levels denoted by * is 0.0001 and ** is 0.005. 40
  • Table XI. Housing Price as a Local Fama-French Factor The analysis of Table VII is repeated by defining the SMB factor more locally using the first two digits of the zip code. SMB portfolios are now formed by sorting median-priced houses by zip into three ranked portfolios within each MSA, and then taking the difference between the average return in the highest and lowest priced groups. Beta Intercept Beta Beta2 SMB SMB2 lnPrice SMB R-Sq MSE Panel A: SMB and SMB2 only 0.00386 0.0471 Estimate 0.0353* 0.00689* * 0.074 8 SE 0.00060 0.00073 0.00017 Panel B: SMB and Beta 0.00423* 0.00431 0.078 0.0470 Estimate 0.03554* * -.00070* 0.00718* * 9 5 SE 0.00061 0.00138 0.00012 0.00076 0.00019 Panel C: Price Effect, SMB and Beta 0.00396 0.02545 0.175 0.0445 Estimate -0.09385* 0.00506* -.00065* 0.00418* * * 6 2 SE 0.00472 0.00131 0.00011 0.00073 0.00018 0.00092 Panel D: With SMB & Beta Interaction 0.00399 0.02546 0.175 0.0445 Estimate -0.09393* 0.00515* -0.00048 0.00423* * * 0.00039 5 2 SE 0.00472 0.00132 0.00033 0.00073 0.00019 0.00092 0.00070 The significance levels denoted by * is 0.0001; ** denotes 0.003. 41
  • 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. 48
  • 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