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Are Pricier Houses Less Risky? Evidence from China∗

Jianhua Gang#, Liang Peng♦, and Jinfan Zhang♥

February 17, 2019

Abstract Recent research shows that pricier houses may have lower investment risk. A main challenge in this analysis is separating the effects of prices and those of location-related variables that are correlated with prices. Using condo price data from China that have a special feature: condos in the same subdivisions have identical locations but different size and prices, we find strong evidence that pricier condos have lower systematic risk, which is measured with their housing market betas, than cheaper ones in the same subdivisions. Key words: housing, risk, segmentation JEL classification: G12, R33

∗ The authors thank Yifan Chen for capable research assistance. # Associate Professor, China Financial Policy Research Center, School of Finance, Renmin University of China, email: jhgang@ruc.edu.cn. ♦ Contact author. Associate Professor, Smeal College of Business, Pennsylvania State University, email: liang.peng@psu.edu. ♥ Associate Professor, School of Management and Economics, Chinese University of Hong Kong (Shenzhen), Shenzhen Advanced Institute of Finance, email: zhangjinfan@cuhk.edu.cn

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1. Introduction

Houses are the largest asset owned by most households (see, e.g. Chetty, Sandor and

Szeidl (2017)), and play an important role in the economy, as manifested in the recent

financial crisis (see, e.g. Goetzmann, Peng and Yen (2012)). Therefore, understanding

their risk is important for homeowners, mortgage lenders, RMBS issuers and investors,

and policy makers. Using U.S. housing data, recent research provides strong evidence

suggesting that housing risk is heterogeneous, which is called risk segmentation by Peng

and Thibodeau (2013). This emerging literature shows that housing risk, measured in

many different ways, may vary across individual houses and be related to local social-

economic characteristics or houses’ attributes.

An important piece of evidence based on house-level data, provided by Peng and Zhang

(2019), is that pricier houses seem to have lower systematic risk. This finding has

important implications for households’ portfolio decisions, because it implies that houses

with different prices are essentially different assets. Therefore, the role of housing in a

mixed-asset portfolio can vary across households with different income or wealth, who

would presumably invest in houses with different price levels. This finding also has

important policy implications. The U.S. government has been promoting homeownership

among low-income households for decades. Should cheaper houses have higher

systematic risk, the benefits and costs of homeownership for low-income households

need to be carefully evaluated.

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A caveat of using U.S. data of single-family houses is that houses with different prices

are also located in different locations with possibly different demographic, geographic,

cultural, social, and economic characteristics. As a result, it is unclear whether lower

systematic risk of pricier houses is driven by house prices, or by location-specific

characteristics that are correlated with house prices. It is fundamentally important to

distinguish the two different relationships. If the true relationship lies between location

characteristics and risk, but mistakenly treated as being between house prices and risk, (1)

home purchases decisions that are based on prices might not achieve desirable investment

goals; (2) mortgage underwriters might wrongly asses risk of underlying houses; (3)

investors of RMBSs may systematically misprice mortgage backed securities; and (4)

policy makers may make problematic proposals or implement polices that are harmful to

home owners and the economy.

This paper aims to separate house prices from location-related characteristics in

analyzing whether pricier houses have lower systematic risk. We achieve this by using a

large dataset from China, which contains transaction prices of condos from 2,073

subdivisions in four major cities – Beijing, Shanghai, Guangzhou, and Shenzhen – from

April 2007 to April 2017. Condos in the same subdivisions have almost identical quality

and virtually the same locations, with their only key differences being their size. We

empirically test whether larger condos have lower systematic risk than smaller ones in the

same subdivisions and thus the same locations. Using a plausible assumption that larger

condos have higher prices that smaller ones in the same subdivisions, we argue that the

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relationship between systematic risk and condo size pertains to prices instead of location-

related characteristics that are correlated with prices.

We conduct our tests in the Capital Asset Pricing Model (CAPM) framework using a

housing market index we construct from our sample as the market portfolio. We assume

that condos with more bedrooms are more expensive that those with fewer bedrooms in

the same subdivisions. We find strong evidence that condos with more bedrooms have

lower betas than those with fewer bedrooms in the same subdivisions. This result is

novel and consistent with a negative relationship between house prices and their

systematic risk, but not consistent with a relationship between systematic risk and

location-specific characteristics because condos in the same subdivisions have the same

locations. We further hold constant the number of bedrooms, and find that condos with

higher prices have lower betas than those with the same number of bedrooms but lower

prices in the same cities. This result indicates that it is prices – not the number of

bedrooms – that affect betas.

This paper contributes to two important literatures. The first literature pertains to the role

of housing in mixed-asset portfolios (see, e.g. Grossman and Laroque (1990), Brueckner

(1997), Fratantoni (1998), Flavin and Yamashita (2002), Yamashita (2003), Cocco

(2005), Yao and Zhang (2005), Chetty and Szeidl (2007), and Chetty, Sandor and Szeidl

(2017), among others). In this literature, houses’ systematic risk is an important input

for households’ portfolio/investment decisions. The second literature pertains to the risk

segmentation of the housing market (see, e.g. Li and Rosenblatt (1997), Zhou and Haurin

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(2010), Ambrose, Buttimer and Thibodeau (2001), Han (2013), Peng and Thibodeau

(2013), Hartman-Glaser and Mann (2016), and Peng and Thibodeau (2017)). This

literature shows that many different risk measures vary across submarkets with different

social-economic characteristics or houses with different price levels.

The rest of this paper is organized as follows. Section 2 describes the data. Section 3

develops the econometric model and the hypothesis. Section 4 presents empirical

evidence. Section 5 conducts robustness checks. Section 6 concludes.

2. Data

This study uses condo-level transaction price data for the four largest cities in China in

terms of GDP, namely Beijing, Shanghai, Guangzhou, and Shenzhen. These four cities

(often referred to as the first-tier cities) have a combined permanent resident population

of over seventy million. Furthermore, these four cities have the most developed housing

markets with the largest samples of condo transactions, according to the data vender

CityRE Data Co.

The vast majority of residents in these cities live in condos that are located in

subdivisions. A typical subdivision consists of multiple buildings each containing several

hundred condos. These condos are highly homogeneous in the sense that they have

identical construction quality and share the same location-related amenities, including

hospitals, public schools, shopping centers, and public transit facilities. Therefore, as

long as they have the same size/number of bedrooms, it is reasonable to treat them as

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homogeneous assets. While each individual condo is not sold or priced in each month,

the data vender calculates monthly average transaction prices for each condo type (the

same subdivision and the same size) from sale prices of sold units.

We obtain our data from CityRE Data Co., which is a leading real estate data vender in

China and complies its housing database from information provided by the Chinese Real

Estate Association (CREA). The dataset we use contains time series of monthly average

transaction prices (quoted as RMB per-square-meter) for each size type of condos, from

one-bedroom to 9-bedroom, in each of more than 2,000 subdivisions in the four cities

over the time period from April 2007 to April 2017. To our best knowledge, this is the

most comprehensive dataset for condo-type-level transaction prices in China.

We clean the data using the following procedure. First, we exclude unusually large (i.e.

six- to nine-bedroom) condos, which constitute less than 1% of the sample. Second, as

there are relatively few five-bedroom condos, we combine them with four-bedroom

condos into a new type, which we still call the four-bedroom condos. If a subdivision has

both four- and five-bedroom condos, we use the average of their prices as the new

average price of the combined type. Third, we delete all negative prices. Fourth, for

each subdivision/size type, we delete prices that are three standard deviations away from

the temporal mean of the price series. Fifth, for size type b condos in subdivision s , we

denote by Rs ,b ,t the log price appreciation from month t −1 to month t , and calculate it

as follows.

Rs ,b ,t = log Ps ,b ,t( )− log Ps ,b ,t−1( ) (1)

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In equation (1), Ps ,b ,t is the average sale price (RMB per square meter) of the size type b

condos in subdivision s in month t . This paper chooses to analyze log price

appreciation rates because they have a more symmetric and Normal-like distribution than

price appreciation rates. However, main results are robust when we analyze price

appreciation rates. We exclude Rs ,b ,t that are lower than -0.4 or greater than 0.4. Finally,

we only keep Rs ,b ,t series that covers at least 60 months.

The cleaning procedure above leads to a final sample of 663, 322, 489, and 595

subdivisions in Beijing, Shanghai, Guangzhou, and Shenzhen respectively. Table 1

summarizes the number of one- to four-bedroom series each city has in our sample. It is

apparent that subdivisions more likely have two-bedroom and three-bedroom condos than

one-bedroom and four-bedroom condos.

Table 2 reports the sample size, minimum, median, maximum, mean, and standard

deviation of all Rs ,b ,t for each size type as well as the whole sample. Note that all size

types have similar minimums and maximums due to our filtering rule that excludes

observations that are lower than -0.4 and greater than 0.4. In terms of sample size, the

two mid-size condos have more samples: two-bedroom condos have 199,514

observations, and three-bedroom condos have 194,173 observations. The smallest and

largest condos have smaller samples: one-bedroom condos have 109,282 observations

and four-bedroom condos have 94,818 observations. In terms of medians, the two mid-

size condos have higher medians: two-bedroom condos have 1.30%, and three-bedroom

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condos have 1.29%. The smallest and largest condos have lower medians: one-bedroom

condos have 1.24%, and four-bedroom condos have 1.21%. In terms of means, the two

mid-size condos have higher means: two-bedroom condos have 1.41%, and three-

bedroom condos have 1.39%. The smallest and largest condos have lower means: one-

bedroom condos have 1.35%, and four-bedroom condos have 1.24%. In terms of

standard deviations, the two mid-size condos have lower standard deviations: two-

bedroom condos have 7.97%, and three-bedroom condos have 8.32%. The smallest and

largest condos have larger standard deviations: one-bedroom condos have 10.06%, and

four-bedroom condos have 11.29%. Figure 1 plots the histogram of Rs ,b ,t for the full

sample, which seems consistent with a symmetric distribution.

We calculate a monthly condo market index of log price appreciation rate, which is

denoted by Mt , by taking equal-weighted averages of the log price appreciation rates

across all series in each month as follows.

Mt =

1Nt

Rs ,b ,t( )s ,b∑ (2)

In equation (2), Nt is the total number of series that have log price appreciation rates

covering month t . Figure 2 illustrates the time series of prices implied by Mt using

RMB 10,000 as the initial value. While equal-weighted averages may not be as ideal as

value-weighted averages in measuring market performance (see, e.g. Goetzmann and

Peng (2002) for discussions regarding differences between equal- and value-weighted

indices), no dataset with information on housing stock or total square footage is currently

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available to allow us to calculate value-weighted averages. Note that our results are

generally robust when we use a price-weighted market index for our tests.

We then calculate market indices for the four size types respectively using the same

algorithm described above, and plot them in Figure 3 using RMB 10,000 as initial values.

We use indices of the four size type indices to develop some basic descriptions of their

price appreciation dynamics. Table 3 reports the minimum, median, maximum, mean,

and standard deviation of monthly index appreciation rates for the four size types and

those of the full sample. There appears to be a pattern in the temporal volatility of index

appreciation rates across the four size types: volatility seems to decrease with condo size.

Specifically, the standard deviation is 2.08%, 1.88%, 1.78%, and 1.63% for the one- to

four-bedroom indices. This is consistent with the notion that larger condos, which are

likely pricier, have lower risk.

3. Model and hypothesis

We develop our hypotheses in a simple log CAPM style model, in which the log risk

premium of the price appreciation rate of the size type b condos in subdivision s is

related to the log risk premium of the market index as follows.

Rs ,b ,t −Ft =α s ,b +βs ,b Mt −Ft( )+ ε s ,b ,t (3)

In (3), Ft is the log gross one-month-yield of Chinese treasury; Mt −Ft is the log risk

premium of the condo market index; α s ,b and βs ,b respectively measure the risk adjusted

risk premium and the systematic risk of size type b condos in subdivision s .

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We use the CAPM framework not because we believe it is the “correct” asset-pricing

model for housing. Asset pricing research keeps evolving and no model is really

“correct”. We use this model for two reasons. First, it is perhaps the most classic asset-

pricing model, which serves as a natural starting point for studying risk and returns of

assets that are not well understood. For example, Cochrane (2005) uses this model to

analyze the stock market beta of venture capital; Driessen, Lin and Phalippou (2012) also

use it to analyze the beta of private equity funds; and Peng and Zhang (2019) use it to

analyze the systematic risk of single family houses in the U.S. Second, betas in this

model measure the sensitivity of different condo size and subdivisions’ price appreciation

rates to the market-average condo price appreciation rates, which seems a natural

measure of their systematic risk.

We use the condo market index as a proxy for the market portfolio because housing is the

largest asset class in China. The Chinese stock market had a total market capitalization

of about $6 trillion in August 2018,1 but the total value of the Chinese real estate market

is about $42 trillion in September 2017, with about 70% being housing.2 Since (1) there

is no reliable database for commercial real estate value appreciation, and (2) the four

first-tier cities have the largest housing markets and the most reliable data for condo

transactions, it seems reasonable to use the condo market index constructed from our

sample to measure the housing market performance in China.

1 See https://www.cnbc.com/2018/08/03/china-loses-status-as-worlds-second-largest-stock-market-to-japan.html. 2 See https://gbtimes.com/china-tops-world-gross-real-estate-value.

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We define four dummies for the four size types of condos, denoted by BR1b , BR2b ,

BR3b , and BR4b , which respectively equal 1 for one-, two-, three-, and four-bedroom

condos and 0 otherwise. To allow heterogeneity in both α and β across subdivisions,

and to allow or test whether α and β vary across different size types of condos in same

subdivisions, we let α s ,b and βs ,b in (3) to be functions of subdivision dummies and size

dummies:

α s ,b =α s + ρ2BR2b + ρ3BR3b + ρ4BR4b (4)

and

βs ,b = βs +λ2BR2b +λ3BR3b +λ4BR4b . (5)

In equations (4) and (5), α s and βs are subdivision dummies, which are used to allow

heterogeneity in α and β across subdivisions. The parameters ρ2 , ρ3 , and ρ4 , as well

as λ2 , λ3 , and λ4 , are used to allow α and β to vary across different size types of

condos in the same subdivisions. Specifically, α s measures alpha of one-bedroom

condos (the base type) in subdivision s , and ρ2 , ρ3 , and ρ4 are the differences between

alphas of two-, three-, and four-bedroom condos and that of one-bedroom condos in the

same subdivision. Similarly, βs measures beta of one-bedroom condos in subdivision s .

λ2 , λ3 , and λ4 are the differences between betas of two-, three-, and four-bedroom

condos and one-bedroom condos’ beta in the same subdivision.

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The null hypotheses we test are that the coefficients of the dummy variables in (5) (λ2 ,

λ3 , and λ4 ) equal 0, which means that larger condos have identical betas with one-

bedroom condos. To empirically test these hypotheses, we plug (4) and (5) into (3) and

have the following empirical model.

Rs ,b ,t −Ft =α s + ρ2BR2b + ρ3BR3b + ρ4BR4b +βs Mt −Ft( )+λ2BR2b Mt −Ft( )+λ3BR3b Mt −Ft( )+λ4BR4b Mt −Ft( )+ ε s ,b ,t

(6)

Note that λ2 , λ3 , and λ4 are respectively the coefficients of the interaction terms

between the size type dummies and the market risk premium.

Note that λ2 , λ3 , and λ4 are identical across subdivisions. Therefore, the model does

not allow the differences between betas of two-, three-, and four-bedroom condos and

betas of the one-bedroom condos to vary across subdivisions. As result, the model

essentially analyzes the across-subdivisions average differences in betas across size types.

However, this is our choice instead of a problem, as our research question pertains to the

average differences. Furthermore, the model would have too many parameters to

estimate if we allow beta differences between different size types to vary across

subdivisions, and our sample size is not large enough to provide sufficient power.

While we do not know prices for each size type in each subdivision, it is plausible that

condos with more bedrooms have higher prices than those with fewer bedrooms in the

same divisions and the same months. Therefore, if we reject the above hypotheses, it

seems reasonable to conclude that pricier condos have different systematic risk than

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cheaper ones. If λ2 , λ3 , and λ4 are negative, we would conclude that pricier condos

have lower systematic risk.

It is worth noting that, while we allow alphas to vary across subdivisions and size types,

we refrain from over-interpreting the results as evidence for heterogeneous risk-adjusted

returns. The main reason is that the CAPM model is not “correct” and there can be

factors missing in the model. As a result, variation of α across size types could be due

to different size types’ heterogeneous exposure to missing factors.

4. Empirical results

We start with building some basic stylized facts by estimating the following simplified

version of the model in (3) for one-, two-, three-, and four-bedroom condos in all

subdivisions separately.

Rs ,b ,t −Ft =α +β Mt −Ft( )+ ε s ,b ,t (7)

This simplified model assumes identical α and β for the same size type across all

subdivisions in all cities. While doing so ignores possible heterogeneity in both α and

β across subdivisions, and does not allow formal tests of differences in α and β across

size types, it provides useful benchmark results.

Table 4 reports the estimation results. First, all four size-types have positive and

statistically significant betas. Second, there is an apparent pattern of the variation of β

across size types. It is monotonically decreasing with condo size: 1.114 for one-bedroom,

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1.030 for two-bedroom, 0.981 for three-bedroom, and 0.844 for four-bedroom condos.

This is consistent with the notion that larger/pricier condos have lower systematic risk.

We then pool all size types from all cities together to formally test whether the

differences in betas estimated above are statistically significant. Note that we do not yet

allow for heterogeneity in alpha and beta across subdivisions.

Rs ,b ,t −Ft =α1 + ρ2BR2b + ρ3BR3b + ρ4BR4b +β1 Mt −Ft( )+λ2BR2b Mt −Ft( )+λ3BR3b Mt −Ft( )+λ4BR4b Mt −Ft( )+ ε s ,b ,t

(8)

In equation (8), α1 and β1 are alpha and beta for one-bedroom condos; BR2b , BR3b ,

and BR4b are dummy variables that respectively equal to 1 for two-, three-, and four-

bedroom condos located in any subdivisions and 0 otherwise; ρ2 , ρ3 , and ρ4 are the

differences between alphas of two-, three-, and four-bedroom condos and that of one-

bedroom condos; λ2 , λ3 , and λ4 are the differences between betas of two-, three-, and

four-bedroom condos and the beta of one-bedroom condos.

Table 5 reports the regression results, which provide very strong evidence for differences

in both alphas and betas across size types. It is apparent that betas of two-, three-, and

four-bedroom condos are lower than betas of one-bedroom condos. The differences,

measured by λ2 , λ3 , and λ4 , are -0.084, -0.133, and -0.270 respectively. All differences

are statistically significant at the 1% level. In terms of alphas, the result indicates that

larger condos have significantly higher alphas. The differences between alphas of two-,

three-, and four-bedroom condos and the alpha of one-bedroom condos, which are

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measured with ρ2 , ρ3 , and ρ4 , are 0.001, 0.001, and 0.002 respectively, all of which are

statistically significant at the 1% level.

Next, we control for heterogeneous alphas and betas across subdivisions and estimate the

model in (6) to test differences in betas across size types using the whole sample as well

as samples from each of the four cities. Note that the model contains 2,069 dummies for

2,069 subdivisions in total. The large number of dummy variables dramatically reduces

the degrees of freedom. Possibly because of this, when we estimate the model, while

coefficients are consistent with those in Table 5 in the sense that all λ2 , λ3 , and λ4 are

negative, only some of them are statistically significant.

We mitigate this problem by use coarser size types. First, we combine one- and two-

bedroom condos into a Small group, and three- and four-bedroom condos into a Large

group. Defining a dummy variable Lb that equals 1 for three- and four-bedroom condos

and 0 otherwise, the model becomes the following.

Rs ,b ,t −Ft =α s + ρLb +βs Mt −Ft( )+λLb Mt −Ft( )+ ε s ,b ,t (9)

In (9), α s is the subdivision dummy that measures alpha of the Small group in

subdivision s ; and ρ is the difference between the alpha of the Large group in

subdivision s and the alpha of the Small group; βs is the subdivision dummy that

measures beta of the Small group in subdivision s ; and λ is the difference between the

beta of the Large group in subdivision s and the beta of the Small group.

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Table 6 reports results of estimating (9) using the full sample and samples from each city.

To interpret the results, note that α s and βs are subdivision-specific betas and alphas of

Small condos. “Yes” in the table means that we allow each subdivision to have its own

alpha and beta for its Small condos. So each regression in Table 6 produces 2,069 α s

estimates and 2,069 βs estimates, which we do not report.

Table 6 provides evidence that larger condos have lower systematic risk. First, using the

whole sample, betas of Large condos are lower than betas of Small condos by 0.042 on

average, which is statistically significant at the 1% level. Using samples from the four

cities separately, beta differences for larger condos are all negative without any exception:

they are -0.09 for Beijing, -1.08 for Shanghai, -0.001 for Guangzhou, and -0.024 for

Shenzhen. However, they are statistically significant for Beijing and Shanghai, but not

for Guangzhou and Shenzhen. The weak result for using samples from individual cities

could be due to smaller samples in each city-level regression.

5. Robustness checks

This section tests whether the results we found earlier are driven by an alternative

mechanism. Owners/renters of condos with more bedrooms are likely older and having

children, and they are probably in later career stages than owners/renters of condos with

fewer bedrooms, who may be younger and have no children. Therefore, income of

owners/rents of condos with more bedroom may be less sensitive to economic shocks

(see, e.g. Zhou and Haurin (2010)). As a result, the demand for condos with more

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bedrooms is less volatile and thus price appreciation rates have lower betas. This

mechanism will lead to the same results we found earlier.

To distinguish the effects of prices and those of the number of bedrooms, we estimate the

following model using samples from all cities for each of the size type separately.

Rc ,s ,b ,t −Ft =α c + ρPc ,s ,b +βc Mt −Ft( )+λPc ,s ,b Mt −Ft( )+ εc ,s ,b ,t (10)

In equation (10), Rc ,s ,b ,t is the log price appreciation from month t −1 to month t for

type b condos in subdivision s in city c , and Pc ,s ,b is the normalized price (RMB per

square meter) of the type b condos in subdivision s in city c in May 2012, which is the

middle point of the sample period.3 We normalize each price by first subtracting the

average price in its city and then dividing the result by the standard deviation of prices in

its city. Therefore, when the normalized price equals 0, the actual price equals the city

average. When the normalized price equals 1 or -1, the actual price is one standard

deviation above or below the city average. The reason why we normalize the prices is to

make it easy for us to interpret the coefficients. For example, it is easy to see that α c and

βc are respectively the alpha and beta for condos with normalized prices being zero,

which are condos with the average price. It is also apparent to see that ρ and λ are

increases in alpha and beta when the actual price increases by one standard deviation.

The null hypothesis we test is whether λ =0 . If λ is 0, then results in our previous

sections are likely driven by the number of bedrooms, not prices. However, if λ is 3 We also use the beginning and the ending month of the sample period to replicate this analysis and results remain strong and robust.

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significantly negative, it is reasonable to conclude that pricier condos have lower betas

not because they have more bedrooms.

Two things are worth noting. First, we implicitly assume that condos with the same

numbers of bedrooms have similar total square meters, so their prices in RMB per square

meter are proportional to total condo prices. Second, the model in (10) does not include

subdivision fixed effects any more. This is because we are using the variation in Pc ,s ,b

across subdivisions to help distinguish the effects of prices from the effects of the number

of bedrooms, and each subdivision only has one value of Pc ,s ,b . Subdivision dummies, if

included, would lead to perfect multicollinearity and cannot be distinguished from the

effects Pc ,s ,b .

Table 7 reports the number of subdivisions and summary statistics of actual prices (RMB

per square meter) in May 2012 for 1-bedroom, 2-bedroom, 3-bedroom, 4-bedroom, and

all condos, including the minimum, median, maximum, mean, and standard deviation of

prices. Note that price series of some condo types in some subdivisions do not cover

May 2012. Such price series constitute only about 5% of the sample, so we exclude these

condos from this table and our analysis in this section.

Table 8 reports results of estimating the model in (10). It is apparent that estimates of λ

are statistically significant and negative for all bedroom types, at the 1% level for one to

three-bedroom condos and at the 10% level for four-bedroom condos. This result

provides strong evidence suggesting that pricier condos have lower risk, when the

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number of bedrooms is held constant. In terms of economic magnitude, estimates

indicate that, when prices increase by one standard deviation, betas decrease by 0.094,

0,058, 0,052, and 0.028 for one- to four-bedroom condos respectively. Furthermore, note

that there is some evidence showing that alphas increase with prices, which, however, is

statistically significant for one- and two-bedroom condos, but not for three- and four-

bedroom condos.

6. Conclusions

This paper aims to test whether pricier houses have lower systematic risk, with the focus

being on separating the effects of house prices and those of location-related variables that

are correlated with house prices. Our identification strategy is based on a special feature

of a condo transaction price dataset from China. This dataset provides price information

for condos that have different size but are located in the same subdivisions and thus have

the same locations. Under a reasonable assumption that larger condos have higher prices

than smaller ones in the same subdivisions, we empirically test whether larger condos

have lower systematic risk, which is measured with their betas of the market risk

premium in a CAPM framework with the average condo market appreciation index being

a proxy for the market portfolio.

In a variety of models, from simpler models that do not allow heterogeneity in levels of

alphas and betas across subdivisions to more complicated ones that allow variation of

average alphas and betas across subdivisions, we find very consistent and generally

robust evidence that larger condos, which are assumed to be pricier, have lower betas

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than smaller ones. Since both larger and smaller condos are located in the same locations,

the result we find this paper is unlikely driven by location-related characteristics that are

related to condo prices.

We also analyze whether it is the number of bedrooms instead of prices that drives the

above result. To do so, we hold constant the number of bedrooms and test whether betas

are related to condo prices for condos with the same number of bedrooms. We find very

strong result that pricier condos have statistically significantly lower betas than cheaper

condos with the same number of bedrooms.

Results in this paper, along with those provided in recent research (see, e.g. Han (2013),

Peng and Thibodeau (2013), Hartman-Glaser and Mann (2016), and Peng and Thibodeau

(2017)), call for future theoretical and empirical research on why and how pricier houses

have lower systematic risk, as well as implications of this phenomenon for homeowners,

mortgage lenders, and policy makers.

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Table 1. Subdivisions in the sample This table reports the number of subdivisions as well as those with one-bedroom, two-bedroom, three-bedroom, and four-bedroom types in Beijing, Shanghai, Guangzhou, and Shenzhen.

City Beijing Shanghai Guangzhou Shenzhen Subdivisions 663 322 489 595 With One-bedroom 546 166 183 248 With two-bedroom 632 303 456 560 With three-bedroom 618 311 471 530 With four-bedroom 271 202 214 350

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Table 2. Summary of log price appreciation by bedroom types This table reports statistics for average monthly log price appreciation rates across time and subdivisions for one-bedroom, two-bedroom, three-bedroom, and four-bedroom types respectively.

% 1-bedroom 2-bedroom 3-bedroom 4-bedroom Full sample Sample size 109,282 199,514 194,173 94,818 597,787 Minimum -39.99% -39.99% -39.98% -39.99% -39.99% Median 1.24% 1.30% 1.29% 1.21% 1.28%

Maximum 39.97% 39.91% 39.98% 39.99% 39.99% Mean 1.35% 1.41% 1.39% 1.24% 1.37%

Std. dev. 10.06% 7.97% 8.32% 11.29% 9.08%

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Table 3. Summary of indices by bedroom types This table reports statistics for the indexes of monthly average log price appreciation rates, for one-bedroom, two-bedroom, three-bedroom, and four-bedroom types respectively.

% 1-bedroom 2-bedroom 3-bedroom 4-bedroom Full sample Sample size 119 119 119 119 119 Minimum -4.17% -2.90% -3.32% -2.48% -3.04% Median 1.22% 1.33% 1.29% 1.10% 1.24%

Maximum 8.58% 7.01% 6.84% 5.19% 6.94% Mean 1.38% 1.43% 1.39% 1.23% 1.38%

Std. dev. 2.08% 1.88% 1.78% 1.63% 1.81%

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Table 4. Systematic risk across size types This table reports results of regressions in equation (7) for one-, two-, three-, and four-bedroom condos respectively. T-statistics calculated using White's heteroscedasticity-consistent standard deviations are reported in parentheses. ***, **, and * indicate significant levels of 1%, 5%, and 10% respectively. One-bedroom Two-bedroom Three-bedroom Four-bedroom

α -0.001*** (-3.77)

0.000 (0.60)

0.000* (1.89)

0.000 (1.09)

β 1.114*** (67.81)

1.030*** (107.05)

0.981*** (95.98)

0.844*** (41.91)

Sample size 109,282 199,514 194,173 94,818 Adjusted R2 0.040 0.054 0.045 0.018

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Table 5. Systematic risk across size types in pooled regression This table reports the result of estimating the model in (8) using all condo types from all subdivisions in all four cities. The sample size is 597,787. The adjusted R2 is 0.04.

Coefficients Standard errors t-statistics

α1 -0.001 0.000 -4.17

ρ2 0.001 0.000 3.66

ρ3 0.002 0.000 4.37

ρ4 0.002 0.000 3.84

β1 1.114 0.148 75.14

λ2 -0.084 0.184 -4.54

λ3 -0.133 0.019 -7.14

λ4 -0.270 0.022 -12.37

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Table 6 Heterogeneous systematic risk: two groups This table reports results of the regression in equation (9) for the whole sample and each of the four cities. T-statistics calculated using White's heteroscedasticity-consistent standard deviations are reported in parentheses. ***, **, and * indicate significant levels of 1%, 5%, and 10% respectively. All Beijing Shanghai Guangzhou Shenzhen

α s Yes Yes Yes Yes Yes

ρ 0.000 (1.41)

0.001** (1.97)

0.001* (1.82)

0.002 (0.34)

0.000 (0.59)

βs Yes Yes Yes Yes Yes

λ -0.042*** (-3.01)

-0.090*** (-5.97)

-0.108*** (-3.99)

-0.001 (-0.02)

-0.024 (-1.19)

Sample size 597,787 212,427 101,726 116,529 167,105 Adjusted R2 0.040 0.089 0.055 0.023 0.065

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Table 7. Summary of prices by condo types This table reports the number of subdivisions and the minimum, median, maximum, mean, and standard deviation of sale prices (RMB per square meter) in May 2012 for 1-bedroom, 2-bedroom, 3-bedroom, and 4-bedroom condos, as well as all condo types in the sample.

1-bedroom 2-bedroom 3-bedroom 4-bedroom Full sample Subdivisions 1,143 1,951 1,930 1,037 6,061

Minimum 6,448 5,766 5,475 5,976 5,475 Median 23,337 21,625 21,816 25,294 22,555

Maximum 123,444 87,755 101,147 122,473 123,444 Mean 24,744. 23,1745 23,489 27,861 24,373

Std. dev. 9,645 9,331 10,227 14,259 10,790

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Table 8. Price vs. bedrooms in affecting betas This table reports results of the regression in equation (10) for each size type across separately. T-statistics calculated using White's heteroscedasticity-consistent standard deviations are reported in parentheses. ***, **, and * indicate significant levels of 1%, 5%, and 10% respectively.

One-bedroom Two-bedroom Three-bedroom Four-bedroom

α c Yes Yes Yes Yes

βc Yes Yes Yes Yes

ρ 0.001*** (2.93)

0.001*** (2.09)

0.000 (1.15)

-0.000 (-0.39)

λ -0.094*** (-4.57)

-0.058*** (-5.05)

-0.052*** (-4.91)

-0.028* (-1.85)

Sample size 100,041 193,089 186,144 85,847 Adjusted R2 0.046 0.061 0.051 0.020

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Figure 1. Histogram of monthly log price appreciation rates

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Figure 2. The market index of house prices

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Figure 3. The index of four different types