Investing in single family
housing
Kevin C.H. Chiang
Outline
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The determinants of home price
appreciation
No-arbitrage between owning and
renting
An application
Popular investments
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Investing in single family housing is
popular.
In U.S., close to 70% of households
invest in single family housing; about
30% of households rent a house or
apartment.
Benefits of owning a house: financial
and emotional.
Is investing in a house a good
deal?
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Financially speaking, yes and no.
On average, the appreciation rate based on
purchase price is close to than that of Tbills.
But the built-in high leverage via mortgage
can make the return on equity substantial.
If one uses the same leverage on other
investments, houses suck (unconditionally).
How about conditionally?
Emotionally speaking, houses rock?
Location, location, location
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The rate of price appreciation is
location-specific.
During the 2004-2007 period, the
median sales price of existing homes
in Riverside, CA went up about 30%.
During the same period, the median
sales price in Pittsburgh went down
about 3%.
The determinants of appreciation
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Population growth (+).
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Employment (+).
Household income (+).
Interest rate (-).
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Immigration accounts for about 1/3 of U.S. population
growth.
Immigrants tend to live in sunbelt cities. Sunbelt cities
have been enjoyed the greatest home price appreciation.
Higher interest rate = higher cost of owning a house =
lower house price.
Cost of renting housing (+).

But this causality runs both way.
Asset bubble
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In addition, housing prices tend to
appreciate madly when the money
supply is too high.
As of 01/2016.
Economic base
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Regional population, employment, and
income is a function of the regional
economy.
Riverside had a strong economy. This lead
to higher population, employment, income,
and home price.
Pittsburgh ran the other way.
Thus, it is important to identify and evaluate
regional economic drivers (economic base)
when investing in a home.
Speculative determinants
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Expectation toward appreciation.
Regulation: tax, mortgage restrictions,
etc.
Example: the property tax in Hong
Kong, Taiwan, and China ranges from
zero to very low. It contributes to
extreme high property prices in these
three regions.
The supply side
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The previous discussions focus on the
demand side of housing.
The supply side is on average less
important than the demand side:
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Cost of land
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Land-locked: Flagstaff.
Sea-locked: Honolulu and coastal cities.
Cost of labor
Cost of materials
Development restrictions
Submarket factors
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Appreciate when net benefits are
created: services received have a
value greater than the taxes and fees
paid for them.
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A new, nice public school just built in your
neighborhood.
Rezoning.
Etc.
Home price too high? Too
low?
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We do not have a good equilibrium asset
pricing model for pricing a house.
The previous demand-supply discussions
are quite general; we do not have a formula.
One way to have a formula is to use a noarbitrage relationship: the cost of using
(owning) a home = the cost of renting a
home.
Cost of ownership, I
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The (annual) cost of owning a house has 6
components.
1. Opportunity cost: the cost of foregone
return that the homeowner could have
earned by investing in something else.
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A conservative measure: the price of housing
times the risk-free rate = p × rf.
2. Cost of property taxes: p × w, where w is
the property tax rate.
Cost of ownership, II
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3. The (federal) tax deductibility of mortgage
interest and property taxes (-): p ×  × (rm
+ w), where  is the (marginal) effective
income tax rate, and rm is mortgage interest
rate.
4. Maintenance (depreciation) costs as a
fraction  of home value: p × .
5. Expected capital gain/appreciation (or
loss) (-): p × g, where g is the appreciation
rate.
6. An additional risk premium to compensate
homeowners for the higher risk of owning
versus renting: p × .
Cost of ownership, III
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Annual $ cost of ownership = p × rf + p × w
– p ×  × (rm + w) + p ×  – p × g + p ×
.
Because every term is a function of p, we
can write the cost as a percentage of p (we
call it the user cost of housing):
User cost = rf + w –  × (rm + w) +  – g + .
Cost of renting
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Annual $ renting costs: R = p × r. Let
us call r the rent rate, i.e., the ratio of
the rent to the house price.
No-arbitrage
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Annual $ renting cost = annual $ cost of
owning.
R (= p × r ) = p × rf + p × w – p ×  ×
(rm + w) + p ×  – p × g + p × .
That is, the rent rate (the inverse of the
price-to-rent ratio) must equal the user cost.
(R / p =) r = rf + w –  × (rm + w) +  – g + .
The lower the user cost, the higher the
price-to-rent ratio.
An example
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r = rf + w –  × (rm + w) +  – g + .
Suppose rf = 4.5%; w = 1.63% (VT);  = 25%; rm =
5.5%;  = 2.5%; g = 3.5%;  = 2%.
The user cost = 4.5% + 1.63% – 0.25 × (5.5% +
1.63%) + 2.5% – 3.5% + 2% = 5.3475%.
For every dollar of house price, the owner pay
5.3475 cents per year in cost.
An investor will be willing to pay up to 18.7 times (1
/ 0.053475) the market rent to purchase a house.
If the market rent is 4% and our inputs are correct,
do houses look expensive? What if 6%?
Some analyses, I
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r = rf + w –  × (rm + w) +  – g + .
Now, let us hold all else equal and look at
one variable at a time.
If interest rates drop, what would happen to
house prices?
If income tax rate is raised, what would
happen to the user cost?
If investors anticipate high price
appreciation, what happen to the user cost?
Some analyses, II
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r = rf + w –  × (rm + w) +  – g + .
Suppose you buy houses and rent them out.
If you expect a high price appreciation,
would you accept a lower rent?
Some cities, e.g., SF, Boston, NYC, LA,
have been characterized by a consistent,
high price-to-rent ratio for the past several
decades. Why?
This makes price-to-rent (or price-toincome) a poor measure for judging whether
house prices are too high.
Appreciation rate, g
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In U.S., the nominal appreciation rate is
about 3.5% (this varies a lot across cities
and over time), which is slightly above
inflation rate.
Construction costs grow less than inflation
rate.
Thus, land is appreciating faster than the
structure (building).
In other words, if you would like to bet on
single family housing, it may be a better idea
to bet on land; surely, it is more risky.
The limitations
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This analysis assumes no arbitrage.
But this is not so for RE transactions.
Thus, we would expect deviations from
the equality, r = rf + w –  × (rm + w) +
 – g + .
These deviations may last for a long
time (why?), but should not last forever
though.
The impact of housing market
on rental market
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In 2007, “apartment building have been one of the
few bright spots in the real estate industry as
people forced out of the home-buying market by
foreclosures or the credit crunch have turned to
renting.”
“But now the specter of job losses is beginning to
spread the gloom into that sector as well. As
would-be renters are doubling up in apartments or
moving in with friends and families, rent growth and
occupancy rates are beginning to fall in many
cities.”
Source: WSJ, Aug. 20, 2008.
An application: Beijing vs.
NYC
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2015 Beijing rent rate: 2%; note that
new properties in China are mostly 70years leasehold.
2015 NYC rent rate: 4%.
Using no-arbitrage argument, what is
the most likely cause for the
difference?
Recalled (from appraisal topic)
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y0 = R0 + g.
Required return (yield) = cap rate +
expected appreciation rate.
This is another way to understand the
difference!
Housing price index, Shanghai
Along with double-digit
appreciation
Meanwhile
Superblock
Meanwhile
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China’s debt has quadrupled since
2007. Fueled by real estate and
shadow banking, China’s total debt
has nearly quadrupled, rising to $28
trillion by mid-2014, from $7 trillion in
2007. At 282 percent of GDP, China’s
debt as a share of GDP, while (likely)
manageable, is larger than that of the
United States or Germany.
Debt to GDP ratio (x axis: change
in the (%) ratio, 2007-2014)
Meanwhile
The consequences of unrealistic
expectation toward appreciation
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Low cap rate?
High RE price?
Oversupply of space? Smog?
High vacancy rate?
Overly leveraged?
Default?
Bubble bursts?
Another consequence
Another statistic
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2015 Beijing price to income ratio: 30.
2015 NYC price to income ratio: 10.
2015 Los Angeles price to income
ratio: 5.
More
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On Sep. 4 (2013), Sunac China Holdings paid
73,000 yuan ($11,900) per buildable square meter,
or about $1,100 per buildable square foot, for a
residential land parcel near Beijing’s embassy
district. (For comparison, the most expensive
property deal in Manhattan in H1 2013
fetched $800 per buildable square foot; the average
for 2012 was $323.)
03/21/2015
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(Bloomberg) -- China doesn’t need the rapid
economic growth of the past and will instead focus
on tasks including returning the blue to Beijing’s
skies, Vice Premier Zhang Gaoli told global
executives gathered in the city.
“It is both impossible and unnecessary to maintain
the very high growth of the past,” said Zhang, a
member of the seven-man Politburo Standing
Committee, the nation’s top decision-making body.
“We’ve paid the price for that,” he said Sunday.
“It’s not sustainable.”
Group assignment
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Please study the housing market in
Burlington and neighboring cities/villages.
Please use the no-arbitrage framework to
analyze the local housing market and
answer the following question: is this a good
time to buy a house here?
Please submit your group report in a week.
References
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http://www.mckinsey.com/insights/economic_studies/debt_and
_not_much_deleveraging?p=1
http://buuea.com/looking-into-the-china-housing-marketbubble-using-gdp-and-affordability-indices/
http://www.globalpropertyguide.com/Asia/china/Price-History
http://qz.com/121852/if-china-has-a-real-estate-glut-why-isbeijing-more-expensive-than-manhattan/
http://www.metropolismag.com/Point-of-View/August2013/The-Real-Problem-with-Chinas-Ghost-Towns/