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Insper Instituto de Ensino e Pesquisa
Ricardo Lins Ribeiro
A Brazilian housing market analysis: pricing and fundamentals
São Paulo
2015
Ricardo Lins Ribeiro
A Brazilian housing market analysis: pricing and fundamentals
Dissertação apresentada ao Programa de
Mestrado Profissional em Economia do
Insper, Instituto de Ensino e Pesquisa, como
parte dos requisitos para obtenção do título
de Mestre em Economia.
Área de Concentração: Finanças
Orientador: Prof. Dr. Ricardo Dias de
Oliveira Brito
São Paulo
2015
RIBEIRO, Ricardo Lins
A Brazilian housing market analysis: pricing and
fundamentals. / Ricardo Lins Ribeiro. – São Paulo, 2015.
Dissertação (Mestrado – Programa de Mestrado Profissional
em Economia) – Insper instituto de Ensino e Pesquisa, 2015.
Orientador: Prof. Dr. Ricardo Dias de Oliveira Brito
1. Real Estate 2. Valuation 3. Brazil
Folha de Aprovação
Ricardo Lins Ribeiro
A Brazilian housing market analysis: pricing and fundamentals
Dissertação apresentada ao Programa de
Mestrado Profissional em Economia do
Insper Instituto de Ensino e Pesquisa, como
parte dos requisitos para obtenção do título
de Mestre em Economia.
Área de Concentração: Finanças
Data da Aprovação: __ / __ / __
Banca Examinadora
__________________________________
Prof. Dr. Ricardo Dias de Oliveira Brito
Orientador
Instituição: Insper
__________________________________
Prof. Dr. Michel Viriato Araujo
Insper
__________________________________
Prof. Dr. Osmani Guillen
BACEN / IBMEC-RJ
Resumo
RIBEIRO, Ricardo Lins. A Brazilian housing market analysis: pricing and
fundamentals, 2015. Dissertação (Mestrado) - Insper Instituto de Ensino e Pesquisa,
São Paulo, 2015.
Este trabalho apresenta evidencias de que o preço dos imóveis no 2ºTri/2015 esteve
sobrevalorizado. Os resultados estão baseados em analises no mercado residencial de
São Paulo onde fundamentos como expectativas de taxa de juros real e PIB real são
responsáveis por explicar parte do movimento da relação price-to-rent. Ao dividir a
amostra em duas partes, no período entre o 1ºTri/2006 até 4ºTri/2012, movimentos na
relação price-to-rent pode ser explicadas pelas variáveis econômicas escolhidas. No
entanto, entre 4ºTri/2012 e 2ºTri/2015 a relação Imputed-to-actual-rent alcança os picos
mais altos, sugerindo que a alta observada na relação price-to-rent não pode ser
explicada pelos fundamentos econômicos propostos no modelo deste trabalho. O
componente de comportamento proposto mostrou importante relevância em explicar a
dinâmica de preço, confirmando a existência de certo momentum esperado nos preços
de imóvel. A conclusão é que outros fatores sugerem explicar os movimentos recentes
no preço dos imóveis que não os baseados na teoria econômica aplicada neste trabalho.
Códigos JEL: R3; G12.
Palavras-chave: Mercado imobiliário; Avaliação; Brasil
Abstract
RIBEIRO, Ricardo Lins. A Brazilian housing market analysis: pricing and
fundamentals, 2015. Dissertation (Mastership) - Insper Instituto de Ensino e Pesquisa,
São Paulo, 2015.
This work presents evidence that home price in 2Q/2105 are overvalued. The results are
based on the analyses of the São Paulo residential market. It was found that
fundamentals, such as real interest rate and real GDP growth forecast, well explain
movements in price-to-rent ratio from 1Q/2006 to 4Q/2012. Nevertheless, from
4Q/2012 to 2Q/2015 the imputed-to-actual-rent ratio reached its peak, suggesting that
the price-to-rent upward trend could not be explained by the economic model proposed.
A behavioural component also showed an important relevance in explaining the pricing
dynamic, confirming the momentum expected in home price and leading to the
conclusion that others factors rather than the fundamentals chosen by this work can
explain the recent trend.
JEL Codes: R3; G12.
Keywords: Real estate; Valuation; Brazil
Executive Summary
The rapid increase in Brazilian home prices over the past several years has raised
concerns about the existence of mispricing in this asset class. A closely related concern
is whether home prices are susceptible to a steep decline that could have a severe impact
on the broader economy. Changes in house prices have important consequences for the
real economy as they affect both homeowners’ wealth and their ability to borrow,
leading to consumers reducing spending to boost saving and improve their weakened
financial condition.
To make inferences about a possible mispricing in the São Paulo housing
market, this work used the financial no arbitrage equilibrium between renting and
owning. The theory argues that, in equilibrium, the annual cost of owning a house is
expected to equal the annual cost of renting. The idea is that if the cost of owning a
house increases, homeowners will prefer to sell their homes and rent a new one, forcing
prices to go down. The opposite is also true. In fact, in both cases home price changes
should be the main factor responsible for reestablishing the equilibrium.
As an illustration, the “user cost” model that reflects the annual cost of
ownership is represented by components such as opportunity cost and expected home
price appreciation. In this context, a house price bubble occurs when homeowners have
unreasonably high expectations about future capital gains, leading them to perceive their
“user cost” to be lower than it actually is and thus pay “too much” to purchase a house
at that moment.
The Imputed-to-Actual-Rent and Imputed-Rent-to-Income are the ratios used to
take into account changes in the price-to-rent ratio that reflect fundamentals and not
necessarily represent mispricing. For instance, an increase in price-to-rent ratio could be
explained by a prior decrease in real interest rate or a positive GDP growth forecast,
both exogenous variables. The Imputed-to-Actual-Rent is calculated by dividing the
annual cost of owning a house by the annual cost of renting and should equal one in
equilibrium.
Analyzing the period from 2006 to the second quarter of 2015 from the city of
São Paulo, changes on Imputed-to-Actual-Rent and Imputed-Rent-to-Income ratios
from 1Q/2006 to 4Q/2012 appear to be well explained by fundamentals. An increase in
the price-to-rent ratio observed at the beginning of 2010 was driven by a combination of
the decrease in real interest rate and an increase in expectation of home price
appreciation, provided by expected real GDP growth. However, the ratio continued to
increase after 4Q/2102 in an unfavorable scenario of rising interest rates and a drop in
expectation of real GDP growth, leading to a conclusion that this last movement could
not be explained by the economic theory. The evidence presented above suggests that
house prices in São Paulo could be overvalued after 2Q-2015.
Summary
1
Introduction ............................................................................................................... 8
2
Literature Review .................................................................................................... 10
3
Model ...................................................................................................................... 14
4
Data ......................................................................................................................... 15
5
Results ..................................................................................................................... 20
5.1.
Dividend Yield .................................................................................................... 21
5.2.
Imputed-to-Actual Rent ratio............................................................................... 22
5.3.
Imputed-to-Actual Rent ratio X Price-to-Rent ratio – normalized ...................... 24
5.4.
Imputed-Rent-to-Income and Price-to-Income ratio ........................................... 26
5.5.
User cost regression ............................................................................................. 28
5.6.
Home price appreciation implicit rate ................................................................. 31
5.7.
Price-to-rent ratio forecast ................................................................................... 32
6
Conclusion............................................................................................................... 33
References ...................................................................................................................... 34
8
1 Introduction
The rapid increase in Brazilian home prices over the past several years has raised
concerns about the existence of mispricing in this asset class. A closely related concern is
whether home prices are susceptible to a steep decline that could have a severe impact on the
broader economy. Changes in house prices have important consequences for the real economy
as they affect both homeowners’ wealth and their ability to borrow (Anenberg and Laufer,
2014). Many analysts argue that such a decline in household wealth would have adverse
macroeconomic effects, as already overextended consumers reduce spending to boost savings
and improve their weakened financial condition (McCarthy and Peach, 2004).
Indeed, home prices have been rising rapidly in Brazil. Since 2008 for instance, real
home prices in São Paulo have increased more than fifty percent (Figure 1.A), roughly double
the increase in rent prices in the same period. Therefore, “how does one tell when rapid
growth in house prices is caused by fundamental factors of supply and demand and when it is
an unsustainable bubble?” (Himmelberg, Mayer and Sinai, 2005). Shiller (2013) suggested in
a press interview that the Brazilian economy apparently has strong signs of a housing price
bubble. Thereafter, studies in this field in Brazil have become extremely relevant.
As a worldwide trend, the housing market gained strong attention after the sub-prime
crises in the US market in the 2007-2008 periods. Himmelberg, Mayer and Sinai (2005)
successfully identify some mispricing in the late 1980s in the US housing market but were not
able to state the same conclusion in 2004, just a few years from the crises. Case and Shiller
(2004) were able to identify, in the same period, elements of a speculative bubble in home
prices in some cities in the US, alerting to a possible price correction. In Brazil, a work by
Tavares (2012) investigated the hypothesis of a real estate bubble in the Rio de Janeiro
housing market and concluded that no signs of a bubble seemed to exist. The author showed
that the strong increase in house prices was well explained by different local factors, such as
an increase in real income and a reduction in the unemployment rate.
The economic analysis of the housing sector relies on ‘no arbitrage’ relationships, like
the economic study of financial and labor markets. Case and Shiller (1987, 1989, 1990) were
pioneers in the study of housing price dynamics, and they emphasized a financial no arbitrage
condition where investors earn equal risk-adjusted returns by investing in housing or other
9
assets. Poterba (1984) and Himmelberg, Mayer and Sinai (2005) focus on the no arbitrage
condition between renting and owning a home. Alonso (1964) and Rosen (1979) examine the
implications for housing prices implied by a spatial no arbitrage condition where individuals
receive similar net benefits from owning in different places.
This work uses the financial no arbitrage equilibrium between renting and owning to
make inferences about a possible mispricing in the São Paulo housing market. Many authors
supported that this approach offers greater precision in comparison to others and, because of
this, it has been broadly used (Glaeser and Gyourko, 2007; Hubbard and Mayer, 2009;
McCarrthy and Peach, 2012). Following Himmelberg, Mayer and Sinai (2005), the theory
argues that, in equilibrium, the annual cost of owning a house is expected to equal the annual
cost of renting. The authors calculate the user cost of owning a house based on the first user
cost model proposed by Poterba (1984), having the opportunity cost and expected home price
appreciation as the main components.
The Imputed-to-Actual-Rent and Imputed-Rent-to-Income ratios ratios were created by
Himmelberg, Mayer and Sinai (2005) to take into account changes in price-to-rent ratio that
could be explained by external factors, such as real interest rate and GDP growth, and not
necessarily represents mispricing. Fundamentals seem to explain most of the movements in
these ratios along the entire period studied. Therefore, the dynamic of home prices and rents
after 4Q/2102 could not be fully explained by the theory proposed here. The model
reasonably predicts the price-to-rent ratio from the first quarter of 2006 to the fourth quarter
of 2012. However, the ratio continues to increase in an unfavorable scenario of rising interest
rates and a significant drop in expectations of real GDP growth. Thus, the conclusion
grounded in economic theory is that home prices in the second quarter of 2015 appear
overvalued and should potentially fall.
This work begins in section 2 with a review of the literature on the definition of a
“bubble” in house prices and a discussion of the behavioral finance theory and equilibrium
models. Section 3 describes the adaptation of the models from Poterba (1984) and
Himmelberg, Mayer and Sinai (2005) to the Brazilian housing market condition. Then, the
data collected is described in section 4 and followed by section 5, which brings a
comprehensive discussion of the results found over all the different exercises conducted.
Finally, the conclusion presents the expectations for home price appreciation based on
economic fundamentals.
10
2 Literature Review
There is very little agreement about the definition of “housing bubble” and its
difference from the term “boom”. For Case and Shiller (2005), the term “boom” is neutral and
suggests that the rise in price may be an opportunity for investors. In contrast, for them, the
term “bubble”, that starts to be used only after 2002, has a negative judgment on the
phenomenon of rising prices. The authors describe “bubble” as “a situation in which
excessive public expectations of future price increases cause prices to be temporarily elevated.
During a housing price bubble, homebuyers think that a home that they would normally
consider too expensive for them is now an acceptable purchase because they will be
compensated by significant further price increases.” In the same way, Stiglitz (1990) provided
a famous definition of asset bubbles: "If the reason that the price is high today is only because
investors believe that the selling price is high tomorrow – when 'fundamental' factors do not
seem to justify such a price – then a bubble exists." Himmelberg, Mayer and Sinai (2005)
think of a housing bubble as being driven by “homebuyers who are willing to pay inflated
prices for houses today because they expect unrealistically high housing appreciation in the
future”.
The behavioral finance theory gained strong attention after the 2007-2008 crises in the
US and became an important alternative to evaluate house price dynamics. Case and Shiller
(2005) demonstrated that an increase in public observation of housing prices leads to public
expectations of future price increases in the same direction. The survey indicates that
elements of a speculative bubble in single-family home prices existed in some cities. For
Shiller (2008), the notion of a speculative bubble could be described as a feedback
mechanism, a social epidemic in which certain public conceptions and ideas lead to emotional
speculative interest in the markets and, therefore, to price increases. For the author, this idea
disseminates among people over time and, consequently, price increases could be above
market fundamentals. Prices stop increasing when the feedback ceases and the public interest
in the investment in housing market drops sharply, the moment the bubble bursts.
As stated before, the economic analysis of the housing sector relies on ‘no arbitrage’
relationships. Case and Shiller (1987, 1989, 1990) presented the financial no arbitrage
condition where investors earn equal risk-adjusted returns by investing in housing or other
assets. Alonso (1964) and Rosen (1979) examine the implications for housing prices through
11
a spatial no arbitrage model. Finally, Poterba (1984) and Himmelberg, Mayer and Sinai
(2005) studied the no arbitrage condition between renting and owning a home.
As Glaser and Gyourko (2007) states, “the spatial equilibrium model requires
homeowners (or renters) to be indifferent between different locations”; since house prices
would be higher in more popular locations or good neighbourhoods, individuals should pay a
premium to live in these places. Rosen (1979) defined three goods in the market: land,
products manufactured by homeowners and amenities associated with the land. For him,
equilibrium in the housing market is obtained by land pricing, in which preferred places
present higher prices due to a strong demand. Therefore, people who cannot afford this are
forced to live in less desirable places. Yet, Alonso (1964) based equilibrium price on the
Pareto principle stating that the house market is in equilibrium when no user can increase
profits by moving to any other location and no homeowner can increase revenue by changing
the price. Glaeser and Gyourko (2007) have shown that “the spatial no-arbitrage condition
fails to yield tight predictions about the relationship between housing prices and income”. The
spatial equilibrium model implies a spatial condition that is very difficult to address, such as
the relationship between changes in housing prices with changes in income and amenities. An
example of that is how home prices should vary with changes in local temperature and
whether people are overpaying for that. This weakness helps explain why economists have
chosen other directions, different from the spatial equilibrium model.
Himmelberg, Mayer and Sinai (2005) contribute with their financial approach in
which there should be no predictable excess return between being an owner and being a
renter. They argue that the correct calculation of the financial return associated with an
owner-occupied property compares with the value of living in that property for a year with the
lost income that one would have received if the owner had invested the capital in an
alternative investment. This line of reasoning is the basis for an economically justified way of
evaluating whether the level of housing is “over” or “under” appreciated.
In general, for Himmelberg, Mayer and Sinai (2005) the housing market is in
equilibrium when the rental cost per year (𝑅𝑡 ) equals the annual cost of ownership(𝑃𝑡 𝑢𝑡 ),
when individuals are indifferent between owning and renting their home. The one-year cost of
owning a house defined as the user cost (𝑢𝑡 ) is calculated and then compared to rental costs to
judge whether the cost of owning is out of line with the cost of renting.
12
𝑅𝑡 = 𝑃𝑡 𝑢𝑡 .
(1)
Based on Poterba (1984) user cost model, Himmelberg, Mayer and Sinai (2005)
defined the user cost of ownership (𝑢𝑡 ) by the sum of six components:
𝑟𝑓
𝑢𝑡 = 𝑟𝑡 + 𝜔𝑡 − 𝜏𝑡 (𝑟𝑡𝑚 + 𝜔𝑡 ) + 𝛿𝑡 − 𝑔𝑡+1 + 𝛾𝑡 .
(2)
To compute the user cost of housing for the United States case, the authors went
𝑟𝑓
through all the six components afore mentioned. For the first component ( 𝑟𝑡 ), which is the
opportunity cost, they used the constant yield to maturity on a 10-year US Treasury note and
subtracted the 10-year expected inflation rate. The second (𝜔𝑡 ) and the third (𝜏𝑡 (𝑟𝑡𝑚 + 𝜔𝑡 ))
components vary between the metro areas, average property tax rates and income tax rates
were collected from the TAXISM model of the National Bureau of Economic Research.
However, data collected from the International Revenue Service showed that 65 percent of
tax-filing households do not itemize their tax deductions, meaning that they do not benefit
from the tax deductibility of mortgage interest and property taxes. The authors decided to
include a reduction of 50 percent in the tax benefit from the user cost of ownership to address
this imprecision. For the fourth component (𝛿𝑡 ), an annual depreciation rate of 2.5 percent
was considered as in Harding, Rosenthal and Sirmans (2004). The expected capital gain or
loss from the fifth component (𝑔𝑡+1 ) should reflect the expected growth rate of future house
prices using the average real growth rate of house prices from 1940-200 from Gyourko,
Mayer and Sinai (2004). Finally, the estimated risk premium (𝛾𝑡 ) obtained by Flavin and
Yamashita (2002) was around 2.0 percent.
The way Himmelberg, Mayer and Sinai (2005) infer whether house prices are too high
is to calculate the imputed rent on housing and compare it to actual rents available in the
market. The imputed rent is the user cost times the level of house price. They create an index
of the imputed-to-actual-rent ratio by dividing the imputed rent index by the index of market
rents:
Imputed-to-Actual-rent ratio =
𝑢𝑡 𝑃𝑡
𝑅𝑡
(3)
13
This index permits the conclusion whether the imputed cost of owning a house relative
to renting the same unit has changed within the metropolitan areas and whether the index in a
certain year is at or close to its previous peak level.
From these analyses, Himmelberg, Mayer and Sinai (2005) achieve two important
results for the US housing market. The imputed-to-actual-rent ratio in 2004 appears fairly
priced; in most metropolitan areas, the imputed rent associated with buying a house in 2004 is
not nearly as high as regards actual rents in the past. Only in a few markets housing appears
more expensive regarding the past, showing that there are important differences between the
areas in the US. Second, deviations between the imputed rent and actual rent appear stronger
when real interest rates were unusually high (early 1980s) or unusually low (2001 – 2004)
suggesting that the pick-up in housing prices in 2004 could be explained by fundamental
economic changes. That said, by observing a high imputed-to-actual-rent ratio in the mid1980s and the subsequently decrease in housing price after that, it was possible to conclude
that this methodology successfully identifies prior periods of excessive valuations in the
housing market.
Another measure from Himmelberg, Mayer and Sinai (2005) is the imputed-rent-toincome ratio which provides a good indicator of whether house prices are supported by
household candidates with or without the ability to pay. In a bubble market, the annual cost of
homeownership is expected to rise faster than incomes, raising imputed rent-to-income to
unsustainable levels. They create an index of the imputed-to-actual-income ratio by dividing
the imputed rent index by the income:
Imputed-Rent-to-Income ratio =
𝑢𝑡 𝑃𝑡
𝐼𝑡
(4)
Looking for local factors in the US housing market, Himmelberg, Mayer and Sinai's
(2005) approach successfully reflects that in the late 1980s the cost of owning was high as
regards income and rent. However, in 2004 these measurements showed little evidence of a
bubble in most of the metropolitan areas analyzed. Lastly, they highlight three main insights.
First, the housing market is not a national, equally distributed phenomenon. This means that
14
the current price in one specific metro area could be fairly priced and at the same time others
could be expensive. Second, you can only compare house prices within one specific area
using the annual cost of ownership. Without considering changes in real long-term interest
rates, expected inflation, taxes and house price appreciation, there could be mispricing. Third,
changes in fundamentals affect cities in different manners. For example, in cities with an
inelastic supply of housing, prices will be higher than rents, and prices will be more sensitive
to change in interest rates.
Finally, it is important to take into account an alert made by Glaeser and Gyourko
(2007) that that the price-to-rent ratio predicted by the no arbitrage condition between renting
and owning a home is very sensitive to variation in different factors such as the level of
maintenance costs, the degree of risk aversion, future price growth, and expected tenure,
which are difficult to measure accurately.
3 Model
From equation 1, equilibrium in the housing market implies that the expected annual
cost of owning a house should not exceed the annual cost of renting. If annual ownership
costs rise without a commensurate increase in rents, house prices must fall to convince
potential homebuyers to buy instead of renting. The opposite happens if annual ownership
costs fall. In Brazil, rent is expected to be reduced due to income tax that homeowners are
obliged to pay and disclose to the authorities, assumed in this work to be 15 percent. This
logic can be summarized by equating the net annual rent with the annual cost of ownership:
(1 − 𝜏𝐴 )𝑅𝑡 = 𝑃𝑡 𝑢𝑡 ,
(5)
Yet, the user cost model(𝑢𝑡 ) proposed in this work for the Brazilian housing market is
derived from equation 2 and consists of four components. First, the cost of foregone interest
that the homeowner could have earned by investing in something other than housing, also
known as the opportunity cost mentioned before and calculated as the house price times the
𝑟𝑓
risk-free interest rate ( 𝑃𝑡 𝑟𝑡 ). It is also necessary to consider an income tax of 15 percent in
this kind of investment (𝜏𝐴𝐹 ). Second, the maintenance costs expressed as a fraction 𝛿𝑡 of
15
home value and third the expected capital gain (or loss) during the year (𝑔𝑡+1 ). The last one is
the additional risk premium to compensate homeowners for the higher risk owning versus
renting (𝑃𝑡 𝛾𝑡 ).
𝑟𝑓
𝑢𝑡 = (1 − 𝜏𝐴𝐹 )𝑟𝑡 + 𝛿𝑡 − 𝑔𝑡+1 + 𝛾𝑡 .
(6)
Important to note that the components (𝜔𝑡 ) and (𝜏𝑡 (𝑟𝑡𝑚 + 𝜔𝑡 )) were withdrawn from
the original model of Himmelberg, Mayer and Sinai (2005) as in equation 2. Different from
the US, in Brazil the homeowner does not pay property tax when the property is rented, it
becomes the tenant's obligation. Also, there is no tax benefit when using mortgages to
finance the purchase. For simplification, no benefit from the Brazilian government such as
using the FGTS, Minha casa, minha vida and similar were considered.
The user cost of housing is just a restatement of the annual total cost of ownership
defined above, but expressed in terms of the cost per dollar of house value. Expressing the
user cost in this way is particularly useful because rearranging the equation 5: (1 − 𝜏𝐴𝐹 )𝑅𝑡 =
𝑃𝑡 𝑢𝑡 as 𝑃𝑡 /𝑅𝑡 (1 − 𝜏𝐴𝐹 ) = 1/𝑢𝑡 , allows us to see that the equilibrium price-to-rent ratio
should equal the inverse of the user cost. Thus, fluctuations in user costs (caused, for example,
by changes in interest rates and taxes) lead to predictable changes in the price-to-rent ratio,
which reflect fundamentals, not bubbles.
4 Data
The Brazilian housing market data-base is not broadly calculated and released. Some
nationwide series are either not available to the public or sometimes do not bring relevant
data. With that being said, the suggestion is to focus on a capital, such as São Paulo, where
local private and public entities started developing a significant data-base relevant to
inference-making.
For the analyses, housing prices (𝑃𝑡 ) were obtained from GEOIMOVEL, a Brazilian
real estate research and consulting company which has gathered the largest and most complete
real estate database in Brazil. The raw data was provided with monthly prices for each
neighborhood as in table 1 below.
16
Table 1 – São Paulo: Zones and neighbourhoods
São Paulo
Central
East
West
South
North
Barra Funda
Consolação
Liberdade
República
Santa Cecília
Belem
Itaim Paulista
Itaquera
Mooca
Penha
São Mateus
Tatuape
Vila Matilde
Butanta
Perdizes
Pinheiros
Pirituba
Vila Leopoldina
Campo Limpo
Cidade Ademar
Ipiranga
Itaim Bibi
Jabaquara
Moema
Saude
Vila Mariana
Santana
Tucuruvi
Vila Maria
Casa Verde
Source: GEOIMOVEL and SECOIV-SP
The prices consist only of vertical and horizontal new homes available for sale for
each month. Tracking is performed from the launching to the final sale to the new owner,
which ensures that the trade has been actually done. It is important to notice that prices could
have been volatile during the period as the number of new homes available each month
varied.
Thereafter, by a compilation of
the monthly price of the thirty neighbourhoods
distributed from the five different zones (Table 1), the city of São Paulo average home price
was generated on a per quarter basis. Yet, prices in this work were deflated by the General
Market Price Index (IGP-M) from FGV, which it is broadly used to adjust rent prices over
time.
Figure 1.A – Real House Price in São Paulo
São Paulo
22,6%
15,1%
16,3%
14,5%
8,7%
1,1%
-0,3%
-1,2%
-3,4%
-4,5%
2006
2007
Source: GEOIMOVEL
Source: GEOIMOVEL.
2008
2009
2010
2011
2012
2013
2014
2015
17
Figure 1.B – Real House Price in São Paulo and Zones
Source: GEOIMOVEL.
Data on district rents ( 𝑅𝑡 ) were obtained between 2006 and 2015 from SECOVI-SP,
the São Paulo State Housing Syndicate. The Syndicate has several key operating sectors of
the real estate production and service chain in Brazil. Prices include vertical and horizontal
residential homes and the raw data was provided on a monthly base for each neighbourhood.
Figure 2.A – Real Rent in São Paulo
250
São Paulo
18,09%
200
15,26%
150
100
3,92%
1,87%
1,79%
1,79%
0,15%
Source: SECOVI-SP.
2013
2014
-3,68%
2015
1º Q - 2010
2012
3º Q - 2009
2011
1º Q - 2009
2010
3º Q - 2008
2009
1º Q - 2008
2008
3º Q - 2007
2007
1º Q - 2007
2006
3º Q - 2006
-2,20%
1º Q - 2006
50
-0,20%
18
Figure 2.B – Real Rent in São Paulo and Zones
250
200
Central
East
West
South
North
São Paulo
150
100
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
50
Source: SECOVI-SP.
São Paulo’s local government divides the city into ninety-six neighbourhoods and five
major zones. This work focuses on the analysis of these five zones and the city of São Paulo
generated by the thirty neighbourhoods' data. These were selected according by both
providers match, SECOVI-SP and GEOIMOVEL, since there could be some missing
neighbourhoods or periods without any record. This means that the numbers could have a bias
for different income profiles.
Figure 3.A – User Cost of Ownership
user cost
12,0%
10,0%
8,0%
6,0%
4,0%
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
2,0%
Source: Author’s calculations.
In order to calculate the user cost of housing (𝑢𝑡 ), a generic Brazilian ten-year
𝑟𝑓
maturity bond was used as the opportunity cost (𝑟𝑡 ), obtained from IDkA– ANBIMA, an
index of constant duration in local currency used to calculate the real interest rate.
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
Source: BCB - Brazil Central Bank.
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
1º Q - 2015
2,0%
1º Q - 2015
4,0%
3º Q - 2014
6,0%
1º Q - 2014
8,0%
3º Q - 2014
10,0%
1º Q - 2014
10Y
3º Q - 2013
Figure 3.B – Real 10-Year Interest Rates
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
2,0%
0,0%
the average nominal
4,0% monthly income for the São Paulo city area.
2,0%
19
Source: ANBIMA.
The capital gain (𝑔𝑡+1 ) expected was obtained from the information released by the
Brazilian Central Bank at Focus-Market Readout. The forecast was calculated using the
average of the forward five-year real GDP expected growth. For simplification, the
depreciation (𝛿𝑡 ) and the risk premium (𝛾𝑡 ) used the same assumptions by Himmelberg,
Mayer and Sinai (2005).
Figure 3.C – Real GDP growth – 5 years Forecast
PIB_5Y
6,0%
4,0%
2,0%
0,0%
10Y
10,0%
Income Data
8,0% (It ) are available only for the city of São Paulo, and there are no records
for zones and districts.
A monthly survey of Employment by PNAD Continua-IBGE provides
6,0%
20
Figure 3.D – Real Income
Real Income
2.500
2.250
2.000
1.750
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
1.500
Source: IBGE.
This work assumes that rental and owner-occupied properties are comparable (Smith
and Smith, 2006). Glaeser and Gyourko (2007) refute arguing is not feasible for large-scale
statistical work involving different markets within a country. For them, rental units tend to be
very different from owner-occupied units, and tenants are different from owners in
economically meaningful ways. The assumption used here tries to simplify these problems.
5 Results
The results found in this section corroborates with the argument that some kind of
mispricing could be occurring at the Brazilian housing economy. This perception is grounded
in several exercises carried out in this work and can be summarized by the several outputs.
Firstly, a dividend yield compression across the period studied. Secondly, a spike in the
Imputed-to-rent ratio after the last quarter of 2012 shows that the equilibrium between owning
and renting has not been respected. Thirdly, even when normalized by its ten year average,
the Imputed-to-rent ratio presented a strong increase after the last quarter of 2012. Fourthly,
the user cost regression showed important relevance when using the user cost model to
explain price-to-rent movements. Fifthly, the implicit expected home price appreciation was
above expected, suggesting prices could be higher by an individual’s expectations. Lastly,
there is a forecast suggesting that the price-to-rent ratio should go down.
The following subsections have a more comprehensive explanation of these exercises
and their impact on the home price.
Source: Author’s calculations.
0,5%
West
0,5%
0,4%
0,4%
0,3%
0,3%
0,2%
0,2%
0,1%
0,1%
1º Q - 2011
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2011
East
1º Q - 2011
South
1º Q - 2011
0,1%
3º Q - 2010
0,1%
3º Q - 2010
North
1º Q - 2010
0,2%
3º Q - 2006
São Paulo
1º Q - 2010
0,2%
3º Q - 2009
0,3%
3º Q - 2009
0,3%
1º Q - 2009
0,4%
1º Q - 2009
0,4%
3º Q - 2008
0,5%
3º Q - 2008
0,5%
1º Q - 2008
0,1%
1º Q - 2008
0,1%
3º Q - 2007
0,2%
3º Q - 2007
0,2%
1º Q - 2007
0,3%
1º Q - 2007
0,3%
1º Q - 2006
0,4%
3º Q - 2006
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
0,4%
3º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
0,5%
0,5%
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
21
5.1. Dividend Yield
The first exercise is to compare the Dividend Yield over time. Basically, this rate
represents the expected return when someone purchases a house and rents it in the market. A
simple way to obtain it is by calculating the inverse of the price-to-rent ratio, dividing rent by
the home price.
As in Figure 4 below, the numbers showed a significant yield compression in the city
of São Paulo and zones in the period, gaining strength after 2008, when real home prices
started to increase significantly as shown in Figure 1.A previously. In periods of high
dividend yield, potential homeowners compete against speculators willing to get exposure in
the real estate market, which leads to a run-up in prices.
Figure 4 – Dividend Yield – São Paulo and Zones
Central
22
However, assuming rigidity in rents, theoretically higher prices decrease the dividend
yield; it is thus expected that the demand for home price falls, since investors leave the
market, forcing prices down again. This was not observed in the city of São Paulo and its five
zones.
5.2. Imputed-to-Actual Rent ratio
As in Himmelberg, Mayer and Sinai (2005), it is crucial to check whether the
condition of equation 6 is met in which, in equilibrium, the annual cost of Renting (𝑅𝑡 ) in
Brazilian reais (R$) should equal the annual cost of ownership(𝑃𝑡 𝑢𝑡 ), represented here by the
user cost (𝑢𝑡 ) times the house price (𝑃𝑡 ) in Brazilian reais (R$). Theoretically, these two
curves should move together over time. The Imputed-to-Actual-Rent ratio from equation 3 is
the first instrument used for the said analysis in this work. The value expected for this ratio in
equilibrium is 1.0 if the parity is correct. Yet, the price-to-rent ratio here could be interpreted
as the number of monthly rents required to purchase an apartment of the same size.
The first result highlighted in Figure 5 is that the ratio is never under 1.0 for all zones
in the city of São Paulo for that entire period. Various reasons could explain this: firstly, home
prices could be overvalued for that entire period; secondly, rent prices could be undervalued,
showing some kind of rigidity; and thirdly, the user cost may be overestimated. Further
discussion will attempt to explain these points.
Breaking down the user cost of ownership (Figure 3.A), real interest rate (Figure 3.B)
and expected house price appreciation (Figure 3.C) explain the most significant movements
on the curves. With this in mind, three periods from Figure 5 could be highlighted: the entire
year of 2006, the end of 2008 and after 4Q/2012. During the first two periods, the user cost
was at its “local peak” and could be explained by the peak of real interest rate and expected
home price appreciation close to its ten-year average. During the period after 4Q/2012, the
user cost went from trough to “local peak” in only two years, caused by a combined sharp
increase in real interest rates with a strong decline in expected home price appreciation. Since
both have different signals in the user cost model, they contributed to a higher user cost at the
same time.
1º Q - 2006
3,50
3,50
3,00
3,00
2,50
2,50
2,00
2,00
1,50
1,50
1,00
1,00
0,50
0,50
2Q/2015.
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
West
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
0,50
1º Q - 2011
1,00
0,50
3º Q - 2010
1,00
1º Q - 2010
North
1º Q - 2010
1,50
3º Q - 2009
2,00
1,50
1º Q - 2009
2,50
2,00
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
São Paulo
3º Q - 2009
3,00
2,50
1º Q - 2009
3,00
3º Q - 2008
3,50
3º Q - 2008
3,50
1º Q - 2008
0,50
3º Q - 2007
1,00
0,50
1º Q - 2008
1,50
1,00
1º Q - 2007
2,00
1,50
3º Q - 2007
2,00
3º Q - 2006
2,50
1º Q - 2007
3,00
2,50
1º Q - 2007
1º Q - 2006
3,00
3º Q - 2006
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
3,50
3º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
1º Q - 2006
3,50
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
3º Q - 2006
1º Q - 2006
23
Figure 5 – Imputed-to-Actual-Rent Ratio – São Paulo and Zones
Central
South
East
Source: Author’s calculations.
After 4Q/2102, the user cost model associated with the price-to-rent ratio could
explain the spike on the Imputed-to-actual-Rent ratio. Figure 6 demonstrates that the price-to-
rent ratio started to increase significantly after the end of 2009. This movement was well
captured by fundamentals such as compressing real interest rates and higher expectations of
home price appreciation until 4Q/2012. However, the price-to-rent ratio continues to increase
after 4Q/2012 unexpectedly, in a new scenario of increasing real interest rates and dropping
expectations of home price appreciation. Prices should have gone down to satisfy the
equilibrium condition. Finally, this work first concludes that fundamentals could not explain
the spike seen in the Imputed-to-Actual-Rent ratio and the overvalued price-to-rent ratio in
500
500
450
450
400
400
350
350
300
300
250
250
200
200
West
1º Q - 2011
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
3º Q - 2010
1º Q - 2010
3º Q - 2009
3º Q - 2011
East
1º Q - 2011
3º Q - 2010
South
1º Q - 2011
3º Q - 2010
North
1º Q - 2010
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
São Paulo
1º Q - 2010
200
3º Q - 2009
250
200
3º Q - 2009
250
1º Q - 2009
300
1º Q - 2009
300
3º Q - 2008
350
3º Q - 2008
400
350
1º Q - 2008
450
400
1º Q - 2008
450
3º Q - 2007
500
3º Q - 2007
500
3º Q - 2006
200
1º Q - 2007
250
1º Q - 2007
300
1º Q - 2006
350
3º Q - 2006
400
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
450
3º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
500
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
1º Q - 2006
24
Figure 6 – Price-to-Rent Ratio – São Paulo and Zones
500
Central
450
400
350
300
250
200
Source: Author’s calculations.
5.3. Imputed-to-Actual Rent ratio X Price-to-Rent ratio – normalized
Now, the Imputed-to-Actual-Rent for districts and zones is calculated from equation 3,
but normalized to its ten-year average, following Himmelberg, Mayer and Sinai (2005). This
allows comparing these ratios against the average ratio over the entire period.
Figure 7 highlights the first major result that matches the author’s conclusion:
“Deviations between the imputed rent and the actual rent appear mostly when real interest
rates were unusually high or unusually low”. This could be verified in all different zones and
2,00
2,00
1,50
1,50
1,00
1,00
0,50
0,50
-
-
-
West
Source: Author’s calculations.
1,50
1,00
0,50
-
Vila Prudente
1º Q - 2011
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
3º Q - 2011
East
1º Q - 2011
South
1º Q - 2011
3º Q - 2010
North
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
-
3º Q - 2006
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
-
3º Q - 2010
0,50
1º Q - 2010
1º Q - 2009
0,50
1º Q - 2010
0,50
3º Q - 2009
São Paulo
3º Q - 2009
1,00
1º Q - 2009
3º Q - 2008
1º Q - 2008
0,50
1º Q - 2009
1,00
3º Q - 2008
3º Q - 2007
1,00
3º Q - 2008
1,50
1º Q - 2008
1,00
1º Q - 2008
1,50
3º Q - 2007
1º Q - 2007
3º Q - 2006
1,50
3º Q - 2007
2,00
1º Q - 2007
1º Q - 2006
1,50
1º Q - 2007
2,00
3º Q - 2006
2,00
3º Q - 2006
1º Q - 2006
2,00
1º Q - 2006
1º Q - 2015
3º Q - 2014
1º Q - 2014
3º Q - 2013
1º Q - 2013
3º Q - 2012
1º Q - 2012
3º Q - 2011
1º Q - 2011
3º Q - 2010
1º Q - 2010
3º Q - 2009
1º Q - 2009
3º Q - 2008
1º Q - 2008
3º Q - 2007
1º Q - 2007
3º Q - 2006
2,50
Q - 2006
Q - 2006
Q - 2007
Q - 2007
Q - 2008
Q - 2008
Q - 2009
Q - 2009
Q - 2010
Q - 2010
Q - 2011
Q - 2011
Q - 2012
Q - 2012
Q - 2013
Q - 2013
Q - 2014
Q - 2014
Q - 2015
1º Q - 2006
25
districts most significantly in two different periods: in 2006, when the real interest rate was
high, and by the end of 2012 and beginning of 2013, when the real interest rate was low.
Nevertheless, a sharp decrease in expectations of house prices started in 4Q/2012,
associated with a rapid increase in real interest rates, causing the imputed-to-actual-rent ratio
to reach levels that pointed to a possible mispricing after the end of 2014. Since the ratio was
normalized by its ten-year average, when comparing the first and second quarters of 2015
against the prior period, it appears to be overpriced by more than fifty percent over the ten-
year average. For São Paulo and major zones, the current ratio is at its peak, and only the
Central zone seems to be slightly below the previous peak.
Figure 7 – Imputed-to-Actual-Rent Ratio x Price-to-Rent Ratio – São Paulo and Zones
(ratios normalized to their 10-year-average)
Central
2,00
Imputed / Actual rent
Price / Rent
26
5.4. Imputed-Rent-to-Income and Price-to-Income ratio
Another exercise chosen by Himmelberg, Mayer and Sinai (2005) is to check whether
rent is undervalued is by using the Price-to-Income and Imputed-Rent-to-Income ratio. Since
data for income is only available for São Paulo, the study focused only on this city. As stated
before, in a bubble market, the annual cost of homeownership is expected to rise faster than
incomes, raising imputed-rent-to-income to an unsustainable high level. The price-to-income
ratio should be interpreted as the number of months an average wealthy individual from São
Paulo needs to work to be able to buy a 60-square-meter apartment in the city.
Figure 8 – Price-to-Income Ratio– São Paulo
São Paulo
300
250
200
150
1º Q - 2006
3º Q - 2006
1º Q - 2007
3º Q - 2007
1º Q - 2008
3º Q - 2008
1º Q - 2009
3º Q - 2009
1º Q - 2010
3º Q - 2010
1º Q - 2011
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
100
Source: Author’s calculations.
Using the same analysis performed on rents, the price-to-income ratio in Figure 8, in
comparison to the Imputed-Rent-to-Income Ratio in Figure 9, appears to be overvalued in
2Q/2015, implying the same conclusion that prices should go down when considering the
levels of income in the same period.
27
Figure 9 – Imputed-Rent-to-Income Ratio– São Paulo
São Paulo
2,0
1,5
1,0
0,5
1º Q - 2006
3º Q - 2006
1º Q - 2007
3º Q - 2007
1º Q - 2008
3º Q - 2008
1º Q - 2009
3º Q - 2009
1º Q - 2010
3º Q - 2010
1º Q - 2011
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
0,0
Source: Author’s calculations.
In the same way, Figure 10 supports the conclusion that the levels of current ImputedRent and Price versus Income seem to be overvalued in comparison to the last 10-year period.
Figure 10 – Imputed-Rent-to-Income Ratio versus Price-to-Income Ratio – São Paulo
(ratios normalized to their 10-year-average)
São Paulo
2,00
1,50
1,00
0,50
1º Q - 2006
3º Q - 2006
1º Q - 2007
3º Q - 2007
1º Q - 2008
3º Q - 2008
1º Q - 2009
3º Q - 2009
1º Q - 2010
3º Q - 2010
1º Q - 2011
3º Q - 2011
1º Q - 2012
3º Q - 2012
1º Q - 2013
3º Q - 2013
1º Q - 2014
3º Q - 2014
1º Q - 2015
-
Source: Author’s calculations.
28
5.5. User cost regression
The next step was to run a simple user cost regression to confirm the statistically
significant relationship between house prices, user costs and rents. Reconstructing equation 5,
moving house price and rent to the left side, results in:
𝑃𝑡 (1 − 𝜏𝐴 )/𝑅𝑡 = 1/ 𝑢𝑡
(7)
Mayer and Sinai (2007) performed this exercise to establish a baseline for explaining
the variation in the price-rent ratio using the user cost model with real interest rates and static
expectations of capital gains based on long-run real house price growth. The expected
coefficient on user cost is 1.0 when the model is used to explain the variation on price-rent
ratio, as stated before. The authors estimated a coefficient on user cost of 0.48 with a R² of
0.28 using the entire sample studied, concluding that the spike observed in house prices was
not entirely supported by fundamentals. Nonetheless, after dividing the sample into two
periods, the authors found that in one period the user cost performance was poor, but during
the other, it showed excess sensitivity. The result was consistent with the view that the run-up
in prices in the 1980s in the US was not supported by fundamentals, while the price growth in
the 2000s was more so. As aforementioned, it seems reasonable to test the model in the
following two periods: 1Q/2006 to 4Q/2012, in which fundamentals appear to explain price
movements, and from 1Q/2013 to 2Q/2015, in which the opposite occurs.
The results found here were exactly the expected, and suggest low influence of
fundamentals to explain house price dynamics from 1Q/2013 to 2Q/2015. However, from
1Q/2006 to 4Q/ 2012, the regression showed a relevant influence of fundamentals. For
example from Table 2 below, the user cost coefficient for the city of São Paulo is 0.57 and
statistically different from zero with a R² of 0.51, and North Zone also with 0.81 and a R² of
0.60.
Several tests were performed to check the robustness of the model. The Jarque-Bera
statistic was not significant; therefore, the standardized residuals were normally distributed.
Ramsey Reset Test for function form showed there is no mis-specification in the model
proposed and the White test confirmed the hypothesis of no heteroskedasticity of the errors.
29
Therefore, the serial correlation test found that the residuals are correlated with their own
lagged values, and the correlogram of the residuals showed autocorrelation in the first three
lags. This result was expected, as Case and Shiller (1988, 1989) and Shiller (1990) stated
“serial correlation in real estate markets is partially due to backwards-looking expectations of
market participants”. To address this problem, the Newey-West HAC method was used to
solve the presence of auto-correlation. After all, despite this weakness, Hubbard and Mayer
(2009) support the user cost model as “the most tractable model suggested by the economic
theory to consider long-run equilibrium price levels and does a reasonably good job of
explaining the price-to-rent ratio across a variety of markets”.
In fact, by trying to find other independent variables for the price-to-rent ratio and the
increased explanatory power R² of the regression, Mayer and Sinai (2007) also tested the
influence of lagged five-year and one-year growth rate. The idea was to check whether the
capital flow to the housing market was motivated by some behavioral response, as suggested
by Shiller (2007). The authors found that the lagged five-year average in house price growth
is positively associated with increases in the price-to-rent ratio and is highly statistically
significant, increasing the explanatory power of the regression studied. This work reached a
similar result by testing the lagged three-year growth rate for the different districts and the
city. As shown on Table 2, the behavioral coefficient showed to be statistically significant in
São Paulo and in the five zones. Moreover, the user cost model and the behavioral coefficient
were responsible for a considerable increase in R² in São Paulo from 0.51 to 0.85 and from
0.60 to 0.91 in the North Zone, showing that these coefficients together explain a certain part
of the price-to-rent variation.
30
Table 2 – User Cost Regressions – São Paulo and Zones
Dependent Variable: Price / Rent
(t-statistics in parentheses)
São Paulo
1Q/06 - 4Q/12
1Q/13 - 2Q/15
Central
1Q/06 - 4Q/12
1Q/13 - 2Q/15
North
1Q/06 - 4Q/12
1Q/13 - 2Q/15
South
1Q/06 - 4Q/12
1Q/13 - 2Q/15
West
1Q/06 - 4Q/12
1Q/13 - 2Q/15
East
1Q/06 - 4Q/12
1Q/13 - 2Q/15
1/User Cost
0.57
(5.45)
0.62
(2.18)
0.81
(5.63)
0.39
(2.12)
0.51
(5.33)
-0.22
-0.21
(-2.50) (-1.05)
0.5
(5.18)
0.35
(2.82)
Constant
206.15 259.4 420.98 420.54 211.61 268.41 447.39 493.37 133.67 185.72 386.01 399.11 276.31 301.88 451.25 460.92 211.14 220.37 417.9 417.48
(9.78) (18.78) (44.03) (23.79) (3.09) (8.86) (11.27) (19.26) (4.77) (12.91) (12.25) (10.73) (7.60) (10.32) (23.41) (22.72) (10.52) (13.56) (19.86) (15.29)
200.4
(9.06)
205.55 380.58 384.71
(7.32) (19.26) (14.85)
Lagged 3-year
growth rate
0.15
(2.05)
-0.15
-0.14
(-2.99) (-0.97)
4907.5
(7.23)
N
-74.89
(-0.04)
28
R - Squared
0.51
0.22
Source: Author’s calculations
-0.1
-0.63
(-0.61) (-3.94)
4137.08
(6.10)
10
0.85
0.17
(1.55)
8204.81
(4.69)
28
0.22
0.27
0.02
-0.05
-0.37
(-0.28) (-1.27)
6431.11
(11.29)
10
0.66
0.26
(3.18)
6139.09
(1.51)
28
0.66
0.6
0.01
-0.13
-0.25
(-1.74) (-1.15)
6206.93
(7.45)
10
0.91
0.02
(0.16)
1976.03
(0.49)
28
0.19
0.19
3700.73
(3.08)
10
0.6
0.09
0.31
(4.30)
-66.95
(-0.03)
28
0.12
0.39
3259.86
(1.79)
10
0.66
0.37
-0.22
-0.32
(-2.85) (-2.44)
2620.42
(1.91)
28
0.37
0.32
10
0.42
0.25
0.38
1º tri - 2006
10,0%
10,0%
8,0%
8,0%
6,0%
6,0%
4,0%
4,0%
2,0%
2,0%
2,0%
2,0%
West
1º tri - 2011
3º tri - 2011
1º tri - 2012
3º tri - 2012
1º tri - 2013
3º tri - 2013
1º tri - 2014
3º tri - 2014
1º tri - 2015
3º tri - 2011
1º tri - 2012
3º tri - 2012
1º tri - 2013
3º tri - 2013
1º tri - 2014
3º tri - 2014
1º tri - 2015
East
1º tri - 2011
3º tri - 2010
1º tri - 2010
3º tri - 2009
1º tri - 2009
3º tri - 2008
1º tri - 2008
3º tri - 2007
1º tri - 2007
3º tri - 2006
1º tri - 2006
1º tri - 2015
3º tri - 2014
1º tri - 2014
3º tri - 2013
1º tri - 2013
3º tri - 2012
1º tri - 2012
3º tri - 2011
1º tri - 2011
3º tri - 2010
North
3º tri - 2010
4,0%
1º tri - 2010
2,0%
1º tri - 2010
4,0%
3º tri - 2009
2,0%
real interest rate, depreciation, risk premium and the observed rent-to-price ratio.
1º tri - 2015
3º tri - 2014
1º tri - 2014
3º tri - 2013
1º tri - 2013
3º tri - 2012
1º tri - 2012
3º tri - 2011
1º tri - 2011
3º tri - 2010
1º tri - 2010
3º tri - 2009
1º tri - 2009
3º tri - 2008
1º tri - 2008
3º tri - 2007
1º tri - 2007
3º tri - 2006
1º tri - 2006
1º tri - 2015
3º tri - 2014
1º tri - 2014
3º tri - 2013
1º tri - 2013
3º tri - 2012
1º tri - 2012
3º tri - 2011
1º tri - 2011
3º tri - 2010
1º tri - 2010
3º tri - 2009
1º tri - 2009
3º tri - 2008
1º tri - 2008
3º tri - 2007
1º tri - 2007
São Paulo
3º tri - 2009
6,0%
1º tri - 2009
4,0%
1º tri - 2009
6,0%
3º tri - 2008
4,0%
3º tri - 2008
8,0%
1º tri - 2008
6,0%
1º tri - 2008
8,0%
3º tri - 2007
6,0%
3º tri - 2006
8,0%
3º tri - 2007
10,0%
1º tri - 2007
1º tri - 2006
8,0%
1º tri - 2007
10,0%
3º tri - 2006
10,0%
3º tri - 2006
1º tri - 2006
10,0%
1º tri - 2006
1º tri - 2015
3º tri - 2014
1º tri - 2014
3º tri - 2013
1º tri - 2013
3º tri - 2012
1º tri - 2012
3º tri - 2011
1º tri - 2011
3º tri - 2010
1º tri - 2010
3º tri - 2009
1º tri - 2009
3º tri - 2008
1º tri - 2008
3º tri - 2007
1º tri - 2007
3º tri - 2006
31
5.6. Home price appreciation implicit rate
Another key way to make inferences about housing market is to calculate the implicit
rate of home price appreciation. “In equilibrium, unusually low levels of the rent-to-price ratio
suggest that housing market participants expect high rates of home price appreciation, one key
ingredient of an asset bubble” (McCarthy and Peach, 2004).
Figure 11 – Expected Home Price Appreciation – São Paulo and Zones
Central
South
Source: Author’s calculations.
Rearranging equations 5 and 6, the implicit rate g t+1 ′ is calculated as a function of
32
𝑟𝑓
𝑔𝑡+1 ′ = (1 − 𝜏𝐴𝐹 )𝑟𝑡 + 𝛿𝑡 + 𝛾𝑡 −
(1−𝜏𝐴 )𝑅𝑡
𝑃𝑡
(8)
Figure 11 presented supports that the current housing market is not characterized by
widespread expectations of rapid future appreciation. The same result was found by McCarthy
and Peach (2004) in the US economy between 1985 and 2001. A linear trend line helps to
identify that expected home price appreciation is falling over that period of time in São Paulo
and in the five zones studied. Despite apparent stability, the average real expected price
increase in the period is 6.7 percent, which could be considered high in comparison to
expectations of future real GDP appreciation and could lead to higher prices, beyond those
explained by fundamentals.
5.7. Price-to-rent ratio forecast
Finally, a static forecast was run from the regression using the sample from 1Q/2006
to 4Q/2012 to predict the following period from 1Q/2013 to 2Q/2015. In Figure 12, it is worth
noticing that the level of the price-to-rent ratio observed after 4Q/2012 remains too high in
comparison to the price-to-rent expected by the forecast. Thus, this argument strongly
suggests that a decrease in home prices is expected.
Figure 12 – Price-to-Rent Ratio: Observed versus Forecast – São Paulo
Source: Author’s calculations.
33
6 Conclusion
The evidence presented herein suggests that house prices in São Paulo could be
overvalued in 2Q-2015. Fundamentals well explained movements on Imputed-to-Actual-Rent
and Imputed-Rent-to-Income ratios from 1Q/2006 to 4Q/2012. An increase in the price-torent ratio observed at the beginning of 2010 was driven by a combination of the decrease in
real interest rates and an increase in expectation of home price appreciation, provided by
expected real GDP growth. However, the ratio continued to increase after 4Q/2102 in an
unfavorable scenario of rising interest rates and a drop in expectation of real GDP growth,
leading to a conclusion that this last movement could not be explained by the economic
theory. In comparison, although Tavares (2012) found no signs of a bubble in the Rio de
Janeiro housing market, she alerts that deterioration in the GDP growth dynamic could have a
negative impact on prices. A similar conclusion could be found in this work.
Also, momentum could explain part of the price-to-rent ratio increase after 4Q/2012.
The capital flow to the housing market could partly be motivated by some behavioral
response, as suggested by Shiller (2007). The behavioral coefficient was the lagged threeyear growth and it showed an important explanatory power on price-to-rent movements, as
demonstrated before.
Yet, the higher increase in home prices relative to income over the period well
explains the dividend yield compression, as tenants could not afford to pay higher rents.
Declining dividend yield and lower house price appreciation could also contribute to a price
decrease as investors and individuals leave the real estate market.
In order to adjust to 2Q/2015 economic fundamentals condition, either rent prices may
rise, or home prices may fall. Rigidity of rent prices is expected since the length of tenant
agreements usually is over 12 months. Hence, if real interest rates and real GDP growth
forecast remain unaltered, expected home prices are more likely to fall in the short term.
Undoubtedly, an individual in São Paulo who faces the dilemma of buying or renting an
apartment in 2Q/2105 should prefer renting instead of buying.
34
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