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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. 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