The Risk Premium on the Euro Area Market Portfolio: The Role of Real Estate

Thomas Nitschka1

Institute for Empirical Research in Economics, University of Zurich

Abstract Incomplete consumption risk sharing implies that the market risk premium is high in times of lack of risk sharing and vice versa. This paper introduces a slight modification of a so far used macroeconomic variable that reflects time variation in the degree of consumption risk sharing to study the implications of incomplete risk sharing for the market price of risk in a sample of 14 developed economies. I particularly focus on euro area countries over the time period from 1970 to 2007. The evidence presented in this paper leaves the impression that for about half of the countries under study the excess return on the stock market fulfils the prediction of the incomplete consumption risk sharing framework. For the other half of the sample, especially for the core European ones, it does not. A potential reason could be that the stock market return is an inadequate proxy of the market return for the latter kind of countries and, based on details about household wealth portfolio composition, presumably better approximated by the return on real estate. However, the cross-sectional asset pricing tests in this paper suggest that the return on real estate does not add any information about systematic sources of risk not already contained in the stock market return.

JEL: G10, G15 Keywords: CAPM, market risk premium, real estate return, excess return predictability

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E-mail: [email protected] , Postal address: Swiss National Bank, Financial Stability, Bundesplatz 1, CH-3003 Bern. This research is part of the URPP Macro-Finance of the University of Zurich and has been conducted during my stay at the Monetary Policy Stance Division of the ECB. I am grateful to Mika Tujula and Bernhard Winkler for comments and for providing me with the euro area data sets used in this paper. Furthermore, I substantially benefited from comments and remarks by an anonymous referee as well as Mathias Hoffmann, Kjetil Støresletten and participants in an ECB-MSN seminar, the 1st URRP conference on Macroeconomics and Finance at the University of Zurich and the EEA Congress 2008. In addition, I gratefully acknowledge that Kenneth French makes his data on value and growth stock portfolios publicly available. The views expressed in this paper do not reflect the view of the ECB or the SNB. Any errors are entirely mine.

The Risk Premium on the Euro Area Market Portfolio: The Role of Real Estate

Abstract Incomplete consumption risk sharing implies that the market risk premium is high in times of lack of risk sharing and vice versa. This paper introduces a slight modification of a so far used macroeconomic variable that reflects time variation in the degree of consumption risk sharing to study the implications of incomplete risk sharing for the market price of risk in a sample of 14 developed economies. I particularly focus on euro area countries over the time period from 1970 to 2007. The evidence presented in this paper leaves the impression that for about half of the countries under study the excess return on the stock market fulfils the prediction of the incomplete consumption risk sharing framework. For the other half of the sample, especially for the core European ones, it does not. A potential reason could be that the stock market return is an inadequate proxy of the market return for the latter kind of countries and, based on details about household wealth portfolio composition, presumably better approximated by the return on real estate. However, the cross-sectional asset pricing tests in this paper suggest that the return on real estate does not add any information about systematic sources of risk not already contained in the stock market return.

JEL: G10, G15 Keywords: CAPM, market risk premium, real estate return, excess return predictability

1

Introduction

This paper focuses on the implications of incomplete consumption risk sharing for asset risk premia (Lustig and van Nieuwerburgh (2005, 2006a,b)). In the theoretical framework of Lustig and van Nieuwerburgh (2005), a currently high level of uninsured consumption risk in the economy should be associated with an expected increase in the risk premium on asset markets. Uninsured consumption risk is mirrored in the ratio of an economy’s collateral to non-collateral wealth as households in this economy can only buffer their consumption streams from idiosyncratic income shocks through borrowing and lending. The availability of collateral, reflected in the ratio of collateral to non-collateral wealth, determines the tightness of borrowing constraints. Empirically, this collateral ratio is approximated by the ratio of housing wealth to income. Short-run variation of the housing-income ratio echoes the temporary variation in the tightness of credit constraints and is hence closely related to the dispersion in consumption growth rates across households and regions in the economy (Lustig and van Nieuwerburgh (2006a,b)). Short-run variations in the collateral to non-collateral ratio thus serve as predictor of the market risk premium (Lustig and van Nieuwerburgh (2005)). This paper assesses the implications of the incomplete consumption risk sharing framework for the market return in a sample of 14 countries, i.e. the predictive power of collateral to noncollateral wealth ratios for the respective stock market excess returns. However, it is difficult to proxy the collateral to non-collateral wealth ratio with housing wealth to income ratios in international data as especially household income data are notoriously difficult to obtain. I propose a simple solution to this data issue. Since housing wealth fluctuations are predominantly driven by house price changes (Slacalek (2006)), I employ house price indexes of 14 industrialized countries to proxy the respective country’s housing wealth changes. As I am interested in the relative availability of collateral that varies over time, I have to scale the house prices. Lustig and van Nieuwerburgh (2005) 1

use labour income for that purpose, I employ GDP as proxy of income. This approach has recently been used by Hott and Monnin (2008) to calculate fundamental values of house prices for the USA, UK, Japan, Switzerland and the Netherlands. They additionally take into account other measures of housing demand such as the level of mortgage interest rates as well as measures of housing supply to calculate fundamental house price values. In addition, the scaling of house prices with GDP to forecast stock market returns is related to Rangvid (2006) who shows that nominal stock prices scaled with nominal GDP predict stock market returns in- and out-of-sample. This finding is connected to the large literature that uses fundamentals such as dividends and earnings to scale stock prices in order to predict stock returns while Rangvid (2006) uses GDP as fundamental. It turns out that the U.S. housing-income ratio and the U.S. house price to GDP ratio are closely related. The two series are cointegrated around a time trend. The respective cointegration residuals predict U.S. annual stock market returns. The correlation of the residuals, however, varies over time. Over the whole sample period for which U.S. data is available, 1952 to 2008, their correlation is about 0.5. Annual data on international house prices and GDP considered in this study starts in 1970. For the 1970 to 2008 period, the correlation between the U.S. housing-income ratio and the U.S. house price to GDP ratio is 0.93. Based on these findings, this paper shows that for about half of the countries under study, short-run variations in the house price to GDP ratio predict the respective stock market excess returns. It is striking that short-term swings in house price to GDP ratios of the three core euro area countries France, Germany and Italy do not show any sign of forecast power for the corresponding stock market returns. This latter finding of no predictability could be due to the possibility that a stock market return is not the adequate proxy for the market portfolio return in these countries. Real estate plays the dominant role in euro area households’ balance sheets. On average, housing wealth 2

accounts for roughly 60 percent of households’ asset wealth in the euro area in the period from the first quarter of 1980 to the first quarter of 2007 as is shown in figure (1). 1 Altissimo et al. (2005) report that housing wealth constitutes about 30 percent of U.S. households’ asset wealth in the years 1995 and 2000. In addition, Norman et al. (2002) emphasize that participation in stock markets is much less widespread in the core European countries than in the U.S. in contrast to participation in housing markets. Moreover, funding of housing in the euro area countries is typically less financial market based than in the U.S. (Tsatsaronis and Zhu (2004)). Hence, the return on real estate has the potential to be a better proxy of the market return for the euro area countries or more general for all countries in which real estate plays such a pronounced role in households’ balance sheet. A straightforward test of this hypothesis would be a regression of housing returns on the proxy of the collateral to non-collateral wealth ratio suggested in this paper. However, this approach would be inappropriate as the short-term variation in house price to GDP ratio quite naturally would have to predict housing returns. The collateral to non-collateral wealth ratio in the Lustig and van Nieuwerburgh (2005) framework has to forecast the market risk premium which is the risk factor in the CAPM. Against this backdrop, I test the performance of national CAPM versions that take into account the return on real estate to assess if it is a better proxy for the market return than a stock market return. I use international value and growth stock portfolio returns compiled by Kenneth French as test assets. The main results are easily summarized. Taking account of the return on real estate helps to diminish the cross-sectional pricing errors of the CAPM for some of the countries under study but not for France, Germany and Italy. Furthermore, the benefit of reduced cross-sectional pricing errors comes both at the cost of implausibly high estimates of the price of real estate risk and the deterioration of the time series performance of the CAPM. 1

The series have been graciously provided to me by the ECB.

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Taken together the main results of this paper suggest that house price to GDP ratios could be used to test the implications of incomplete consumption risk sharing for predictions of asset risk premia. The predictive regressions reveal that short-run variations in the house price to GDP ratio forecast stock market excess returns. But this implication of the incomplete consumption risk sharing framework of Lustig and van Nieuwerburgh (2005) is not fulfilled in the core euro area countries. This finding could be due to the negligible role of equity in euro area households’ wealth portfolio which provides a rationale to use other asset returns in addition to stocks in empirical tests of the CAPM. However, the consideration of real estate, the dominant component in most households’ portfolios, does not improve the overall performance of the CAPM in any of the countries regarded in this paper. The remainder of the paper is organized as follows. Section two discusses implications of incomplete consumption risk sharing for the risk premium on the market portfolio and provides evidence for the predictability of the market risk premium. Section three compares the cross-sectional and also partly the time series performance of CAPM versions with or without consideration of the real estate return. Finally, section four concludes.

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Incomplete consumption risk sharing and time series predictability of the market risk premium

2.1

Basics

The basic idea of the consumption risk sharing literature is that consumers desire to insulate their consumption stream from idiosyncratic income shocks. However, consumption risk sharing is incomplete both within and across countries (Asdrubali et al. (1996), Sørensen and Yosha (1998)) even though risk sharing, i.e. isolating consumption from idiosyncratic income shocks, seems to have increased internationally in recent years (see e.g. Artis and Hoffmann (2007)).

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One way to buffer idiosyncratic income shocks is to borrow and lend. This credit channel seems to be particularly important for households. However, households’ access to credit markets varies over the business cycle (e.g. Gertler and Gilchrist (1994)). This observation is the point of departure of Lustig and van Nieuwerburgh (2005, 2006,a,b). They assess the implications of undiversified, idiosyncratic risk on the risk premium on asset markets. Lustig and van Nieuwerburgh (2005) model an economy in which households face common and idiosyncratic income shocks. Idiosyncratic income shocks can be smoothed through borrowing and lending. Loans are only granted on the basis of collateral. The more collateral available in this economy, the higher the number of households that are able to insure their idiosyncratic income risks. In Lustig and van Nieuwerburgh (2005, 2006a,b) the ratio of an economy’s collateral wealth relative to wealth that is not accepted as collateral serves as a proxy for the tightness of credit constraints faced by households. Aggregate shocks, measured by this collateral to non-collateral ratio, directly affect the distribution of consumption across households. In times of relative scarcity of collateral assets more households are bound by credit constraints. Hence the dispersion in consumption growth rates at the household and regional level increases (Lustig and van Nieuwerburgh (2006a)). In addition, households will demand higher risk premia when collateral wealth is relatively low because their ability to insure idiosyncratic consumption risk is limited (Lustig and van Nieuwerburgh (2006b)). Empirically, real estate seems to be the ideal candidate as measure of collateral wealth. Since it is difficult to borrow only against human capital, human wealth is regarded as non-collateral wealth. Lustig and van Nieuwerburgh (2005) use after-tax labour income to proxy for human wealth. This approach is valid under the assumption that labour income represents the dividend paid from human capital (Campbell (1996), Jagannathan and Wang (1996)). Lustig and van Nieuwerburgh (2005) find the housing-income ratio to be cointegrated around a time trend. Short-run fluctuations of the housing-income ratio should reflect the temporary tightening or relaxation of households’ credit constraints and are closely related to 5

consumption dispersion across households and regions. Hence, as predicted by the model, the temporary variation in the housing-income ratio predicts expected risk premia on the market portfolio approximated by the excess return on a broad U.S. stock market index in annual data for the time period from 1926 to 2002. The construction of housing-income ratios for a wider cross-section of countries is difficult because of the sheer lack of household income data and the often rather ad hoc assumptions necessary to calculate housing wealth data. The next subsection suggests a simple alternative.

2.2

Approximating collateral scarcity

Nitschka (2008) employs a euro area version of the housing wealth to income ratio to show that the decisive risk factor in recently derived models of currency excess returns is predictable by the short-run swings in the housing-income ratio. However, euro area housing wealth compiled by the ECB is constructed backwards thus relying on rather ad hoc simplifying assumptions. 2 The use of this euro area housing wealth series may hence not be innocuous even though it serves to illustrate the importance of housing wealth for euro area households as is mirrored in figure (1). An assessment of the incomplete consumption risk sharing framework for asset risk premia outlined above requires approximating the relative availability of collateral. Calculating housing wealth to income ratios is one way to proxy collateral scarcity. However, income series are hard to obtain in international data and the construction of housing wealth series is generally problematic to some extent. I try to circumvent these issues by using annual, nominal house price to nominal GDP ratios to approximate the relative availability of collateral. This use of house price to GDP instead of housing wealth to income ratios can be justified by acknowledging that swings in housing wealth are predominantly driven by house price changes (Slacalek (2006)). Since I am interested in the relative availability of collateral that 2

I thank an anonymous referee for pointing this fact out to me

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varies over time, I am predominantly concerned about fluctuations in housing wealth not the correct level. House prices mirror most of the variation of housing wealth over time. But I have to scale house prices to obtain a measure of relative collateral availability. The scaling of house prices with GDP to forecast stock market returns is related to Rangvid (2006) who shows that nominal stock prices scaled with nominal GDP as proxy for fundamentals instead of dividends or earnings predict stock market returns. In addition, Hott and Monnin (2008) calculate fundamental values of house prices in a variety of countries. They augment house price to GDP ratios by taking into account the level of mortgage interest rates as well as measures of housing supply. To alleviate remaining concerns about this data issue, the next subsection compares the properties of the house price to GDP ratio in the U.S. with the original housing-income ratio of Lustig and van Nieuwerburgh (2005).

2.3

Housing-income vs. house price to GDP ratio: The U.S. experience

In the U.S., housing wealth and income cointegrate around a time trend (Lustig and van Nieuwerburgh (2005)). Table 1 displays the cointegration properties of the logarithmic, annual U.S. nominal house price to nominal GDP ratio for the sample period from 1952 to 2008. The Johansen cointegration test results strongly support the view of a cointegration relation between the nominal house price and nominal GDP. In the test I allow for a deterministic time trend and two lags in the vector autoregressive representation of the two variables as suggested by standard information criteria. Therefore, a vector error correction representation of the form

⎛ Δh ⎞ Γ(L)⎜⎜ t ⎟⎟ = α[ht −1 + γ 1 y t −1 + γ 2 timetrend + η t ] + ε t ⎝ Δy t ⎠

(1)

must exist (Engle and Granger (1987)) where ht denotes the natural logarithm of the nominal house price, yt represents the natural logarithm of nominal GDP. Bold upper-case letters 7

highlight matrices, bold lower-case letters represent vectors. The vector of cointegration coefficients, β = [1,−γ1 ,−γ 2 ]' , describes the long-run relationship of the house price with GDP and the time trend if the coefficient on the house price is normalized to unity. The estimation of the cointegration vector via dynamic ordinary least squares with four leads and lags (Stock and Watson (1993)) delivers

βˆ = [1 − 1.29 i − 0.02 timetrend ]' if the cointegration ( −3.31)

( −1.75 )

coefficient of the house price is normalized to unity. Temporary fluctuations in the cointegration relation among house price and GDP, henceforth abbreviated hy t , are thus governed by hy t = ht − 1.29 y t − 0.02timetrend + η t

(2)

Figure (2) visualizes the resulting cointegration residual. It mirrors the unprecedented rise in house prices relative to fundamentals to its peak in 2007 and the recent sharp decline back to its more fundamental level at the end of 2008. Lustig and van Nieuwerburgh (2005) emphasize that the cointegration vector of the collateral to non-collateral wealth ratio should be [1 -1]. However, the estimates of the cointegration vector in this paper are obtained for the sample period from 1952 to 2008 and are in the range of cointegration coefficient estimates reported by Lustig and van Nieuwerburgh (2005) for the sample period from 1949 to 2002 (cf. Table II in Lustig and van Nieuwerburgh (2005)). Finally, I update the original dataset of Lustig and van Nieuwerburgh (2005) that is freely available at http://hlustig2001.squarespace.com and conduct a comparison of the forecast ability of the housing wealth to income cointegration residual with hy t . Table 2 reports estimates from long-horizon regressions of the form:

rte,t + h = α + β h xt + ε t + h

(3)

where rte,t + h denotes the return on the S&P 500 stock index in excess of the risk-free rate, here the 3-month t-bill, at time horizon t+h. The regressor, xt , is either hy t or the residual from the

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cointegration relation between residential real estate wealth and income from Lustig and van Nieuwerburgh (2005), my t . The forecast horizon, h, is in years. The t-statistics are NeweyWest corrected (Newey and West (1987)) and appear below the regressor estimates in parenthesis. The row below the estimates reports the adjusted R 2 statistic at the respective forecast horizon. Asterisk indicates significance at the 95% confidence level. The results reported in panel A rely on the sample period from 1952 to 2008. Panel B reports estimates from the sample period from 1970 to 2008. I rescaled hy t as proposed by Lustig and van Nieuwerburgh (2005) such that it takes values between zero and unity to indicate collateral scarcity, i.e. hy t =

hy tmax − hy t where max and min refer to the maximum and minimum hy tmax − hy tmin

value in the sample. We should hence observe positive slope coefficients in the regressions. Table 2 shows that both short-term variations in the housing-income and temporary swings in the house price to GDP ratio predict excess returns on the U.S. stock market. The predictive power is most emphasized at rather long time horizons as reported in Lustig and van Nieuwerburgh (2005). The performance of hy t is at least as pronounced as the predictive ability of the residual from the housing wealth to income ratio. Furthermore, panel A of table 2 displays that hy t is a statistically significant predictor at all forecast horizons for the longer sample from 1952 to 2008 thus attenuating concerns about inference from long-horizon regressions in rather small samples. Not reported but available upon request are results from forecast regressions based on quarterly data which support the impression left by the forecast exercise reported in table 2. This subsection shows that the house price to GDP ratio behaves similarly to the housingincome ratio in terms of cointegration properties and forecast power for excess returns on the stock market. It is hence a valid empirical approximation of collateral scarcity in the spirit of the Lustig and van Nieuwerburgh (2005) framework. I exploit this finding in the subsequence

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to study the implications of incomplete consumption risk sharing for asset markets in international data.

2.4

House price to GDP ratios and the market risk premium: International evidence

Against the backdrop of the previous subsection, I assess the forecast implications of the Lustig and van Nieuwerburgh (2005) framework by using house price to GDP ratios as proxy for collateral scarcity for the following countries: Australia, Belgium, Canada, Denmark, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, Switzerland and the United Kingdom. Annual house price indexes are from the Bank for International Settlements and constitute the best available international house price series even though the house price indexes are not complied at the same basis across countries. But since I am focused on country-specific, temporary variation in relative availability of collateral, this latter caveat should be negligible. Annual GDP data is from the IMF’s International Financial Statistics. Due to the availability of house price data, the sample runs from 1970 to 2007. For expositional purposes, I do not report the cointegration properties of all the countries’ house price to GDP ratios in tables. In general, there is evidence for cointegration according to the Johansen cointegration test. It is weaker than for the U.S., but this can be attributed to the shorter sample period. The estimates of the GDP cointegration coefficients are in the range of 0.5 to 1.1 and thus comparable to the U.S. experience. Tables 3a and 3b report estimates from

rte,t,+i h = α + β h,i hyti + ε ti+ h

(4)

where rte,t,+i h denotes the annual return on the MSCI stock index in excess of the risk-free rate at time horizon t+h of country i. I use the respective country’s 3-month call money market rate or the 3-month t-bill rate as risk free rate. Newey and West (Newey and West (1987))

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corrected t-statistics appear in parenthesis. Asterisk denotes significance at the 95% confidence level. Table 3a summarizes the results for the six euro area countries Belgium, France, Germany, Italy, the Netherlands and Spain. It is apparent that the U.S. evidence is roughly corroborated by the results for Belgium, the Netherlands and Spain. For these countries, hy t forecasts the risk premium on the respective stock market. But we do not find any sign in favour of stock return predictability for the three biggest euro area countries. The main findings in table 3a hence provide a mixed picture and highlight that there are substantial differences among the euro area countries in terms of predictive power of the house price to GDP ratio for stock market returns. This information would have been lost when an aggregate of the euro area were considered. Table 3b provides the corresponding long-horizon regression estimates for the remaining countries of the sample. Again, there is a rather mixed picture. Short-run fluctuations in the house price to GDP ratio of Australia, Japan, Norway and Switzerland do not explain the time series variation in the corresponding stock market returns. For Canada, Denmark, Sweden and the UK they do. A potential explanation why there is no forecasting power of the house price to GDP ratio for stock market returns in some countries could be that the underlying theory is very general. Short-run variation in the housing-income ratio or house price to GDP ratio respectively should predict the market price of risk, consistent with the finding of Nitschka (2008) that the aggregate euro area housing-income ratio predicts that risk factor that is common to all euro area investors who hold foreign currency. Components of the market return other than equity, such as the return on foreign currency, hence perfectly fulfil the predictions of the Lustig and van Nieuwerburgh (2005) framework in the euro area. It could be the case that the market price of risk is not adequately captured by the excess return on the stock market for all of the countries under study. E.g., housing wealth is the dominant component of euro area 11

households’ asset wealth while equity plays a minor role in euro area households’ balance sheets (Altissimo et al. (2005)). Figure (1) displays the shares of equity and housing wealth in euro area households’ asset wealth portfolio for the time period from the first quarter of 1980 to the first quarter of 2007. The share of housing is always around 60 percent of total asset wealth, while equity seems to be far less important. In the course of the stock market surge in the late 1990s, the share of equity rises to about 20 percent of euro area households’ asset wealth but declines subsequently. Furthermore, Norman et al. (2002) highlight that stock market participation in the core European countries is more limited than in the U.S. In 1997, 6.2% of German and 12.0% of French households participated in the stock market. In Italy 7.8% of households are engaged in the stock market while in the U.S. 19.2% of households hold stocks in 1998. A direct way of testing if the return on real estate is a better approximation of the market return than the stock market return would be a long-horizon regression of the return on housing, defined as change in house prices, on hy t . But such an exercise would simply be inappropriate because house prices are employed to construct hy t and predictability of house price changes in excess of a risk-free rate by hy t do not necessarily answer the question if the return on real estate could be used as proxy of the market return. The next section pursues an indirect way of assessing this question as the time series evidence has clear implications for empirical tests of the CAPM. Differences in the exposure to the market return should explain the cross-sectional differences in asset returns. If the return on real estate is a more appropriate proxy of the market return for those countries for which the house price to GDP ratio does not predict the respective stock market return, we should observe a non-negligible impact of the housing return on the performance of the CAPM.

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3

The market risk premium and real estate: Empirical tests of the

CAPM

Based on the evidence from the forecast exercises, this section assesses the role of the return on housing in empirical tests of the CAPM. In particular, I am concerned with the question if the return on real estate adds any information about systematic sources of risk in excess of the information contained in stock market returns for that countries for which hy t does not predict the stock market excess return. Such a finding would indicate that the lack of predictive power of hy t could be due to the inappropriateness of the stock market return as proxy for the return on the market portfolio for these particular countries. The capital asset pricing model of Sharpe (1964) and Lintner (1965) implies that any return on asset i, R i , in excess of the risk-free rate, R f , is determined by its sensitivity to the risk premium on the market portfolio which comprises all risky assets, i.e. E ( R i ) − R f = β Mi ( E ( R M ) − R f ) with R M the return on the market portfolio, β Mi =

(5)

cov( R i , R M ) and E(.) denotes the var( R M )

expectation operator. This paper explicitly takes account of housing in tests of the CAPM by considering two versions of it: i) the stock market excess return is the only proxy of R M ii) stock market as well real estate excess return comprise the market return. The focus of the empirical, cross-sectional tests lies on the pricing errors of the different model specifications. Irrespective of the proxy of the market return, the plain vanilla static CAPM considered in this paper is not a good description of the data (Jagannathan and Wang (1996), Lettau and Ludvigson (2001)). Hence, the aim of the remainder of the paper is merely to assess if the cross-sectional evidence allows inferring if the lack of predictability of the 13

stock market excess return for some of the countries under study is the direct consequence of the stock return being a bad proxy of the market return. This paper does not attempt to provide another solution to well known asset pricing puzzles such as the value/growth phenomenon based on a CAPM that features the return on real estate. I estimate the beta representation of the two CAPM versions outlined above via a FamaMacBeth (Fama and MacBeth (1973)) cross-sectional regression for each of the countries under study. The CAPM of each country is confronted with international value (high book-tomarket value ratio) and growth (low book-to-market value) stock portfolios. The value and growth stock portfolio data is complied by Kenneth French and available on his website http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. Kenneth French computes one value and one growth portfolio each for a variety of countries. I employ the respective value and growth portfolios of Australia, Belgium, Canada, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, Switzerland and the UK leading to 26 test assets. The sample period runs from 1977 to 2007 restricted by the availability of the Canadian value and growth portfolio. All variables are observed at the annual frequency. Quarterly estimates (not reported but available upon request) qualitatively corroborate all of the subsequently reported findings. The first stage of the Fama-MacBeth regression (Fama and Mac Beth (1973)) is a time series regression of the test asset returns on the respective risk factors to obtain the exposure to the risk factors, i.e. here i i rte, j = μ + β EQ rti , EQ + β RE rti , RE + ε ti

(6)

with r e, j the return on the value and growth portfolios in excess of the risk-free rate. The market portfolio excess return is proxied by both the excess return on a stock market index ( r i , EQ ) and the return on real estate ( r i , RE ) or solely the stock market return of country i. The second step is a cross-sectional regression of the test asset returns on the estimated exposures at each point in time to assess if differences in the sensitivities to the risk factors 14

explain the differences in the average asset returns. Since the test asset returns are excess returns, I do not include a constant in the second stage regression

i i rt e , j = λ EQ ,i βˆ EQ + λ RE ,i βˆ RE + v ti , ∀t

(7)

to obtain the risk prices λ. Tables 4a and 4b report the results. The t-statistics in parenthesis below the estimates are Shanken (1992) corrected to correct for the fact that the second stage regressors are generated in the first stage time series regression. The column R² gives the cross-sectional R² adjusted for the number of regressors as employed by Jagannathan and Wang (1996) that could take negative values if the fit is really poor. The columns mspe and mape display mean squared and mean absolute pricing errors in percentage points respectively. Table 4a reports the risk price estimates in percentage points, fit of the model and pricing errors for the euro area countries. Given the importance of housing in euro area households’ balance sheets and the results from the long-horizon regressions from section 2, one would expect the CAPM version that features the return on real estate to perform better than the version that uses the stock market return only for the three biggest euro area countries. As table 4a shows, this is not the case. Neither the fit of the model nor pricing errors are improved. The additional consideration of the return on real estate does not improve the performance of the CAPM at least for France, Germany and Italy. Regarding both table 4a and 4b, there are countries for which the cross-sectional performance is improved by the consideration of the real estate return. However, this benefit comes at the cost of implausibly high risk price estimates. Belgium is a good example. The return on real estate in excess of the risk-free rate is estimated to be about five percent p.a. The actual average excess return on real estate is about 0.5 percent. The estimate is about ten times too high. 15

In addition, table 5 reports the p-value of the Gibbons, Ross and Shanken test (Gibbons et al. (1989)) which tests the null of the pricing errors in the first stage time series regression of the Fama-MacBeth regression jointly being equal to zero. Apparently, the time series performance of the CAPM is not too bad, but the consideration of the real estate return either leaves the time series performance unaffected or it significantly worsens the ability of the CAPM to explain the time series of the test asset returns. As an alternative cross-sectional test, I test the Black (1972) version of the CAPM and explicitly allow for a constant term in the second stage. The estimates of the constant should then reflect the risk-free rate. This approach helps to improve the cross-sectional fit in terms of the R² but the risk-free rate is clearly overestimated. These results are not reported as they do not alter any of the conclusions drawn above but are available upon request. Taken together, the cross-sectional exercises convey the notion that the lack of predictability of stock market returns by the house price to GDP ratio is not due to the fact that a stock market return is a bad proxy for the market return per se.

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Summary

This paper tests the empirical implications of incomplete consumption risk sharing for the return on the market portfolio. Times of high consumption risk, reflected in collateral scarcity, should be associated with high expected asset returns. Lustig and van Nieuwerburgh (2005) empirically approximate collateral scarcity with the ratio of housing wealth to income. This paper shows that the ratio of nominal house prices to nominal GDP can be used for that purpose which facilitates international comparisons that are otherwise restricted by the lack of income data. The predictions of the Lustig and van Nieuwerburgh (2005) framework for the time variation in the market return are fulfilled for about half of the countries under study. The other half, in

16

particular the core euro area countries France, Germany and Italy, shows no sign of predictability. This latter finding could be due to the fact that real estate constitutes the dominant component in euro area households’ wealth portfolio and hence the return on real estate could be a more adequate proxy for the market return for these countries. However, cross-sectional tests of the CAPM taking both the stock market and real estate excess return as proxy of the market portfolio return into account leave the impression that the return on real estate does not add any information about systematic sources of risk in excess of the information contained in stock market returns. This observation is true for all countries under consideration in this paper, but particularly pronounced for the core euro area countries.

References Altissimo, F., E. Georgiu, T. Sastre, M. T. Valderrama, G.L Sterne, M. Stocker, M. Weth, K. Whelan and A. Willman (2005) Wealth and Asset Price Effects on Economic Activity. ECB Occasional Paper Series No. 29. Artis, M.J. and M. Hoffmann (2007) The Home Bias and Capital Income Flows between Countries and Regions. IEW working paper 316, University of Zurich Asdrubali, P., B. E. Sørensen and O. Yosha (1996) Channels of Interstate Risk Sharing: the United States 1963-1990. Quarterly Journal of Economics 111, 1081-1110. Campbell, J. Y. (1996) Understanding Risk and Return. Journal of Political Economy 104, 298-345. Engle, R.F. and C.W.J. Granger (1987) Co-Integration And Error Correction: Representation, Estimation and Testing. Econometrica 55, 251-276. Fama, E.F. and J.D. MacBeth (1973) Risk, Return and Equilibrium: Empirical Tests. Journal of Political Economy, 81, 607-631. Gertler, M. and S. Gilchrist (1994) Monetary Policy, Business Cycles, and the Behaviour of Small Manufacturing Firms. Quarterly Journal of Economics 109, 309-340. Gibbons, M.R., Ross, S.A. and J. Shanken (1989) A Test of the Efficiency of a Given Portfolio. Econometrica 57, 1121-1152. Hott, C. and P. Monnin (2008) Fundamental Real Estate Prices: An Empirical Estimation with International Data. Journal of Real Estate Finance and Economics 36, 427-450.

17

Jagannathan, R. and Z. Wang (1996) The Conditional CCAPM and the Cross-Section of Expected Returns. Journal of Finance 51, 3-53. Lettau, M. and S. Ludvigson (2001) Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time Varying. Journal of Political Economy 109, 1238-1287. Lintner, J. (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics , 47, 13-37. Lustig, H. and S. van Nieuwerburgh (2005) Housing Collateral, Consumption Insurance and Risk Premia. Journal of Finance 60, 1167-1219. Lustig, H. and S. van Nieuwerburgh (2006a) How much does Household Collateral constrain Regional Risk Sharing? working paper UCLA and NYU Stern Lustig, H. and S. van Nieuwerburgh (2006b) Can Housing Collateral explain Long-Run Swings in Asset Returns? working paper UCLA and NYU Stern Newey W.K. and K.D. West (1987) A simple, positive semidefinite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703-708. Nitschka, T., (2008) Idiosyncratic Consumption Risk and Predictability of the Carry Trade Premium: Euro Area Evidence. IEW working paper 387, University of Zurich Norman, B., M. Sebastia-Barriel and O. Weeken (2002) Equity wealth and consumption – the experience of Germany, France and Italy in an international context. Bank of England Quarterly Bulletin Spring 2002. Rangvid, J. (2006) Output and Expected Returns. Journal of Financial Economics 81, 595624. Shanken, J. (1992) On the estimation of beta-pricing models. Review of Financial Studies 5, 1-33. Sharpe, W. F. (1964) Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19, 425-442. Slacalek, Jiri (2006), “What Drives Personal Consumption? The Role of Housing and Financial Wealth”, DIW discussion paper 647. Sørensen, B.E. and O. Yosha (1996) International Risk Sharing and European Monetary Unification. Journal of International Economics 45, 211-238. Stambaugh, R.F. (1982) On the Exclusion of Assets from Tests of the Two-Parameter Model: A Sensitivity Analysis. Journal of Financial Economics 10, 237-268. Tsatsaronis, K. and H. Zhu (2004) What drives housing price dynamics: cross-country evidence. BIS Quarterly Review

18

Tables

Table 1: Cointegration characteristics of U.S. house price to GDP ratio Panel A: Johansen Cointegration Test Trace

L-Max

r=0

23.50***

22.65***

r=1

0.27

0.27

Notes: This table presents test statistics of the Johansen cointegration test allowing for a time trend and two lags as suggested by standard information criteria. The Trace test tests the null of r cointegrating relationships against the alternative of p, the number of variables in the tested system, cointegrating relations. The L-Max test tests the null of r cointegrating relations against the alternative of r+1. * denotes significance at 90%, ** at 95% and *** at 99% level. The variables under consideration are a log U.S. house price index and log U.S. GDP. Both of the series are annual and nominal. The sample spans the period from 1952 to 2008.

19

Table 2: Long-horizon regression (U.S. stock market excess return) h=1

h=2

h=3

h=5

h=8

h=9

h=10

Panel A: 1952 - 2008 hy t

0.38 *

0.72 *

1.10 *

1.97 *

2.94 *

3.13 *

3.17 *

R2

0.05

0.09

0.19

0.42

0.62

0.61

0.56

my t

0.05

0.07

0.33

1.05 *

2.03 *

2.26 *

2.47 *

R2

0.00

0.00

0.01

0.15

0.38

0.39

0.42

( 2.13)

( 0.31)

( 3.00)

( 0.24 )

( 5.15 )

( 0.72 )

( 6.13)

(1.99 )

( 5.01)

( 2.78)

( 4.81)

( 2.96 )

( 5.03)

( 3.23)

Panel B: 1970 - 2008 hy t

0.23

0.39

1.05 *

2.32 *

3.79 *

4.03 *

4.02 *

R2

0.00

0.01

0.07

0.33

0.75

0.78

0.74

my t

0.14

0.37

0.87 *

1.57 *

2.55 *

2.78 *

2.85 *

R2

0.00

0.01

0.12

0.31

0.72

0.74

0.78

( 0.72 )

( 0.80 )

( 0.84)

(1.26 )

( 2.20 )

( 2.33)

( 4.89 )

( 4.58 )

(8.34 )

( 9.66 )

(8.80 )

(10.11)

( 9.48)

(10.85)

Notes: This table reports estimates from long-horizon regressions of the form:

rte,t + h = α + β h xt + ε t + h where rte,t + h denotes the return on the S&P 500 stock index in excess of the risk-free rate, here the 3-month t-bill, at time horizon t+h. The regressor, xt , is either the temporary deviation from the long-term trend in the ratio of a residential house price index and GDP in the U.S., abbreviated with hy t . Or it is the residual from the cointegration relation between residential real estate wealth and income from Lustig and van Nieuwerburgh (2005), my t . All of the variables are observed at annual frequency and expressed in natural logarithms. The house price GDP ratio is calculated as ratio of nominal values. Housing wealth and income are denominated in real, per household terms. The forecast horizon, h, is in years. The t-statistics are Newey-West corrected (Newey and West (1987)) and appear below the regressor estimates in parenthesis. The row below the estimates reports the adjusted R 2 statistic. Asterisk indicates significance at the 95% 20

confidence level. The results reported in panel A rely on the sample period from 1952 to 2008. Panel B reports estimates from the sample period from 1970 to 2008. Both regressors are normalized as in Lustig and van Nieuwerburgh (2005) such that a value of unity indicates collateral scarcity and values near zero plentiful supply of collateral. Hence we should observe positive estimates of the slope coefficients.

21

Table 3a: Long-horizon regression (Euro Area countries) h=1

h=2

h=3

h=5

h=8

h=9

h=10

BEL

0.01

0.09

0.25

0.51 *

0.85 *

0.94 *

0.96 *

R2

0.00

0.00

0.03

0.13

0.36

0.47

0.59

FRA

− 0.18

− 0.24

− 0.28

0.13

0.16

0.07

− 0.10

R2

0.00

0.00

0.00

0.00

0.00

0.00

0.00

GER

0.36

0.86

2.08

2.48

0.83

1.02

1.71*

R2

0.00

0.00

0.04

0.04

0.00

0.00

0.02

ITA

− 0.14

− 0.08

0.07

0.57

0.74

0.65

0.52

R2

0.00

0.01

0.07

0.33

0.75

0.78

0.74

NL

0.11 *

0.20 *

0.31 *

0.28 *

0.30

0.29

0.28

R2

0.03

0.06

0.11

0.06

0.07

0.07

0.08

ESP

0.39 *

0.70 *

0.98 *

1.21*

1.03 *

1.02 *

1.02 *

R2

0.25

0.32

0.35

0.34

0.22

0.21

0.25

( 0.11)

( −0.77 )

( 0.60 )

( −0.80 )

( 2.14 )

( 3.32 )

( 0.64)

( −0.60 )

( 0.74)

( −0.29 )

( 2.40)

( 3.18)

(1.82 )

( −0.55)

(1.40)

( 0.21)

( 3.34 )

( 3.37 )

( 3.54 )

( 0.22 )

(1.39)

(1.23)

( 2.34 )

( 3.40)

( 3.77 )

( 0.32 )

( 0.35)

(1.37 )

(1.94 )

( 2.38 )

( 4.45)

( 0.13)

( 0.67 )

(1.12 )

(1.82 )

( 2.23)

( 4.57 )

( −0.18 )

( 2.02 )

( 0.84 )

(1.74 )

( 2.36 )

Notes: This table reports estimates from long-horizon regressions of the form:

rte,t,+i h = α + β h,i hyti + ε ti+ h where rte,t,+i h denotes the return on the MSCI stock index return in excess of the risk-free rate at time horizon t+h of country i. The regressor, hy ti , is the temporary deviation from the longterm trend in the ratio of a residential house price index and GDP of country i. The variables are observed at annual frequency and expressed in natural logarithms. The house price to GDP ratio is calculated as ratio of nominal values. The forecast horizon, h, is in years. The t-statistics are Newey-West corrected (Newey and West (1987)) and appear below the regressor estimates in parenthesis. The row below the estimates reports the adjusted R 2 statistic. Asterisk indicates significance at the 95% confidence level. The sample period runs from 1970 to 2007 with the exception of Spain for which the sample starts 1973. The regressor is normalized as in Lustig and van Nieuwerburgh 22

(2005) such that a value of unity indicates collateral scarcity and values near zero plentiful supply of collateral.

23

Table 3b: Long-horizon regression (other countries) h=1

h=2

h=3

h=5

h=8

h=9

h=10

AUS

− 0.15

0.17

0.63

0.71

0.03

− 0.31

− 0.11

R2

0.00

0.00

0.00

0.01

0.00

0.00

0.00

CND

− 0.01

0.14

0.39

0.63

0.68 *

0.72 *

0.92 *

R2

0.00

0.00

0.02

0.08

0.14

0.12

0.22

DK

0.14

0.27

0.37

0.48

0.75 *

0.77 *

0.69 *

R2

0.00

0.01

0.03

0.06

0.34

0.26

0.20

JPN

0.04

− 0.20

− 0.26

0.08

0.33

0.40

0.61

R2

0.00

0.00

0.00

0.00

0.00

0.00

0.00

NOR

0.15

0.06

0.08

0.55

0.22

0.00

− 0.04

R2

0.00

0.00

0.00

0.00

0.00

0.00

0.00

SWE

− 0.14

− 0.15

0.00

0.68

1.53 *

1.49 *

1.37 *

R2

0.00

0.00

0.00

0.03

0.27

0.29

0.39

CH

− 0.10

− 0.23

− 0.29

− 0.16

0.24

0.28

0.24

R2

0.00

0.00

0.00

0.00

0.00

0.00

0.00

UK

− 0.31

− 0.19

0.33

0.76

1.22 *

1.32 *

1.32 *

R2

0.00

0.00

0.00

0.07

0.20

0.23

0.22

( −0.56 )

( −0.08)

( 0.99 )

( 0.17 )

( 0.50 )

( −0.56 )

( −0.45 )

( −0.99 )

( 0.42 )

( 0.46 )

(1.22 )

( −1.05)

( 0.14 )

( −0.33)

( −0.51)

( −0.56 )

(1.34 )

(1.02 )

(1.33)

( −1.21)

( 0.17 )

( 0.00 )

( −0.50 )

( 0.81)

(1.40 )

(1.68 )

(1.51)

( 0.25 )

(1.09 )

(1.05)

( −0.25 )

(1.55)

( 0.05)

( 2.10 )

( 3.55 )

( 0.69 )

( 0.52 )

( 3.74 )

( 0.55)

( 2.91)

( −0.58)

( 2.11)

( 4.82 )

( 0.75)

( 0.00 )

( 3.34 )

( 0.67 )

( 4.23)

( −0.13)

( 2.81)

( 3.96 )

(1.16 )

( −0.14 )

( 3.07 )

( 0.63)

( 5.52 )

Notes: The sample period runs from 1970 to 2007 with the exception of Denmark for which the sample starts 1971. For further details, please refer to the notes below table 3a.

24

BEL

Table 4a: Risk price estimates (Euro Area countries) mspe λ EQ λ RE R2 -0.26 13.14 12.64 ( 2.22 )

9.90 (1.73)

FRA

( 2.17 )

( 2.07 )

0.19 ( 0.22 )

13.97 ( 2.09 )

12.06 (1.89 )

− 3.85 ( −1.40 )

12.38 ( 2.15 )

10.81 (1.90 )

ESP

( 0.38)

( 2.19 )

( 2.05 )

NL

0.74

13.50 13.17

ITA

( 2.20 )

12.51 11.94

GER

5.37

5.71 ( 2.28 )

13.30 ( 213)

10.43 (1.71)

4.74 (1.73)

mape 2.91

-0.03

10.60

2.66

-0.48

15.56

3.14

-0.48

15.44

2.18

-0.50

16.10

3.19

-0.50

16.03

3.20

-0.89

20.81

3.72

-0.72

18.85

3.62

-0.74

19.09

3.57

-0.48

15.73

3.21

-0.96

22.11

3.96

-0.77

19.22

3.49

Notes: This table shows risk price estimates in percentage points p.a. from the estimation of the beta representation of the CAPM confronted with value and growth excess returns of the countries under study. The risk prices are obtained through a Fama-MacBeth cross-sectional regression (Fama and MacBeth (1973)) of international value and growth excess returns ( r e, j ) on the market portfolio excess return of country i. The market portfolio excess return is proxied by both the excess return on a stock market index ( r i , EQ ) and on real estate ( r i , RE ) or solely the stock market return of country i, i.e. i i rte, j = μ + β EQ rti , EQ + β RE rti , RE + ε ti

in the first step to obtain the exposure to the risk factors and i i rte , j = λ EQ ,i βˆ EQ + λ RE ,i βˆ RE + vti , ∀t

to obtain the risk prices λ. The t-statistics in parenthesis below the estimates are Shanken (1992) corrected to correct for the fact that the second stage regressors are generated in a time series regression. The column R² gives the cross-sectional R² adjusted for the number of regressors allowing for negative values. The columns mspe and mape display mean squared and mean absolute pricing errors respectively. All data is measured at the annual frequency. The sample period runs from 1977 to 2007.

25

AUS

Table 4b: Risk price estimates (other countries) mspe λ EQ λ RE R2 -0.35 13.99 10.27 ( 2.22 )

10.23 ( 2.22 )

CND

( 2.16 ) (1.98)

( −2.40 )

( 2.11)

(1.88)

5.11 (1.47 )

16.50 ( 2.09 )

10.23 (1.64 )

4.66 (1.62 )

12.51 ( 2.23)

10.84 ( 2.19 )

UK

− 3.18

16.29 11.87

CH

(1.40 )

( 2.07 ) (1.62 )

SWE

3.04

11.26 8.04

NOR

( −0.32 )

7.81 6.55

JPN

− 0.74

1.40 ( 0.80 )

9.69 ( 2.20 )

6.03 (1.77 )

2.65 (1.11)

Notes: see the notes below table 4a

26

mape 3.19

-0.30

13.39

3.11

-0.75

18.95

3.69

-0.60

16.83

3.62

-1.01

23.78

3.87

-0.45

15.71

3.00

-1.06

27.90

4.56

-0.79

19.48

3.68

-0.97

23.15

3.91

-0.73

18.64

3.56

-0.50

16.17

3.21

-0.34

14.06

3.09

-0.77

19.53

3.48

-0.39

14.34

2.96

Table 5: Time series restrictions on pricing errors

BEL

p-value GRS r EQ + r RE r 0.69 0.68

AUS

p-value GRS r EQ + r RE r 0.68 0.67

FRA

0.70

0.65

CND

0.68

0.67

GER

0.69

0.68

JPN

0.65

0.26

ITA

0.70

0.66

NOR

0.70

0.71

NL

0.70

0.71

SWE

0.70

0.37

ESP

0.69

0.45

CH

0.69

0.38

UK

0.68

0.16

EQ

EQ

Notes: This table shows the p-value of the Gibbons, Ross and Shanken (1989) test if all pricing error estimates from the first stage time series regressions of the Fama-MacBeth (Fama and MacBeth (1973)) regressions reported in table 4a and 4b are jointly zero. All data is measured at the annual frequency. The sample period runs from 1977 to 2007.

27

Figures 0.7 housing

Share of wealth component in asset wealth

0.6

0.5

0.4

0.3

0.2 equity 0.1

0 1980Q1

1985Q1

1990Q1

1995Q1 time

2000Q1

2005Q1

Figure 1: Share of housing wealth and equity in euro area households’ asset wealth for the time period from the first quarter of 1980 to the first quarter of 2007.

28

short−run variation in U.S. house price to GDP ratio

0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 1952

1960

1970

1980 time

1990

2000

Figure 2: Short-run movements in the cointegrated relation between nominal house prices and nominal GDP in the U.S for the sample period from 1952 to 2008.

29