Accounting Data, Market Values, and the Cross Section of Expected Returns Worldwide Akash Chattopadhyay Matthew R. Lyle Charles C.Y. Wang Working Paper 15-092 Accounting Data, Market Values, and the Cross Section of Expected Returns Worldwide Akash Chattopadhyay Harvard Business School Matthew R. Lyle Kellogg School of Management Charles C.Y. Wang Harvard Business School Working Paper 15-092 Copyright © 2015 by Akash Chattopadhyay, Matthew R. Lyle, and Charles C.Y. Wang Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author. Accounting Data, Market Values, and the Cross Section of Expected Returns Worldwide Akash Chattopadhyay Harvard Business School Matthew R. Lyle Kellogg School of Management Charles C.Y. Wang∗ Harvard Business School June 2015 Abstract Under fairly general assumptions, expected stock returns are a linear combination of two firm fundamentals—book-to-market ratio and return on equity. This parsimonious relation is pervasive, producing expected return proxies (ERP) that predict the cross section of out-of-sample returns in 26 of 29 international equity markets. The average slope coefficient on the ERP is a highly significant 1.05. In contrast, factor-model-based proxies fail to exhibit predictive power worldwide. Integrating the model with a dynamic information structure, we show analytically, and verify empirically, that the importance of return on equity in forecasting future stock returns depends on the quality of the accounting information. This extension also reconciles our model with alternative characteristic-based forecasters. These findings suggest that a tractable accounting-based valuation model provides a unifying framework for obtaining reliable proxies of expected returns worldwide. Keywords: Expected returns, discount rates, fundamental valuation, present value, information quality, international equity markets. JEL: D83, G12, G14, M41 Chattopadhyay (achattopadhyay@hbs.edu) is a doctoral candidate in Accounting and Management at Harvard Business School. Lyle (m-lyle@kellogg.northwestern.edu) is Assistant Professor of Accounting Information and Management and The Lawrence Revsine Research Fellow at Kellogg School of Management. Wang (charles.cy.wang@hbs.edu) is Assistant Professor of Business Administration at Harvard Business School. For helpful comments and suggestions, we are grateful to Ryan Buell, Craig Chapman, Peter Easton, Ian Gow, Jeremiah Green (FARS discussant), Daniel Malter, Jim Naughton, Tatiana Sandino, Pian Shu, Beverly Walther, Clare Wang, James Zeitler, and to workshop participants at University of Alberta, Arizona State University, Citadel Quantitative Research, Duke University, Harvard Business School, University of Illinois, Kellogg School of Management, University of Miami, National Chengchi University, as well as participants at the 2015 FARS conference and Minnesota Empirical Accounting Research Conference. We thank Kyle Thomas for excellent research assistance. Lyle is grateful for generous funding provided through the Lawrence Revsine Research Fellowship. ∗ Accounting Data, Market Values, and Expected Returns Worldwide 1 1 Introduction Estimating expected returns has been a centerpiece in financial economics since at least the derivation of the CAPM (Sharpe, 1964). Over the past thirty years, the central organizing theoretical and empirical question in asset pricing is understanding what drives the variation in expected returns (Cochrane, 2011). Capital markets research in accounting has also developed a large and growing literature examining how different firm attributes or policies—e.g., disclosure policies (Botosan, 1997), audit quality (Chen, Chen, Lobo, and Wang, 2011), or corporate governance and regulatory institutions (Hail and Leuz, 2006)—affect expected returns. Despite its importance, empirical research in this area remains problematic, and results are often controversial because the key dependent variable—expected returns—is not directly observable, notoriously difficult to measure, and there is no well-accepted standard for its estimation. We posit that such a standard should, by definition, produce empirical proxies that on average forecast the cross-section of future returns and across multiple equity markets. Despite extensive work on this measurement problem, to our knowledge no such method exists. Factor-based models, like the capital asset pricing model or the Fama and French (1993) factor model, are unreliable proxies of ex ante expected returns as they fail to exhibit out-of-sample predictive ability in the U.S. (Lee, So, and Wang, 2014; Lyle and Wang, 2015). The accounting literature’s development of the implied cost of capital (ICC) class of expected return proxies (ERPs), as an alternative to factor-based proxies, have so far failed to produce a well-accepted standard.1 This may be in part due to the restrictive assumptions that underly ICC models (e.g., constant expected returns, adhoc terminal growth assumptions), the difficulties in their implementation (e.g., solving 1 Recent examples of papers that explore the performance of these and other expected-return proxies include: Botosan and Plumlee (2005); Botosan, Plumlee, and Wen (2011); Easton and Monahan (2005); Lyle, Callen, and Elliott (2013); Lee et al. (2014); Lyle and Wang (2015); Wang (2015). Accounting Data, Market Values, and Expected Returns Worldwide 2 non-linear equations by numerical methods that may or may not converge, or that may converge to multiple solutions), and, perhaps most saliently, the lack of evidence that ICCs, in the cross section, line up well with true expected returns (Easton and Monahan, 2005; Lee et al., 2014). These empirical challenges are exacerbated in international settings (Lee, Ng, and Swaminathan, 2009). Varying degrees in the integration with global markets, differences in regulatory and governance institutions, the relative paucity in international data, and differences in accounting reporting standards represent significant barriers to a uniform standard or framework for estimating firm-level expected returns worldwide. Indeed, prior work has shown that factors known to explain the in-sample variation of returns in the United States do not necessarily explain the cross section of returns in other markets internationally (Fama and French, 2012; Hou, Karolyi, and Kho, 2011). It is perhaps unsurprising, therefore, that there is no well-accepted and theoretically-motivated standard for estimating firm-level expected returns not only in the U.S. setting, but also across international markets. In this paper we show, both analytically and empirically, that a simple and parsimonious accounting-based approach can offer a step forward to solving to this long-standing measurement problem. We derive, under fairly general assumptions, an accounting-based ERP that can forecast the cross-section of future returns worldwide and lines up well with true expected returns. Our work validates and builds on, in three ways, the findings of Lyle and Wang (2015) (subsequently referred to as LW15), who apply the log-linearization of Vuolteenaho (2002) to derive a tractable model of time-varying expected rate of return that is a linear function of the book-to-market ratio (BM) and return-on-equity (ROE). First, we show analytically that the accounting-based model of expected returns in LW15 is quite robust in that it can be applied to a broad set of accounting systems. Like LW15, we show that a parsimonious solution for estimating firm-level expected returns Accounting Data, Market Values, and Expected Returns Worldwide 3 requires only a linear combination of two accounting fundamentals: BM and ROE. But we derive this solution under more generalized and milder assumptions: 1) the book-tomarket ratio is a weakly stationary process and that 2) expected growth rates in market and book are mean-reverting. Thus we generalize LW15 by showing that this linear relation between expected returns and fundamentals holds for a much broader class of accounting systems, rather than just those conforming to the assumptions implicit in the Vuolteenaho (2002) approach.2 Second, we extend to and validate in an international setting the empirical findings of LW15, who focus only on U.S. equities. Our simple accounting-based ERPs perform well across the world: they significantly and reliably predict the cross section of stock returns in 26 of 29 equity markets worldwide. They also line up well with true expected returns. Fama-MacBeth (FM) regression tests—regressing one-month-ahead returns on ex-ante proxies of expected returns—yield an average predictive slope coefficient of 1.05 (relative to the absolute benchmark of 1). For 21 (20) of the 29 countries the predictive slope is not significantly different from 1 at the 10% (5%) level. Portfolio-based tests yield similar conclusions. Finally, we build upon LW15 by examining, both analytically and empirically, how the quality of accounting information affects the relation between accounting numbers and expected returns. By relating the accounting-based model of expected returns to a dynamic information structure, we show analytically that, holding all other sources of information constant, higher-quality accounting information—defined by lower measurementerror variance—increases the importance of ROE in determining expected returns. These predictions are supported by our empirical tests. Relying on measures of country-level earnings quality derived from Leuz, Nanda, and Wysocki (2003) and employing an instruThe log-linearization approach of Vuolteenaho (2002) assumes that in the long-run book values and market value must converge, consistent with mark-to-market accounting and inconsistent with conservatism in accounting systems. We thank Stephen Penman for pointing this out this critical assumption. 2 Accounting Data, Market Values, and Expected Returns Worldwide 4 mental variables estimation strategy, we document that, all else equal, higher earnings quality elevates the importance of ROE in inferring expected returns. Together, we contribute to the literature by providing a simple accounting-based ERP that can be applied to international markets and by demonstrating how the quality of accounting systems impacts the importance of accounting-information in this proxy. Our work relates to the extensive value-relevance literature in accounting that connects prices to accounting data, and in particular to the seminal work of Ohlson (1995) and Feltham and Ohlson (1995) that relate firm values to accounting data through the residual income model. Our approach to deriving firm values is similar; however, unlike the prior papers, we do not assume clean surplus, risk neutrality, and importantly allow both growth rates in book and stock values to vary stochastically through time. Our work also relates to the rich implied cost of capital literature in accounting (e.g., Botosan, 1997; Gebhardt, Lee, and Swaminathan, 2001; Claus and Thomas, 2001; Gode and Mohanram, 2003; Easton, 2004) in that we also seek to infer expected returns implied by observed stock prices and accounting data. Our approach, though similar in principle, has several distinct practical advantages. Ours is motivated by a fairly general model, applicable to broad classes of accounting systems, easy to implement, and does not require solving non-linear equations. Further, our ERPs line up well with true expected returns across international equity markets. Our paper is also related to the large body of research in accounting and finance linking stock returns to firm characteristics (e.g., Banz, 1981; Rosenberg, Reid, and Lanstein, 1985; Bernard and Thomas, 1990; Fama and French, 1992; Jegadeesh, Jegadeesh, Titman, and Titman, 1993; Haugen and Baker, 1996; Sloan, 1996; Daniel, Grinblatt, Titman, and Wermers, 1997; Piotroski, 2000; Fama and French, 2008; Penman, Reggiani, Richardson, and Tuna, 2013).3 Our study differs from these in that we contribute by showing whether See Green, Hand, and Zhang (2013) or Lewellen (2015) for a summary of the firm characteristics that have been identified to be associated with future returns. 3 Accounting Data, Market Values, and Expected Returns Worldwide 5 and how investors can combine firm characteristics to form ERPs that line up well with true expected returns, a subject that has received relatively little (but growing) attention (e.g., Lewellen, 2015; Lyle et al., 2013; Lyle and Wang, 2015; Lee et al., 2014). Aside from LW15, closest to the present study is Lewellen (2015), which also studies how firm characteristics can be combined to form reliable ERPs using historical FM regressions, and Haugen and Baker (1996), which also assesses the usefulness of historical FM regressions. Our work differs from these in that we focus on two firm characteristics motivated by valuation theory instead of a large set of ad hoc [and in the case of Haugen and Baker (1996) short-lived] predictors. Moreover, our analyses are focused on a large set of international markets, for which there is relatively little evidence on the performance of cross-sectional-regression-based estimates of firm-level expected returns.4 Our findings suggest that an accounting-based valuation model can serve as a unifying framework for estimating firm-level expected rates of return across markets worldwide. Though the primary contribution of this paper is to demonstrate that a simple and reliable ERP that lines up well with true expected returns can be obtained from a linear combination of only two firm fundamentals, we wish to emphasize a subtler but important contribution of our analytical work. In relating our accounting-based expected returns model to a dynamic information setting, we are able to offer new insights that would not be possible using traditional CAPM or ICC expected return models. First, this framework allows us to analyze how accounting information quality impacts expected returns through fundamentals. How accounting information quality impacts expected returns is a long standing question in accounting research, a question that is difficult to address in large part because models of expected returns that allow for information quality variation (e.g., Lambert, Leuz, and Verrecchia, 2007) are not functions of actual accounting data. Our analytical approach takes a step towards dealing with this issue. Second, this extension Lewellen (2015) studies the U.S. market exclusively. Haugen and Baker (1996) focuses mainly on the U.S. but performs an analysis on France, Japan, Germany, and the U.K. 4 Accounting Data, Market Values, and Expected Returns Worldwide 6 provides a framework for understanding why various characteristics (accounting data and valuation ratios) relate to future stock returns: they carry information about future ROE. This analytical result suggests that the empirical approach used by Ou and Penman (1989), coupled with our parsimonious model, may offer an exciting area of potential future research in accounting and characteristic-based asset pricing. The remainder of the paper is organized as follows. Section 2 presents the accountingbased model for estimating expected returns. Section 3 discusses the estimation of the model and presents our empirical findings. Section 4 presents our theoretical and empirical analyses of the role of accounting-information quality. Section 5 concludes the paper. 2 The Model In this section, we derive a model of expected returns that is a linear combination of BM and expected ROE, as in LW15. However, our derivation relies on a milder set of assumptions, that generalize the result of LW15 and allow for the application of this model to a wide range of accounting systems. 2.1 Main Assumptions and Set Up Two main assumptions anchor the present model. First, instead of relying on the log-linearization of Vuolteenaho (2002), we make the mild assumption that the log bookto-market ratio (bm) is covariance-stationary with finite first moment:5 Bt+j Mt+j j→∞ 5 lim Et log = bm < ∞. (1) This assumption is consistent with that of Daniel et al. (1997), who assume that a long-term bookto-market ratio is measurable. Accounting Data, Market Values, and Expected Returns Worldwide 7 Unlike the assumption required in Vuolteenaho (2002)—that book and market values are equal in the limit, consistent with mark-to-market accounting—this milder assumption applies to broad classes of accounting systems, including, for example, those expected to be conservative. Aside from generalizability, the weak stationarity assumption is also motivated and supported empirically in untabulated tests.6 Second, we assume that expected growth rates in the market value of equity, Et [gm,t+1 ] ≡ µt , and the book value of equity, Et [gb,t+1 ] ≡ ht , are time-varying and mean-reverting. We model them to follow AR(1) processes: µt+1 = µ + κ(µt − µ) + ξt+1 , and ht+1 = µ + ω(ht − µ) + t+1 , (2) (3) where κ and ω represent the levels of persistence in expected market and book growth, respectively; µ represents the unconditional average expected growth rates for both market and book; and the book and market growth innovations (ξt+1 , be IID with zero means and bounded variances. The AR(1) assumption for expected market growth is consistent with time-varying and persistent expected returns and follows prior research (e.g., Campbell, 1991; van Binsbergen and Koijen, 2010; P´stor and Stambaugh, 2012; Lyle and Wang, 2015). The a assumption for expected book growth captures the idea that competitive forces drive a tendency of accounting rates of returns to revert to a steady-state mean (e.g., Beaver, 1970; Penman, 1991; P´stor and Veronesi, 2003; Healy, Serafeim, Srinivasan, and Yu, a 2014). The above also assumes that expected market and book growth revert to a common mean, which is not only consistent with the stationarity in bm but also motivated by the idea that in the long-run abnormal growth in book values should converge to 0 due to Analyzing the aggregate annual bm series across countries using standard Dickey-Fuller tests, we reject the null of non-stationarity for the vast majority of countries. 6 t+1 ) are assumed to Accounting Data, Market Values, and Expected Returns Worldwide 8 competition (e.g., Ohlson, 1995). In untabulated tests we also find empirical support for these assumptions.7 Under these two main assumptions, we can relate bmt , µt , and ht parsimoniously. Letting Mt , Bt , Gm,t+1 , and Gb,t+1 denote market value, book value, growth in market value, and growth in book value, respectively, we can relate two periods’ market and book values as follows: Bt+1 = Gb,t+1 Bt and Mt+1 = Gm,t+1 Mt . (4) Taking logs and subtracting log market (m) from log book (b) values yields bmt = bmt+1 + gm,t+1 − gb,t+1 . (5) Iterating Eq., (5) forward, using the Eq., (1) assumption, and taking expectations conditional on information known at time t, bmt can be expressed as ∞ bmt = bm + i=1 Et [gm,t+i − gb,t+i ]. (6) Given the stationarity of bm (so that bmt is bounded for any t), this expression implies that growth rates of book and market values must be expected to converge, T →∞ lim Et [gm,t+T − gb,t+T ] = 0, (7) implying a common mean assumption in these expected growth rates. Finally, under the In a vast majority of the countries in our sample, we find substantial support for the hypothesis that the realized aggregate series in the growth in market and book values are generated by ARMA(1,1) processes, consistent with expected book and market growth being AR(1) (Hamilton, 1994). Moreover, in all of the countries in our sample, we are unable to reject the null that the mean growth in book and the mean growth in market values are different from one another. 7 Accounting Data, Market Values, and Expected Returns Worldwide 9 AR(1) structure, bmt can be simplified as 1 1 (µt − µ) − (ht − µ). 1−κ 1−ω bmt = bm + (8) 2.2 Expected Returns Our goal is to solve for next period expected returns, conditional on information known at time t. Expected log-returns, is defined as: Mt+1 + Dt+1 Mt Et [rt+1 ] = Et log , (9) where Mt and Dt are the time-t market value and dividends, respectively. Armed with the bm ratio in Eq., (8) and assuming, as in P´stor and Veronesi (2003), a that accounting satisfies clean surplus and that dividends are proportional to book value over the next interval, we show in the Appendix that expected returns is a linear combination of the book-to-market ratio and expected ROE: Et [rt+1 ] = A1 + A2 bmt + A3 Et [roet+1 ], (κ−ω)(1−ρ) µ, (1−ω) (10) where A1 = K − (1 − κ + ρκ)bm − A3 log(1 + δ) + A3 = ρ(κ−ω)+1−κ ; 1−ω A2 = 1 − κ + ρκ, and δ is the proportion of dividends paid out of book; the constants K and ρ are by-products of a log-linearization around the unconditional bm ratio and close to zero in value. Thus, even under these rather mild assumptions, as in LW15, expected log returns can be determined by a constant, bm, and expected roe.8 The intuition for why bm and roe provide information on expected returns resides in the present value relation between prices, expected future payoffs, and expected returns. 8 (ω−κ)k1 1−ωk1 µ, one. The interpretation of the coefficients in this paper, however, is slightly different. In LW15, A1 = 1−κk A2 = 1 − κk1 , and A3 = 1−ωk1 , where k1 is a linearization constant assumed to be close to 1 Accounting Data, Market Values, and Expected Returns Worldwide 10 Accounting fundamentals provide information on expected future payoffs (cash flows), while market prices provide information on how those future payoffs are discounted. Thus combining market values with accounting numbers, rather than the latter per se, reveal expected returns. Consider for illustration the classic Gordon Growth Model, which relates market values (Mt ) to dividends (Dt ) as well as constant dividend growth (g) (i.e., expected future payoffs) and constant expected returns (r): 1+g . r−g Mt = Dt This model implies that expected returns is a function of expected future fundamentals and market prices: Dt (1 + g) + g. Mt r = While contrived, this example illustrates the intuition that expected returns are revealed by combining market values and “adding back” expected future payoffs. Moreover, assuming that dividends are proportional to book value, future payoffs can be expressed in terms of accounting fundamentals.9 Our model can be interpreted using this intuition, but it is more general in that we allow expected returns and future payoffs, expressed in terms of accounting fundamentals, to be dynamic. Following the intuition above, holding expected future payoffs fixed (e.g., holding fixed current book value and expected future roe), lower market values reflect higher expected returns [i.e., positive A2 in (10)]. Simi9 Alternatively, similar intuition can be gleaned from a classic steady-state residual income model: Mt = B t + (roe∗ − r)Bt , r−g where r is expected returns, g is the growth in book value and net income, and roe∗ is the steady-state return-on-equity. Accounting Data, Market Values, and Expected Returns Worldwide 11 larly, holding market prices fixed, greater expected future payoffs (e.g., higher future roe) reflects higher expected returns [i.e., positive A3 in (10)]. 3 Model Calibration and Main Empirical Tests This section describes the process of estimating Eq., (10), including the data require- ments and key inputs, to compute the model-implied estimates of expected returns. We then present our main empirical tests to assess the out-of-sample cross-sectional performance of these estimates. 3.1 Data and Calibration To calibrate the model we make the following assumptions on the relations between realized and expected returns and roe: ri,t+1 = Et [ri,t+1 ] + ηi,t+1 , roei,t+1 = Et [roei,t+1 ] + νi,t+1 , (11) (12) where (ηi,t+1 , νi,t+1 ) are IID noise terms with zero mean and finite second moment.10 Substituting into Eq., (10) and applying the AR(1) assumption to expected log book growth yields the following estimable equation relating one-period ahead realized returns to current bm ratios and roe: ri,t+1 = β1 + β2 bmi,t + β3 roei,t + ζi,t+1 , 10 (13) The uncorrelatedness and zero mean assumptions follow from the properties of conditional expectations (e.g., Angrist and Pischke, 2008). Accounting Data, Market Values, and Expected Returns Worldwide 12 where β1 = K + 1 − κ + (κ−ω)(1−ρω) 1−ω µ − (1 − κ + ρκ)bm − ωA3 log(1 + δ), β2 = A2 = 1 − κ + ρκ, β3 = ωA3 = ω ρ(κ−ω)+1−κ , and ζi,t+1 = A3 ( t − ωνt ) − ηt+1 . Again, K = 1−ω log(1 + δ exp(bm)) and ρ = δ exp(bm) 1+δ exp(bm) are by-products of the log linearization. Calibrating the model requires us to specify the frequency with which expected returns and expected roe evolve according to the assumed dynamics. For example, LW15 choose quarterly and annual frequencies. A challenge in the international setting is that the mandatory frequency of interim reporting is not uniform across markets in different countries; moreover, some countries changed their mandatory interim financial-reporting frequency during our sample period (e.g., Link, 2012). Because annual reporting is required in all countries in our sample, a natural empirical specification would be to match annual stock returns to annual bm and roe. Given that fundamental data for most countries becomes available for a suitable cross section only between the early and mid-1990s, using annual data imposes serious limitations on the time series data available to us. The lack of consistency in quarterly reporting across countries also limits the usefulness of switching to interim reporting. Our approach to resolving this empirical issue, similar to that of Fama and French (1992), is to match one-month-ahead returns to annual fundamental data (i.e., matching one-month-ahead returns to bm and annual roe). This can be thought of as treating the annual version of Eq., (13) as the sum of 12 equations that contain monthly returns and news. In this framework, each of the 12 months in a given year is an estimation equation, using the same BM and annual ROE, and the sum of the 12 estimated monthly coefficients translates to the coefficients of an annual model. We assume fundamental data to be known publicly and observable to the researcher four months after the fiscalyear-end date.11 Thus, in computing a firm’s BM, we use its market capitalization on the This assumption is necessitated by the sparseness of the earnings announcement date variable for a number of countries in Compustat Global. However, among those firms in our sample with earnings announcement dates, greater than 90 percent of them report annual earnings within four months of the fiscal year end. 11 Accounting Data, Market Values, and Expected Returns Worldwide 13 last trading day of the fourth month after the last fiscal-year-ending month. Our data on returns and fundamentals come from Compustat Global and Compustat North America (in the case of Canada and the U.S.).12 Monthly returns are computed using Compustat’s price variable (variable prccd from the price file) by applying adjustments for splits and dividends using the respective adjustment factors (variables ajexdi and trfd from the price file).13 Gross annual ROE is calculated as ROEi,t = 1 + Xi,t Booki,t−1 , where Xi,t is Net Income before Extraordinary Items (variable ib from the fundamentals file) and Booki,t−1 is the lag Book Value of Common Equity (variable ceq from the fundamentals file). We make forecasts of expected future monthly (log) returns by estimating Eq. (13), via FM regressions, using historical realized monthly returns, the bm ratio, and roe that are observable as of the forecast date to avoid look-ahead bias. To ensure some stability in the FM coefficients, we use a training (or burn-in) sample consisting of 40 months in each country, after which out-of-sample forecasting and testing begins. We use a “cumulative” window approach, or recursive estimation, in that all historical data available at the time of the forecast are used to estimate Eq., (13) in order to form expected returns. In other words, we forecast one-month-ahead expected r at the end of each calendar month by applying historically-estimated FM coefficients on the bm and roe values observed as of the forecast date. Embedded in our country-specific and recursive estimation choices are the implicit assumptions that 1) expected market growth and expected book growth follow AR(1) processes with a common long-run mean; 2) these model parameters are country-specific and may be time-varying; and 3) expected dividend payout ratios are country-specific and While our use of Compustat for international fundamentals and returns data follows some prior literature (e.g., Bushman and Piotroski, 2006, Novy-Marx, 2013), the international capital markets literature has also used Datastream as a common alternative. Though ex ante we do not expect our findings to be influenced by this choice, we re-estimate our main results, in untabulated robustness tests, for a set of major countries using Datastream and find nearly identical results. 13 12 Specifically, log gross returns from t to t + 1 is computed as log prccdt+1 ×trf dt+1 ajexdit+1 × ajexdit prccdt ×trf dt Accounting Data, Market Values, and Expected Returns Worldwide 14 time-varying. The latter assumption differs slightly from LW15, which assumes that the model parameters are industry-specific. These implementation choices reflect a tradeoff between parsimony and realism necessitated by the relative sparsity, both in time series and cross-section, of international equity fundamentals data. 3.2 Sample Selection We began with a set of 34 countries whose capital markets and related institutions have been commonly studied in the international asset pricing literature – Australia, Austria, Belgium, Canada, China, Denmark, Finland, France, Germany, Greece, Hong Kong, India, Indonesia, Israel, Italy, Ireland, Japan, Malaysia, Netherlands, New Zealand, Norway, Pakistan, the Philippines, Portugal, Singapore, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Thailand, the United Kingdom, and the U.S. These include the 31 countries examined by Leuz et al. (2003) and the 23 countries recognized to have developed capital markets (e.g., Ang, Hodrick, Xing, and Zhang, 2009; Fama and French, 2012). We impose three sets of filters to mitigate the influence of unusual observations on our estimation and calibration of the paper’s model. First, in each country and on each forecast date, we eliminate very small and illiquid firms—any firm belonging to the bottom 2 percent of the cross-section in either market capitalization or liquidity.14 Second, we exclude observations whose stock price belongs to the bottom 5 percent of the cross-section or is trading below 1 unit of the home currency. Third, to further ensure the reliability of the cross-sectionally-estimated coefficients, we impose the requirement that each cross section, after applying the above filters, must have at minimum 100 observations. Following prior research (e.g., LaFond, Lang, and Skaife, 2007), we proxy for a stock’s liquidity using the proportion of zero-return days over the prior month. This approximation is necessitated by a lack of a well-populated trading-volume variable in the Compustat Global price files. 14 Accounting Data, Market Values, and Expected Returns Worldwide 15 These restrictions, in conjunction with a minimum of 40 months of data, eliminate the following 5 countries from our empirical analyses: Austria, Ireland, New Zealand, Singapore, and Portugal. Thus, the empirical analyses in our paper examine the efficacy of our model-implied ERPs for a set of 29 countries worldwide. We also take measures to ensure that our data are not corrupted by inconsistencies arising from the use of different currencies to report financial data within a given country. For the eurozone countries that switched currencies following adoption of the euro, we convert all pre-adoption financial data to euro using the conversion rate mandated by the European Central Bank. This translation simply makes the within-country currency amounts comparable pre- and post-euro conversion. For all other occasions where companies switch currencies, we drop the two years surrounding the change.15 3.3 Summary Statistics Table 1 summarizes, by country, our data on the model inputs of Eq., (13). It reports time-series averages of the distributional statistics of bm and roe. With the exception of South Korea, all countries on average have (cross-sectional) median bm values that are negative, such that book values tend to be smaller than market values. There is wide variation in the central tendency in bm across countries, ranging from a median bm of 0.11 in South Korea to -1.17 in China. Despite this variation in central tendency, the spread in the distribution appears similar across most countries. In contrast, the (time-series) averages of (cross-sectional) median and mean roe values are relatively uniform across all the countries in our sample. The last two columns of Table 1 report the initial and final dates for which we have fundamentals and returns data for each country (after imposing the sample selection 15 We set the one-month-ahead returns to missing whenever the given fiscal year’s financials are reported in a different currency than the following year’s financials. This adjustment affects less than 1% of the sample. Accounting Data, Market Values, and Expected Returns Worldwide 16 requirements described above). There is some variation in how early the data begins. For three countries (Canada, Japan, and the U.S.), data became available in the mid- to late-1980s; for most countries data became available in the early- to mid-1990s. For a small handful of countries (Belgium, China, Finland, Greece, Israel, Norway, Pakistan, and the Philippines), data are not available until the 2000s. Table 2 presents FM coefficients from monthly regressions of one-month-ahead returns (r) on bm and roe, i.e., the time-series mean of the cross-sectionally-estimated coefficients. These two fundamental variables explain between 1% to almost 5% of the cross sectional variation contemporaneous volatility, averaging 2.2%.16 Our findings suggest that roe exhibits a stronger association with returns compared to bm. The FM coefficient on roe is positive and significant (at the 10-percent level) in 27 of the 29 countries in our sample; on the other hand, the coefficient on bm is significant (at the 10-percent level) for 21 of the 29 countries. These patterns suggest that roe is more reliably and systematically associated with realized returns compared to bm. Finally, we form the model-implied expected one-month-ahead return proxy on each forecast date using historically estimated FM coefficients. Recall, at the end of each calendar month after the initial 40-month burn-in period, we construct a forecast of one-month-ahead returns by applying the cumulative average of all the cross-sectional coefficients from estimating Eq., (13) to the currently available annual bm and roe. Table 3 reports the time-series average of the cross-sectional distributional summary As noted in Lewellen (2015), FM R2 is not an indicator of predictive power, but reflects the degree to which the ERP explains contemporaneous volatility. To see why, consider the following simple example. Suppose that expected returns are constant for all firms (i.e., no cross-sectional variation), but news has the following structure: ri,t+1 i,t+1 16 = = er + i,t+1 , Ct+1 × erpi,t , where Ct+1 is a cross-sectional random variable taking a positive or a negative value with 50% probability in a given time period. In this case, even though the proxy (erpi,t ) has no predictive ability, in crosssectional regressions it will completely explain the ex post contemporaneous volatility in realized returns, i.e., 100% R2 . Accounting Data, Market Values, and Expected Returns Worldwide 17 statistics for the estimated expected one-month-ahead log returns. On average, we observe substantial variation in the (cross-sectional) mean expected returns, consistent with time-varying expected returns. There is also substantial cross-sectional variation in the ERP in all countries. Comparing the mean expected return to the mean realized return, reported in the last column, suggests that our ERPs are on average similar to future average realized returns for all the countries. The next section provides a more comprehensive assessment of the ERPs’ performance. 3.4 Cross-Sectional Validation Tests We next turn to validating the model-implied ERPs and assessing their reliability across worldwide markets. We first examine how the proxies, on average, are associated with future returns, and compare their performance with standard factor-model-based proxies. 3.4.1 Regression Based Tests Our primary test for assessing the reliability of our ERPs is the standard regressionbased test as employed by, for example, Lewellen (2015) and Lyle and Wang (2015). In particular, we separately estimate for each country cross-sectional predictive regressions of 1-month-ahead r on our ERPs: ri,t+1 = δ0 + δ1 Et [ri,t+1 ] + wi,t+1 . (14) True expected returns implies δ0 = 0 and δ1 = 1. In particular, having a slope coefficient close to 1 suggests that the magnitudes of the cross-sectional differences in the ERP are informative of the magnitude of differences in expected returns, which facilitate inferences in regression settings. More generally, positive and significant δ1 coefficients Accounting Data, Market Values, and Expected Returns Worldwide 18 imply positive return sorting ability on average. To reduce the influence of unusually large values in our estimates, we winsorize the expected return measures at the top and bottom 1 percent. Table 4 reports FM regression estimates of Eq., (14) for the 29 countries in the sample. The results in this table indicate that the model-implied ERPs strongly and significantly predicts realized returns for a vast majority of the countries. Coefficients on expected returns (the “predictive slope coefficient”) are statistically significant at the 5-percent and 10-percent levels for 24 and 26 of the 29 countries, respectively. Greece, Pakistan, and South Africa’s predictive slope coefficients do not differ significantly from 0 at the 10% level; in the case of Pakistan, the slope is also indistinguishable from 1. The average slope coefficient across the 29 countries is 1.05. Based on the F-test for the null hypothesis that the slope is equal to 1 (reported in the last row of Table 4), we reject the null for only 9 (10) of the 29 countries at the 10-percent (5-percent) level. Furthermore, we fail to reject the null that the constant term is equal to 0 at the 5-percent level for all but 2 countries in our sample. In the aggregate, these regression-based test results suggest that our accounting-based ERPs line up well with true expected returns and are reliably associated with the cross section of future returns across international markets.17 3.4.2 Portfolio Sort Tests We supplement the above parametric return regression tests with a portfolio-level analysis. To conduct these non-parametric tests, we construct equal-weighted portfolios at the end of each calendar month based on the quintile rankings of the ex ante ERP, and summarize the average 1-month-ahead returns realized by each portfolio. Our choice of quintile portfolios is intended to ensure that, for any given country on any given month, In untabulated robustness tests, we find that winsorizing the inputs at the top and bottom 1 percent of each cross section yields ERPs that produce virtually identical results. 17 Accounting Data, Market Values, and Expected Returns Worldwide 19 there are at least 20 stocks in each portfolio. Table 5 provides further evidence that, consistent with the regression tests of Table 4, the model-implied proxies exhibit significant ability to predict the cross-section of future returns. We document in column (6) significant average spreads between the top and bottom quintile portfolios for 24 countries. Though these results are statistically slightly weaker, they are broadly consistent with the regression-based tests. In fact, the portfolio sorts are robust enough that for the majority of the countries (20), even the spread between the portfolio median returns, reported in column (7), are statistically significant. On the basis of these results we conclude that reliable firm-level expected stock returns that are applicable to worldwide markets can be constructed with a linear combination of bm and roe. These findings also demonstrate, consistent with Lewellen (2015), that firm-level ERPs obtained from FM regressions exhibit strong cross-sectional predictive properties. 3.5 Robustness Tests We provide in this section analyses on the sensitivity of the ERPs to variations in the training sample period. We also assess the performance of factor-model-based ERPs to contextualize our main findings. 3.5.1 Sensitivity to Training Sample Window We begin by assessing the sensitivity of our proxies to the choice of the burn-in period. Our baseline results use the first 40 months of data as the training sample before constructing ERPs and conducting out-of-sample tests. Our choice of 40 months, which we view to be a relatively short training period, was motivated by the relatively short sample of available data in certain countries (e.g., Israel and Pakistan). Thus, we are Accounting Data, Market Values, and Expected Returns Worldwide 20 limited in the amount by which we can extend this training sample for the cross section of countries. Table 6 reports the regression-based tests of Table 4, but using training windows of 30, 40, and 50 months. For nearly all countries, these variations in the training sample period do not affect our inferences. For Finland and the Netherlands, widening the training sample and reducing the testing window reduces the statistical significance slightly, with t-statistics of 1.56 and 1.33, respectively. Reducing the training window to 30 months marginally affects one country—Switzerland—predictive coefficients remain positive and large in magnitude with borderline t-statistics of 1.63. Overall, however, our main findings on the association with the cross section of future returns across countries are not very sensitive to the training window period. 3.5.2 Factor-Based Estimates To contextualize our main empirical results, we assess the performance of firm-level ERPs derived from the global and regional four-factor models described in Fama and French (2012). These are global and regional versions of the Fama and French (1993) three-factor model augmented with the momentum factor, but calculated based on portfolios that encompass 23 countries in four regions: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Switzerland, Sweden, U.K., and U.S. The monthly global and regional factor returns are obtained from Ken French’s data library.18 At the end of each calendar month (t), one-month-ahead factor-based ERPs for a firm 18 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html Accounting Data, Market Values, and Expected Returns Worldwide 21 (i) are constructed as follows: ˆ ˆ ˆ Et [ri,t+1 ] = rft+1 + γi,RM RF Et [RM RFt+1 ] + γi,SM B Et [SM Bt+1 ] ˆ ˆ ˆ ˆ +ˆi,HM L Et [HM Lt+1 ] + γi,W M L Et [W M Lt+1 ]. γ ˆ (15) ˆ ˆ ˆ ˆ Here Et [RM RFt+1 ], Et [SM Bt+1 ], Et [HM Lt+1 ], and Et [W M Lt+1 ] represent the expected global or regional market, size, value, and momentum factor returns, respectively, which we estimate based on the trailing average 40-month realized factor returns. γi,j represents ˆ the factor j loadings for a firm, estimated in time-series for each firm i using monthly stock and factor returns over the 40 months prior to the forecast date. Risk-free rates are proxied by US treasury yields. Because the global and regional factors are calculated using US-Dollar-denominated returns, for consistency in this exercise we convert all price series to US Dollars and compute US-Dollar-denominated returns for all firms in our sample. Table 7 reports the results of regression-based tests for the global- and regional-factorbased ERPs for the 29 countries in our sample alongside the results for our model-implied ERPs. To facilitate comparisons, we use a common set of firm-year observations for which all three ERPs are available. The performance of our model-implied ERPs on this subset of common observations remain substantively unchanged. Strikingly, with the exception of one country, the global- and regional-factor-based ERPs do not exhibit out-of-sample return predictability. The exception is in Pakistan, for which the global four-factor model exhibits a modest slope coefficient of 0.2548 that is significant at the 10% level. For the remaining countries the slope coefficients are either significantly negative (4 countries) or indistinguishable from zero at the 10-percent level. We also consider the recent Fama and French (2014) five-factor model, which augments Fama and French (1993)’s original three-factor model with a profitability factor and Accounting Data, Market Values, and Expected Returns Worldwide 22 an investment factor. Fama and French (2014) show that this expanded model better explains the cross section of average returns in-sample compared to the three-factor model. We complement their findings by assessing the out-of-sample performance of five-factor-based ERPs, reported in the second-to-last row of Table 7. Our regressionbased tests of this model are restricted to the U.S. since profitability and investment factor returns are not available globally. As with the four-factor model, we find that this expanded model does not produce ERPs that are robustly associated with future returns. We document a negative but insignificant slope coefficient. Finally, we consider a variation of the new factor model that incorporates only the market, value, and profitability factors, representing the factor-based counterpart to our paper’s characteristic-based model. The out-of-sample performance, reported in the last row of Table 7, continues to be poor, as the proxy exhibits a negative and significant slope coefficient at the 10-percent level. Juxtaposed against the performance of our model-implied ERPs, these results overall show that the out-of-sample cross-sectional predictive ability of our model-implied ERPs dramatically outperform that of alternative factors-based proxies. We note that findings need not necessarily invalidate the factor models per se, but could be consistent with the possibility that firm characteristics better capture time-varying factor loadings and premiums (e.g., Cochrane, 2011), which are notoriously difficult to estimate (Fama and French, 1997). This evidence is also consistent with and generalizes the findings of LW15 across international markets and accounting systems, broadly echoing the views of Campbell, Polk, and Vuolteenaho (2010) that accounting information is useful in explaining firm level expected rate of returns. More strongly, our evidence suggest that accountingbased valuation models provide a unifying framework for estimating firm-level expected rates of returns around the world. Accounting Data, Market Values, and Expected Returns Worldwide 23 4 Accounting Quality: Implications and Tests While the empirical evidence presented above establishes the usefulness of accounting information in estimating expected returns across the world, accounting systems, and the quality of the information they produce, can significantly vary from one market and institutional setting to another. This section analyzes, both analytically and empirically, how our model of expected returns is affected by the quality of accounting information provided to investors. 4.1 Model Setup and Key Implication To investigate this issue analytically, we extend the baseline model of expected returns to a setting where information is imperfect. To introduce the concept of imperfections in the accounting system vis-`-vis return prediction, we assume that investors do not a directly observe expected growth in book value, ht , but learn about it dynamically over time using realized accounting reports.19 In the spirit of Dechow, Ge, and Schrand (2010), we assume that investors observe financial reports of book growth, gb,t+1 , which reflects both “true” firm performance r (gtrue,t+1 ) and noise (ξt+1 ) from the accounting system: r gb,t+1 = gtrue,t+1 + ξt+1 , and true gtrue,t+1 = ht + ξt+1 . (16) (17) It follows that observed reports of book growth (gb,t+1 ) have two sources of noise: (1) true true “fundamental” or “innate” noise (ξt+1 ) and (2) measurement errors from the ac- Unlike related studies in the literature (e.g., van Binsbergen and Koijen, 2010), we do not assume that investors need to filter expected returns; our rationale is that since investors set prices, given their expectations of book growth they must also set expected market returns. Our setting is thus closely related to that of P´stor and Veronesi (2003, 2006), except that we do not assume an exogenous discount a factor. 19 Accounting Data, Market Values, and Expected Returns Worldwide 24 r counting system (ξt+1 ). We assume that the noise in the reports is captured by two true r 2 independent error terms, ξt+1 ∼ N (0, σ 2 ) and ξt+1 ∼ N (0, σr ).20 Mapping this back into the assumptions about growth in book value (3), we have: r true gb,t+1 = ht + ξt+1 + ξt+1 . (18) Since investors observe only realized growth in book values, they form expectations of book growth by making inferences (or learning) about the unobserved ht using relevant information to optimally update their beliefs over time. We denote ft = E[ht |Ft ] as the investors’ beliefs about mean book growth given Ft , where Ft = {gb,τ }τ ∈{0,1,...,t} represents the history of accounting reports available to investors. Assuming that ht is also conditionally Gaussian, it can be shown that investors’ optimal dynamic updates to their beliefs take the following form: ωvt (gb,t+1 − ft ), 2 σ 2 + σr + vt f t+1 = µ + ω(ft − µ) + (19) where vt = E[(ft − E[ft |Ft ])2 |Ft ] is the conditional variance of ft with respect to investors 2 filtration Ft , or the dispersion in investors’ prior beliefs; σh is the conditional variance of 2 ht ; and vt+1 = ω 2 vt + σh − 2 ω 2 vt .21 2 σ 2 +σr +vt Using this updating rule, we show in the Appendix that when the accounting system is imperfect, expected stock returns are a linear combination of bm and roe: E[rt+1 |Ft ] = C1 (t) + C2 (t)ft−1 + C3 bmt + C4 (t)roet , 20 (20) While the assumption of Gaussian error terms is common and somewhat restrictive, the assumption of independence is without loss of generality. 21 This follows directly from Theorem 13.4 of Liptser and Shiryaev (1977). Accounting Data, Market Values, and Expected Returns Worldwide 25 in which the coefficient on roe takes the following form ωvt−1 . 2 + σr + vt−1 C4 (t) = A3 σ2 (21) This model provides the key insight that, all else equal, better accounting information quality elevates the importance of roe in forecasting future returns. Specifically, conditional on the dispersion of investors’ prior beliefs (vt−1 ), the volatility in the underlying fundamentals (σ 2 ), and the persistence in expected returns and expected roe, the 2 coefficient on roe is increasing with accounting information quality (or decreasing in σr ). The above analytical approach also allows a reconciliation of our model to the various alternative firm characteristics and signals (e.g., valuation ratios and accounting data) that relate to future stock returns. In particular, generalizing the above to include multiple information sources in investors’ information set, if a signal systematically forecasts future payoffs (i.e., future roe), conditional on bm, it follows that such a variable is also systematically associated with expected returns. This insight suggests that the empirical approach used by Ou and Penman (1989), coupled with our parsimonious model, may offer an exciting area of potential future research in accounting and characteristic-based asset pricing. 4.2 Empirical Tests We proceed to empirically test the prediction that, all else equal, higher-quality accounting information leads investors to place greater weight on roe. Accounting information quality, specifically the variance in measurement errors in the context of the model above, is difficult to measure. We adopt the methodology of Leuz et al. (2003), which creates a composite country-level measure of accounting quality by averaging a given country’s rankings across four dimensions. Accounting Data, Market Values, and Expected Returns Worldwide 26 The first two dimensions of information quality capture the extent to which firms in a given country engage in earnings smoothing. The first earnings-smoothing measure (Variability) takes each country’s median ratio of firm-level standard deviation of operating earnings divided by the firm-level standard deviation of cash-flow from operations, and ranks these median ratios across countries in descending order. A lower ratio implies a greater degree of earnings smoothing, and hence lower earnings quality, resulting in a higher rank. The second earnings-smoothing measure (Correlation) takes the magnitude of the contemporaneous correlation between changes in accounting accruals and changes in operating cash flows in each country, and ranks this correlation across countries in ascending order. This correlation is estimated by pooling all firm-years within a country; a greater magnitude implies greater earnings smoothing and lower earnings quality, resulting in a higher rank. The third and fourth dimensions of information quality proxy for the extent of the use of accruals to manage earnings in a given country. The third measure (Accruals Magnitude) takes the median of the ratio between the absolute value of firm accruals and the absolute value of firm cash-flow from operations in a given country, and ranks this measure across countries in ascending order. A higher median ratio implies a greater use of accruals to manage earnings, and lower earnings quality, resulting in a higher rank. The fourth and final dimension of poor information quality (Small Loss Avoidance) takes the ratio between instances of small profits and instances of small losses, calculated by pooling all firm-years within a country, and ranks the measure across countries in ascending order. Small profits and small losses are calculated using earnings scaled by total assets, where small losses are defined as in the range [−0.01, 0) and small profits are defined as in the range [0.00, 0.01]. A higher ratio implies greater use of managerial discretion in managing earnings, and lower earnings quality, resulting in a higher rank. Our main empirical test, reported in Table 8, explores cross-country variations be- Accounting Data, Market Values, and Expected Returns Worldwide 27 tween this proxy, Poor Information Quality, and the median roe coefficient, generated from monthly regressions of Eq., (13). Column (1) of the table reports OLS estimates of regressions of each country’s median roe coefficient on its Poor Information Quality measure and a control for the size of each country’s equity market.22 The rationale for such a control is to address the “all else equal” aspect of the theoretical predictions. Holding accounting information quality constant, the presence of more of information intermediaries may reduce the importance of roe. Consistent with this intuition, our result shows a negative and significant coefficient on market size. Moreover, consistent with the model predictions, we report a negative coefficient on Poor Information Quality, but it is not statistically signficant.23 We interpret the lack of significance in Poor Information Quality as, at least in part, a result of errors in measuring countries’ accounting systems’ measurement error variances—the underlying theoretical variable of interest—which is consistent with the coefficient’s attenuation to 0. We resolve this issue empirically by using an instrumentalvariables approach to identify the effect of information quality on the importance of roe. Our instruments capture the quality of governance institutions in a given country. Our identifying assumption is that the strength of such institutions affects the importance of roe in forecasting future returns only by improving the information quality produced by firms in equity markets. Our instrument, Quality of Governance Institutions, is constructed using data from the World Bank’s Worldwide Governance Indicators project, which compiles five metrics on countries’ governance institutions.24 Rule of Law captures perceptions of the quality of contract enforcement, property rights, and the courts; Accountability captures perceptions of the extent to which citizens have the ability to Specifically, we take the log of the median total market capitalization over the relevant time frame for a given country. 23 These results exclude Greece, Pakistan, and South Africa, for which the model does not generate reliable proxies. Taiwan is also exluded because information on the strength and quality of its governance institutions is unavailable. 24 http://info.worldbank.org/governance/wgi/index.aspx#home 22 Accounting Data, Market Values, and Expected Returns Worldwide 28 exert their voices and influence to create accountability in society, including freedom to select their government and the presence of a free media; Political Stability measures perceptions of the likelihood of political instability; Government Effectiveness captures perceptions of the quality of public services and the robustness of the policy formulation process; and Control of Corruption captures perceptions of the extent to which public power is exercised for private benefits. We take the median value of each variable over the relevant time frame for each country and then standardize each measure using the crosssection of countries. Our final country-level variable, Quality of Governance Institutions, is the simple average of the five standardized governance measures. Columns (2) and (3) report the first- and second-stage results, respectively, of an instrumental-variables estimation in which we instrument Poor Information Quality with Quality of Governance Institutions. The first-stage estimation results suggest that higherquality or stronger governance institutions in a country are significantly associated (at the 1% level) with higher-quality accounting information, consistent with economic intuition. In the second stage we find that, all else equal, better earnings quality increases the importance of roe in forecasting returns. Specifically, improving a country’s earnings-quality rank by 1 unit increases the roe coefficient by about 0.001, representing an economically significant increase of approximately 10 percent for the median country. Consistent with measurement errors influencing the OLS results, the magnitude of the coefficient in the instrumental-variables specifications is substantially larger compared to the baseline OLS specification. Finally, the last column of the table reports the reduced-form OLS estimates from regressing the median roe coefficients on the governance-quality variable and the market size control. Consistent with our instrumental-variables estimates, these results show that stronger and higher-quality governance institutions elevate the importance of roe in forecasting returns. Table 9 provides further analyses of the impact of information quality on the roe coef- Accounting Data, Market Values, and Expected Returns Worldwide 29 ficient by examining the four different dimensions of Poor Information Quality separately. Broadly speaking, the results in this table are consistent with those in Table 8. However, whereas results using Variability are substantially, Accruals Magnitude, in contrast, produces the strongest results. Overall, these findings as consistent with the theoretical model and with the intuition that roe plays a reduced role in forecasting returns when accounting information is poor. 5 Conclusion We show that, under fairly general assumptions, expected returns is related to bm and roe. This parsimonious linear relation is not only theoretically applicable to various accounting systems, but also supported empirically: the model-implied expected return proxies (ERPs) line up well with true expected returns across international markets. Our work promotes an accounting-fundamentals approach to expected returns, and contributes to the stream of empirical studies devoted to developing the estimation of, and understanding the behavior of, expected returns. It also provides a practical tool that can be used to analyze investment choices in international equity contexts. 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Accounting Data, Market Values, and Expected Returns Worldwide 35 Appendix Expected Returns Derivation This subsection describes in detail the derivation of expected returns as a function of bm and expected roe. We begin with the observation that expected stock returns are given by: Et [rt+1 ] = µt + Et log 1 + Dt+1 Mt+1 . (A.1) We follow P´stor and Veronesi (2003) and assume that dividends are proportional to a book value over the next interval, such that: log 1 + Dt+1 Mt+1 = log 1 + δ Bt+1 Mt+1 = log (1 + δ exp(bmt+1 )) . (A.2) Log-linearization around the unconditional mean of bm, bm, and using Eq., (8), we have: log 1 + Dt+1 Mt+1 ≈ log(1 + δ exp(bm)) + δ exp(bm) (bmt+1 − bm) 1 + δ exp(bm) (A.3) = log(1 + δ exp(bm)) + 1 δ exp(bm) 1 (µt+1 − µ) − (ht+1 − µ) . (A.4) 1−ω 1 + δ exp(bm) 1 − κ Taking conditional expectations and substiting for expected growth in market using (8) yields: Et log 1 + Dt+1 Mt+1 κ ω (µt − µ) − (ht − µ) 1−κ 1−ω κ−ω = K + ρ κ(bmt − bm) − (ht − µ) , 1−ω = K +ρ δ exp(bm) . 1+δ exp(bm) (A.5) (A.6) where K = log(1 + δ exp(bm)) and ρ = Finally, under the proportional dividend assumption and clean-surplus accounting, growth in book and ROE can be related: log(ROEt+1 ) = log((Bt+1 + Dt+1 )/Bt ) = Accounting Data, Market Values, and Expected Returns Worldwide 36 log(1 + δ) + log(Bt+1 /Bt ) and Et [roet+1 ] = log(1 + δ) + ht . Combining this with (A.1) and (A.6) above obtains the desired linear expression as summarized in Eq., (10) in the body of the paper: Et [rt+1 ] = K+ (κ − ω)(1 − ρ) ¯ µ − (1 − κ + ρκ)bm − A3 log(1 + δ) 1−ω A1 + [1 − κ + ρκ]bmt A2 + ρ(κ − ω) + 1 − κ Et [roet+1 ]. 1−ω A3 (A.7) Expected Returns under Incomplete Information This subsection derives expected returns when investors do not directly observe book growth. To solve for stock returns in this setting, we must first solve the present-value problem; we do so by applying the law of iterated expectations to Eq., (6). (See the appendix of P´stor and Veronesi, 2009, for a simple and related example.) We deduce: a bmt = bm + 1 1 (µt − µ) − (ft − µ). 1−κ 1−ω (A.8) Now, using the log-linearization in the previous subsection, we have: log 1 + Dt+1 Mt+1 ≈ log(1 + δ exp(bm)) + δ exp(bm) (bmt+1 − bm) 1 + δ exp(bm) (A.9) = log(1 + δ exp(bm)) + δ exp(bm) 1 1 (µt+1 − µ) − (ft+1 − µ) . (A.10) 1−ω 1 + δ exp(bm) 1 − κ Taking expectations conditional on Ft , we have: Accounting Data, Market Values, and Expected Returns Worldwide 37 E log 1 + Dt+1 Mt+1 Ft = K +ρ κ ω (µt − µ) − (ft − µ) , (A.11) 1−κ 1−ω where K and ρ are given in the prior subsection. This implies that expected returns are given as follows: E[rt+1 |Ft ] = A1 + A2 bmt + A3 (ft − y). Here A1 = K − ρκbm − (1 − κ)bm − A3 y + ρ(κ−ω)+1−κ ; 1−ω (κ−ω)(1−ρ) µ, (1−ω) (A.12) A2 = ρκ + (1 − κ), and A3 = y = log(1 + δ) From the updating rule (Eq., (19)), we can express this in term of current roe by noting that: ft − µ = ω(ft−1 − µ) + ωvt−1 (roet − y − ft−1 ). 2 σ 2 + σr + vt−1 (A.13) Plugging this into the expected-returns Eq., (A.12), we have: E[rt+1 |Ft ] = A1 + A2 bmt + A3 µ − y + ω(ft−1 − µ) + Re-arranging, we obtain: E[rt+1 |Ft ] = C1 (t) + C2 (t)ft−1 + C3 bmt + C4 (t)roet , σ2 (A.14) ωvt−1 (roet − y − ft−1 ) . 2 + σr + vt−1 (A.15) Accounting Data, Market Values, and Expected Returns Worldwide 38 where C1 (t) = A1 + A3 µ(1 − ω) − y 1 + C2 (t) = A3 ω + C3 = A2 , C4 (t) = A3 σ2 ωvt−1 . 2 + σr + vt−1 σ2 ωvt−1 2 + σr + vt−1 , ωvt−1 2 + σr + vt−1 , σ2 Table 1. Summary Statistics of Model Inputs Table 1 reports summary statistics by country for inputs to the regression of Eq., (13), bmt and roet . The distributional summary statistics reported here are time-series averages of the corresponding cross-sectional statistics. N represents the average number of observations per cross section in a particular country. Min Date and Max Date, respectively, denote the first and last calendar month for which data are available for the country in question, after imposing our sample selection requirements. bm Country Australia Belgium Canada China Denmark Finland France Germany Greece Hong Kong India Indonesia Israel Italy Japan Malaysia Netherlands Norway Pakistan Philippines South Africa South Korea Spain Sweden Switzerland Taiwan Thailand UK US q5 -2.11 -1.57 -1.58 -2.25 -1.76 -1.69 -1.76 -1.94 -1.77 -1.68 -2.05 -1.78 -1.67 -1.72 -1.55 -1.64 -2.09 -1.81 -1.59 -2.51 -1.99 -1.24 -2.07 -2.10 -1.78 -1.41 -1.50 -2.16 -2.04 q25 -1.13 -0.68 -0.83 -1.56 -0.65 -0.95 -0.94 -1.05 -0.85 -0.67 -0.84 -0.81 -0.51 -0.90 -0.71 -0.79 -1.17 -0.91 -0.71 -1.08 -1.06 -0.40 -1.08 -1.20 -0.91 -0.72 -0.65 -1.16 -1.12 Med -0.61 -0.22 -0.38 -1.17 -0.15 -0.45 -0.45 -0.56 -0.31 -0.05 -0.09 -0.19 -0.07 -0.43 -0.27 -0.34 -0.62 -0.36 -0.16 -0.49 -0.53 0.11 -0.62 -0.62 -0.36 -0.29 -0.14 -0.52 -0.60 q75 q95 Mean -0.72 -0.32 -0.42 -1.23 -0.27 -0.50 -0.46 -0.60 -0.38 -0.12 -0.17 -0.26 -0.21 -0.44 -0.35 -0.41 -0.70 -0.33 -0.16 -0.63 -0.57 0.06 -0.70 -0.67 -0.39 -0.35 -0.20 -0.63 -0.70 sd 0.78 0.70 0.74 0.61 0.83 0.67 0.84 0.80 0.79 0.91 1.08 0.95 0.75 0.84 0.67 0.70 0.81 0.96 0.91 1.18 0.87 0.76 0.77 0.83 0.88 0.59 0.77 0.88 0.77 q5 q25 Med 0.12 0.09 0.09 0.08 0.08 0.12 0.10 0.08 0.08 0.11 0.13 0.11 0.10 0.08 0.05 0.10 0.13 0.09 0.17 0.11 0.19 0.06 0.12 0.11 0.10 0.08 0.11 0.13 0.11 roe q75 0.20 0.15 0.15 0.15 0.15 0.19 0.16 0.15 0.15 0.18 0.22 0.21 0.18 0.14 0.09 0.16 0.22 0.17 0.28 0.18 0.27 0.13 0.18 0.20 0.16 0.15 0.19 0.22 0.17 q95 0.43 0.36 0.34 0.30 0.34 0.34 0.31 0.37 0.36 0.37 0.42 0.47 0.47 0.29 0.20 0.30 0.47 0.42 0.52 0.41 0.54 0.28 0.38 0.41 0.31 0.29 0.38 0.46 0.38 Mean 0.13 0.08 0.06 0.09 0.05 0.11 0.08 0.06 0.09 0.11 0.12 0.10 0.09 0.07 0.04 0.10 0.12 0.03 0.16 0.12 0.21 0.03 0.12 0.02 0.08 0.07 0.10 0.14 0.08 sd 0.25 0.24 0.30 0.21 0.29 0.18 0.25 0.34 0.18 0.23 0.26 0.41 0.30 0.24 0.18 0.19 0.30 0.37 0.29 0.32 0.26 0.31 0.21 0.48 0.22 0.18 0.27 0.27 0.36 N Min Date Max Date -0.18 0.28 0.11 0.64 0.00 0.63 -0.82 -0.37 0.24 0.78 -0.01 0.48 0.01 0.71 -0.12 0.62 0.14 0.75 0.52 1.25 0.55 1.47 0.37 1.10 0.25 0.67 0.02 0.73 0.10 0.57 0.06 0.55 -0.16 0.42 0.19 1.38 0.41 1.23 0.07 0.82 -0.08 0.76 0.59 1.20 -0.27 0.35 -0.10 0.56 0.08 0.94 0.09 0.50 0.32 0.91 0.02 0.43 -0.20 0.37 -0.17 0.06 -0.24 0.03 -0.33 0.00 -0.09 0.03 -0.39 0.00 -0.13 0.05 -0.25 0.04 -0.37 0.01 -0.11 0.02 -0.11 0.05 -0.21 0.05 -0.34 0.00 -0.33 0.02 -0.21 0.02 -0.13 0.02 -0.10 0.05 -0.25 0.04 -0.60 -0.03 -0.21 0.06 -0.12 0.04 -0.05 0.11 -0.40 0.00 -0.14 0.06 -0.70 -0.02 -0.20 0.04 -0.16 0.02 -0.27 0.03 -0.10 0.04 -0.34 0.03 287 1993m11 2014m9 106 2001m5 2014m3 170 1985m5 2010m9 1,188 2001m5 2014m8 134 1999m5 2014m8 105 2001m5 2014m9 441 1991m5 2014m9 388 1991m5 2014m9 141 2002m5 2010m9 250 1995m8 2014m9 967 1997m8 2014m9 210 1999m5 2014m9 183 2008m5 2014m8 181 1998m5 2014m9 2,530 1989m2 2014m9 322 1993m3 2014m9 131 1997m5 2011m8 118 2001m5 2014m9 195 2004m12 2014m9 138 2007m5 2014m9 186 1997m11 2014m9 893 1994m5 2014m9 114 1998m5 2014m4 246 1998m5 2014m9 171 1998m5 2014m9 488 1999m5 2014m9 289 1993m5 2014m9 656 1990m6 2014m9 3,249 1984m5 2014m9 39 40 Table 2. Summary Statistics of Estimated Coefficients Table 2 reports the coefficients on bmt and roet . The coefficients are estimated by Fama and MacBeth (1973) cross-sectional regressions, in which monthly log-returns are regressed on firm characteristics for each calendar month. We assume accounting data is known four months after the fiscal-year end date. Publicly available financial data on book values and ROE are matched to one-month-ahead returns for twelve months, starting four months after the fiscal-year end date as in Lewellen (2015). The estimation uses the cross-section of firms in a given country for a particular calendar month. Columns (1)–(3) report the Fama-MacBeth coefficients and standard errors (in square brackets below coefficients). Column (4) reports the average number of firms per cross section, column (5) reports the total number of months included in the Fama-Macbeth estimates, and column (6) reports the average of the cross-sectional-regression adjusted R2 values. Levels of significance are indicated by *, **, and ***, representing 10 percent, 5 percent, and 1 percent, respectively. (1) Country Australia Belgium Canada China Denmark Finland France Germany Greece HongKong India Indonesia Israel Italy bm 0.0033*** [0.001] 0.0047*** [0.001] -0.0004 [0.001] 0.0051*** [0.001] 0.0000 [0.002] 0.0091*** [0.002] 0.0030*** [0.001] 0.0025*** [0.001] 0.0006 [0.002] 0.0067*** [0.001] 0.0016 [0.002] 0.0060*** [0.002] 0.0007 [0.002] 0.0021** [0.001] (2) roe 0.0103*** [0.004] 0.0242*** [0.006] 0.0095** [0.004] 0.0031 [0.005] 0.0136*** [0.004] 0.0318*** [0.009] 0.0155*** [0.003] 0.0103*** [0.002] 0.0287*** [0.008] 0.0223*** [0.007] 0.0129** [0.005] 0.0136*** [0.003] 0.0234*** [0.006] 0.0182*** [0.004] (3) cons 0.0048* [0.002] 0.0015 [0.004] -0.0004 [0.003] 0.0086 [0.008] 0.0003 [0.004] -0.0014 [0.005] 0.0021 [0.003] -0.0016 [0.003] -0.0133 [0.009] -0.0015 [0.005] 0.0026 [0.007] 0.0090 [0.006] -0.0008 [0.009] -0.0019 [0.004] (4) N 286 106 170 1,182 134 106 440 387 141 250 963 210 182 181 (5) No. of Periods 252 139 300 161 185 108 282 282 100 229 207 186 77 198 (6) Adj R2 0.019 0.020 0.016 0.022 0.028 0.039 0.019 0.015 0.021 0.020 0.029 0.015 0.017 0.025 41 Table 2. Continued (1) Country Japan Malaysia Netherlands Norway Pakistan Philippines South Africa South Korea Spain Sweden Switzerland Taiwan Thailand UK US bm 0.0067*** [0.001] 0.0064*** [0.001] 0.0034* [0.002] 0.0013 [0.001] -0.0004 [0.002] 0.0036** [0.002] 0.0027** [0.001] 0.0097*** [0.002] 0.0029** [0.001] 0.0012 [0.001] 0.0022** [0.001] 0.0063** [0.003] 0.0074*** [0.001] 0.0022*** [0.001] 0.0030*** [0.001] (2) roe 0.0069*** [0.002] 0.0238*** [0.005] 0.0113** [0.006] 0.0211*** [0.006] 0.0105** [0.005] 0.0100* [0.006] 0.0010 [0.004] 0.0159*** [0.004] 0.0256*** [0.007] 0.0120*** [0.003] 0.0080* [0.005] 0.0314*** [0.007] 0.0208*** [0.006] 0.0083*** [0.002] 0.0047*** [0.001] (3) cons -0.0007 [0.004] 0.0009 [0.006] 0.0002 [0.004] 0.0014 [0.004] 0.0120* [0.006] 0.0095 [0.006] 0.0098*** [0.003] -0.0054 [0.006] 0.0001 [0.004] 0.0001 [0.004] 0.0027 [0.003] -0.0015 [0.007] 0.0002 [0.005] 0.0045* [0.003] 0.0065** [0.003] (4) N 2,522 321 131 118 195 138 185 889 115 246 170 486 289 654 3,244 (5) No. of Periods 309 260 172 152 116 79 204 246 184 198 198 186 258 293 366 (6) Adj R2 0.017 0.017 0.030 0.024 0.022 0.010 0.015 0.022 0.031 0.029 0.024 0.048 0.019 0.011 0.011 42 Table 3. Summary Statistics of Expected Return Proxies Table 3 reports summary statistics by country for the monthly ERPs calculated using Eq., (13). The rightmost column reports the average monthly realized log return. The summary statistics reported here are time-series averages of the corresponding cross-sectional statistics. Expectedreturn proxies for a particular calendar month are calculated using firm fundamentals and the cumulative rolling average of the estimated cross-sectional coefficients as of the end of the previous calendar month. For calculating cumulative averages, we use a burn-in period of forty months. Country Australia Belgium Canada China Denmark Finland France Germany Greece Hong Kong India Indonesia Israel Italy Japan Malaysia Netherlands Norway Pakistan Philippines South Africa South Korea Spain Sweden Switzerland Taiwan Thailand UK US q5 -0.0034 -0.0061 -0.0043 -0.0105 -0.0023 -0.0120 -0.0031 -0.0072 -0.0126 -0.0167 -0.0043 -0.0038 -0.0108 -0.0077 -0.0110 -0.0075 -0.0081 -0.0080 0.0047 -0.0013 -0.0023 -0.0227 -0.0071 -0.0132 -0.0028 -0.0147 -0.0263 0.0023 0.0014 q25 0.0029 0.0013 0.0007 -0.0054 0.0027 -0.0043 0.0023 -0.0033 -0.0064 -0.0079 0.0002 0.0026 -0.0043 -0.0034 -0.0051 -0.0018 -0.0026 0.0027 0.0076 0.0071 0.0034 -0.0135 0.0004 -0.0029 -0.0003 -0.0072 -0.0106 0.0043 0.0045 Median 0.0050 0.0037 0.0020 -0.0027 0.0040 0.0006 0.0036 -0.0020 -0.0042 -0.0047 0.0014 0.0064 -0.0028 -0.0019 -0.0020 0.0010 0.0000 0.0051 0.0092 0.0090 0.0063 -0.0087 0.0025 -0.0007 0.0012 -0.0049 -0.0058 0.0053 0.0059 q75 0.0069 0.0055 0.0032 -0.0004 0.0049 0.0051 0.0047 -0.0008 -0.0019 -0.0017 0.0026 0.0102 -0.0016 -0.0006 0.0006 0.0033 0.0021 0.0071 0.0106 0.0107 0.0086 -0.0045 0.0042 0.0010 0.0023 -0.0032 -0.0023 0.0063 0.0069 q95 0.0095 0.0098 0.0062 0.0028 0.0069 0.0117 0.0074 0.0017 0.0055 0.0038 0.0053 0.0149 0.0036 0.0017 0.0040 0.0064 0.0048 0.0111 0.0132 0.0132 0.0132 0.0007 0.0075 0.0039 0.0046 -0.0001 0.0030 0.0082 0.0084 Mean 0.0043 0.0030 0.0016 -0.0032 0.0035 0.0003 0.0030 -0.0023 -0.0041 -0.0055 0.0011 0.0061 -0.0031 -0.0023 -0.0026 0.0004 -0.0007 0.0040 0.0091 0.0081 0.0060 -0.0096 0.0018 -0.0019 0.0010 -0.0059 -0.0076 0.0053 0.0055 sd N Mean Returns 0.0040 0.0021 -0.0002 0.0028 -0.0003 0.0024 0.0018 -0.0029 -0.0104 0.0010 0.0048 0.0082 0.0013 -0.0025 -0.0035 0.0008 -0.0014 0.0014 0.0137 0.0044 0.0092 -0.0041 0.0008 -0.0012 0.0020 -0.0002 0.0021 0.0042 0.0051 0.0053 268 0.0057 76 0.0047 153 0.0048 1,118 0.0033 110 0.0078 68 0.0047 421 0.0035 366 0.0072 93 0.0088 229 0.0041 928 0.0070 182 0.0063 108 0.0041 150 0.0049 2,371 0.0050 301 0.0051 98 0.0068 88 0.0030 148 0.0057 78 0.0050 158 0.0078 855 0.0066 90 0.0067 212 0.0027 145 0.0064 449 0.0111 272 0.0026 599 0.0027 3,004 Table 4. Return Regressions Table 4 reports the results of Fama-MacBeth regressions of one-month-ahead log returns on the ERPs for each country. Expected returns are winsorized at the top and bottom one-percent. Standard errors are reported in brackets below the coefficient estimates. The last row reports the p-value for the F-test of the null hypothesis that the slope coefficient is equal to 1. Levels of significance are indicated by *, **, and ***, representing 10 percent, 5 percent, and 1 percent, respectively. Australia ˆ E[ri,t+1 ] Cons N R2 p-Value 0.5577** [0.238] 0.0007 [0.003] 67,239 0.016 0.064 India ˆ E[ri,t+1 ] Cons N R2 p-Value 0.7374** [0.299] 0.0029 [0.008] 191,194 0.008 0.380 South Africa ˆ E[ri,t+1 ] Cons N R2 p-Val -0.0378 [0.170] 0.0146*** [0.003] 32,104 0.012 0.000 Belgium 1.0484*** [0.319] -0.0017 [0.005] 9,991 0.025 0.880 Indonesia 1.0454*** [0.227] 0.0056 [0.005] 33,691 0.013 0.842 South Korea 1.5412*** [0.245] 0.0105 [0.007] 209,537 0.017 0.028 Canada 0.7340** [0.335] -0.0028 [0.003] 45,514 0.016 0.428 Israel China 0.4085** [0.204] 0.0121 [0.009] 178,906 0.008 0.004 Italy Denmark 1.5072*** [0.530] -0.0004 [0.005] 20,186 0.025 0.340 Japan 0.9429*** [0.155] -0.0001 [0.003] 730,374 0.013 0.713 Switzerland 0.7494* [0.409] 0.0016 [0.004] 28,656 0.018 0.540 Finland 0.4111* [0.221] -0.0013 [0.007] 6,779 0.014 0.010 Malaysia 1.4109*** [0.206] -0.0004 [0.006] 78,049 0.012 0.047 Taiwan 0.9327*** [0.167] 0.0097* [0.006] 82,991 0.013 0.687 France 1.3956*** [0.347] -0.0042 [0.003] 118,351 0.012 0.255 Netherlands 0.8810** [0.406] -0.0043 [0.005] 16,696 0.024 0.770 Thailand 0.6660*** [0.141] 0.0082* [0.005] 69,932 0.015 0.019 Germany 1.7270*** [0.333] -0.0002 [0.003] 102,838 0.009 0.030 Norway 1.1139** [0.440] -0.0029 [0.005] 13,307 0.025 0.796 UK 1.1200*** [0.255] -0.0022 [0.003] 174,792 0.007 0.638 Greece 0.2810 [0.303] -0.0116 [0.011] 9,236 0.012 0.021 Pakistan 1.0769 [0.879] 0.0004 [0.012] 16,883 0.019 0.931 US 1.2794*** [0.350] -0.0039 [0.004] 1,096,559 0.008 0.425 Hong Kong 0.8958*** [0.170] 0.0102* [0.005] 52,309 0.016 0.541 Philippines 1.1622** [0.487] -0.0033 [0.008] 6,050 0.012 0.741 1.6767*** 1.3071*** [0.414] [0.255] 0.0158** 0.0010 [0.007] [0.004] 8,183 0.015 0.111 Spain 29,548 0.02 0.231 Sweden 1.0350*** 1.0922*** [0.249] [0.253] -0.0000 0.0030 [0.004] [0.004] 16,290 0.027 0.888 41,673 0.022 0.716 43 Table 5. Stock Returns of Portfolios Sorted on Expected Return Estimates Table 5 reports the country-specific average one-month-ahead log returns for each quintile portfolio of the ERP. Quintile portfolios are constructed for each calendar month between and including Min Date and Max Date in Table 1. Column (6) [(7)] reports the average spread in mean [median] log returns between the fifth and first quintile portfolios. Column (8) reports the average spread in mean net returns between the fifth and first quintile portfolios. OLS standard errors are used in significance tests, using the time-series of mean or median quintile spreads. Levels of significance are indicated by *, **, and ***, representing 10 percent, 5 percent, and 1 percent, respectively. (1) Country Q1 (2) Q2 (3) Q3 (4) Q4 (5) Q5 (6) Spread Mean Q5 - Q1 0.0054** 0.0115*** 0.0077** 0.0053** 0.0124*** 0.0053 0.0127*** 0.0106*** 0.0070 0.0173*** 0.0027 0.0164*** 0.0203*** 0.0118*** 0.0112*** 0.0156*** 0.0095** 0.0149*** 0.0045 0.0147** 0.0018 0.0294*** 0.0120*** 0.0178*** 0.0050* 0.0083*** 0.0163*** 0.0053*** 0.0070*** (7) Spread Median Q5 - Q1 0.0040** 0.0034 0.0035 0.0037 0.0117*** 0.0030 0.0088*** 0.0085*** 0.0075 0.0142*** 0.0029 0.0049 0.0125*** 0.0122*** 0.0100*** 0.0105*** 0.0089*** 0.0194*** 0.0135** 0.0090** -0.0009 0.0238*** 0.0107*** 0.0180*** 0.0042 0.0090*** 0.0120*** 0.0031** 0.0033* Australia Belgium Canada China Denmark Finland France Germany Greece HongKong India Indonesia Israel Italy Japan Malaysia Netherlands Norway Pakistan Philippines South Africa South Korea Spain Sweden Switzerland Taiwan Thailand UK US -0.0008 -0.0048 -0.0087 0.0060 -0.0083 -0.0008 -0.0075 -0.0124 -0.0205 -0.0076 0.0026 0.0046 -0.0043 -0.011 -0.0099 -0.0122 -0.0084 -0.0122 0.0073 0.0003 0.0116 -0.0224 -0.0064 -0.0125 0.0004 -0.0029 -0.0062 0.0001 -0.0010 0.0045 0.0031 -0.0002 0.0095 -0.0013 -0.0010 0.0006 -0.0043 -0.0118 0.0051 0.0098 0.0080 0.0099 -0.0009 -0.0030 -0.0037 -0.0047 -0.0001 0.0132 0.0047 0.0113 -0.0074 0.0000 0.0018 0.0037 0.0043 -0.0014 0.0038 0.0034 0.0036 0.0005 0.0026 0.0121 0.0037 0.0010 0.0024 0.0000 -0.0107 0.0072 0.0109 0.0119 0.0116 -0.0014 -0.0013 -0.0009 -0.0019 0.0033 0.0125 0.0085 0.0124 -0.0040 0.0029 0.0047 0.0015 0.0076 0.0062 0.0035 0.0049 0.0044 0.0057 0.0018 0.0116 0.0044 0.0057 0.0043 0.0010 -0.0085 0.0089 0.0124 0.0145 0.0116 0.0001 0.0006 0.0020 -0.0006 0.0056 0.0124 0.0095 0.0121 0.0035 0.0075 0.0052 0.0039 0.0070 0.0087 0.0053 0.0067 0.0046 0.0067 -0.0010 0.0113 0.0041 0.0045 0.0052 -0.0018 -0.0135 0.0097 0.0053 0.021 0.0159 0.0008 0.0013 0.0034 0.0011 0.0027 0.0118 0.0149 0.0134 0.0069 0.0056 0.0053 0.0054 0.0054 0.0102 0.0053 0.006 44 Table 6. Sensitivity of Slope Coefficients to Choice of Training-Window Table 6 reports the country-specific slope coefficients (Coefficient) and their standard errors (Std-Errors) from Fama Macbeth regressions of one-month-ahead returns on our ERP for three different choices of the training sample: 30, 40, and 50 months. As in previous tables, ERPs are winsorized at the top and bottom one percent. Levels of significance are indicated by *, **, and ***, representing 10 percent, 5 percent, and 1 percent, respectively. Country 30 Coefficient Australia Belgium Canada China Denmark Finland France Germany Greece Hong Kong India Indonesia Israel Italy Japan Malaysia Netherlands Norway Pakistan Philippines South Africa South Korea Spain Sweden Switzerland Taiwan Thailand UK US 0.5377** 1.1157*** 0.7240** 0.6219*** 1.5511*** 0.3762* 1.4150*** 1.6229*** 0.3539 1.0999*** 0.6593** 1.0364*** 1.5416*** 1.4037*** 0.9316*** 1.3204*** 1.0520** 1.0765*** 1.1853 1.1133** 0.0768 1.5205*** 1.4020*** 1.1000*** 0.6475 0.8927*** 0.7789*** 1.0398*** 1.2317*** Std-Errors [0.229] [0.293] [0.325] [0.217] [0.498] [0.194] [0.340] [0.325] [0.273] [0.221] [0.287] [0.215] [0.338] [0.319] [0.151] [0.204] [0.463] [0.406] [0.778] [0.447] [0.168] [0.240] [0.312] [0.310] [0.398] [0.182] [0.151] [0.248] [0.340] Coefficient 0.5577** 1.0484*** 0.7340** 0.4085** 1.5072*** 0.4111* 1.3956*** 1.7270*** 0.2810 0.8958*** 0.7374** 1.0454*** 1.6767*** 1.3071*** 0.9429*** 1.4109*** 0.8810** 1.1139** 1.0769 1.1622** -0.0378 1.5412*** 1.0350*** 1.0922*** 0.7494* 0.9327*** 0.6660*** 1.1200*** 1.2794*** Training Window Length (months) 40 Std-Errors [0.238] [0.319] [0.335] [0.204] [0.530] [0.221] [0.347] [0.333] [0.303] [0.170] [0.299] [0.227] [0.414] [0.255] [0.155] [0.206] [0.406] [0.440] [0.879] [0.487] [0.170] [0.245] [0.249] [0.253] [0.409] [0.167] [0.141] [0.255] [0.350] Coefficient 0.5121** 1.0493*** 0.6712* 0.3607* 1.5028*** 0.4055 1.5498*** 1.8278*** 0.3900 0.9459*** 0.8766*** 1.0672*** 1.6719*** 1.1941*** 0.9353*** 1.4479*** 0.5172 1.2056** 1.2935 1.7600*** -0.1389 1.6199*** 0.9543*** 1.0477*** 0.6700* 0.9518*** 0.6077*** 1.2122*** 1.2442*** 50 Std-Errors [0.246] [0.354] [0.345] [0.216] [0.559] [0.260] [0.346] [0.342] [0.356] [0.173] [0.311] [0.239] [0.420] [0.252] [0.160] [0.197] [0.389] [0.481] [0.835] [0.413] [0.175] [0.220] [0.256] [0.259] [0.404] [0.159] [0.138] [0.262] [0.358] 45 Table 7. Return Regressions: Factor-Based-Model Expected-Return Estimates Table 7 reports the results of Fama-MacBeth regressions of future returns on different ERPs. Columns under the heading CLW report regressions of one-month-ahead log returns on ERPs generated using our model. FF Global and FF Regional report regression of realized net returns on ERPs generated using firm-specific loadings on the Fama-French global four factors and the regional four factors, respectively. The analyses are conducted on a common set of firm-year observations for which all three ERPs are available. Expected factor returns are estimated based on trailing 40-month averages, and factor loadings are estimated based using data available in the 40 months prior to the forecast date. All ERPs are winsorized at the top and bottom one percent. Columns under ˆ the heading E[ri,t+1 ] reports the slope coefficient on the ERP, Cons reports the coefficient on the constant term, and p reports p-values corresponding to the F-test of the null that the slope coefficient is equal to 1. Levels of significance are indicated by *, **, and ***, representing 10 percent, 5 percent, and 1 percent, respectively. CLW Country Australia Belgium Canada China Denmark Finland France Germany Greece HongKong India Indonesia Israel Italy Japan Malaysia Netherlands Norway Pakistan Philippines South Africa South Korea Spain Sweden Switzerland Taiwan Thailand UK US 5-Factor 3-Factor ˆ E[ri,t+1 ] 0.5118** 1.0179*** 0.6762** 0.4280** 1.8370*** 0.4113* 1.3492*** 1.8069*** 0.3077 0.9409*** 0.6986** 1.0291*** 1.7038*** 1.2827*** 0.9156*** 1.3741*** 0.7986** 1.1222** 1.1666 1.2317** -0.0113 1.4888*** 1.0916*** 1.0790*** 0.6836* 0.9569*** 0.6741*** 1.2105*** 1.3091*** Cons 0.0010 -0.0014 -0.0029 0.0107 -0.0008 -0.0013 -0.0032 0.0004 -0.0121 0.0107** 0.0028 0.0060 0.0150** 0.0014 -0.0002 -0.0006 -0.0040 -0.0030 -0.0013 -0.0031 0.0145*** 0.0105 -0.0000 0.0033 0.0018 0.0110* 0.0081 -0.0032 -0.0042 p 0.040 0.955 0.346 0.006 0.082 0.010 0.329 0.020 0.027 0.735 0.309 0.902 0.105 0.266 0.604 0.079 0.615 0.784 0.851 0.665 0.000 0.047 0.719 0.759 0.443 0.806 0.023 0.423 0.387 ˆ E[ri,t+1 ] -0.0646 -0.2259 0.0019 -0.0091 -0.2906* -0.0532 0.0248 -0.0250 -0.0282 -0.2072* -0.0760 -0.2348** -0.3198** -0.1420 -0.0061 -0.0487 -0.3039 -0.1384 0.2548* -0.1299 0.0103 -0.0035 -0.1363 0.0253 -0.1285 -0.0812 -0.0398 -0.0126 -0.0916 FF Global Cons 0.0000 -0.0206** 0.0234 0.0269** 0.0344*** 0.0103 0.0105 -0.0126 -0.0127 -0.0047 0.0215* 0.0286*** 0.0191** 0.0092 -0.0141 0.0077 0.0119 0.0037 0.0157* 0.0188** 0.0391*** 0.0278 -0.0067 0.0144 -0.0096 0.0027 -0.0123 0.0089 0.0234* p 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ˆ E[ri,t+1 ] FF Regional Cons 0.0117*** 0.0068 0.0121*** 0.0222** 0.0116** -0.0004 0.0080** 0.0048 0.0020 0.0137*** 0.0220** 0.0275*** 0.0160* 0.0052 0.0038 0.0066 0.0100* 0.0081 0.0166* 0.0168* 0.0167*** 0.0160* 0.0093* 0.0142** 0.0081** 0.0158** 0.0167*** 0.0077*** 0.0132*** 0.0127*** 0.0134*** p 0.000 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.647 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.031 0.000 0.000 0.007 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.004 N 65,323 9,881 43,572 172,649 19,808 6,720 115,243 100,427 9,076 51,098 183,590 32,330 7,813 29,006 689,158 76,099 16,516 12,941 16,233 5,829 31,379 204,755 16,077 40,711 28,247 81,380 67,837 167,791 1,073,567 1,073,567 1,073,567 -0.0184 0.0293 -0.2129*** -0.1790 -0.0238 -1.1041** -0.0100 -0.0961 0.7506 0.1255 -0.0390 -0.1740 -0.1703 -0.2367 0.0268 0.1005 0.2923 -0.1867 -0.0925 0.3035 0.1978 -0.0710 0.2966 -0.0925 -0.0425 0.2080 -0.1973* -0.1381 -0.0677* -0.0406 -0.1034* 46 Table 8. Earnings Quality and Importance of ROE Table 8 reports the results of OLS and instrumental-variables (IV) regressions of country-level median roe coefficients, from monthly regressions of Eq., (13), on measures of earnings quality. Our overall earnings quality measure follows Leuz et al. (2003): a simple average of a country’s in-sample ranks on four dimensions of earnings quality: earnings smoothness, correlation of accruals and cash flows, accruals magnitude, and loss avoidance. These four variables are defined in Table 9. A higher score on each of these dimensions, and on the overall earnings-quality measure, implies lower or poorer earnings quality. The leftmost column reports the results of an OLS regression of the median roe coefficients on overall earnings quality. The second and third columns report the first and second stage results, respectively, of instrumental variables regressions where earnings quality is instrumented with a measure for a country’s quality of governance institutions. This quality of governance measures combines information on a country’s Rule of Law, Accountability, Political Stability, Government Effectiveness, and Control of Corruption, as reported by the World Bank’s Worldwide Governance Indicators project. Rule of Law captures perceptions of the quality of contract enforcement, property rights, and the courts; Accountability captures perceptions of the extent to which citizens have the ability to exert their voices and influence to create accountability in society, including freedom to select their government and the presence of a free media; Political Stability measures perceptions of the likelihood of political instability; Government Effectiveness captures perceptions of the quality of public services and the robustness of the policy formulation process; and Control of Corruption captures perceptions of the extent to which public power is exercized for private benefits. We take the median value of each variable over the relevant time frame for each country and then standardize each measure using the cross-section of countries. Our final country-level measure is the simple average of these standardized measures. In the last column we report reduced-form versions of the IV estimation. The F-statistic on the instrument is reported in the last row. In each of these regressions we control for the log of a given country’s median total market capitalization over the relevant time frame. Levels of significance are indicated by *, **, and ***, representing 10 percent, 5 percent, and 1 percent, respectively. OLS Poor Information Quality (Leuz et al., 2003) Quality of Governance Institutions Log Market Size Constant Observations First Stage F -0.0023*** [0.001] 0.0750*** [0.023] 25 -0.0001 [0.000] -3.9260*** [1.264] -0.1859 [0.883] 20.6885 [23.082] 25 9.65 IV First Stage IV Second Stage -0.0007** [0.000] 0.0027* [0.001] -0.0029*** [0.001] 0.0898*** [0.018] 25 47 Reduced Form -0.0030*** [0.001] 0.1041*** [0.025] 25 Table 9. Earnings Quality and Importance of ROE: Alternative Measures Table 9 reports the same specifications reported in Table 8 but uses Leuz et al. (2003)’s four measures of poor Information quality. Variability measures the extent to which a country’s firms engage in earnings smoothing. In descending order, we rank each country’s median ratio of firm-level standard deviation of operating earnings to the firm-level standard deviation of cash-flow from operations. A lower ratio implies a greater degree of earnings smoothing and thus lower earnings quality, resulting in a higher rank in Poor Information Quality. Correlation also measures the extent of earnings smoothing in a country. Across countries, in ascending order, we rank the magnitude of the contemporaneous correlation between changes in accounting accruals and changes in operating cash flows. This correlation is estimated by pooling all firm-years within a country. A greater magnitude of correlation implies greater earnings smoothing and lower earnings quality, resulting in a higher rank on Poor Information Quality. Accruals Magnitude proxies for the extent of the use of accruals to manage earnings. We rank, in ascending order, the median of the absolute value of firm accruals scaled by the absolute value of firm cash-flow from operations. A higher median ratio implies a greater use of accruals in managing earnings and lower earnings quality, resulting in a higher rank on Poor Information Quality. Lastly the Small Loss Avoidance measure ranks across countries, in ascending order, the ratio of instances of small profits to instances of small losses: this ratio is calculated by pooling all firm-years within a country. Small profits and small losses are calculated using earnings scaled by total assets. Small losses are defined as in the range [−0.01, 0) and small profits are defined as in the range [0.00, 0.01]. A higher ratio implies greater use of managerial discretion in managing earnings and lower earnings quality, and results in a higher rank in Poor Information Quality. Our instruments and control variables remain the same as in Table 8. Levels of significance are indicated by +, *, **, and ***, representing 15 percent, 10 percent, 5 percent, and 1 percent, respectively. OLS Poor Information Quality Quality of Governance Log Market Size Constant Observations First Stage F -0.0022*** [0.001] 0.0701*** [0.021] 25 0.0001 [0.000] Variability IV IV First Stage Second Stage -0.0009 [0.001] -2.9232 [2.059] -0.2771 [1.332] 22.4796 [35.373] 25 2.02 OLS 0.0000 [0.000] Correlation IV IV First Stage Second Stage -0.0006* [0.000] Accruals Magnitude OLS IV IV First Stage Second Stage -0.0002 [0.000] -0.0006** [0.000] Small Loss Avoidance OLS IV IV First Stage Second Stage -0.0000 [0.000] -0.0008* [0.000] -0.0032** [0.001] 0.1107*** [0.041] 25 -4.5851*** [1.537] -0.0022*** 0.0738 [0.001] [1.253] 0.0725*** 14.2393 [0.019] [33.039] 25 25 8.90 -4.8061*** [1.474] -0.0029*** -0.0027*** -1.4518+ [0.001] [0.001] [0.919] 0.0982*** 0.0860*** 53.8144** [0.030] [0.027] [24.410] 25 25 25 10.63 -3.3898+ [2.145] -0.0037*** -0.0022*** 0.9117 [0.001] [0.001] [1.142] 0.1203*** 0.0731*** -7.7792 [0.025] [0.018] [30.393] 25 25 25 2.50 -0.0022** [0.001] 0.0835*** [0.023] 25 48