Analysing the relationship between implied cost of capital metrics and realised stock returns

Transcription

1 Analysing the relationship between implied cost of capital metrics and realised stock returns by Colin Clubb King s College London and Michalis Makrominas Frederick University Cyprus Draft: September 2017 Comments most welcome, please do not quote.

2 Abstract We extend the analytical framework linking realised stock returns and ICC estimates used in Easton and Monahan (2005) and Mohanram and Gode (2013) (based on Vuolteenaho (2002)) by incorporating insights from studies by Pettengill, Sundaram, and Mathur (1995) and Hughes, Liu, and Liu (2009). We use the theoretical work of Hughes et al (2009) to structure our analysis of the relationship between realised returns and the ICC in order to: (i) take account of the impact of market news on the association between the ICC and realised stock returns; (ii) provide an alternative measure of discount rate news ; and (iii) take account of the expected theoretical difference between the implied cost of capital and the expected rate of return. Our empirical results, based on both cross-sectional and timeseries analysis and employing an adjustment for analyst earnings forecast error, are generally consistent with the implications of our analytical framework. Specifically, our cross-sectional regression results (a) provide robust support for a coefficient close to one for most ICC estimates after taking account of market news, (b) provide cash flow news and discount rate news coefficient estimates close to one, and (c) provide evidence for the role of a growth/leverage based variable as a control for the expected difference between the ICC and expected stock returns. Time-series results for individual firms confirm strong mean reversion in ICC estimates as assumed in our analytical framework and provide strong corroborative evidence for a positive association between market new adjusted implied risk premiums and realised returns. Overall, our paper provides further robust support for the relevance of realised returns as a benchmark for establishing the usefulness of ICC measures, consistent with theoretical expectations.

3 1. Introduction Previous research has provided evidence on the relationship between a variety of implied cost of capital (ICC) estimates and realised stock returns. This research is important as reliable cost of capital estimates are required for optimal investment decision-making by both managers and investors, and the explanatory power of implied cost of capital estimates for future realised stock returns provides a potentially important basis for evaluating the usefulness of ICC metrics in this role. As highlighted in many prior studies, however, the comparison of ICC estimates with realised stock returns is affected by the impact of new information on stock returns and by potential bias in analysts earnings forecasts used to generate ICC estimates. As a result, more recent theoretical and empirical analysis of this relationship has focused on controlling for the effect of cash flow news and discount rate news on realised stock returns and adjusting analysts earnings forecasts for predictable bias. While such controls have led to improved empirical results providing clear evidence of a positive relationship between ICC estimates and realised returns, notably by Mohanram and Gode (2013), multivariate regression results incorporating cash flow news and discount rate news variables are not entirely consistent with theoretical expectations. In the current paper, we extend the analytical framework linking realised stock returns and ICC estimates used in Easton and Monahan (2005) and Mohanram and Gode (2013) (based on Vuolteenaho s (2002) analysis of the relationship between realised and expected returns) by incorporating insights from prior studies by Pettengill, Sundaram, and Mathur (1995) and Hughes, Liu, and Liu (2009). We use the theoretical work of Hughes et al (2009) to structure our analysis of the relationship between realised returns and the ICC in order to: (i) take account of the impact of market movements or market news on the association between the implied cost of capital and realised stock returns, as implied by Pettengill et al (1995); (ii) provide an alternative measure of discount rate news based on mean-reverting expected returns; and (iii) take account of the expected theoretical difference between the implied cost of capital and the expected rate of return highlighted by Hughes et al (2009). Our empirical results, which also employ an adjustment for analyst earnings forecast error based on Larocque (2013), are generally consistent with the implications of our analytical framework. More specifically, our cross-sectional regression results: (a) provide robust support for a coefficient close to 1

4 one for most ICC estimates (including those based on Ohlson and Juettner-Nauroth (2005) and Gebhardt, Lee, and Swaminathan (1999)) after taking account of market news; (b) provide cash flow news and discount rate news coefficient estimates close to one; (c) provide evidence for the role of a growth/leverage based variable as a control for the expected difference between the ICC and expected stock returns. Additional time-series results for sample firms provide strong evidence of mean reversion in ICC estimates and further strong evidence of a positive association between market news adjusted ICC estimates and realised returns as predicted by theory. In summary, our paper contributes to the literature by extending analysis of the relationship of the relationship between realised returns and ICC metrics and providing strong empirical support for a positive association broadly consistent with theoretical expectations. The remainder of the paper is organised as follows. Section 2 provides a review of previous work on ICC and realised returns and highlights the issues which motivate the current study. Section 3 develops our analytical framework linking the ICC to realised stock returns. Section 4 outlines the data, ICC estimation methods, and empirical models and methods used in the study. Section 5 reports and discusses our empirical findings based on cross-sectional and time-series analysis of the association between ICC measures and realised stock returns. Section 6 summarises and concludes the paper. 2. Previous research and motivation Assumptions regarding expected equity return underpin significant financial decisions regarding investment, valuation and capital budgeting. While a large volume of literature in finance and accounting has been devoted to measuring the cost of equity, the problem of validating measures of expected equity return continues to be an important research issue. We review here some of the key papers which have used accounting based valuation models to infer the ICC with a particular focus on evidence on the association of ICC estimates with realised stock returns. The development of valuation models linking stock prices with future earnings or dividends based on various assumptions regarding expected performance and asymptotic growth rates has led to a number of alternative approaches to estimating the ICC. Such approaches include Botosan (1997) who uses the dividend discount model with a target price as terminal value, Gebhardt et al (2001) who 2

5 employ the residual income model using short term analyst earnings forecasts and an industry specific asymptotic growth rate, Claus and Thomas (2001) who implement the residual income model with an economy wide growth rate, and Gode and Mohanram (2004) who implement the Ohlson and Juettner- Nauroth (2005) abnormal earnings growth model where short-term earnings growth assumptions are based on analyst earnings forecasts and long-term growth is based on an economy-wide long term growth rate. Easton (2004) identifies the price-earnings / growth (PEG) valuation model as a special case of the Ohlson and Juettner-Nauroth (2005) model and develops a procedure for simultaneously estimating the ICC and the long-run growth rate given short-run analyst earnings forecasts. Further studies by Botosan and Plumlee (2005), Easton and Monahan (2005), Botosan et al (2011), Hou et al (2012), and Mohanram and Gode (2013) provide evidence on the usefulness of a range of ICC estimates using the association of ICC estimates with known risk factors and with realised stock returns as the main basis for comparison. Botosan and Plumlee (2005) assess the association of ICC estimates with a range of variables intended to proxy for risk factors and provide evidence that only two of their ICC measures, based on the dividend and PEG models, are significantly related to market, leverage, information, and residual risk proxies. However, given that interest in the ICC method has been reanimated in recent years due to perceived limitations of the ability of asset factor models to provide reliable estimates of the cost of capital, this approach appears to have some limitations. These are discussed by Easton and Monahan (2016) who highlight the apparent conceptual inconsistency of using the asset factor model approach to evaluate ICC metrics and question the ability of measures such as book-to-price to proxy for true risk factors. 1 An alternative approach which does not suffer the conceptual issues related to the risk factor approach is to evaluate the efficacy of alternative ICC measures to predict future realized returns. This approach, however, has generated mixed results as indicated below. In univariate tests of association, Gode and Mohanram (2004) find that ICC estimates derived from the Ohlson and Juettner-Nauroth (2005) model are only weakly correlated with future realized 1 Berk (1995) questions the interpretation of book-to-price and size as risk factors, a perspective which is developed by Clubb and Naffi (2007) where they are interpreted as valuation factors rather than risk factors in a returns model based on Vuolteenaho (2000). 3

6 returns. Easton and Monahan (2005), using a methodology based on the Vuolteenaho (2002) return decomposition model, evaluate seven ICC estimates and conclude that none of these estimates show a meaningful association with realized returns, even after controlling for shocks related to cash flow news and discount rate news. An important feature of the Easton and Monahan study is the use of changes in the estimated ICC between consecutive years as the basis for estimating discount rate news. Botosan et al (2011), on the other hand, provide more supportive results on the association of a wide range of ICC estimates with realised returns when additional information on the change in analysts target prices (interpreted as cash flow news) and changes in firm-specific betas and interest rates (interpreted as expected return news) are included as additional explanatory variable for returns. While their results are generally consistent with the expected positive association between realised returns and ICC, the incremental explanatory power of ICC beyond their extensive set of cash flow and expected returns news control variables is however generally small. Laroque (2013) also provides some further evidence of a positive association between ICC estimates and realised returns after controlling for cash flow and expected return news using procedures outlined in Callen and Segal (2010). Finally, Mohanram and Gode (2013) show that adjusting analysts forecasts for predictable errors resulted in a positive association between returns and a range of ICC estimates using a similar methodology to Easton and Monahan (2005). 2 With the exception of Mohanram and Gode (2013) and Laroque (2013), research on ICC estimation has typically used analyst earnings forecasts under the assumption that these forecasts match the market s earnings expectations. Other research, however, documents important shortcomings in analyst forecasts such as upward bias (O Brien (1998)), sluggishness (Mendenhall (1991)) and/or underreaction (overreaction) to bad (good) news (Easterwood and Nutt (1999)). Furthermore, studies by Elgers and Lo (1994) and Ali et al (1992) show that analyst forecasting errors can be predicted using 2 Christodolou et al (2014) provide evidence that realised stock returns revert to an estimate of the long-run cost of equity based on accounting information. Firm cost of equity estimates, however, are extracted from estimation of time-series accounting information dynamics based on Ohlson (1995) and Clubb (2013) and hence their approach differs from the ICC methodology of reverse-engineering the stock price using accounting information. The Christodolou et al (2014) analysis therefore provides support for a significant association between realised stock returns and an accounting-based cost of capital estimate in the long-run but does not address the issue of the cross-sectional relationship between ICC estimates and short-run stock returns considered in the literature reviewed here. 4

7 information available at the time (or prior) to the forecast. More recently, Hughes et al (2008) model expected forecasting error based on factors related to overreaction (accruals, sales growth, long-term growth, growth in PP&E) as well as factors related to underreaction (past return, past error, forecast revision). The potential impact of analyst errors on ICC estimates, highlighted in Claus and Thomas (2001) and Easton and Monahan (2005), raises the question of whether the validity of ICC estimates can improve by correcting for analysts expected error. Only a small number of studies consider the return predictability of ICC estimates after adjusting the imputed forecasts for analyst error. Guay et al. (2011) adjust forecasts for errors related to analyst underreaction (past return), size effects, analyst following and book to market. They find that once predictable errors have been removed the return predictability of ICC estimates improve, but the improvement is limited at portfolio level and for some ICC estimates. Larocque (2013) extends Ali et al (1992) to construct an error-correction model encompassing past forecast error, recent return, size and a control for measurement error but fails to find an improvement in ICC return predictability once analyst forecast have been adjusted. More positively, as previously indicated, Mohanram and Gode (2013) use the Hughes et al (2008) model to remove predictable errors for analysts forecasts and document a substantial improvement in the association of ICC estimates and future realized returns when controlling for cash flow news and discount news. While the study by Mohanram and Gode (2013) provides the strongest evidence to date that a wide range of ICC metrics based on the residual income and abnormal earnings growth models can provided significant explanatory power for future realised stock returns with a consistently positive ICC coefficient, their results are not entirely consistent with theory. Specifically, the coefficient for most ICC metrics turns out to be significantly different from the theoretical expectation of 1 and the coefficient for discount rate news is either significantly negative (rather than positive as expected by theory) or insignificantly different from 0. Based on the insight of Pettengill et (1995) that the relationship between realised returns and expected returns will be affected by returns on the market portfolio in a simple CAPM setting (and, for example, will be negative when realised returns on the market are below the risk-free rate), we propose a market news adjustment to ICC estimates to control for the impact of unexpected market returns on the association between realised returns and ICC 5

8 metrics. While such market news is incorporated within the theoretical measures of cash flow news and discount rate news provided by the Vuolteenaho (2002) return decomposition, it is unclear that the empirical proxies used for these news variables in Easton and Monahan (2005) and Mohanram and Gode (2013) fully capture market news. The following section of the paper develops an analytical framework which incorporates all three news measures and provides the basis for our empirical analysis in sections 4 and 5 of the paper. Given the importance of controlling for analyst forecast bias suggested by the findings of Mohanram and Gode (2013), our subsequent empirical analysis also uses an error correction model to control for predictable analyst forecast errors based on Laroque (2013). While the use of this methodology did not significantly improve her findings, she provided other evidence on the utility of the adjustment procedure which suggests its potential usefulness on our larger sample of US stocks. In summary, previous research has provided weak or mixed evidence on the association between ICC metrics and realised stock returns. We develop an analytical framework which builds on the Vuolteenaho (2002) based framework of Easton and Monahan (2005) and Mohanram and Gode (2013) by incorporating theoretical insights from Hughes et al (2009) and taking account of the possible impact of market return news on the association between ICC metrics and realised returns in the spirit of Pettengill et al s (1995). Based on our framework, the empirical analysis extends previous research in three important respects; first, the impact of market news on the return/icc relationship is exposed; second, broad support is provided for ICC and news variables coefficients with sign and magnitude predicted by theory: third, evidence of bias in ICC estimates as estimates of expected stock returns is indicated. We interpret our analysis and empirical findings as contributing significantly to the growing evidence on the usefulness of ICC based approaches to estimating the cost of capital. 3. Modelling the relationship between realised stock returns and the implied cost of capital Our analysis of the relationship between realised stock returns and the implied cost of capital integrates insights from previous studies by Pettengill et al. (1995), Vuolteenaho (2002), Easton and Monahan (2005), and Hughes et al. (2009). First, we assume an underlying single factor asset pricing model as in Hughes et al (2009) and show how the relationship between realised stock returns and 6

9 expected stock returns is affected by realised market returns, as highlighted previously by Pettingill et al (1995). Second, we combine this model of realised returns with the return decomposition model of Vuolteenaho (2002) where realised stock returns are expressed as the summation of expected returns, cash flow news, and discount rate news and confirm that realised stock returns can be expressed as the sum of expected returns adjusted for (or conditional on) market returns and firm-specific cash flow and discount rate news. Third, given results in Hughes et al (2009) on differences between ICC and expected returns, we consider the impact of using the implied cost of capital (rather than expected returns) in our model of realised returns and show how this leads to a division of realised stock returns into three main elements: (i) (ii) (iii) market news adjusted implied cost of capital, firms specific news based on changes in the implied cost of capital and cash flow news, error related to the difference between the implied cost of capital and expected returns. Fourth, we consider the implications of this division of realised stock returns for empirical analysis of the relationship between stock returns and implied cost of capital. Finally, we propose a linear regression model for assessing this relationship empirically. 3.1 Realised returns and market news adjusted expected returns Following Hughes et al (2009), our analysis assumes that expected returns are generated by the following single factor market model (firm subscripts are suppressed for presentational clarity): μ t+1 t+1 t = r f + λβ t (1) t+1 t+1 where μ t is expected return for period t+1 as at end of period t, β t is beta for period t+1 estimated (and known with certainty) at the end of period t, λ is the market risk premium (assumed constant over time), and r f is the risk-free rate (again assumed constant over time). Also consistent with Hughes et al. (2009), we assume that: β t+1 t = β + σ β ε βt (2) where ε βt, t = 0,1,., are standard normal variates, and that β t+s t = β for s > 1 so that: μ t+s t = r f + λβ μ, for s > 1 (3) 7

10 Drawing on the observation of Pettengill et al (1995) that the relationship between realised returns and beta is conditional on realised market returns, realised returns for t+1 can be written as: r t+1 = μ t+1 t + (λ t+1 λ)β t+1 t + ε t+1 (4) where λ t+1 represents the realised market return for period t+1 less the risk-free rate and ε t+1 is a mean zero disturbance term reflecting idiosyncratic firm risk during period t+1. Subtracting r f from both t+1 sides of equation (4) and substituting for β t using equation (1) then gives: r t+1 t+1 where r t+1 r t r f and μ t μ t+1 t r f. = λ t+1 λ μ t t+1 + ε t+1 (5) 3.2 Realised returns, market news adjusted expected returns, and firm-specific cash flow and discount rate news Vuolteenaho (2002) and Easton and Monahan (2005) show that if earnings are measured on a clean surplus basis and the log of the book-to-market ratio has an unconditional mean (i.e, is meanreverting), realised stock returns for period t+1 may be written (approximately) as: r t+1 = μ t+1 t + ρ j (x t+1+j t+1+j t+1 x t ) j=0 ρ k (μ t+1+k t+1 μ t+1+k t ) k=1 (6) where x t t+1+j denotes the expectation of the log of one plus accounting return on equity for period t+1+j as at the end of period t and ρ can be viewed as a discount factor for aggregating changes in expectations of future accounting return on equity and future expected stock returns. 3 Equation (6) indicates that realised returns are equal to expected returns plus total firm news for the period, where total firm news is divided into cash flow news, k=1 j=0 ρ j (x t+1+j t+1 x t+1+j t ), and discount rate news, ρ k (μ t+1+k t+1 μ t+1+k t ). Using equation (3) to simplify the discount rate news component of equation (6) and re-expressing in terms of excess returns over the risk-free rate gives: r t+1 t+1 = μ t + ρ j (x t+1+j t+1+j t+1 x t ) j=0 t+2 ρ(μ t+1 μ ) (7) 3 As discussed in Easton and Monahan (2005), ρ lies between 0 and 1 and is likely to be positively related to the price-to-net dividend ratio. Empirical estimation of ρ based on firms divided into price-to-dividend quartiles suggests that it lies between 0.92 and 1. 8

11 where μ μ r f and, which from comparison with equation (5), implies that: ε t+1 = ρ j (x t+1+j t+1+j t+1 x t ) j=0 t+2 ρ(μ t+1 μ ) ( λ t+1 λ 1) μ t t+1 (8) Equation (8) indicates that firm-specific news, represented by ε t+1 in equation (5), is equal to cash flow news plus discount rate news minus market news given by ( λ t+1 λ contains both market-related cash flow news and market-related discount rate news. 1) μ t t+1, where market news 3.3 Realised returns, market news adjusted implied cost of capital, firm-specific cash flow and discount rate news, and error in the implied cost of capital In order to provide an expression for evaluating the relationship between realised stock returns for period t+1 and the ICC at the end of period t, denoted by π t, we define excess ICC (over the riskfree rate) as π t π t r f, add and subtract ( λ t+1 π λ t ρ(π t+1 π t )) from the right hand side of equation (5), and make use of equation (8) to obtain: r t+1 = λ t+1 λ π t + [ ρ j (x t+1+j t+1 x t+1+j t ) ρ(π t+1 j=0 π t ) ( λ t+1 λ 1) π t ] t+1 + {(μ t π t+2 t ) ρ ((μ t+1 μ ) (π t+1 π t ))} (9) Equation (9) indicates that excess realised returns can be expressed as the sum of the following three components: Market news adjusted excess ICC equal to λ t+1 π λ t = π t + ( λ t+1 1) π λ t, where ( λ t+1 1) π λ t represents a measure of market news based on excess ICC (rather than excess expected returns as in equation (5)) Firm-specific news (given by the term in square brackets) equal to cash flow news plus discount rate news minus market news, where discount rate news and market news are based on excess ICC (rather than excess expected returns as in equation (8)), and ICC error (given by the final term in curly brackets) resulting from use of excess ICC instead of excess expected return (i) as the main explanatory variable i.e., (μ t t+1 π t ) and (ii) as the t+2 basis for measuring discount rate news i.e., ρ ((μ t+1 μ ) (π t+1 π t )). 9

12 3.4 Implications for empirical analysis of relationship between realised stock returns and ICC We develop the empirical implications of the previous analysis by re-expressing equation (9) in the form of two alternative theoretical cross-sectional regression models. For presentational clarity, we index all relevant variable with a firm subscript i = 1,2, n, where n represents the total number of firms. In addition, we define the mean cross-sectional bias of the ICC as an estimate of expected returns at date t+1 as (μ t t+1 π t ), such that the bias for any individual firm i can be expressed as follows: t+1 (μ it π it ) = (μ t t+1 π t ) + θ it+1 where θ it+1 represents the difference between the mean cross-sectional ICC bias and the firm i ICC bias for expected returns at date t+1. Hughes et al (2009) suggest that mean cross-sectional bias is likely to be positive under reasonable assumptions (i.e., expected returns may be expected to exceed the implied cost of capital). follows: Our first theoretical cross-sectional regression model simply involves rewriting equation (9) as r it+1 = α 0,t+1 + α 1,t+1 ( λ t+1 λ π it ) + α 2,t+1 ( (ρ i ) j (x t+1+j it+1 x it +α 3,t+1 (ρ i (π it+1 j=0 t+1+j ) π it )) + υ it+1 (10) where, from a direct comparison with equation (9), the model intercept is α 0,t+1 = μ t t+1 π t, the coefficient for market news adjusted ICC is α 1,t+1 = λ λ t+1, the coefficients for cash flow and discount rate news are α 2,t+1 = 1 and α 3,t+1 = 1 respectively, and υ it+1 is a mean zero disturbance term. 4 Given that the cross-sectional regression model represented by equation (10) contains complete measures of cash flow and discount rate news (i.e., they contain both firm specific and market news), it is logical ) 4 t+2 To see that υ it+1 in equation (10) is a mean zero disturbance term, note that υ it+1 = ρ i ((μ it+1 μ i ) (π it+1 π it )) + θ it+1 where μ t+1 i = μ t+1 it λσ iβ ε iβt (as equations (1) and (2) imply μ it = λβ t+1 it = λβ i + λσ iβ ε iβt = μ t+2 i + λσ iβ ε iβt ). It follows that υ it+1 = ρ ((μ t+1 π t+1 ) + θ it+2 (μ t t+1 π t ) + θ it+1 + λσ iβ ε iβt ) + θ it+1. Given that ε iβt, θ it+1, and θ it+2 are all mean zero variables and making the mild assumption t+2 that (μ t+1 π t+1 ) (μ t t+1 π t ) 0 (i.e. assuming that the mean bias of the ICC vis-à-vis expected returns is approximately constant over time, consistent with the previous analysis of Hughes et al (2009)), it follows that υ t+1 can be regarded as a mean zero disturbance term. 10

13 that the coefficient for these variables should equal 1 and that the coefficient for market news adjusted ICC should in effect undo the market news adjustment i.e., α 1,t+1 ( λ t+1 π λ it ) = λ ( λ t+1 λ t+1 λ π it ) = π it. On the other hand, if we assume that market news for firm i can be split into a market cash flow news component, m CF it+1, and a market discount rate news component, m it+1, where m it+1 DR CF + m DR it+1 = ( λ t+1 λ 1) π it, and that this market news is not captured by cash flow and discount rate news variables, then the following alternative theoretical cross-sectional regression model is implied by equation (9): r it+1 = α 0,t+1 + α 1,t+1 ( λ t+1 λ π it ) + α 2,t+1 ( (ρ i ) j (x t+1+j it+1 x it +α 3,t+1 (ρ i (π it+1 j=0 t+1+j ) m CF it+1 ) π it ) m DR it+1 ) + υ it+1 (11) where the coefficient on market news adjusted ICC is now α 1,t+1 = 1 (and α 0,t+1 = μ t t+1 π t, α 2,t+1 = 1 and α 3,t+1 = 1). A possible rationale for the omission of market news from cash flow news based on analyst forecasts is provided in Appendix A. The cross-sectional regression models represented by equations (10) and (11) indicate that while use of market news adjusted ICC in place of unadjusted ICC does not alter the explanatory power of one particular cross-sectional regression (because λ t+1 λ is a scale factor applied to each firm s ICC estimate in the date t+1 regression), it will affect the time-series distribution of the regression coefficient over the whole sample period and hence inferences based on the time-series mean (such as those based on Fama-MacBeth t statistics). In particular, if market news is not well captured by empirical estimates of cash flow and discount rate news, equation (11) implies that market news adjustment of ICC estimates should generate a time-series mean coefficient more reliably close to 1. 5 On the other hand, if market 5 Based on equation (11), if the realised excess market return deviates significantly from λ over time and market news represented by ( λ t+1 1) π λ t is not reflected in estimates of cash flow and discount rate news for firms, the mean time-series coefficient for ICC without market news adjustment (equal to the time series mean of λ t+1 ) will λ be volatile and may be significantly different from 1. The coefficient for the market news adjusted ICC in this setting, on the other hand, is exactly 1 in all years. 11

14 news is well captured by cash flow and discount rate news proxies, equation (10) suggests that the mean coefficient based on ICC estimates without market news adjustment should be more reliably close to 1. 6 In summary, our analytical framework provides the basis for our empirical approach which accommodates the possibility that cash flow and discount rate news proxies do not fully capture market news. More specifically, it provides a basis for testing whether market news adjustment of ICC estimates leads to an improved specification of the relationship between realised stock returns and the ICC. In section 4, we outline our empirical research models based on this analysis after discussing our dataset and the alternative ICC metrics used in the study. 4. Data, variable estimation methods, and empirical models 4.1 Data We consolidate consensus analyst forecasts from the I/B/E/S summary file, accounting data from COMPUSTAT and market data from CRSP. Risk free rates are obtained from the publicly available feed of U.S. Treasury. All data is collected 6 months prior to estimation date so as to allow accounting data to become publicly available and thus incorporated into analyst forecasts and stock prices. Since I/B/E/S coverage starts from 1981 and given our data requirement of 1-year ex-post market return our full sample covers the period between 1982 and To facilitate meaningful estimates from the Ohlson and Juettner-Nauroth (2005) (OJ hereafter) or abnormal earnings growth model, we eliminate firm-year observations with negative earnings per share estimates. Likewise, we eliminate some observations for which the numerical solutions for the Gebhardt et al (2001) and Claus and Thomas (2001) (GLS and CT respectively hereafter) specifications of the residual income valuation model do not converge to valid estimates. We furthermore sacrifice three years of observations in the interest of adjusting implied cost of capital for predictable analyst errors. Finally, we remove observations with extreme values of prices (P0 <0.5 or P0 >500). 6 This is the converse of the case considered in footnote 4. Specifically, based on equation (10), if the realised excess market return deviates significantly from λ over time and market news represented by ( λ t+1 1) π λ t is completely reflected in cash flow and discount rate news, the mean time-series coefficient for market news λ adjusted ICC (equal to the time series mean of ) will be volatile and may be significantly different from 1. λ t+1 The coefficient for the ICC without market news adjustment in this case, on the other hand, will be exactly 1 in all years. 12

15 4.2 Implied cost of capital metrics Following the extant literature we deduce implied cost of capital estimates by employing variants of the residual income valuation (RIV) model and the abnormal earnings growth (AEG) model. While both RIV and AEG models are economically equivalent to the dividend discount model, these models present the advantage of utilizing more reliable input in the form of book values and/or analysts earnings forecasts. In total, we compute four alternative implied cost of capital estimates based on the GLS specification of the RIV model, the CT specification of the RIV model, the OJ model as implemented by Mohanram and Gode (2013), and the PEG specification of the AEG model from Easton (2004) Implied cost of equity capital based on GLS P t = y t + As in Ohlson (1995), we reformulate the basic dividend discount valuation to: τ=1 R τ α (x t+τ ), where R equals 1+cost of capital, y t is the book value of equity, x t is the value of accounting earnings, and x t α = x t (R 1)y t 1 is the value of residual earnings. The implementation of the model requires assumptions regarding future earnings, dividends and book values as well as an appropriate terminal value. We directly apply the consensus (median) analysts earnings per share forecasts (hence forth eps t) to obtain eps 1 and eps 2. To estimate expected book values of equity we begin with the beginning of year book value per share (BV 0) and progressively apply the clean surplus relation (y t = y t 1 + x t d t ) to obtain BV 1-BV 2. In doing so we assume a constant dividend payout rate from year 1 to perpetuity set equal to the latest, historical payout rate. In addition: the payout rate is bounded between 0 and 1, and, payout rates that are greater than 0.5 and less than 1 are circumvented to 0.5. We then combine earnings per share and book values per share expectations to obtain return on equity (ROE) forecasts for the future two years. We thereon assume that ROE converges to the industry median by year 12. We assign each firm according to Fama French (2007) 48 industry classification and estimate the long run ROE as the 10 year historical moving median of all companies listed in the designated industry. 7 ROE estimates for years 3 to 12 are taken through linear interpolation between year 2 ROE and the industry long run ROE median anchored at year 12. A 7 We include inactive companies to mitigate survivorship bias. 13

16 terminal value based on the industry ROE of the last year completes the valuation. There are is no closed form solution to obtain implied cost of capital estimates under the current implementations of the residual income model (a 12th-degree polynomial). We thus obtain numerical solutions with errors less than or equal to 10 (-10) (maximum 50 Newton iterations) Implied cost of equity capital based on CT In this implementation we similarly apply the consensus (median) analysts earnings per share forecasts to obtain eps 1 and eps 2 and then use the analysts long term growth prediction (hence forth ltg) to estimate eps 3-eps 5. When the ltg estimate is not available this variable is set equal to the industry median. A terminal value is obtained by assuming that all future earnings grow at the rate of inflation set equal to the long term risk free rate (10 year government bond) minus 3% (r f-3%) Implied cost of equity capital based on the OJ model The abnormal earnings growth model or OJ model expresses the value of a firm's stock as a function of the cost of capital, expected earnings, and long term earnings asymptotic growth. The functional form of the model is given by: P 0 = eps 1 r [1 + g 2 R γ ] where g 2 = [%Δ eps 2 + r dps 1 eps 1 ] r, R equals 1+the cost of capital, r is the cost of capital and γ is the long term asymptotic growth rate. Rearranging for r one obtains: r = Α + Α 2 + eps 1 P 0 (g (γ 1)) where A = 1 {(γ 1) + dps 1 }, γ is the long term asymptotic earnings growth rate and g is the short 2 P 0 term earnings growth rate. Following the assumptions made in Mohanram and Gode (2013) we equate the short term rate with the geometric mean of the two year growth in earnings per share (eps 2/eps 1-1) and the long term growth rate (ltg). Where the short term growth is lower than ltg, the short term growth rate is set equal to ltg. Furthermore, as in the RIV models dps 1 is set equal to the latest historical dividend payout while the asymptotic growth rate (γ-1) equals rf-3%. 14

17 4.2.4 Implied cost of equity capital based on PEG ratio Setting the asymptotic growth rate equal to zero, such as (γ-1 = 0), and assuming a zero dividend payout rate the OJ model simplifies to: r = (eps 2 eps 1 )/P 0,or equivalently to r = ( eps 1 ) g, P where g is the short term earnings growth rate. The assumption that (γ-1 = 0) corresponds to a special case of the OJ model where the expected abnormal earnings growth between year 1 and year 2 is an unbiased estimate of expected abnormal earning growth in all subsequent periods (Easton (2004)). Following the assumptions made in the full OJ model we set g equal to the average of the two year growth in earnings per share (eps 2/eps 1-1) and the long term growth rate (ltg) when the two year growth in earnings is greater than ltg, or equal to ltg when the two year growth rate is less than ltg. 4.3 Adjusting implied cost of capital for predictable analyst errors Implied cost of capital estimates are calculated using analysts forecasts under the assumption that these forecasts are in line with the market s earnings expectations. Nevertheless analysts forecasts are subject to well documented biases including optimism (O Brien (1998)) and sluggishness (Guay et al (2011)). Deviations between analysts forecasts and market expectations embedded in implied cost of capital estimates are likely to impair the return predictability of these estimates. On the other hand, accounting for expected bias should mitigate the mismatch between earnings forecasts and market prices thus improving the implied cost of capital estimates. A number of research papers including Guay et al (2011) and Hughes et al (2008) construct multivariate models to predict analyst errors using contemporary and/or historical variables. In a more recent development, Larocque (2013) models analyst expected error as a function of lagged error, abnormal stock return, market value and a control for measurement error, and finds that that erroradjusted forecasts are improved estimates of market s earnings expectations. To that end we opt to replicate the Larocque (2013) model. The description of the model and estimated coefficients can be found in Appendix B. To construct an out-of-sample test, we run 3-year rolling regressions of the multivariate forecasting model and apply the coefficients of each regression to the subsequent year's realizations of the corresponding explanatory variables to get predicted values of analysts expected forecasting errors. 15

18 Finally, we correct the analyst earnings forecasts by subtracting the estimated values of expected forecasting errors from the original values of these forecasts. Using the corrected earnings we repeat the estimation procedure of alternative implied cost of capital specifications thus obtaining a set of adjusted ICC estimates. 4.4 Empirical regression models Cross-sectional analysis of relationship between realised returns and ICC metrics Our main empirical analysis is based on cross-sectional estimation of regression models developed from our analytical framework. In addition, however, we also provide some time-series tests of mean reversion in our ICC estimates Based on equations (10) and (11), the main empirical regression model for examining the explanatory power of alternative ICC metrics for stock returns is as follows: RET i,t+1 = α 0 + α 1 MIRP i,t + α 2 CNEWS i,t+1 + α 3 DNEWS i,t+1 + α 4 GRLVG i,t. +ε i,t+1 (12) where: RET i,t+1 is the excess realised return for firm i over the risk-free rate during year t+1; MIRP i,t = IRP i,t MNEWS t+1 where: IRP i,t ICC i,t r ft is the implied risk premium for firm i at the end of year t based on the difference between estimated implied cost of capital, ICC i,t, and the 10 year US Treasury bond rate, r ft, at that date; MNEWS t+1 is the market news adjustment estimated as the ratio of the excess realised market returns over the risk-free rate to the market equity risk premium (assumed to be 6% in most of our analysis); CNEWS i,t+1 is cash flow news at date t+1 using the method employed by Easton and Monahan (2005); 8 8 CNEWS is measured using a similar approach to Easton and Monahan (2005) and Mohanram and Gode (2013) as follows: ρ CNEWS i,t+1 = {roe it+1 froe it+1,t+1 )} + {froe it+1,t+1 froe it,t+1 } + (1 ρω t ) {froe it+1,t+2 froe it,t+2 } where froe ij,k is the forecasted return on equity of firm i, for the fiscal year k, based on the consensus earnings forecast released in year j. As such the first term of CNEWS represents the realized forecast error on the eps forecast made at the end of fiscal year t+1 (scaled by beginning book value per share), the second term represents the forecast revision between the time of the estimation of implied cost of capital until the end of the fiscal year, and the third term represents the revision in the two-year forecasted return on equity adjusted by a capitalization factor equal to ρ/(1- ρ *ω t). Estimates of ρ are taken from Easton and Monahan (2005) and vary between and across five quintiles based on dividend to price ratios. The term ω t captures time series persistence in ROE and is estimated through a pooled rolling regression for each of the 48 Fama and French (1997) industries using 10 years of lagged data, such as: roe i,t τ = ω 0 + ω t roe i,t τ 1, where τ takes the values between 0 and 16

19 DNEWS i,t+1 ρ(irp i,t+1 IRP i,t) is the estimated discount rate news measured for firm i for year t+1, where ρ is an estimate of the Vuolteenaho (2002) capitalisation factor as estimated by Easton and Monahan (2005); GRLVG i,t = GR i,t LVG i,t where: LVG i,t 1 + D i,t E i,t where D i,t is the estimated market value of debt and E i,t is the estimated market value of equity for firm i as at the end of year t; GR i,t is equal to one plus the growth rate for firm i as estimated at the end of year t where the growth rate varies according to the ICC metric under consideration. For GLS it is based on the 10-year industry ROE median, for CT it is based on the inflation adjusted long-term risk free rate, and for OJ and PEG models it is based on the average of short term growth rate (eps 2/ eps 1-1) and long term rate (ltg) earnings growth rate when (eps 2/ eps 1-1) is greater than ltg, or equal to ltg when (eps 2/ eps 1-1) is less than ltg. While the rationale for including MIRP i,t, CNEWS i,t+1, and DNEWS i,t+1 follows directly from our analysis in section 3, the inclusion of GRLVG i,t requires some explanation. Also the calculation of DNEWS i,t+1 differs from that in previous research and requires some further explanation. The rationale for including GRLVG i,t is based on the Hughes et al (2009) analysis of factors which cause the ICC to be a biased indicator of next period expected stock returns. As indicated in our analysis summarised in equations (10) and (11) in section 3, the intercept term captures average bias, while the disturbance term υ it+1 includes the effect of firm-specific bias represented by θ it+1, and θ it+2 (see earlier discussion in footnote 3). The analysis of Hughes et al (2009) and Lambert (2009) suggest that the downward bias in ICC will be positively related to volatility of cash flows and expected returns and that this bias will be amplified for firms with higher growth and higher leverage. We therefore include GRLVG i,t in equation (12) to provide an additional control for the bias of (even accurate) ICC estimates as indicators of expected returns. The definition of DNEWS i,t+1 ρ(irp i,t+1 IRP i,t), where ρ is an estimate of the Vuolteenaho (2002) capitalisation factor as estimated by Easton and Monahan (2005), differs from the definition used by Easton and Monahan (2005) and Gode and Mohanram (2013) due to our assumption that expected returns follow a mean-reverting process as in Hughes et al (2009) (see our equation (3) 9. CNEWS is a firm-specific, model independent variable which varies across firm-year observations but remains constant across alternative ICC models. 17

20 and its use to obtain equation (7)). The alternative assumption made by Easton and Monahan (2005) and Gode and Mohanram (2013) is that expected returns follow a random walk with ρ/(ρ 1) (rather than simply ρ) used to determine DNEWS i,t+1. As reported in section (5), our assumption of mean reversion appears to result in a more reasonable coefficient for DNEWS closer to the theoretical benchmark of 1. In our empirical analysis reported in section (5), we estimate equation (12) cross-sectionally for each year over our 32 year sample period and calculate Fama-MacBeth (1973) t-tests on the annual mean coefficents with Newey-West (1987) autocorrelation adjusted standard errors. For comparative purposes, we also estimate a regression of the form of equation (12) but with IRP i,t in place of MIRP i,t. In addition, we estimate some additional regressions where CNEWS i,t+1, DNEWS i,t+1, and GRLVG i,t are excluded in order to determine the importance of these variables as explanatory variables for stock returns. If our analysis represented by equation (11) is correct and CNEWS i,t+1 and DNEWS i,t+1 do not adequately capture MNEWS t+1, we expect α 1, α 2, and α 3 to equal approximately 1. Given Hughes et al (2009) suggest that the average excess of expected returns and implied cost of capital may be of the order of 2.3% for plausible volatility assumptions, we also expect α 0 > 0. Finally, given that our GRLVG i,t variable has an overall mean over all ICC metrics of about 2.0, and assuming an average impact of this ICC bias variable of say 1% to 2% (or 0.01 to 0.02), one might expect a positive coefficient for α 4 of the order of to While the precise magnitude of α 4 cannot be readily predicted, we clearly expect it to be positive and statistically significant but of much smaller magnitude in comparison to α 1, α 2, and α Time series analysis of ICC mean reversion and association with realised returns In addition to our cross-sectional analysis, we run firm-by-firm time series tests on mean reversion in our implied cost of capital estimates to provide further evidence on our previous assumption that ICC reverts immediately to its long-run mean. We also run further time-series tests of the association between realised returns and estimated ICC to check for consistency with our main crosssectional results. The time-series models we run are summarised below, a more detailed rationale for the proposed models is provided in Appendix C. 18

21 To test for mean reversion, we estimate the following simple AR1 model for each firm / ICC time-series where the number of consecutive ICC estimates is at least 20 years: ICC t+1 = a 0 + a 1 ICC t + e t+1 (13) where, assuming a 0 > 0 and 0 a 1 < 1, the long-run mean ICC estimate is given by a 0 (1 a 1 ). As discussed in Appendix C, our analysis suggests that it is likely that the residuals in equation (13) will serially correlated. For this reason, we estimate equation (13) using maximum likelihood rather than OLS. For approximate consistency with our calculation of DNEWS in equation (12), we expect a 1 to be close to 0, thereby indicating rapid mean reversion of the ICC (and the underlying expected returns). As discussed further in Appendix C, our analytical framework in section 3 also suggests the following time-series estimation of the relationship between excess realised stock returns and the market news adjusted implied return risk premium for each firm / ICC time series: RET t+1 = b 0 + b 1 MIRP t +e t+1 (14) where b 1 is expected to equal 1 and b 0 is expected to equal 0 for the special case where the ICC measures next period expected returns without error i.e, where π t = μ t t+1 in terms of our analytical framework. Given our argument in section 3.4 based on Hughes et al (2009) that in general π t < μ t t+1, we show in Appendix C that it is likely that b 1 in equation (14) will be biased above 1 and that b 0 will be positive, reflecting the average downward bias of the ICC as an estimator of the expected stock return. 5. Empirical results 5.1 Descriptive statistics for model variables Table 1 Panel A provides descriptive statistics for key variables used to estimate ICC metrics. Mean price and book value per share figures for our sample imply an average price to book ratio above 2.0, while the average industry median ROE (based on the 48 industries in Fama and French (1997)) for our sample period is 14%. Mean short term forecast eps growth is 59% but this is inflated by some large positive figures, suggesting that the median figure of 19% is a more representative summary statistic. The mean long-term earnings forecast growth of 15% is close to the median of 14% indicating no undue influence of extreme values on this figure. Indeed, as expected, the standard deviation 10% 19

22 implies a moderate spread of long-term eps growth forecasts, in marked contrast to the distribution of short-term growth rates. Table 1 Panel B provides summary statistics for estimated implied risk premia for the four alternative ICC metrics used in the study. The OJ model provides the highest mean and median implied risk premia estimates consistent with higher long-run earnings growth for this model. The residual income based models, GLS and CT, have the lowest median implied risk premia reflecting lower long term growth compared with the abnormal earning growth based metrics (OJ and PEG). Overall, implied risk premia are somewhat low compared with previous research findings based on the equity risk premium (the median IRP varies between 3.15% for CT and 5.47% for OJ), possibly reflecting the tendency of the ICC approach to underestimate expected returns highlighted by Hughes et al (2009). Table 2 provides the correlation matrix between implied risk premia based on our four ICC metrics. In general, these are statistically significant at the 1% for all years for all metrics with the exception of one year in the case of CT metric. There are, however, clear differences between the metric, the Pearson correlation coefficient exceeding 0.60 only for association between the OJ and PEG metrics. The correlation for the latter of 0.94 is unsurprising given that the PEG model is a special case of the more OJ abnormal earnings growth model. It would seem that the common short-term growth rate used in PEG and OJ estimates of the ICC drive this high pairwise correlation and that the substantially higher median and mean implied risk premium for the OJ model is due to long-term growth assumed in the latter. Finally, Table 3 provides descriptive statistics for all variables used in the estimation of equation (12). The table indicates that controlling for predictable analyst forecast error using the Larocque (2013) methodology results in substantially lower estimated risk premiums, consistent broadly with analyst optimism. In relation to the news variables included in our main empirical analysis, CNEWS is on average only 0.34% but has a substantial standard deviation of 8.65%, while DNEWS for all four metrics is on average close to zero with a standard deviation ranging between 1.47% for GLS and 7.55% for CT. The variation in CNEWS and to a lesser degree DNEWS is therefore consistent with volatile stock returns which deviate substantially from expected returns. The MNEWS variable has a mean of 0.94 and median of 1.53 indicating a tendency for market returns to exceed our expected market 20

23 risk premium of 6% in most years but for large negative market returns to pull the mean market return close to the assumed expected market risk premium. The substantial number of negative values for MNEWS (the 25 th percentile is negative) highlights the problem of an expected negative association between implied risk premium estimates and realised excess stock returns in several years and hence the potential usefulness of using MIRP in place of IRP in empirical tests of the association between stock returns and ICC metrics. 5.2 Cross-sectional findings for implied risk premiums excluding market news adjustment Table 4 provides regression results for the explanatory power of implied risk premiums for excess realised stock returns without an adjustment for market news. Panel A reports results based on estimation of the ICC metrics using analysts earnings forecasts unadjusted for error and Panel B reports results based on ICC metrics estimated using error-corrected analyst earnings forecasts. The univariate results based on IRP reported in Panel A have very low R 2 and counterintuitively negative slope coefficients. Addition of CNEWS and DNEWS variables greatly improves explanatory power and all coefficients for these news variables are significantly positive at the 1% level for all four ICC metrics. The improved explanatory power of the GLS based model is particularly strong, the adjusted R 2 increasing from 1.80% for the univariate model to 10.42% for the models with the additional news variable. However, for all ICC metrics, the coefficient for IRP is remains negative. Panel B of Table 4 shows a major improvement in the performance of the IRP variable when it is based on ICC estimated using Larocque (2013) error-corrected analyst earnings forecasts. Similar to results reported by Mohanram and Gode (2013) based on the Hughes et al (2008) error adjustment procedure, the analyst error adjustment leads to highly significant positive coefficients for IRP in GLS, OJ, and PEG univariate regressions which are in excess of 1 (the IRP coefficient however remains significantly negative for the CT regression). Inclusion of CNEWS and DNEWS variables adds further to the explanatory power of the regression models, adjusted R 2 increasing to 10% or above for GLS, OJ, and PEG based metrics. There are also substantial reductions in estimated coefficients for IRP, although these remain significantly above the theoretical value of 1 (1.40 for GLS and 1.55 and 1.91 respectively for OJ and PEG metrics). Interestingly, the coefficient for DNEWS based on our assumption of mean reversion in expected returns is consistently positive in regressions for all metrics 21

24 and is relatively close to the benchmark of 1, most notably for GLS. In summary, the results in Table 4 confirm previous findings of improvements in the explanatory power of ICC for realised stock returns when ICC estimates are adjusted for analyst forecast error and when cash flow and discount rate news variables are included in the regression model. Table 5 provides further evidence on the positive association of ICC estimates with realised stock returns using a portfolio based methodology employed by Hou et al (2012). More specifically, Table 5 provides strong support for the hypothesis that a portfolio of the top IRP decile of stocks have significantly higher one-year ahead realised returns than a portfolio of the bottom IRP decile of stocks for all four ICC metrics. These results, based on analyst error-corrected ICC estimates, are in contrast to the results reported by Hou et al (2012) for an average of unadjusted analyst earnings forecast based ICC estimates where there was no statistically significant difference between top and bottom decile portfolio returns. The results reported in Table 5 therefore reinforce the regression results in Table 4 Panel B highlighting the important contribution of analyst error correction to establishing the validity of ICC estimates. 5.3 Cross-sectional findings for market news adjusted implied risk premiums Table 6 provides regression results for the explanatory power of implied risk premiums for realised stock returns when the implied risk premium is adjusted for market news i.e., when the variable MIRP is used in place of IRP. In addition, the growth / leverage variable GRLVG, intended to capture the impact of variation in the bias of ICC as an estimator for expected returns as highlighted in Hughes et al (2009), is also included in the full model results (based on equation (12)). As previously, Panel A reports results based on estimation of the ICC metrics using analysts earnings forecasts unadjusted for error and Panel B reports results based on ICC metrics estimated using the Larocque (2013) errorcorrected analyst earnings forecasts. In addition Results reported in Panel A of Table 6 indicate that the coefficient for MIRP is positive in a simple univariate regression model and is statistically significant at the 10% level for GLS and PEG metrics. The addition of CNEWS and DNEWS variables results in additional explanatory power together with statistically significant positive coefficients for MIRP for all metrics at the 5% level or better. 22

25 However, the results in Panel A based on unadjusted analyst earnings forecasts fall well short of the benchmark coefficient of 1 for MIRP and the GRLVG is statistically insignificant in all regressions. Panel B of Table 6 indicates that analyst error correction in the estimation of ICC metrics combines with the market news adjustment of the implied risk premium to generate results where coefficients for MIRP, CNEWS and DNEWS coefficients are generally closest to the benchmark of 1 (only for DNEWS is the null hypothesis that the coefficient equals 1 widely rejected) and the coefficient for GRLVG is positive as expected and statistically significant at the 5% level or better for CT, OJ and PEG metrics. Focusing on the results for the full model represented by equation (12), GLS, CT, OJ, and PEG coefficients for MIRP are 1.14, 0.63, 1.07, and 0.82 respectively, all of which are significantly positive at the 1% level and, with just the exception of the CT model, insignificantly different from the benchmark of 1. Furthermore, for all metrics, the coefficient for CNEWS is significant at the 1% level and generally close to the benchmark of 1. DNEWS coefficients vary across metrics but are significantly positive in all cases (although below 1 for OJ, PEG, and CT models and above 1 for GLS). Finally, the GRLVG variable is significant and positive for all metrics except GLS and of a reasonable magnitude in relation to expectations discussed in section 4. Given that GRLVG should capture cross-sectional variation in the bias of the IRP as an estimate of true expected returns and the intercept should capture common bias across all firms for a particular IRP, the significantly positive intercepts for GLS and PEG regressions and significantly positive GRLVG coefficients for CT, OJ, and PEG regressions in Panel B of Table 6 are consistent with the Hughes et al (2009) hypothesis that ICC estimates are downwardly biased estimates of the true expected return. The results for all four ICC metrics in Panel B of Table 6 are broadly consistent with equation (11) in our analytical framework. In other words, our results support the assumption that CNEWS and DNEWS estimated using the methods described in section 4.3 of this paper provide useful firm-specific news but do not fully capture market news. With market news adjustment of implied risk premia, results are close to theoretical expectations for these three metrics. Which metric performs best according to our analysis? It could be argued that the OJ model performs best in terms of a small and statistically insignificant intercept together with highly significant MIRP and CNEWS coefficients very close to the theoretical ideal of 1. The GLS regression, on the other hand, has the highest average adjusted R 2 and 23

26 a MIRP coefficient that is also not significantly different from 1, suggesting that the GLS metric has a similarly meaningful association with stock returns to the OJ metric. The PEG model association with realised returns is similar in many respects to OJ model but is a little weaker in terms of explanatory power and proximity of coefficients to theoretical expectations. The CT model has coefficients of correct sign but there is some statistical evidence that the MIRP coefficient is less than 1 counter to expectations and its explanatory power is slightly weaker than the other models. Finally, as discussed in Appendix A(iii), it is useful to consider the effect of excluding any possible impact of market news on our measure of cash flow news. Results from estimating our full model given by equation (12) where CNEWS is replaced with an alternative cash flow news variable, CNEWS*, which has been orthogonalied with respect to market news are reported in Panel C of Table 6. For all metrics, the removal of the market news impact on cash flow news leads to increased average adjusted R 2, most notably increasing from 12.61% (in Panel B) to 20.47% for the case of the OJ model. Furthermore, for GLS, OJ, and PEG, the positive coefficient for MIRP is highly statistically significant and remains statistically indistinguishable from its theoretical value of 1 at the 10% level and above. While the coefficient for CNEWS* is substantially higher than that for CNEWS (in Panel B) and is greater than 1 at the 1% level, the coefficients for DNEWS and GRLVG strengthen slightly compared with the previous results based on unadjusted CNEWS. Taking the results reported in Panels B and C of Table 6 together, we conclude that there is some evidence that market news impacts on CNEWS and that excluding this impact from cash flow news leads to a stronger association between realised returns and implied cost of capital metrics. In relation to the relative performance of the ICC metrics, the results in Panel C of Table 6 confirm the previous results in Panel B that the OJ and GLS metrics are most closely associated with realised stock returns. 5.4 Mean reversion of ICC estimates and time-series findings for market news adjusted implied risk premiums As discussed in section and Appendix C, we carry out additional firm-by-firm time series tests of mean reversion in ICC estimates in order to provide evidence on the accuracy of the Hughes et al (2009) assumption that expected rates of return and related ICC estimates are mean-reverting. In addition, we also provide results on firm-by-firm time series test of the contemporaneous relationship 24

27 between excess realised returns and estimates of the market news adjusted implied risk premium which broadly corroborate our previous cross-sectional findings on the robust relationship between ICC metrics and realised returns. Results on mean reversion of our ICC estimates are summarised in Table 7 and Figure 1 and provide broad support for our approach to measuring DNEWS based on the assumption of mean reversion. Panel A of Table 7 indicates that the mean intercept from estimating equation (13) for our sample of 1,133 firms with 10 or more annual observations lies in the range of 0.06 to 0.08 and that individual firm intercepts for all ICC metrics are generally highly statistically significant as evidenced by the very large proportion of statistically significant positive intercepts (based on a 1% level binomial test, the requirement for rejection of the null hypothesis of a zero average intercept is 137 significantly positive intercepts at the 10% level out of 1,133 which is clearly much less than actual figures ranging from 888 for the CT model to 982 for the OJ model). Rapid mean reversion of all ICC metrics to a longrun average is supported by low but statistically significant mean slope coefficents which range between 0.05 for PEG and OJ models to 0.14 for the CT model. The estimated mean long-run ICC for all metrics is therefore only slightly above the mean intercepts and ranges from 7% for the CT model to 9% for the OJ model. Furthermore, as shown in Panel B of Table 7 and in Figure 1, the overall cross-firm distribution of the long-run average ICC for all metrics is very similar and relatively symmetric, with a range of 6% to 7% between the 5 th percentile firm and the 95 th percentile firm for all metrics. Finally, our expectation that the intercept from an AR1 regression based on the ICC is a downwardly biased estimate of the intercept from an AR1 regression based on the true expected return (as indicated by the intercepts in equations (C2) and (C4) in Appendix C when φ 3 < 0) suggests that the long-run expected return is likely to be in a range somewhat above the long-run ICC range of 7% to 9% shown in Table 7. For example, if the OJ model provides an accurate measure of the ICC, the long-run average ICC of 9% may imply a long-run expected rate of return of 10% or above. As an alternative time-series perspective on the relationship between ICC estimates and realised stock returns, we provide evidence from firm-by-firm time series regressions of realised excess returns on IRP and MIRP variables in Panels A and B of Table 8. Broadly consistent with the cross-sectional results shown in Panel B of Table 4, the results in Panel A of Table 8 provide support for a positive 25

28 association between realised returns and IRP for the GLS, OJ, and PEG metrics. Thus, for these metrics, the mean slope coefficient is equal to 1.87 for PEG, 2.24 for OJ, and 2.60 for GLS and the number of positive statistically significant coefficients at the 10% level equal to 239 for PEG, 286 for OJ and 285 for GLS substantially exceed that expected by chance at the 1% level according to a binomial test. The mean coefficients for these models are, however, substantially greater than the theoretical expectation of 1 and the number of intercepts significantly different from zero is greater than expected by chance. There is also evidence that the number of slope coefficients out of all 1,133 firms which significantly deviate from the expected value of 1 is greater than expected by chance. Panel B of Table 8 provides evidence on the impact of using market news adjusted implied risk premiums in our time-series regressions which is broadly consistent with the analytical framework in section 3 and further analysis in Appendix C. As expected, and consistent with the previous analysis of Pettingill et al (1995), the use of MIRP in place of IRP as the explanatory variable for realised returns leads to substantially improved results. Most notably, mean/median slope coefficients are close to 1 for GLS (0.83/0.84), OJ (0.95/0.84), and PEG (0.84/0.85) and the number of positive coefficients at the 10% level for these metrics (534, 605, and 509 for GLS, OJ, and PEG respectively) greatly exceeds the binomial test cut-off of 137 at the 1% level. However, despite the close proximity of mean and median slope coefficients to 1, the number of coefficients for which it is possible to reject the null hypothesis of 1 at the 10% level is substantially greater than the 1% binomial test cut-off of 137 (i.e., 216, 209, and 206 for GLS, OJ, and PEG respectively), thus providing evidence of a small but statistically significant deviation of the slope coefficient from 1. Consistent with our expectation of downward average bias in the ICC as an estimate of expected stock returns, mean intercepts are positive and statistically significant in terms of the number of observed positive estimates exceeding the 1% binomial test cut-off for all metrics. Finally, as in our cross-sectional results, OJ, GLS, and PEG metrics are superior to the CT model in terms of overall association with stock returns, with the OJ and GLS metrics performing slightly more strongly than the PEG model both in terms of the number of sample firms showing the expected positive association with realised returns and in terms of mean adjusted R 2 across firm-level regressions. 26

29 Overall, our time-series results corroborate our previous cross-sectional results that for all ICC metrics there is a highly significant positive association between realised stock returns and MIRP and that in the case of OJ, GLS, and PEG the estimated slope coefficient is close to the predicted value of 1. Estimation of firm AR1 time-series models for all metrics also strongly supports our theoretical assumption of rapid mean reversion in the ICC (and hence expected returns) towards a long-term average of similar magnitude for all metrics (in the 7-9% range based on the means across our sample of 1,133 firms). Interestingly, the means of the long-run average firm ICC estimates in Panel A of Table 7 are broadly in line with (but slightly lower than) the means of the annual average IRP estimates reported in the final row of Panel B of Table 1 based on a long-run average risk-free rate of 4%. 5.5 Summary of relationship to previous research findings Our findings extend previous findings by Mohanram and Gode (2013) which highlighted the usefulness of removing predictable analyst forecast errors on the explanatory power of ICC metrics for realised returns. Specifically, we show how an alternative adjustment procedure based on Laroque (2013) has a similarly significant impact on this relationship, our results in Table 4 Panel B indicating that application of this procedure to our dataset generates IRP, CNEWS and DNEWS coefficients substantially closer to theoretical expectation of 1 than in Mohanram and Gode (2013), with the notable exception of the CT metric (see their Table 8 Panel B). The use of an alternative DNEWS measure based on the Hughes et al (2009) assumption of mean-reverting expected returns also contributes to DNEWS coefficients much closer to the theoretical ideal of 1 in comparison to the previous findings in Mohanram and Gode (2013), where some such coefficients were even perversely negative. The market news adjustment of IRP estimates and the addition of an ICC bias variable GRLVG, also motivated by the analysis of Hughes et al (2009), generates theoretically plausible coefficients for MIRP and news variables in Table 6 Panels B and C for all ICC metrics. The proximity of MIRP coefficients to 1 is comparable to the previous findings of Botosan et al (2011) but is achieved using a more parsimonious model which reflects our focus on evaluating ICC metrics. More specifically, the use of the change in analysts target prices and other information including the change in beta over the return interval by Botosan et al (2013) raises issues regarding the extent of the role of the ICC in driving their regression results. Our adoption of the Easton and Monahan (2005) and Gode and Mohanram 27

30 (2013) approach to estimating CNEWS and DNEWS provides a more focused analysis of the importance of ICC estimates in explaining realised returns because (i) DNEWS is based directly on the relevant ICC metric and (ii) CNEWS is simply a common control variable used in all regressions based on an ROE forecast model which is not directly affected by actual changes in the stock price of firms over the return interval. Our cross-sectional analysis combining a particular IRP measure with the related DNEWS variable based on the change in the IRP therefore provides a more complete representation of the role of the given metric per se in explaining realised returns. 9 Finally, we extend previous research on the implied cost of capital by providing additional firmbased time-series results on the association between realised stock returns and the implied cost of capital. Our results show that after adjusting ICC estimates for realised market returns in the spirit of Pettengill et al s (1995) empirical analysis of the CAPM, there is a robust positive association between stock returns and ICC metrics with slope coefficients for OJ, GLS, and PEG close to (but on average slightly less than) the expected value of 1. We interpret these results as providing strong corroboration of our previous cross-sectional results on the relevance of ICC estimates for explaining realised stock returns. 6. Conclusion This paper provides a framework for analysing the relationship between realised stock returns and the implied cost of capital which integrates insights from previous research by Pettengill et al (1995), Hughes et al (2009), Vuolteenaho (2002), and Easton and Monahan (2005). This framework suggests that interacting the firm s implied risk premium with market news (represented by realised excess market returns over the risk-free rate scaled by the market risk premium) in a regression model for stock returns which also includes cash flow news and discount rate news variables may lead to results more consistent with theoretical expectations. Specifically, if cash flow news and discount rate 9 The average adjusted R-squared reported for our full model reported in Table 6 Panels B and C is in the 10%- 20% range. Results reported in Botosan et al s (2013) Table 6 (p.1108) are typically in the 25%-30% range. However, as can be seen from comparing the results for their model 1 which excludes the ICC metric (i.e., only contains other information) with their model 2 results which includes an ICC metric, the incremental role of the ICC metrics are generally small in their study. For example, while the average R-squared for their model 1 excluding ICC is 25.9%, this rises only modestly to 27.3% when the OJ metric is added and to 28.0% for the GLS metric. 28

31 news exclude (or only imperfectly reflect) market news, our framework suggests that market news adjusted ICC estimates, along with cash flow news and discount rate news, will be required to jointly explain stock returns. The likely bias of the implied cost of capital as a measure of expected stock returns identified in previous research is also incorporated into the framework via inclusion of a further variable based on the interaction of expected earnings growth and financial leverage. Empirical results reported in the paper provide substantial support for the relevance of the proposed analytical framework and also highlight the importance of controlling for predictable analyst forecast error when estimating the ICC. Cross-sectional results indicate that market news adjusted implied risk premiums for three of our four ICC metrics based on earnings forecasts adjusted for predictable analyst errors are positively related to stock returns with coefficients statistically indistinguishable from unity as predicted by theory (estimated coefficients for CNEWS and DNEWS variables are also strongly positive, the former generally statistically indistinguishable from 1 as suggested by theory, the latter generally somewhat less than 1). Positive mean intercepts together with a positive coefficient for our growth leverage interaction variable provide also support to our hypothesis that the ICC is a downwardly biased estimate of expected returns. In addition, firm-based time-series analysis strongly confirms the positive association between market news adjusted implied risk premiums and realised excess stock returns with mean slope coefficients only slightly less than unity and further supports our assumption of rapid mean reversion in firm based ICC estimates (and hence expected returns) over time. In summary, our paper contributes to the research literature by demonstrating conceptually and empirically the relevance of implied cost of capital metrics for explaining realised stock returns. Incorporating market news information into the analysis of the relationship between stock returns and ICC metrics based on analyst forecasts adjusted for predictable error yields results which are closely related to theoretical expectations. This in turn highlights the importance of ICC estimates based on residual income and abnormal earning growth models as inputs into assessments of a firm s required rate of return on investment. 29

32 Table 1: Summary statistics of implied risk premia metrics and relevant inputs PANEL A: Summary statistics for inputs to implied risk premia metrics Variable N Mean StdDev 25 th Pcl Median 75 th Pcl 95 th Pcl Price 45, BVPS 45, Payout 45, IROE 1, eps 1 45, eps 2 45, ltg (%) 45, stg (%) 45, γ-1 (%) 32 (Years) PANEL B: Summary statistics of implied risk premia metrics by year (%) GLS CT OJ PEG Year N Mean Median Mean Median Mean Median Mean Median , , , , , , , , , , , , , , , , , , , , , , All Years 45,

33 Notes: Panel A presents summary statistics for inputs to implied cost of capital estimation. Price is the stock price measured at the time of implied cost of capital estimation. BVPS is the beginning of year book value deflated by number of shares outstanding. Payout is the latest realized payout rate. Furthermore, the payout rate is bounded between 0 and 1, and, payout rates that are greater than 0.5 and less than 1 are circumvented to 0.5. IROE is the industry median rate of return across all 48 industries based on the Fama and French (1997) classification. eps 1 and eps 2 are analyst mean earnings per share forecasts for future years 1 and 2. ltg is the mean long term growth rate projected by analysts. stg is the short term earnings growth equal to (eps 2 - eps 1)/eps 1. γ -1 is long term asymptotic earnings growth rate. Panel B presents annual mean and median statistics of implied risk premia. GLS is the implied risk premium imputed from Gebhardt et al. s (2001) implementation of the residual income valuation model. CT is the implied risk premium imputed from Thomas s (2001) implementation of the residual income valuation model. OJ is the risk premium implied by the full Ohlson and Juettner-Nauroth (2003) model. PEG is the risk premium implied from the price to earnings growth ratio. The 10-year Treasury bill rate is subtracted from the ICC to obtain the implied risk premium. 31

34 Table 2: Correlation matrix of implied risk premium metrics GLS 1 CT OJ PEG GLS CT OJ PEG (31/1) (32/0) (32/0) (1,259) (1,259) (1,259) (32/0) 1 (32/0) (32/0) (1,259) (1,259) (1,259) (32/0) (32/0) 1 (32/0) (1,259) (1,259) (1,259) (32/0) (32/0) (32/0) (1,259) (1,259) (1,259) Notes: Results above the unit diagonal correspond to Pearson correlation coefficients. Results below the unit diagonal correspond to Spearman Rank non-parametric statistics. Correlations for each year in the period are calculated and the mean annual coefficient reported. The first parenthesis gives the number of years in which the correlation statistics is positive and statistically significant at 1% (significant/non-significant). The second parenthesis gives the median of the number of observations used in the calculation of the statistic. GLS is the implied risk premium imputed from Gebhardt et al. s (2001) implementation of the residual income valuation model. CT is the implied risk premium imputed from Thomas s (2001) implementation of the residual income valuation model. OJ is the risk premium implied by the full Ohlson and Juettner-Nauroth (2003) model. PEG is the risk premium implied from the price to earnings growth ratio. The 10-year Treasury bill rate is subtracted from the ICC to obtain the implied risk premium. 1 32

35 Table 3: Descriptive statistics of analysis variables Variable N Mean StdDev 25 th Pcl Median 75 th Pcl 95 th Pcl GLS 45, CT 45, OJ 45, PEG 45, A_GLS 34, A_CT 34, A_OJ 34, A_PEG 34, CNEWS DNEWS GLS 38, DNEWS CT 38, DNEWS OJ 38, DNEWS PEG 38, GRLVG GLS 44, GRLVG CT 44, GRLVG OJ 43, GRLVG PEG 43, R_RP 44, M_RP 32 (Years) MNEWS 32 (Years) Notes: All variable expressed as % except MNEWS and GRLVG variables (see definitions below). GLS is the implied risk premium imputed from Gebhardt et al. s (2001) implementation of the residual income valuation model. CT is the implied risk premium imputed from Thomas s (2001) implementation of the residual income valuation model. OJ is the risk premium implied by the full Ohlson and Juettner-Nauroth (2003) model. A_GLS, A_CT, A_OJ and A_PEG are the corresponding implied risk premium metrics after adjusting for analyst expected error. CNEWS is a measure of cash flow news as in Easton and Monahan (2005) and is estimated as CNEWS i,t+1 = (roe i,t+1 froe i,τ+1,t+1 ) + (froe i,τ+1,t+1 froe i,τ,t+1 ) + ρ (froe 1 ρω i,τ+1,t+2 froe i,τ,t+2 ) where froe i,j,k is the forecasted return on equity of t firm i, for the fiscal year k, based on the consensus earnings forecast released in year j. The first term of CNEWS represents the realized forecast error on the eps forecast made at the end of fiscal year t (scaled by beginning book value per share), the second term represents the forecast revision between the time of the estimation of implied cost of capital until the end of the fiscal year, and the third term represents the revision in the two-year forecasted return on equity adjusted by a capitalization factor equal to ρ/(1- ρ *ω t). Estimates of ρ are taken from Easton and Monahan (2005) and vary between and across five quintiles based on dividend to price ratios. The term ω t captures time series persistence in ROE and is estimated through a pooled rolling regression for each of the 48 Fama and French (1997) industries using 10 years of lagged data, such as : roe i,t τ = ω 0 + ω t roe i,t τ 1, where τ takes the values between 0 and 9. DNEWS is measure of discount rate news and is calculated as: DNEWS i,t+1 = ρ ( IRP i,t+1 IRP i,t) where IRP is the implied cost of capital metric and ρ is the coefficient as defined in CNEWS. GRLVG is an interactive term of growth x leverage. Growth corresponds to the earnings growth rate applied in estimation of implied cost of capital metrics as described in section 4 Leverage is defined as long term debt scaled by market value equity (stock price x number of shares outstanding). R_RP is the realized one-year forward stock return premium. M_RP is the realized one year forward market return premium. MNEWS is a measure of market-wide news and is estimated as the one-year ahead realized market risk premium scaled by the constant long-term expected risk premium (6%). The sample size varies according to data availability. 33

36 Table 4: Relation between implied risk premium metrics and future returns controlling for cash flow news and discount rate news Panel A: Implied risk premium metrics unadjusted for analyst forecast error Metric Intercept IRP CNEWS DNEWS Adj_R2 GLS 0.08 *** % (3.09) (-1.26) 0.09 *** ** *** % (3.47) (-2.77) (9.22) 0.10 *** *** 1.85 *** % (3.55) (-1.61) (4.21) (7.37) CT 0.08 *** * % (2.75) (-1.44) 0.08 *** *** *** % (3.12) (-3.01) (3.72) 0.09 *** * *** 0.22 *** % (3.81) (-1.90) (3.70) (3.40) OJ 0.11 *** ** % (-4.26) (-2.37) 0.11 *** *** *** % (4.18) (-3.34) (5.40) 0.12 *** ** *** 0.60 *** % (4.27) (-2.43) (3.72) (4.97) PEG 0.09 *** ** % (3.09) (-2.37) 0.09 *** *** *** % (3.82) (-3.61) (5.63) 0.10 *** ** *** 0.56 *** % (4.04) (-2.46) (3.74) (5.24) Panel B: Implied risk premium metrics adjusted for analyst forecast error Metric Intercept IRP CNEWS DNEWS Adj_R2 A_GLS *** % (0.44) (7.80) 0.06 ** 2.21 *** *** 9.37% (2.14) (5.04) (6.24) *** *** 1.16 *** 12.44% (0.74) (6.41) (5.40) (8.49) A_CT ** % (2.69) (-2.24) *** *** % (0.74) (-3.45) (4.91) 0.09*** *** 1.80 *** 5.93% (3.41) -(1.52) (5.11) (3.41) A_OJ *** % -(0.36) (8.61) *** *** % (-0.77) (8.50) (4.77) *** *** 0.45 *** % (0.78) (8.33) (5.36) (5.59) A_PEG *** % (0.95) (8.27) *** *** % (1.18) (8.00) (6.43) *** *** 0.46 *** % (1.32) (9.94) (5.14) (5.44) Notes: Table 4 presents regressions with RET i,t+1 as the dependent variable. RET i,t+1 is the 12 month buy and hold return following the estimation of date of implied risk premium metrics minus the risk free rate. IRP is the implied risk premium corresponding to a specific implied risk premium metric. The four implied risk premium metrics 34

37 used (GLS, CT, OJ, PEG) are defined in section 4. PANEL A presents results using implied risk premium metrics without adjustments for analyst expected error. CNEWS is a measure of cash flow news as in Easton and Monahan (2005) and is estimated as CNEWS i,t+1 = (roe i,t+1 froe i,τ+1,t+1 ) + (froe i,τ+1,t+1 froe i,τ,t+1 ) + ρ 1 ρω t (froe i,τ+1,t+2 froe i,τ,t+2 ) where froe i,j,k is the forecasted return on equity of firm i, for the fiscal year k, based on the consensus earnings forecast released in year j. The first term of CNEWS represents the realized forecast error on the eps forecast made at the end of fiscal year t (scaled by beginning book value per share), the second term represents the forecast revision between the time of the estimation of implied cost of capital until the end of the fiscal year, and the third term represents the revision in the two-year forecasted return on equity adjusted by a capitalization factor equal to ρ/(1- ρ *ω t). Estimates of ρ are taken from Easton and Monahan (2005) and vary between and across five quintiles based on dividend to price ratios. The term ω t captures time series persistence in ROE and is estimated through a pooled rolling regression for each of the 48 Fama and French (1997) industries using 10 years of lagged data, such as: roe i,t τ = ω 0 + ω t roe i,t τ 1, where τ takes the values between 0 and 9. DNEWS is measure of discount rate news and is calculated as: DNEWS i,t+1 = ρ ( IRP i,t+1 IRP i,t) where IRP is the implied cost of capital metric and ρ is the coefficient as defined in CNEWS. PANEL B presents multivariate regressions using implied risk premium metrics adjusted for analyst expected error. Mean coefficients for annual cross-sectional regressions are reported in all panels. T-statistics in parenthesis are based on Newey- West standard errors. *** (**)(*) denotes statistical significance at 1% (5%) (10%) for tests of coefficients different from zero. +++ ( ++ ) ( + ) denotes statistical significance at 1% (5%) (10%) for tests of coefficients different from one. 35

38 Table 5: Realized risk premia on ICC-premia sorted portfolios Panel A: Average value weighted realized risk premia based on ICC sorted deciles High - Low GLS *** (2.96) (6.77) (6.69) (6.71) (7.73) (8.39) (12.41) (14.63) (7.64) (18.37) (11.11) CT *** (8.80) (4.78) (4.05) (2.73) (6.93) (7.35) (10.77) (12.15) (12.29) (15.24) (4.94) OJ *** (2.90) (8.60) (2.58) (7.14) (6.24) (9.14) (9.96) (11.45) (15.33) (13.44) (6.86) PEG *** (5.06) (7.81) (3.58) (6.49) (5.71) (10.41) (9.66) (9.02) (17.28) (12.96) (5.03) Panel B: Median value weighted realized risk premia based on ICC sorted deciles High - Low GLS (2.96) (6.77) (6.69) (6.71) (7.73) (8.39) (12.41) (14.63) (7.64) (18.37) (4.68) CT (8.80) (4.78) (4.05) (2.73) (6.93) (7.35) (10.77) (12.15) (12.29) (15.24) (5.08) OJ (2.90) (8.60) (2.58) (7.14) (6.24) (9.14) (9.96) (11.45) (15.33) (13.44) (9.67) PEG (5.06) (7.81) (3.58) (6.49) (5.71) (10.41) (9.66) (9.02) (17.28) (12.96) (2.04) Notes: Table 5 Panel A (B) presents value weighted time-series averages (median) of 1-year realized risk premia on ICC sorted portfolios. For each year, 10 portfolios based on levels of alternative ICC estimates are generated. The four implied risk premium metrics used (GLS, CT, OJ, PEG) are defined in section 4. To obtain t+1 realized risk premia, monthly returns (minus the risk-free rate) for the 12 months following the ICC estimation date are compounded. Aggregate returns are weighted by market capitalization. Time-series mean (median) returns for each portfolio and corresponding t-statistic (in parentheses) are reported. The High minus Low portfolio returns are calculated as the difference between the value weighted return of the 10 th decile minus the value weighted return of the 1 st decile. *** denotes statistical significance at 1% for differences in means t-tests. ( ) denote statistical significance at 1% (5%) for the Wilcoxon-Mann-Whitney test of differences in medians. 36

39 Table 6: Relation between implied risk premium metrics and future returns controlling for market news, cash flow news, discount rate news and growth x leverage Panel A: Implied risk premium metrics unadjusted for analyst forecast error Metric Intercept MIRP CNEWS DNEWS GRLVG Adj_R2 GLS 0.07 *** 0.57 ** % (3.50) (2.69) 0.07 *** 0.53 ** *** % (3.07) (2.33) (6.42) 0.08 *** 0.33 * *** 1.78 *** % (3.96) (1.66) (5.25) (11.22) 0.05 ** 0.60 *** *** 1.84 *** % (2.11) (3.21) (5.33) (5.33) (1.17) CT 0.06 *** % (2.87) (1.30) 0.06 *** *** % (2.35) (1.34) (4.41) 0.07 *** 0.22 ** *** 0.25 ** % (2.88) (2.24) (5.49) (4.93) ** *** 0.25 *** % (1.39) (2.29) (5.53) (4.92) (1.33) OJ 0.09 *** % (4.09) (1.26) 0.09 *** *** % (3.67) (1.54) (3.67) 0.10 *** 0.29 ** *** 0.54 *** % (4.30) (2.36) (4.58) (7.05) 0.08 *** 0.31 ** *** 0.57 *** % (3.40) (2.48) (4.68) (7.68) (0.99) PEG 0.08 *** 0.22 * % (3.69) (1.84) 0.07 *** 0.29 * *** % (2.81) (1.75) (5.43) 0.08 *** 0.37 ** *** 0.56 *** % (4.63) (2.29) (4.63) (4.63) 0.06 *** 0.38 ** *** 0.54 *** % (2.82) (2.22) (4.70) (5.97) (1.52) Panel B: Implied risk premium metrics adjusted for analyst forecast error Metric Intercept MIRP CNEWS DNEWS GRLVG Adj_R 2 GLS ** % (1.57) (2.45) 0.09 *** 1.19 *** 1.36 *** 10.5% (6.22) (4.15) (6.22) 0.06 ** 1.52 *** 1.65 *** *** % (2.69) (3.60) (5.25) (6.91) 0.05 ** 1.14 *** 1.44 *** 1.26 *** % (2.07) (3.81) (5.39) (8.42) (-0.34) CT 0.07 *** % (2.83) (0.18) *** *** % (0.04) (2.80) (5.06) *** *** 0.01 *** % (1.44) (2.89) (6.30) (4.56) *** *** 0.20 *** ** 10.9% (-0.59) (2.95) (8.19) (4.28) (2.23) OJ *** 5.77% (1.50) (4.07) 37

40 0.05** 1.19 *** 0.49 *** % (2.32) (5.21) (5.66) 0.04 * 1.19 *** 1.04 *** 0.54 *** % (1.88) (4.42) (4.95) (5.75) *** 1.05 *** 0.58 *** ** 12.61% (1.38) (4.22) (4.79) (6.79) (2.54) PEG 0.05* 0.67 ** 5.14% (2.03) (2.71) 0.07** 1.38 *** 0.44 *** % (2.88) (5.03) (6.33) 0.06** 0.78 ** 1.07 *** 0.52 *** % (2.58) (2.73) (4.71) (5.64) 0.05* 0.82 *** 1.12 *** 0.55 *** *** 12.3% (2.01) (2.83) (4.77) (6.59) (2.83) Panel C: Implied risk premium metrics adjusted for analyst forecast error - CNEWS* excludes market news effect Metric Intercept MIRP CNEWS* DNEWS GRLVG Adj_R 2 GLS 0.09*** 1.25 *** 2.37 *** *** ** 18.97% (3.47) (4.70) (6.11) (7.13) (-2.15) CT ** *** ** % (1.25) (2.48) (9.49) (2.47) (1.11) OJ *** 1.75 *** *** *** 20.47% (-1.04) (5.82) (8.46) (6.75) (3.86) PEG 0.06** 1.02 *** 1.99 *** *** *** 14.69% (2.34) (4.24) (5.72) (6.89) (2.99) Notes: Table 6 presents regressions with RET i,t+1 as the dependent variable. RET i,t+1 is the 12 month buy and hold return following the estimation of date of implied risk premium metrics minus the risk free rate. IRP is the implied risk premium corresponding to a specific implied risk premium metric. The four implied risk premium metrics used (GLS, CT, OJ, PEG) are defined in section 4. Panel A presents results using implied risk premium metrics without adjustments for analyst expected error. Panel B presents multivariate regressions using implied risk premium metrics adjusted for analyst expected error. MNEWS is a measure of market-wide news and is estimated as the one-year ahead realized market risk premium scaled by the constant long-term expected risk premium (6%). CNEWS is a measure of cash flow news as in Easton and Monahan (2005) and is estimated as: CNEWS t+1 = (roe t+1 froe τ+1,t+1 ) + (froe τ+1,t+1 ρ froe τ,t+1 ) + (froe 1 ρω τ+1,t+2 froe τ,t+2 ) where froeij,k is the forecasted return on equity of firm i, for the fiscal t year k, based on the consensus earnings forecast released in year j. The first term of CNEWS represents the realized forecast error on the eps forecast made at the end of fiscal year t (scaled by beginning book value per share), the second term represents the forecast revision between the time of the estimation of implied cost of capital until the end of the fiscal year, and the third term represents the revision in the two-year forecasted return on equity adjusted by a capitalization factor equal to ρ/(1- ρ *ωt). Estimates of ρ are taken from Easton and Monahan (2005) and vary between and across five quintiles based on dividend to price ratios. The term ωt captures time series persistence in ROE and is estimated through a pooled rolling regression for each of the 48 Fama and French (1997) industries using 10 years of lagged data, such as: roe i,t τ = ω 0 + ω t roe i,t τ 1, where τ takes the values between 0 and 9. DNEWS is measure of discount rate news and is calculated as: DNEWS i,t+1 = ρ ( IRP i,t+1 IRP i,t) where IRP is the implied cost of capital metric and ρ is the coefficient as defined in CNEWS. GRLVG is an interactive term of growth x leverage. Growth corresponds to the earnings growth rate applied in estimation of implied cost of capital metrics as described in section 4 Leverage is defined as long term debt scaled by market value equity (stock price x number of shares outstanding). Panel C presents results for implied risk premium metrics adjusted for analyst expected error where CNEWS* is the residual from a first-pass regression of CNEWS on (MNEWS t+1 1)IRP i,t. Mean coefficients for annual cross-sectional regressions are reported in all panels. T-statistics in parenthesis are based on Newey-West standard errors. *** (**)(*) denotes statistical significance at 1% (5%) (10%) for tests of coefficients different from zero. +++ ( ++ ) ( + ) denotes statistical significance at 1% (5%) (10%) for tests of coefficients different from one. 38

41 Table 7: Estimated mean reversion of implied cost of capital metrics based on AR1 model for 1,133 firms with 10 or more observations for period Panel A: Summary results from time series regression model ICC i,t+1 = a 0 + a 1 ICC i,t + e t+1 Metric Intercept (a 0) Slope (a 1) π = a 0/(1 a 1) GLS Mean estimate Median estimate No. 10% level 1,034 *** 237 *** CT Mean estimate Median estimate No.pos.@10% level 1,007 *** 386 *** OJ Mean estimate Median estimate No.pos.@10% level 1,083 *** 283 *** PEG Mean estimate Median estimate No.pos.@10% level 1,069 *** 286 *** Panel B: Cross-firm distributional statistics for a 0, a 1, and π Metric Mean Stdv 5 Pcl 25 Pcl 50 Pcl 75 Pcl 95Pcl GLS a a π CT a a π OJ a a π PEG a a π Notes: Panel A presents results of AR(1) firm-specific regressions for alternative implied cost of capital metrics (GLS, CT, OJ, PEG) as defined in section 4. Maximum likelihood estimates correcting for first order autocorrelation of residuals are reported. No.pos.@10% level denotes the number of firm coefficients which are significantly positive at the 10% level. *** indicates that the number of significant coefficients is above that expected by chance at the 1% level based on a binomial test (for our sample of 1133 firms, the number of significant coefficients must exceed 137 based on a 1% binomial test). +++ denotes significance of the median of π for a particular ICC at the 1% level based on the Mann- Whitney-Wilcoxon test. Panel B presents distributional statistics for a 0, a 1, and π based on 1,133 firm estimates for the alternative ICC metrics. 39

42 Table 8: Time-series regressions of realized return on implied risk premia for 1,133 firms with 10 or more observations for period Panel A: Results for model RET i,t+1 = b 0 + b 1 IRP i,t +e t+1 Metric b 0 b 1 Mean Adj. R 2 GLS Mean estimate % Median estimate No. 10% level 175 *** 285 *** No. b 1 10% level 158 *** CT Mean estimate % Median estimate No. 10% level 414 *** 78 No. b 1 10% level 195 *** OJ Mean estimate % Median estimate No. 10% level 159 *** 286 *** No. b 1 10% level 149 *** PEG Mean estimate % Median estimate No. 10% level 242 *** 239 *** No. b 1 10% level 144 *** Panel B: Results for model RET i,t+1 = b 0 + b 1 MIRP i,t +e t+1 b 0 b 1 Mean Adj. R 2 GLS Mean estimate % Median estimate No. 10% level 321 *** 534 *** No. b 1 10% level 216 *** CT Mean estimate % Median estimate No. 10% level 376 *** 282 *** No. b 1 10% level 250 *** OJ Mean estimate % Median estimate No. 10% level 305 *** 605 *** No. b 1 10% level 209 *** PEG Mean estimate % Median estimate No. 10% level 340 *** 509 *** No. b 1 10% level 206 *** Notes: Panel A presents results from firm-specific regressions of realized risk premium against implied risk premia (IRP) for alternative ICC metrics (GLS, CT, OJ, PEG) as defined in section 4. Panel B presents results from firm specific regressions of realized risk premium against implied risk premia adjusted for market news (MIRP) for alternative ICC metrics. No. 10% level denotes the number of firm coefficients which are significantly positive at the 10% level. No. b 1 10% level denotes the number of firms with significant t-statistics at the 10% level based on the alternative null hypothesis that b 1 1. *** indicates that the number of significant coefficients is above that expected by chance at the 1% level based on a binomial test (for our sample of 1133 firms, the number of significant coefficients must exceed 137 based on a 1% binomial test). 40

43 Figure 1: Distributional Properties of Long Term Implied Cost of Capital Estimates Notes: Graph 1 presents the histogram and related distributional statistics of the long-run Implied Cost of Capital based on alternative metrics. Observations which are 5 standard deviations away from the mean (on average < 1% of the sample) are excluded. The alternative ICC metrics (GLS, CT, OJ, PEG) are defined in section 4. 41