Pricing and Mispricing in the Cross-Section

Transcription

1 Pricing and Mispricing in the Cross-Section D. Craig Nichols Whitman School of Management Syracuse University James M. Wahlen Kelley School of Business Indiana University Matthew M. Wieland Kelley School of Business, Indianapolis Indiana University October 2012 We appreciate helpful comments and suggestions from workshop participants at the Boston Area Research Colloquium; The Ohio State University; Ohio University; Indiana University Finance Department; Kelley School of Business, Indianapolis; Florida State University; and the University of Texas at Austin. Comments and suggestions welcome.

2 Pricing and Mispricing in the Cross-Section Abstract This study examines the extent to which parsimonious and general cross-sectional valuation models, restricted to include only publicly-available historical accounting information, explain share pricing in the cross-section and identify mispriced shares. A model that includes historical book value components, earnings components, dividends, and growth explains a fairly large proportion of the cross-sectional variation in share prices, with an average adjusted R-square of 60.0 percent in annual estimations across the 21-year study period, We find surprising variation in explanatory power across time, with R-squares ranging from roughly 24 percent in bubble years like 1999 to roughly 70 percent in We also find these valuation models explain greater proportions of the variation in share prices among firms with less developed information environments (firms not covered by analysts), but smaller proportions of the variation in share prices among firms with richer information environments (firms with analyst coverage), suggesting these share prices impound additional information beyond these accounting fundamental variables. We also examine whether the residuals from these cross-sectional valuation models indicate model misspecification or mispricing. Portfolios based on the lowest (highest) quintile of value residuals each year generate an average annual size-adjusted return of 12.4 percent (- 2.4 percent). A hedge-portfolio strategy, controlling for other firm characteristics that explain returns, including size, market-to-book, accruals, and lagged returns generates an average annual abnormal return of 17.8 percent. This study contributes new evidence on the mapping of accounting fundamentals into share prices, as well as a new and straightforward approach to using accounting fundamentals to identify mispriced shares.

3 Pricing and Mispricing in the Cross-Section 1. Introduction Accounting-based market multiples, such as price-earnings or market-to-book value ratios, are heuristics that are widely used in practice, teaching, and research, for understanding the expectations impounded into share price, explaining value, and identifying mispriced stocks. However, multiplesbased valuation is ad hoc, simplistic (utilizing only a single value indicator, such as earnings or book value), and it is difficult to incorporate indications of value from more than a single multiple, especially when those multiples give conflicting conclusions. In this paper, we examine the ability of book value and earnings components to explain share prices and identify mispriced stocks using simple crosssectional regressions. This approach provides flexibility in choice of accounting fundamentals used to explain price, and allows for simultaneous consideration of earnings and book values (and their components). The choice of firms used in the cross sectional price regression forms the comparable universe, and the fitted values from the regression represent the share values justified by the accounting fundamentals, relative to the share prices of the comparable firms. The value residuals, measured as the differences between share prices and fitted values, reflect either model misspecification or mispricing. If they reflect mispricing, then they should predict returns. This is what we find. The ability of accounting fundamentals to explain price in parsimonious, cross-sectional regressions provides a baseline for fundamental analysis of financial statement information for valuation purposes. The baseline can be a useful benchmark to accounting scholars, practitioners, financial statement users, and standard setters for understanding how the mapping of accounting fundamentals into share prices varies across time, firms, industries, information environments, economic conditions, and accounting regimes. In this study, we establish this baseline and contribute new evidence on how 1

4 the mapping of accounting fundamentals into share prices varies across time, by information environment, and by industry. We find that accounting fundamentals explain a majority of the cross-sectional variation in share prices. 1 In particular, we use annual estimations across a 21-year study period, , in which we regress share prices on historical financial statement variables, including book value components (i.e., net operating assets and net financial liabilities), earnings components (i.e., cash flows from operations, accruals, and other income items), dividends, and growth. We find that our model explains on average 60.0 percent of the cross-sectional variation in share prices. Moreover, we find surprising variation in the ability of accounting fundamentals to explain prices over time. Our model exhibits high explanatory power in the years 1988 through 1993 (adjusted R-squares between 65 and 70 percent), low explanatory power in the bubble period of the late 90s (the lowest adjusted R-square of only 23.6 percent occurs in 1999), and high explanatory power again in recent years (adjusted R-squares in the 65 to 70 percent range). These findings contribute more recent evidence to the literature examining the relevance of financial statement information (e.g., Collins, et al. 1997; Francis and Schipper 1999; Lev and Zarowin 1999; Curtis 2012; among others), indicating that, although share prices departed from fundamentals during the late 1990s, share prices exhibited a strong return to fundamentals in the 2000s, suggesting financial statements continue to provide highly relevant information. We also predict and find that accounting fundamentals explain more of the variance in share prices among firms with poorer information environments, but less of the variance among firms with richer information environments. We use analyst coverage as a proxy for the richness of the firm s information environment. We assume that investors in firms with analyst coverage likely have access to a wider array of firm-specific information than is available to investors in firms that analysts choose not 1 This is consistent with Bernard (1994). 2

5 to cover. Firms covered by analysts tend to have larger market capitalizations, larger investor bases, more active institutional investors, and greater trading volume. As such, these firms are likely to receive more coverage from the financial press, provide more disclosure, and issue more frequent management forecasts and guidance. Financial analysts presumably develop research reports, with forecasts, value estimates, and trade recommendations, using more elaborate and dimensional models than the simple models used in this study. In addition, analysts forecasts, recommendations, and reports can incorporate more information than that to which we constrain our parsimonious models. Insofar as capital market participants utilize analysts forecasts and recommendations, as well as additional information available, then share prices for firms covered by analysts should incorporate much more information than share prices for firms not covered. Therefore, we predict financial statement information about firm fundamentals will explain less of the variation in share prices among covered firms than among firms not covered. Conversely, we predict financial statement information is proportionately more relevant for investors, and therefore will explain a greater proportion of the cross sectional variation in share prices, for firms that have relatively poor information environments. Indeed, we find that the cross-sectional value model has an average adjusted R-square of 55.8 percent for covered firms, and 68.4 percent for firms without coverage. Our findings show that financial statement information is extremely relevant to investors in firms not covered by analysts; in five of our sample years our model explains in excess of 75.0 percent of the cross sectional variation in prices. In addition, we demonstrate the importance of analysts forecasts to the information set available to investors in covered firms. When we include forecasts of future earnings for the analyst coverage sample, the adjusted R-squares jump to an average of 69.0 percent. We also find that, in the presence of analyst earnings forecasts, the role of the accounting fundamentals is reduced, but not eliminated. In particular, accounting book values and historic operating cash flows continue to have incremental explanatory power for prices, whereas the explanatory power of accruals disappears. 3

6 In supplemental analysis, we examine whether the fit of the valuation models improves by grouping all sample firms into one of the 12 Fama-French industries each year and estimating the crosssectional valuation model. 2 The average adjusted R-square increases from 55.8 percent to 63.7 percent among covered firms, and from 68.1 percent to 74.0 percent among firms without analyst coverage. 3 We also find that our model explains cross-sectional variation in share prices very well in all of our sample industries, with the average annual adjusted R-square ranging from a low of 60.0 percent for the telephone and television transmission industry to a high of 75.9 percent in the consumer durables industry. We also find considerable variation across industries in the mapping of accounting fundamentals into share prices. In general, the annual industry valuation model explains observed share prices very well in all industries, for firms with or without analyst coverage. Studying the errors from accounting-based cross-sectional valuation models examining components of share prices that appear orthogonal to accounting fundamentals is also an important step forward in this literature. A better understanding of conditions when market prices seem out of line with accounting fundamentals provides a foundation for examining (a) how to improve the specification and fit of the valuation models themselves, (b) how to improve the accounting information variables that help explain prices, and (c) how to identify potential market mispricing of accounting fundamentals. We examine whether residuals from accounting-based cross-sectional valuation models identify mispriced shares, and whether analyst coverage reduces the potential for mispricing. Our approach is intriguing for its simplicity because, unlike other valuation approaches in the literature (such as Frankel and Lee, 1998), our approach only utilizes historical accounting data and does not require analysts forecasts; it can be applied to all firms, whether covered by analysts or not; and it only relies on fitted 2 Barth, et al. (2005) show that valuation model parameter estimates vary across the 17 industries in their study. Fama-French estimate varying risk premia across 12 industries that are economically homogeneous and sufficiently large to produce meaningful annual valuation parameter estimates. 3 Pooled versus industry-specific estimations will differ in power because of differences in sample sizes, noise from classifying firms into industries, and other factors. It is therefore not entirely appropriate to simply compare adjusted R-squares across pooled versus industry samples; nonetheless, these comparisons are descriptive. Estimating the value model by industry-year improves the fit of the model considerably. 4

7 values and residuals from a cross-sectional regression and does not require specification of a particular valuation model, discount rates, or long-term growth rates. We take a portfolio-based approach to test the degree to which the valuation model residuals represent mispricing. Each year we form portfolios by taking long positions in the quintile of firms with the most negative value residuals as a percentage of price (potentially under-priced shares), and short positions in the quintile of firms with the highest positive value residuals as a percentage of price (potentially over-priced shares). We hold the portfolios for twelve months and measure cumulative size-adjusted abnormal returns. If this fundamental cross-sectional valuation approach identifies mispriced shares, then we should observe positive abnormal returns to the long portfolios and negative abnormal returns to the short portfolios. If the residuals to the cross-sectional valuation models simply represent shares for which the valuation models are misspecified, then we should not observe consistent abnormal returns to either the long or short portfolios. We find that firms with low value residuals outperform firms with high value residuals by 14.8 percent on average over our 21-year study period. This suggests that the departure of price from the value justified by accounting fundamentals reflects at least some degree of mispricing. If analyst coverage improves the information environment and share pricing for the firms they follow, our approach should be less successful in identifying mispriced shares among firms that are covered compared to firms not covered. Consistent with this, low value residual firms outperform high value residual firms by 11.0 percent for firms with analyst coverage, but by 28.6 percent for firms without analyst coverage. Our return results are robust across alternative specifications, including annual cross-sectional Fama-MacBeth regressions that control for other known predictors of returns, and time-series regressions that control for the Fama-French factors as well as a momentum factor. Like prior studies, we demonstrate that parsimonious valuation models, restricted to include only historical accounting information, explain the majority of the cross-sectional variation in share 5

8 prices in the capital markets. Our study contributes new evidence by showing that, although share prices departed from fundamentals during the late 1990s, the capital markets exhibited a strong return to financial statements for relevant information about firm fundamentals during the 2000s. In addition, we show that accounting-based models are extremely relevant in explaining the cross-sectional variation in prices among firms not covered by analysts. We also show that, even among firms with richer information environments characterized by analysts coverage, financial statement information about firm fundamentals, particularly balance sheet components and cash flows, continue to provide substantial information to explain cross-sectional variation in share prices. In addition, we show that estimating the value model within industries increases the explanatory power considerably. We also contribute a new straightforward approach to identify mispriced shares. Our approach simply uses the value residuals from our cross-sectional valuation model to identify under- and overpriced shares. In particular, we predict and find that our fundamental cross-sectional valuation approach predicts future abnormal returns, particularly among firms without analyst coverage. Our approach and findings should be of interest to accountants, analysts, investors, researchers, and teachers interested in financial statement analysis and the relations between accounting information and share prices. We organize the remainder of the paper as follows. In section 2 we describe the research design, methods, and samples, including the cross-sectional valuation models. In section 3, we describe the results from the various cross-sectional value model estimates and the portfolio tests. Section 4 provides concluding remarks. 2. Research Design and Sample In this section we describe our research design, beginning with the cross-sectional regression model we use to explain share prices and estimate value residuals. We then describe the model 6

9 residuals and the abnormal returns tests we use to distinguish the extent to which the residuals represent model misspecification versus market mispricing. Finally, we describe the sample. 2.1 Cross-Sectional Value Models Our research design is guided by three objectives pertinent to our research questions: parsimony, generality, and availability. We seek to test the extent to which parsimonious and general valuation models using available historical accounting data can explain pricing and identify mispricing in the broad cross-section of firms. Initially, we consider only how historical accounting variables map into share prices. Later, we explore how this mapping changes when we include analyst forecasts of future earnings. We begin our analysis by developing a model to explain price that includes available historical data on components of book value, earnings, and growth. We know from prior research that different components of book value and earnings can have different valuation implications. Therefore, we seek to increase the fit of the valuation model by decomposing book value of shareholders equity and net income into components with potentially different valuation implications. We decompose shareholders equity into net operating assets and net financial liabilities (i.e., BV = NOA NFL). If firms create value for shareholders through net operating assets, and if net financial liabilities are more likely to be value neutral, then this decomposition allows the valuation parameters to vary accordingly. In addition, this decomposition allows valuation parameters to capture differences arising from historical cost-based measurements for net operating assets and fair value-based measurements for net financial liabilities (Penman and Zhang, 2002). We also decompose net income into accruals and cash flows from operations, and we include a variable to capture other income items that typically exhibit less persistence. Components of earnings, such as accruals and cash flows, have different implications for future earnings persistence and 7

10 differential explanatory power for share value (Lipe, 1986; Dechow, 1994; Sloan, 1996). 4 In addition, accruals and cash flows provide explanatory power for market value incremental to book value and abnormal earnings (Barth et al, 1999). 5 Other income includes transitory elements, such as extraordinary items and income from discontinued segments, which typically provide less information about future earnings and are therefore likely to have lower explanatory power for share value. By decomposing net income, we allow the valuation parameters to vary across components based on their differential implications for future earnings and share prices. 6 To capture differences in valuation attributable to differences in dividend policy, we also include dividends per share (DIV). In addition, to capture valuation effects of growth, we include two variables representing growth in operating income per share (OIGR) as well as growth in sales per share (SALEGR), thereby allowing the model to capture whether sales and income growth are priced differently. We estimate parameters from the following annual cross-sectional model based on the discussion above: (1) P is share price measured at the end of the third-month following the fiscal year-end; NOA is net operating assets per share; NFL is net financial liabilities per share; ACC income before extraordinary items less CFO per share; CFO is cash flow from operations per share; NIoth is net income less operating income per share, DIV is lagged all-inclusive dividends per share, OIGR is the change in operating income per share, and SALEGR is the change in sales per share. 7 4 In supplemental tests we also include a dummy variable for firm-years with losses, interacted with earnings per share, to allow for differential pricing of positive versus negative income. After including this interaction, the results from the valuation model estimations and the returns tests are equivalent to those reported here in the paper. 5 Barth et al. (2005) decompose net income into accruals and cash flows and find smaller equity value prediction errors relative to a base model. 6 In supplemental analyses, we also decompose net income to components consisting of revenues, expenses, and other income items. The results (untabulated) are unchanged from those reported in the paper. 7 We measure price at the end of the third month to allow the market time to incorporate the financial statement information into share prices. We measure all-inclusive dividends using clean surplus accounting, as lagged BV plus NI minus current BV. 8

11 We refine the analysis and valuation model by analyzing two sub-samples with differing information environments, characterized as the set of firms covered by analysts and the set of firms not covered. Firms that are covered by analysts have richer information sets and market prices likely incorporate greater amounts of information from outside the financial statements that have implications for future earnings. We therefore expect our models to explain less of the variation in share prices of covered firms than for firms that are not covered by analysts. We further refine the analysis by estimating the cross-sectional valuation model parameters yearly by industry using 11 of the 12 industries in the Fama-French classification system (excluding firms in the financial services industry). Annual estimation of the value model by industry permits the valuation parameters to vary by industry and year insofar as they differ in levels of profitability, risk, growth, combinations of accruals and cash flows, levels of investments in assets, use of net financial leverage, accounting conservatism, cost of capital, dividend payout policies, and other value determinants Cross-Sectional Value Residuals We apply the coefficient estimates to the current values of these independent variables to project a share value estimate as follows: (2) We subtract Value from Price to obtain the residual. We deflate the value residual by price to measure the portion of price unexplained by accounting fundamentals, which we denote VRES. VRES reflects a combination of model misspecifications and/or market mispricing, if any. Value residuals will arise from model misspecification when the model does not capture all of the value-relevant information impounded in price. While potential misspecification can arise for many 8 Barth et al. (1999) finds the valuation of accruals and equity book value vary across industries. 9

12 reasons, some obvious sources in the cross-section include when (a) a firm s current period earnings differ from the persistent future stream of earnings the market expects (e.g., because of transitory gains or losses in current period earnings), (b) the market expects a firm s future earnings growth to differ from that in current period earnings growth, (c) a firm s share price reflects asset values not reflected in book value (such as off-balance sheet intangible assets), and (d) a firm s share price reflects an abnormally high or low level of risk. Value residuals can also arise from market mispricing. If the market has temporarily over- or under-priced a firm s shares, relative to the fundamentals included in the model and the set of firms used to estimate the model, then VRES will be positive or negative, respectively. We do not attempt to discriminate between residuals that reflect model misspecification or mispricing. Instead, we attempt to maximize the fit of the valuation models in order to reduce misspecification, thereby increasing the likelihood that the residuals reflect mispricing. To examine whether the value residuals identify mispriced stocks, we calculate abnormal returns for each firm-year by compounding the firm s raw return over a one-year holding period and then subtracting the return on the CRSP size-based decile portfolio to which the firm belongs at the beginning of the holding period. 9 We begin the return accumulation period on the first day of the fourth month following fiscal year-end (i.e., immediately after estimating the value model, projecting value, and calculating the residuals, VRES). This allows the market time to incorporate the financial statement information into share prices. We end the accumulation period one year later, on the last day of the third month following the subsequent fiscal year end, and thereby capture price movements caused by investors reacting to information and events during the year that confirm or refute their beliefs about the firm s value. If a firm delists, we include the delisting return in the calculation of returns, place the funds available after delisting into the size-based decile, and continue cumulating returns through the end of the period. 9 Berk (1995) suggests that firm size is a catchall risk proxy. 10

13 We examine the abnormal returns to portfolios based on the quintile ranks of VRES. For each portfolio, we compute equal-weighted average abnormal returns. If the models identify mispriced stocks then we expect to find larger positive abnormal returns to firms in the bottom quintile (the most negative value residuals), and more negative abnormal returns to firms in the top quintile (the most positive value residuals). As discussed later, we verify the robustness of our portfolio based tests using Fama-MacBeth cross-sectional regressions and Fama-French time-series regressions Sample Selection Our sample includes all calendar-year end firms with information available on the CRSP/Compustat merged database during We remove firms in the financial services industry (SIC codes between 6000 and 6999). We merge this file with I/B/E/S to identify which firm-years had at least one outstanding analyst forecast for the next period. Our sample consists of 53,331 firm-year observations, of which 36,664 have analyst coverage and 16,667 do not. We mitigate the effects of outliers in the parameter estimation procedure by winsorizing the variables in the models at the top and bottom percentile. 10 We require at least 15 observations per industry-year to estimate model coefficients and we delete observations when the model indicates projected share value is negative Sample Description We report sample descriptive statistics in Table 1. Panel A describes the full sample. The average share price is $17.76, while the average book value per share is $8.54. Thus, for the typical firm in our sample, price consists of roughly equal parts book value and present value of future residual income. In decomposing book value, we find that the typical sample firm has net operating assets of $13.14 per share and net financial liabilities of $4.56 per share. On average, net operating assets are approximately three times net financial liabilities. Average earnings per share equals $0.54, consisting of $1.65 per 10 To further ensure our results are not driven by outliers, in untabulated analysis we also delete observations in the top and bottom percentile based on VRES. Results are qualitatively similar to those reported below. 11 The results reported in the paper hold (a) with or without deleting observations with negative projected share values, and (b) with or without firms with share price less than $5. 11

14 share in cash from operations, $-1.14 per share in accruals. The transitory items in income (NIoth) average $-1.03 per share. Panels B and C report descriptive statistics for firms with versus without analyst coverage, respectively. Firms covered by analysts have higher prices on average ($22.08) than firms with no coverage ($8.25). Covered firms have an average book value per share of $9.94 while firms not covered have an average book value per share of $5.46. Overall, these statistics suggest that firms covered by analysts derive a greater portion of value from expected future residual income than do firms without coverage. 12 Firms covered by analysts finance a greater proportion of their net operating assets using net financial liabilities. In particular, covered firms have net operating assets of $15.52 and net financial liabilities of $5.56 (a multiple of less than 3). In contrast, firms without coverage have net operating assets of $7.90 and net financial liabilities of $2.38 (a multiple greater than 3). Surprisingly, firms in the analyst coverage sample have greater standard deviation in earnings (1.89) and cash flows (2.83) than firms without analyst coverage (standard deviations of 1.44 and 2.13, respectively). These differences highlight the importance of understanding how well valuation models based on historical accounting measures explain share prices and identify mispriced stocks for firms with or without analyst coverage. We address this question in the next section. Table 2 presents univariate correlations among the variables we use to model the relationship between price and accounting fundamentals. Panel A contains correlations for the full sample. Price exhibits positive correlations with BV, NOA, IB (income before extraordinary items), CFO, DIV, OIGR, and SALEGR. The correlations provide further support for decomposing book value and earnings. Net operating assets exhibits greater correlation to price relative to net financial liabilities, and cash flow from operations exhibits a greater correlation than accruals. Panels B and C report similar relationships for the samples with and without analyst coverage. 12 This is consistent with analysts promoting the information environment, greater expected future earnings streams, and/or less risk inherent in the future earnings streams of firms covered by analysts. 12

15 3. Empirical Results In this section we present the results from our cross-sectional price regressions and return prediction tests. We first describe the results from estimating our cross-sectional model for the full sample, then split the sample into firms with analyst coverage and those without. For covered firms we also examine how the mapping of accounting fundamentals changes when we include analyst forecasts in our model. We then test whether our value residuals help identify mispriced shares and predict future abnormal returns. We also report the results from additional analysis and robustness checks. 3.1 Broad Cross-Sectional Value Model Estimation Table 3 presents coefficients from the yearly estimations of our model for the full sample (Panel A) as well as the samples with analyst coverage (Panel B) and without (Panel C). In addition to the mean coefficient estimates, we report the average t-statistic, the number of times the variable is significantly positive and negative at the 5% level, a Z-statistic testing whether the time-series average of the t- statistics is significant (Baginski and Wahlen 2003), and the Fama-MacBeth (FM) t-statistic testing whether the time-series average of the coefficient estimates is significant. To illustrate, consider the intercept, which reflects the mean effect of all the influences on price omitted from our model. The intercept for the full sample in Panel A averages 6.74 across the 21 annual estimations, and is significantly different from zero based on the time-series distribution of the annual estimates (FM t- statistic of 17.87). The t-statistic averages across the 21 regressions, which is also significantly different from zero (Z-statistic = 32.16) based on its time-series distribution. Across the 21 years, the intercept is significantly positive (>1.96) 21 times and never significantly negative (<-1.96). The results in Panel A show that components of book value, earnings, dividends, operating income growth and sales growth explain on average 60.0 percent of the cross-sectional variation in share prices. However, the model did a relatively poor job of explaining share prices during the bubble years from 1997 to 2000, with the poorest explanatory power occurring in On average, every 13

16 dollar of net operating assets per share contributes $0.70 to price per share, whereas prices appear to reflect net financial liabilities on a dollar-for-dollar basis (average coefficient on NFL is 0.99). Both are significantly positive. The difference in coefficients between NOA and NFL highlights the difference in measurement rules for these groups of balance sheet accounts, and confirms the importance of recasting book value of equity into its components. Accruals and cash flows differ in their implications for prices. In particular, a dollar of accruals per share contributes $3.16 to price, whereas a dollar of operating cash flow contributes $4.20 to price. These differences are consistent with prior research demonstrating lower persistence of accruals relative to cash flows (e.g., Sloan 1996). NIoth captures the difference between net income and operating income, and includes many items that are transitory in nature. Consistent with this, the average coefficient on NIoth is Surprisingly, dividends and operating income growth are negatively associated with prices. A dollar of dividends per share reduces prices by $.40 on average. However, this effect is not consistent across periods, as DIV is significantly negative in 10 periods but significantly positive in 5 periods. In particular, dividends seemed to lose favor in the 90s, and corresponded to much lower prices in the bubble years of 1998 (coefficient estimate = -1.30) and 1999 (coefficient estimate = -3.51). A dollar of growth in operating income per share corresponds to prices that are lower by $.20, but again the effect is not consistent across periods (significantly positive in 4 periods, significantly negative in 10 periods), and seems strongest in the mid- to late-90s. Finally, sales growth is positively associated with prices, and is significant in 15 periods. The general patterns we observe for the full sample extend to our subsamples. As predicted, we find that the average adjusted R-square is lower for the analyst coverage sample in Panel B (55.8 percent) than for the sample of firms without analyst coverage in Panel C (68.1 percent). We also observe that, for the analyst coverage sample in Panel B, the mean coefficients on accruals (3.20) and 14

17 cash flows (4.28) are considerably higher than the coefficients for the sample without coverage in Panel C (accruals = 1.88, cash flows = 2.56). We believe the effect of analyst coverage on the information environment is associated with both findings, at least to some extent. The lower coefficient on earnings components likely stems from the higher uncertainty about future prospects and persistence surrounding firms without coverage (for example, a much higher proportion of these firms experience losses). The higher adjusted R-square indicates that accounting fundamentals such as earnings, book values, and dividends do a better job of summarizing the available value-relevant information for firms without analyst coverage than for those with analyst coverage, indicating coverage enables market prices to incorporate more information than that contained in summary historical accounting variables. For firms covered by analysts, share prices departed sharply from fundamentals in the late 1990s, when the adjusted R-square was only 32.3 percent in 1998, 19.8 percent in 1999, and 48.0 percent in However, share prices for firms not covered by analysts exhibited a much shorter and less dramatic departure from fundamentals during the bubble years. In particular, the adjusted R- squares were 57.5 percent in 1998, 30.3 percent in 1999, and 60.9 percent in These adjusted R- squares indicate that during the bubble years market pricing made a more severe and prolonged departure from accounting fundamentals among firms followed by analysts. In recent years, particularly 2004 to 2008, market prices made a striking return to fundamentals, with accounting information exhibiting a strong resurgence in value relevance. During this period the adjusted R-squares were much higher than average for covered firms and for firms not covered. 13 In panel D, we summarize the adjusted R-squares from our estimations in Panels A, B, and C. Of particular note, the minimum for both subsamples (19.8% for firms without coverage, 30.3% for firms with coverage) occurs at the peak of the bubble, and the maximum for both samples (66.6% for firms 13 Differences in R-square across samples or over time could also result from differential scale effects in the cross-section or in time-series (Brown, Lo, and Lys 1999). Later, we report analyses to alleviate the concern that the R-square differences we observe are simply the result of scale effects. 15

18 without coverage, 81.3% for firms with coverage) occurs in The intercept in 1999 is extremely high compared to the historical average. As previously mentioned, the intercept summarizes the crosssectional average impact of other influences on prices omitted from our model. For 1999, the high intercept and low R-squares are consistent with a bubble period in which investors set prices with seemingly diminished attention to fundamentals. For 2006 in contrast, the coefficients on almost all the fundamentals are high relative to their historical average. Coupled with the high R-squares, this suggests that fundamentals were the main influence on prices in Cross-Sectional Models Including Analyst Forecasts Prices reflect expectations of the future, and for our firms with analyst coverage we have forecasts of future earnings. In Table 4 we examine how analyst forecasts affect the mapping of historic accounting fundamentals into share prices of covered firms. Panel A provides a summary of our results. Because not all firms with analyst coverage have data available for forecasts of one-year ahead earnings per share, two-year ahead, and expected long-run earnings growth (which we denote FY1, FY2, and LTG, respectively) we first provide a benchmark estimation of the fundamentals only using a constant sample (25,943 firm-year observations with all necessary forecast data). The results are qualitatively similar to those reported in Panel B of Table 3, although the R-square of 51.6% is slightly lower than reported in Panel B (55.8%). The remaining results summarize the effects of adding FY1, FY2, and LTG, one variable at a time. The most dramatic effect on the model occurs with the addition of FY1. FY1 enters the regression with a positive coefficient that is highly significant in every period (Z-statistic = 17.28, FM t-statistic = 15.85). Not only does FY1 cause the adjusted R-square to jump from 51.6% to 63.3%, but it results in many of the accounting fundamentals becoming insignificant or playing a reduced role. For example, cash flows and accruals were positive and significant in all 21 years in the model with fundamentals. Once FY1 is added, cash flows are positive (negative) and significant in only 5 (2) years. Accruals are positive 16

19 (negative) and significant in 2 (8) years. In contrast, FY1 does not subsume the information in book value components to the same extent. NOA and NFL continue to be significantly positive in 19 and 20 years, respectively, and are never significantly negative. Finally, the inclusion of FY1 sharpens the role of dividends in valuation. In the fundamentals only model dividends were not consistently significant. Once FY1 is included, dividends are significantly negative (positive) in 10 (1) periods, and the time-series average becomes significant (FM t-statistic = -2.05, Z-statistic = -3.16). FY2 loads significantly positive in all 21 years and improves the adjusted R-square to 67.7%. FY1 switches signs, and becomes significantly negative in 13 years. The remaining coefficients are generally similar to the model with FY1, with one notable exception. CFO attains significance in 12 periods, compared to only 5 when only FY1 is added. The inclusion of FY2*(1+LTG) increases the adjusted R- square to 69.0% and leads FY2 to become negative in 11 periods. Panel B reports the annual regressions for the full information model including fundamentals and forecasts, FY1, FY2, and FY2*(1+LTG). We summarize the effects on model fit in Panel C. The fundamentals explain approximately half the variation in prices (51.6%), but including forecasts increases the explanatory power of the model to nearly 70%. Interestingly, including the analyst forecast variables in the model only partially moderates the apparent departure of share prices from fundamentals in the bubble years. For example, the average adjusted R-squares of the model remain relatively low: 37.0 percent in 1998, 25.6 percent in 1999, and 53.5 percent in Value residuals and future returns The results in the prior section demonstrate that accounting fundamentals explain most of the cross-sectional variation in price, particularly for firms without analyst coverage. Our next analysis examines the economic content of the value residual by asking whether deviations of prices from the values indicated by the accounting fundamentals derive from mispricing or model misspecification. 17

20 In Table 5, we report returns to quintiles ranked on VRES. The portfolios based on the lowest quintile of VRES are associated with positive future abnormal returns, and the portfolios based on the highest quintile of VRES are associated with negative future abnormal returns for each of the samples, but are strongest among firms not covered by analysts. For example, in the no analyst coverage sample: the lowest VRES quintile portfolios experienced 21.1 percent size-adjusted returns on average, while the highest VRES quintile portfolios experienced -7.5 percent size-adjusted returns, such that the spread in returns across extreme VRES quintiles averaged 28.6 percent per year. These results confirm that value residuals reflect mispricing, at least in part, and that the effect is stronger for firms where accounting fundamentals do a better job of summarizing value-relevant information. In Table 6 we narrow our focus to firms with analyst coverage, and compare returns to value residuals based on fundamentals only to value residuals estimated including fundamentals and analyst forecasts. For the fundamentals only model, a sort on VRES results in a significant spread in returns across extreme quintiles. In contrast, we find no significant returns across extreme quintiles when VRES is estimated based on fundamentals and analyst forecasts. This suggests that the mispricing we see in the value residuals from the fundamentals only model is associated with the pricing of analyst forecast information. This is consistent with prior research (e.g., La Porta 1996) which finds mispricing associated with analyst growth forecasts. Because we decompose earnings into operating cash flows and accruals, the relation between VRES and future returns in Table 5 could simply reflect the accrual anomaly among relatively neglected stocks that have no analyst coverage. In Table 7, we examine whether our results for the sample firms without coverage are distinct from the accruals anomaly as well as other firm characteristics that predict returns, such as size and book-to-market. We use an approach similar to Bernard and Thomas (1990) by estimating the following regression to simulate a zero-investment portfolio: (3) 18

21 AR i,t+1 represents one-year-ahead abnormal returns measured as the raw return less the size-adjusted market return. rvres i,t equals the VRES quintile ranking standardized to range between zero and one, equaling one (zero) when VRES falls in the bottom (top) decile. We control for the effects of other factors associated with future returns by creating quintiles based on ranks of the following five characteristics: (1) size (MVE); (2) the book-to-market ratio (BTM); (3) accruals (ACC), measured as operating income less cash flow from operations, deflated by total assets, (4) prior size-adjusted abnormal returns (AR_LAG), and (5) BETA. We scale all quintile ranks to range from 0 to 1, so the coefficients can be interpreted as the spread in returns across extreme portfolios on each characteristic after controlling for the return implications of the other characteristic portfolios. In particular, given that rvres is standardized to range between zero and one, the slope coefficient, β 1, represents the return to a zero-investment hedge portfolio after controlling for the effects of the other factors. We estimate the regressions in each annual period, and report the time-series mean coefficients. We report t-statistics based on the time-series distribution of the coefficient estimates. The coefficient on VRES equals in Table 7 and is statistically significant. This suggests a spread in returns of 17.8 percent across extreme VRES quintiles (in contrast to the 28.6 percent spread in the portfolio results in Table 5). This suggests that economically and statistically significant returns remain after controlling for other firm characteristics, alleviating the concern that our results merely reflect the accrual anomaly or risk premia in disguise. Overall, the results confirm our findings in Table 5, and suggest that VRES predicts returns and is distinct from other factors that predict returns. As a final check on the robustness of our results, we estimate time-series factor model regressions of monthly excess returns on the Fama-French factors and the momentum factor: (4) Where r p,t denotes the value-weight return on all firms in VRES portfolio p for month t; rf t denotes the one-month Treasury bill rate (from Ibbotson Associates) for month t; MKT t denotes the value-weighted 19

22 return on all NYSE, AMEX, and NASDAQ stocks (from CRSP) minus the one-month Treasury bill rate (from Ibbotson Associates) for month t; HML t denotes the average return on the two value portfolios (small value + big value) minus the average return on the two growth portfolios (small growth + big growth) for month t; SMB t denotes the average return on the three small firm portfolios (small value + small neutral + small growth) minus the average return on the three big firm portfolios (big value + big neutral + big growth) for month t; WML t denotes the average return on the two high prior return portfolios (small high + big high) minus the average return on the two low prior return portfolios (small low + big low) for month t. The intercepts reflect the average monthly return generated by each portfolio after controlling for the portfolio s exposure to the asset pricing factors including in the regression. In Table 8 we report results for the full sample (Panel A), analyst coverage sample (Panel B), without analyst coverage sample (Panel C), constant sample fundamentals only (Panel D), and constant sample full information (fundamentals and forecasts, Panel E). The results confirm that our value residuals predict returns for the full sample, analyst coverage sample, and without analyst coverage sample. For the full sample, the low VRES portfolio generates a statistically significant return of 1.40% per month, while the high VRES portfolio does not generate significant returns. The hedge portfolio, constructed by subtracting the high VRES portfolio returns from the low VRES portfolio returns, generates monthly returns of 1.48% after controlling for known risk factors. On an annual basis, this amounts to approximately 17.7%, and is similar in magnitude to the return we present in Table 5 (14.8%). Interestingly, the results also confirm that the long side contributes most of the returns to the strategy. We believe this is powerful evidence, as returns from a long position are more likely to survive transactions costs and limits to arbitrage arguments. The results for the samples with and without analyst coverage are similar. As in Table 5, the analyst coverage sample generates weaker returns; the alpha for the hedge portfolio is a statistically significant 1.09% per month, or 13% on an annual basis. The returns for the without analyst coverage 20

23 sample (17% on an annual basis) are nearly identical to those reported in Table 7 (17.8%), suggesting the VRES strategy predicts future abnormal returns for firms without analyst coverage, after controlling for differential exposure to risk. In Panels D and E we focus on the constant sample of firms with analyst coverage, and compare the ability of value residuals to predict returns from the fundamentals only model (Panel D) and the full information model (Panel E). Consistent with our findings in Table 6, the fundamentals only model generates statistically significant hedge returns of.786% per month, or 9.4% on an annual basis. In contrast, the returns to the full information model are substantially weaker; the intercept for the hedge portfolio is.363% per month, or 4.4% on an annual basis, and is not statistically significant. These results confirm our finding in Table 6 that the mispricing reflected by the value residuals in the fundamentals only model pertain to the pricing of analyst forecasts. 3.3 Results from Industry-Specific Value Model Estimation As noted earlier, our pooled yearly regressions constrain coefficients to be the same across all industries, despite substantial differences in economic characteristics, competitive structure, accounting conventions, composition of the asset base, risk, and growth. To refine our analysis, we next report results for our value model estimated within industry each year in Table 9. We classify companies into industries based on the Fama-French 12 industry classification (and exclude the financial services industry from our analyses). We report industry mean (averaged across the 21 years in our sample) coefficient estimates for the full sample in Panel A. We observe substantial variation in parameter estimates across industries. For example, the coefficient on NOA per share ranges from 0.25 for consumer nondurables to 1.61 for the healthcare industry. The coefficient on net financial liabilities remains close to 1 on average, but ranges from a low of.39 to a high of 2.76 (again, consumer nondurables and healthcare, respectively). The coefficients on accruals and cash flows are lowest for 21