How Does Firm-Specific Fundamental Information Drive Stock Returns? Theory and Evidence. PETER CHEN Hong Kong University of Science & Technology

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1 How Does Firm-Specific Fundamental Information Drive Stock Returns? Theory and Evidence PETER CHEN Hong Kong Universy of Science & Technology GUOCHANG ZHANG * Hong Kong Universy of Science & Technology July 2004 ABSTRACT: This study examines the role of firm-specific information in driving stock returns. Based on Zhang s (2000) model that relates value to the scale and profabily of underlying operations, we show that return is related to earnings yield, profabily (ROE) change, scale change (equy capal investment), growth opportuny change, and discount rate change. Empirical results confirm the predicted effects of all identified factors. Our model explains about one fifth of firm-level return variations in cross-sectional samples, wh profabily-related factors (earnings yield and profabily change) playing the dominant role, followed by scalerelated factors (capal investment and growth opportuny change) and, finally, discount rate change. Further analysis uncovers how the role of fundamentals varies wh size, book-tomarket, and growth. There also exist size, book-to-market, and growth effects unexplained by fundamentals. Keywords: Stock returns, Firm-specific information, Earnings yield, Profabily (ROE), Scale, Capal investment, Growth JEL Classification Codes: G12, G14, G31 * Correspondence: Guochang Zhang, School of Business and Management, Hong Kong Universy of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. Phone: (852) ; Fax: (852) ; acgzhang@ust.hk. We appreciate the comments of Murray Carlson, Adlai Fisher, Alan Kraus, Charles Lee, and workshop participants at the Hong Kong Universy of Science and Technology, UBC, and UC - Berkeley.

2 How Does Firm-Specific Fundamental Information Drive Stock Returns? Theory and Evidence An issue that is of immense interest to both capal market participants and researchers is what moves stock prices. In any given period, different stocks can exhib vastly different performances. For example, is common that the prices of some stocks more than double in a year whereas the prices of other stocks drop to below half over the same period. The standard valuation approach suggests that stock price changes should be driven by information that signals changes in fundamental values. However, has been a challenge to identify specific sources of information that can effectively explain observed price movements. A series of studies have been undertaken to tackle this issue, including, among others, Roll (1988), Cutler, Poterba and Summers (1989), and Mchell and Mulherin (1994). Relying on the insights from established asset price theories, existing studies mainly focus on macroeconomic and market-wide information (and, to a lesser extent, industry-level information), but the power of such information to account for stock returns is limed especially in a crosssectional context. In this study, we turn to a source of information that has not received adequate attention in explaining stock price movements, namely, firm-specific fundamental information. In practice, firms financial data are regularly reported to investors to convey about the state of operations, and such data are used as an essential basis for investors trading decisions. Our purpose here is to show how, and to what extent, firm-level information causes stock prices to change. We first develop a theoretical model of stock return based on fundamental information that measures operating activies and then evaluate the effectiveness of such information in explaining differences in returns across firms. 1

3 To develop a model of stock return (price change), we start wh the model of Zhang (2000) that links equy value to fundamental characteristics of underlying operations. 1 According to Zhang (2000), equy value equals the value generated from assets in place plus the value of real options that reflect flexibilies in potentially adjusting the scale of operations (abandonment and growth options). This model is consistent wh the standard view of equy value (e.g., Brealey and Myers (2003)), except that establishes valuation from the perspective of value generation (as opposed to value distribution, i.e., dividends, as in the tradional lerature). 2 Equy value hinges on two basic attributes of operations: scale (invested equy capal) and profabily (ROE), and valuation amounts to forecasting the scale and profabily of future operations. It follows that return as change in value (plus dividends) is driven primarily by changes in expectations about the scale and profabily in future periods. Our analysis identifies the following firm-level fundamentals as core factors in driving returns: earnings yield, profabily change, capal investment, and growth opportuny change. These factors convey information about future cash flows, and they are complemented by change in discount rate to form the full set of information in the setting. Most of the variables in the model can be measured wh publicly available data, so the model can be easily estimated and applied in the empirical context. We estimate the return model wh a comprehensive firm-level data set for period and find that all five factors affect returns as predicted and are highly significant. Specifically, return is posively related to earnings yield, profabily change, capal investment, and growth opportuny change, and negatively related to change in discount rate. Furthermore, the effects of profabily and growth opportuny shocks on returns are greater for firms wh higher profabily, as predicted by the theory. These qualative properties hold in all size, book-to-market, and growth groups. 2

4 Sub-sample analysis reveals that the role of fundamental factors varies in particular ways wh firm size, book-to-market ratio, and growth opportuny, and, for a given amount of fundamental information, the effect on return can differ by several times, depending on a firm s specific characteristics. Interestingly, the analysis also uncovers the existence of size and book-tomarket effects (Fama and French 1992, 1995) and growth effect that are not explained by our cash flow fundamentals or discount rate change. Although size, book-to-market ratio, and growth effects are somewhat correlated, evidence suggests that they are separate effects driven by different underlying forces. The model explains 17.4% of the variation of annual firm-level returns in our pooled crosssectional sample, and approximately 20% of the variations in annual samples and in partioned subsamples on average. In our empirical sample, profabily-related factors (earnings yield and profabily change) play the most important role in driving returns, followed by scale-related factors (capal investment and growth opportuny change), wh discount rate change as the least important information source. In the pooled sample, the two profabily-related factors explain 11.58% of the return variation (or 66.55% of the variation explained by the model); scale-related factors together explain 5.81% of total return variation (or 33.39% of the explained variation); and, finally, change in discount rate has an explanatory power of 1.68% (or 9.66% of the explained variation). This ranking is unchanged in all size, book-to-market, and growth deciles. While cash flow factors dominate discount rate change in driving cross-sectional returns for all sub-samples considered, there exist substantial variations in the importance of these two sources of information, particularly discount rate change, across firms. The importance of cash flow information tends to decrease wh size and book-to-market ratio and increases wh growth opportuny, whereas the importance of discount rate change varies in oppose ways. 3

5 Our study contributes to the on-going research that seeks to uncover sources of fundamental information underlying stock price movements. 3 Early studies view dividends as the primarily information variable and rely on ex post dividends to infer whether stock prices are too volatile to be justified by fundamentals. 4 In a recent study, Vuolteenaho (2002) classifies news as eher related to cash flows or to the discount rate and assesses how important each type of news is in driving returns. He finds that, empirically, cash flow news is more important than discount rate news, which is consistent wh our findings. However, Vuolteenaho (2002) (as well as other prior studies) does not develop an explic return function based on (realized) fundamental information; instead, he uses the variance decomposion technique to make inferences from the second moments of the sample data. 5 To our best knowledge, our study is the first to advance a model of stock return based on observable firm-specific information, derived from a formal model of equy value. Our theoretical model is useful in several ways. First, enables us to trace down the return-generating factors and estimate the magnude of their impact on return. Second, the model provides us wh a more solid basis for empirical analysis, and the results we obtain are robust across time periods and subsamples of firms wh different characteristics. It has been shown previously that empirical results from ad hoc model specifications can be unreliable; see, e.g., Boudoukh, Richardson, Shen and Whelaw (2002). 6 Finally, our theoretical model incorporates a broader set of fundamental information (beyond dividends) to explain returns, and can be potentially useful for re-examining issues such as whether stock prices are too volatile. Our study complements the existing research that relies on common factors to explain returns of individual stocks. While common factors are found to be moderately successful in explaining time-series returns (see, for example, Roll (1988)), they are typically much less effective in accounting for return variations in cross-sectional samples. 7 Our study shows that firm-specific 4

6 information is more promising in accounting for return differences across firms (although most of variations remain unexplained). The next section develops a theoretical model of stock return based on firm-level fundamentals. Section II describes the empirical research design and the sample. Section III estimates the return model. Section IV examines differences in the role of fundamental factors across firms. Section V evaluates the relative importance of sub-groups of factors in driving returns. Section VI summarizes the study. I. Modeling the Relation between Return and Firm-Specific Information This section establishes the theoretical relation between stock return and firm-level fundamental information and examines the properties of the return function. We first introduce the equy value model of Zhang (2000) from which the return function is to be derived. A. A Model of Equy Value (Zhang (2000)) Zhang (2000) develops an equy value model based on (observed) accounting data that measure the fundamental characteristics of underlying operations. It starts by defining value as the present value of future cash flows and then models the link between accounting data and future cash flows. 8 Equy value is shown to hinge on two basic attributes of operations, scale and profabily, and valuation amounts to forecasting the scale and profabily of operations in the future, condional on current scale and profabily as conveyed by accounting data. Profabily (ROE) plays an essential role in this model; not only measures a firm s abily to generate value from invested capal but also indicates how the firm is likely to adjust s scale of operations moving forward. The valuation model embeds the firm s decisions to create value whin the set of available investment opportunies characterized by a set of real options (options to grow or abandon the operations). 9 In what follows, we introduce a simplified version of Zhang s model. 5

7 Let V t be the value of an all-equy financed firm at date t (end of period t), B t the corresponding book value of equy, which measures the amount of (equy) capal invested in the firm, X t the earnings generated in period t, and g t the firm s growth opportuny as perceived at t, defined as the percentage by which the scale of operations (capal invested) may grow. Define q t X t /B t-1 as period t profabily. Then, following Zhang (2000), equy value can be expressed as, V = B P q ) + k E ( X + ) + B g C( q ) (1) t t ( t t t 1 t t t where E t (X t+1 ) is the expected next-period earnings to be generated from assets in place, k is the earnings capalization factor, and P(q t ) and C(q t ) are, respectively, the put option to abandon operations and the call option to expand operations, both normalized by operating scale (B t ). 10 The option values relate to both the benef from exercising the options and the likelihood of exercising the options, and are functions of profabily. Intuively, (1) says that equy value equals the value of maintaining the existing operations (capalization of earnings from existing assets) plus the value of growth and abandonment options. The importance of the different value components in (1) hinges on the firm s profabily and growth opportuny. To simplify the analysis, we further assume that q t follows a random walk process. Then, k E t (X t+1 )=B t q t /r t, 11 and valuation function (1) becomes V t = B P( q ) + q / r + g C( q )] B * v( q, g, r ) (2) t [ t t t t t t t t t where v ( qt, gt, rt ) P( qt ) + qt / rt + gtc( qt ). Thus, equy value can be viewed as a product of two basic elements: scale of operations, Bt, and value per un of invested capal, v, which is determined primarily by profabily (q t ) but also depends on growth opportuny (g t ) and the discount rate (r t ). As shown in Zhang (2000), v is an increasing and convex function of profabily q t. When profabily is sufficiently low, the firm would abandon operations to lim operating losses and divert the resources to alternative uses. As profabily increases, the chance that the firm will 6

8 remain in operation increases, and so does firm value. Wh higher profabily, not only are the existing assets more productive, the growth option also becomes more valuable. The flexibily to reduce the scale of operations when profabily is low and to increase the scale when profabily is high makes the valuation function a convex function of q t. It can also be shown that v increases wh growth opportuny g t, but the effect of g t is concentrated mostly in high profabily regions (where the growth option is in the money ). Finally, v decreases wh discount rate r t. B. The Return Model To derive the return function, we totally differentiate (2) to obtain dvt dbt v qt, gt, rt ) + Bt [ v1 dqt + C( qt ) dgt + v3drt = ( ] (3) where v 1 dv/dq t and v 3 dv/dr t. Note that dv/dg t = C(q t ). Let D t+1 be the dividends paid in period t+1, net of capal contribution. Stock return in period t+1, denoted R t+1, equals dvt + Dt dbt Bt Bt Bt Rt + 1 = v [ ] + v1 [ dqt ] + C( qt ) [ dgt ] + v3 [ Vt Vt Vt Vt Vt dbt Bt Bt Bt Dt + 1 = + v1 [ dqt ] + C( qt ) [ dgt ] + v3 [ drt ] +. Bt Vt Vt Vt Vt drt ] + Dt + 1 Vt (4) Assuming the clean surplus relation, db t =X t+1 -D t+1, then D t+1 = X t+1 db t. 12 Replacing dividends D t+1 in (4) wh accounting variables X t+1 and db t+1 and rearranging, we obtain the following return function, 13 X t + 1 Bt Bt dbt Bt R t + = [ ] + v1 [ dq] + [(1 ) ] + C( qt ) [ dgt ] + v3 V V V B V B [ V t 1 t t t t t t t dr ]. (5) According to (5), the following factors drive stock returns: i) earnings yield X t+1 /V t, ii) profabily change dq t, iii) proportional change of equy capal db t /B t, referred to as (equy) capal investment, iv) growth opportuny change dg t, and v) discount rate change dr t. 7

9 In the empirical analysis below, earnings yield and profabily change are categorized as profabily-related information, and capal investment and growth opportuny change as scalerelated information. Together, they revise expectations about future cash flows. These cash flow related factors are complemented by discount rate change to form the full information set in the model. Intuively, (5) says that return arises from value generated in the contemporaneous period plus changes of expected future value generation due to changes in scale and profabily of operations, adjusted for the effect of discount rate change. Next, we discuss in more detail how the individual factors influence return. C. Factors Driving Stock Returns Earnings yield (X t+1 /V t ): Earnings X t+1 represent value generated in the contemporaneous period (period t+1). Earnings normalized by beginning equy value (V t ) translate into return. According to (5), the coefficient on X t+1 /V t is one, condional on the other factors in the model. Profabily change (dq t ): As profabily is central to value generation, profabily change dq t is central to return. The model requires that dq t be adjusted by the (beginning) book to market ratio B t /V t when translated into return. This is because profabily change affects value generation via invested capal (B t ) whereas return is defined relative to beginning equy value (V t ). The coefficient on dq t (after adjusted by the book to market ratio) is v 1 (i.e., dv/dq t ), which is an increasing function of q t given that v is increasing and convex in q t. Also, the coefficient is expected to be non-negative given the non-negativy of equy value. Capal Investment (db t /B t ): Capal investment, defined as proportional change of invested equy capal, db t /B t, affects return because investment changes the capal base on which value is generated. The model requires that db t /B t be adjusted by (1-B t /V t ), reflecting the fact that return relates the net value creation from capal investment over and above the cost of capal. The intuion is as follows: An increase in capal base (scale) due to capal investment raises the 8

10 expectations about future value generation and, hence, equy value. On the other hand, capal investment also reduces current period s dividends, given earnings. The coefficient of db t /B t captures the overall of these two effects. 14 Growth Opportuny Change (dg t ): Since value also depends on growth opportuny, i.e., the extent to which the operating scale can potentially grow, return depends on change in growth opportuny. Ceteris paribus, a posive shock of growth opportuny increases equy value, which increases return. The impact of dg t on return should be greater for firms that have higher profabily (and hence are more capable of exploing growth opportunies). The model specifies that dg t should be adjusted by B t /V t (for the same reason as explained above). The coefficient on dg t, after adjusted by B t /V t, is C(q t ), which is posive and increasing in q t. Change in Discount Rate (dr t ): The discount rate determines how future cash flows are priced. An increase in discount rate reduces the present value of given future cash flows, which lowers equy value and return. Thus, the coefficient on dr t should be negative. II. Empirical Research Design and Data A. Empirical Research Design and Variables We adopt two empirical versions of the return model for estimation. The basic version arising from theoretical model (5) is a linear specification: R = α + β x + γ q + δ b + ω g + ϕ r + e, (6) where R is annual stock return of firm i in year t, measured from 2 days after year t-1 earnings announcement to 1 day after year t earnings announcement; x = X /V is earnings yield of firm i in year t, equal to earnings to common shareholders in year t (X ) (#237) 15 divided by beginning market value of equy (V -1 ); q =(q q -1 ) B -1 /V -1 is profabily change of firm i in year t, adjusted by the ratio of equy book value (# 60) to market value at period beginning, where profabily is 9

11 measured by return on equy, q = X /B -1 ; b =[(B B -1 )/B -1 ] (1- B -1 /V -1 ) is (equy) capal investment, or proportional change in equy book value, of firm i in year t, adjusted by one minus the beginning book to market ratio; g = (g g -1 ) B -1 /V -1 is growth opportuny change of firm i in year t, adjusted by beginning book to market ratio; r =(r t -r t-1 )B -1 /V -1 is discount rate change in year t (the same period over which firm i s return is calculated), adjusted by firm i s beginning book to market ratio; α, β, γ, δ, ω and ϕ are regression coefficients; and e is a residual term. This linear specification is intended to provide an inial indication of the performance of the return model. The theoretical predictions are β=1, γ>0, δ=1, ω>0, and ϕ<0. In (6), the regression coefficients are treated as constant across observations. According to theoretical model (5), the coefficients on q and g should increase wh profabily. To capture the varying impacts of these factors, we also adopt a piece-wise linear specification for empirical analysis, R = α + β x + δ b + γ q + ω g + γ + ω M M M q M g + γ + ω H H H q H g + ϕ r + e (7) where M and H are, respectively, dummy variables for the medium- and high-third profabily ranges of a sample. The coefficients on the dummy terms represent the incremental slope coefficients in the higher-profabily ranges above that in the low-profabily range. The theoretical predictions are γ H > γ M > 0 and ω H > ω M > 0. The predictions on other coefficients in (7) remain the same as in (6) above. B. Data Of the five factors in the return model (5), data for the first three (earnings yield, profabily change, and capal investment) are readily obtained from financial statements. Growth opportuny is not observable, and we use analyst consensus forecast of long-term growth rate as a proxy. 16 Thus, 10

12 growth opportuny change is measured by revision of the consensus forecast. Discount rate change is proxied by change in the yield of 10-year US government bond (over the return period). We extract annul stock returns from CRSP daily files for all firms wh annual earnings announcement dates available in the COMPUSTAT quarterly file, earnings and equy book values from the COMPUSTAT annual file, and consensus analyst forecasts of long-term earnings growth from the I/B/E/S database. The sample is the common of these three data sets for year 1983 through year To ensure that the growth opportuny measure impounds current year s earnings information, we take the first consensus forecast available after an annual earnings announcement. We exclude observations wh negative book equy and trim 0.5% of the extreme observations at the top and the bottom end of the distribution for each of the following variables, R, x, b, q and g. The final sample consists of 27,897 firm-year observations for period C. Descriptive Statistics Table I about here Panel A of Table I presents the descriptive statistics of the overall sample. Annual return has a mean (median) of 15% (10%). Earnings yield has a mean (median) of 6% (7%), implying a priceto-earnings ratio of 16.7 (14.3). Change in annual profabily has a mean (median) of -1.55% (- 0.01%). Capal investment (proportional change in equy capal) has a mean (median) of 13% (10%). Growth opportuny change, or revision of consensus analyst forecasts of long term growth rate, has a mean (median) of -0.53% (-0.09%). Change in discount rate has a mean (median) of % (-0.51%). Finally, the beginning book-to-market ratio has a mean (median) of 0.59 (0.53). Panel B shows the statistics of annual samples. The mean annual stock return fluctuates widely from year to year, ranging from a low of -6% in 1987 and to a high of 35% in The 11

13 mean return does not exhib an obvious increasing or decreasing trend over time, though the variabily of return across firms becomes greater in more recent years. The mean earnings yield shows a slow declining trend from 1983 to 2001, ranging from 10% in 1983 to 3% in 1998 and The mean profabily change fluctuates whin the range from % to 0.66%, and is typically below the median value, suggesting the presence of extreme small (or very negative) values in annual samples. The mean capal investment remains relatively steady whin the range between 8% (1984) and 19% in 1995, which increases slightly in more recent years. The mean growth opportuny change is negative for all the years except for 1983, but the median is zero for about half of the years and negative for remaining years. The mean discount rate change varies from 2.63% to 1.45%. Finally, the mean book to market ratio exhibs a declining trend. It has a high of 0.87 in year 1983 and a low of 0.44 in year A. Results from the Pooled Sample III. Empirical Estimation of the Return Model Table II about here Table II reports the pooled sample results for regression equations (6) and (7). All five factors are found to be statistically significant at the one-percent level, and the signs of their coefficients are as predicted by the theoretical model. Specifically, return is posively related to earnings yield, profabily change, capal investment, and growth opportuny change, and is negatively related to discount rate change. The (adjusted) R 2 is 16.01% for linear regression (6), and increases to 17.4% for the piece-wide linear regression (7). Earnings yield (x) obtains a coefficient of 0.97 (t=27.71) in the linear model and 1.09 (t=30.79) in the piece-wise linear model. These estimates are close to the theoretical value of 1. 12

14 Profabily change ( q) has a coefficient of 0.76 (t=20.34) in the linear regression. In the piece-wise linear regression, the coefficient is 0.32 for the low-profabily range, and increases to 1.30 in the middle-profabily range and to 1.35 in the high-profabily range. The coefficient increases are significant (t=13.54 and respectively), confirming that the impact of profabily change on return is greater in higher-profabily ranges. The estimated return model (linear version) implies that a profabily (ROE) increase of 1% on average increases stock prices by 0.45% for the pooled sample (assuming a sample average bookto-market ratio of 0.59). However, according to the piece-wise linear regression, this effect differs substantially for firms wh different profabilies. The average price increase due to a 1% increase in ROE is 0.19% in the low-profabily range, 0.96% in the medium range, and 0.99% in the high range. Capal investment ( b) (after adjusted by 1-B/V) has a coefficient (δ) of 0.31 in both the linear and the piece-wise linear regression (t=23.38 and respectively). Thus, at a book to market ratio of 0.59, given earnings, a 1% increase in capal base (at the expense of cutting down current dividends) is associated wh an incremental return of 0.13%. The coefficient is significantly posive, suggesting that on average capal investments lead to posive (net) value creation. However, the estimated coefficient (0.31) is substantially below the theoretical value of Growth opportuny change (dg) has a coefficient of 2.97 (t=26.17) in the linear regression. This means that ceteris paribus an increase of growth opportuny (as measured by forecasted longterm earnings growth rate) of 0.01 leads to an average equy value increase by 1.75% (assuming a book to market ratio of 0.59). In the piece-wise linear regression, the coefficient on growth change is 2.49 in the low-profabily range, and increases to 2.69 in the medium range and further to 5.34 in the high range. This is consistent wh the prediction that the impact of growth opportuny change on return is greater for firms wh higher profabily. 13

15 Finally, the coefficient on discount rate change is in both regressions, highly significant. This means that a discount rate increase of 1% causes stock prices to drop by 4.72% (assuming a book-to-market ratio of 0.59). B. Results from Annual Samples Table III about here Table III presents the return model estimations from annual samples, wh results for the linear version of the model in Panel A and those for the piece-wise linear version in Panel B. The qualative properties demonstrated in the pooled sample also hold in annual samples, though the magnudes of coefficient estimates vary from year to year. Details follow. Earnings yield obtains a posive and significant coefficient at the one percent level for 16 (17) of the 19 years in the linear (piece-wise linear) regression model, posive but not significant for two years (one year) in the linear (piece-wise linear) model, and negative and significant for one year (1999) in both versions of regression models. 19 The annual coefficient estimate fluctuates around the theoretical value of one, wh a mean value across the 19 year period of 0.90 in linear regression (6) and 1.01 in piece-wise linear regression (7). In linear regressions, the coefficient on profabily change (γ) is posive and significant in 17 of the 19 years, and is posive but insignificant in two remaining years (1983 and 1984). In piecewise linear regressions, the base coefficient on profabily change (γ 0 ), obtained from the lowprofabily range, is generally posive (17 of 19 years, significant in 9 years). The coefficient increases as we move to higher-profabily regions. The dummy coefficient for the medium range (γ M ) is posive in all years, significant in 15 years, and that for the high-profabily range (γ H ) is posive in 18 years, significant in 15 years. These results generally confirm that return is posively 14

16 related to profabily change, and that the impact of profabily change is greater for firms wh higher profabily. In both linear and piece-wise linear regressions, the coefficient on capal investment (δ) is generally posive (in all but two years) and significant (in 16 years). However, as in the pooled sample, the magnude of this coefficient is well below the theoretical value of one. In linear regressions, the coefficient on growth opportuny change (ω) is posive in all 19 years, significant in 18 years (except 1987); the mean estimate is In the piece-wise linear regressions, the base coefficient on growth opportuny change (ω 0 ), obtained for the lowprofabily range, is also significantly posive in all years except for 1987, and s mean value for the 19 yeas is The dummy coefficient for the medium-profabily range (ω M ) fluctuates around zero (wh a mean of 0.37), and is insignificant in all but one year. On the other hand, the dummy coefficient for the high profabily range (ω H ) is generally posive (in 16 years) and significant at the one percent level (in 9 years), wh a mean value of This shows that the impact of growth opportuny shocks on return is similar in the low- and the medium-profabily range but is greater in the high-profabily range. The negative relation between return and discount rate change is generally confirmed. For both regression equations, the coefficient on discount rate change is negative in 14 of the 19 years, significant in 10 years. In the remaining five years, the coefficient has a wrong (posive) sign, significant in 4 years. Annual regressions also reveal that the coefficients on profabily change and growth opportuny changes tend to increase over time in our sample period. Based on the linear regression estimates, the correlation between profabily change coefficient and year is 0.53 (p<0.001), and that between growth opportuny change coefficient and year is 0.55 (p<0.001). 15

17 The annual explanatory power ranges from 8.94% (year 1987) to 32.92% (year 1984), wh an average of 19.65%, for the linear regression, and ranges from 10.43% to 35.15%, wh an average of 21.66%, for the piece-wise linear regression. There is indication that the model is less effective in explaining cross-sectional returns in years wh major market corrections (such as 1987 and 1999). IV. Cross-Sectional Differences in the Effects of Individual Factors In this section, we explore the properties of the return model in more details to examine how the roles of fundamental factors vary across firms. The theoretical model presented above is developed for a generic firm. The factors identified there convey basic economic information and hence have general validy. In the empirical context, however, the extent to which these factors affect return can vary from firm to firm, due to differences in firm characteristics not captured in the theoretical model. Since we are interested in how the returns of different firms respond to fundamental information, we regress return directly on the factors (whout adjusting the explanatory variables as before) in this section. Specifically, we use the following regression equation, 20 R = α ' + β ' x + γ ' q' + δ ' b' + ω ' g' + ϕ ' r' + e, (6 ) where q =(q q -1 ) is profabily change of firm i in year t; b =(B B -1 )/B -1 is capal investment (proportional change in equy book value) of firm i in year t; g = (g g -1 ) is growth opportuny change of firm i in year t; r =(r t -r t-1 ) is discount rate change in year t that coincides wh the return period for firm i. The coefficients in (6 ) are distinguished from those in (6) by a prime. 16

18 A. Differences across Book-to-Market Partions Prior studies (e.g., Fama and French (1992, 1995)) find that stock returns are related to the ratio of book to market value of equy (B/M). In this subsection, we examine whether there exist systematic differences in the effects of fundamental factors on return across different B/M groups. We partion the pooled sample by the B/M ratio into deciles, and then run separate regressions. The result for regression model (6 ), reported in Table IV, shows that in all B/M deciles, the regression coefficients have the same signs as predicted by the theoretical model. However, the magnudes of coefficients generally vary across B/M deciles in particular ways, as explained below Table IV about here First, the intercept of the regression model exhibs an increasing trend as the B/M ratio increases. The estimated value is 0.06 for the lowest B/M decile and is 0.21 for the highest B/M decile (a difference of 27% in return), and increases monotonically wh the B/M ratio. This increasing trend is consistent wh the book-to-market effect found in prior studies (e.g., Fama and French 1992). The result here suggests that the B/M effect is not subsumed by our fundamental factors. Second, the coefficient of earnings yield (β ) decreases wh the B/M ratio. The coefficient value is 3.40 in the lowest B/M group (decile 1), and is 0.29 in the highest B/M group (decile 10); declines monotonically as the B/M ratio increases. This coefficient measures the marginal effect on return of earnings yield, holding all other factors constant. Third, the coefficient of profabily change (γ ) increases wh the B/M ratio. Its value ranges from 0.18 in decile 1 to 0.77 in decile 10. This coefficient measures the marginal effect on return of profabily change. Observe that the trend of profabily change coefficient across the B/M deciles goes in the oppose direction to that of earnings yield coefficient (β ). 17

19 Fourth, the coefficient on capal investment (δ ) exhibs an increasing trend wh the B/M ratio. The estimated value varies between 0.16 (decile 4) and 0.45 (decile 10). This coefficient measures the return effect of a one-percent increase in capal base. The coefficients of growth opportuny change (ω ) and discount rate change (ϕ ) do not exhib obvious trends across B/M deciles. Unexpected earnings affect both earnings yield and profabily change (relative to the previous year). Thus, stock price reactions to unexpected earnings reflect the combined effect of unexpected earnings yield and profabily change. As discussed above, the return effect of earnings yield is greater for lower B/M firms, but that of profabily change is greater for higher B/M firms. The coefficient values reported in Table IV suggest that for a given unexpected ROE (i.e., earnings normalized by equy book value), the stock prices of high B/M firms react more strongly than the prices of low B/M firms. For example, the average price increase associated wh an unexpected ROE increase of 1% for firms in B/M decile 1 (lowest) is 3.4*1%* *1% = 0.69%, whereas that for firms in B/M decile 10 (highest) is 0.29*1%* *1% =1.16%. B. Differences across Size Partions Previous studies also report that the behavior of stock returns varies wh firm size (e.g, Fama and French (1992, 1995)). To gain insight along the size dimension, we partion the overall sample into deciles by firm size (measured by period-beginning market value of equy) and run regression for each decile. The result reported in Table V shows that the general properties demonstrated in the pooled and annual samples above also hold in all size groups. The explanatory power of the linear regression model ranges from 15.5% to 21.8%. There is no indication that the explanatory power of the return model increases or decreases wh size Table V about here

20 As we move across different size deciles, most coefficients show a general changing trend. First, the regression intercept (α ) decreases wh size, ranging from 0.14 for decile 1 (smallest) to 0.04 for decile 10 (largest), suggesting that firms in the smallest size decile on average earn 10% higher in annual return than firms in the largest decile, and this difference is beyond what is explained by fundamentals. Thus, the size effect persists after controlling for fundamental information. Second, the coefficient on earnings yield (β ) generally increases wh size, although a few deciles are out of this trend. This indicates that stock prices of larger firms tend to react more strongly to earnings yield. The coefficient value for the largest group (decile 10) is 1.39, which is more than twice as large as that for the smallest group (decile 1) of Third, the coefficient on profabily change (γ ) decreases wh size, indicating that a given profabily change has a greater impact on return for smaller firms than for larger firms. This coefficient is 0.57 in the smallest decile, about two times the value of 0.27 in the largest decile. Fourth, the coefficient of growth opportuny change (ω ) generally increases wh size, ranging from 1.59 (in decile 2) to 3.57 (in decile 10). This means that a one percent increase of forecasted long-term growth rate on average raises stock prices by 1.59% for firms in decile 2 and by 3.57% for firms in decile 10. The coefficient on capal investment (δ ), while fluctuates across size deciles, does not exhib an obvious changing trend. The coefficient of discount rate change (ϕ ) remains relatively steady across different size groups. C. Differences across Growth Partions Table VI about here

21 We further examine how in the properties of our return function change wh growth opportuny. Similar to above analysis, we partion the pooled sample by growth opportuny (proxied by analyst forecast of long term growth rate) into deciles, and then run separate regressions for the deciles. The results are reported in Table VI. Again, the qualative properties predicted by the theoretical model hold in all growth deciles. On the other hand, there are also systematic differences in the magnudes of regression coefficients across growth deciles. The coefficients of all four cash flow factors, namely, earnings yield, profabily change, capal investment, and growth opportuny change, all exhib a generally increasing trend as growth increases, indicating that cash flow information has a greater impact on return for high-growth firms than for low-growth firms. On the other hand, the effect of discount rate change exhibs a declining trend, suggesting (perhaps surprisingly) that discount rate change affects low-growth firms more than high-growth firms. The regression intercept exhibs a non-monotonic trend. The result shows that controlling for fundamentals, the average return is lowest for medium-growth firms, higher for low-growth firms, and highest for high-growth firms. The trend of the intercept coefficient across the growth deciles is not consistent wh the trend across B/M partions shown above. An implication is that the B/M ratio is not a close proxy for growth. V. Relative Importance of Different Factors in Driving Returns In this section, we examine the relative importance of various factors in driving stock returns. 21 We employ two measures for the importance of a factor (or groups of factors): relative explanatory power (REP) and incremental explanatory power (IEP). The REP of factor x (which belongs to the set of factors in model (7)) is defined as REP(x) = R 2 of regression using x alone to explain return / R 2 of regression model (7). The IEP of factor x is defined as 20

22 IEP(x) = [R 2 of regression model (7) R 2 of regression model (7) excluding x] / R 2 of regression model (7). 22 Intuively, REP measures the importance of a particular factor (or subset of factors) in explaining returns relative to the full model (7), and IEP measures the uniqueness of the information conveyed by a particular factor (or subset of factors) in explaining returns. We first evaluate the importance of subsets of factors in terms of REP and IEP. Following the theoretical model, we categorize the factors into three groups: profabily related (earnings yield and profabily change), scale related (capal investment and growth opportuny change), and discount rate related Table VII about here The results from the pooled sample, Panel A of Table VII, show that profabily-related information is the dominant force driving returns, eher in terms of REP or IEP. The REP of profabily-related factors (x and q) is 66.55%, meaning that earnings yield and profabily change alone are capable of explaining 66.55% of the return variation in the pooled sample that is explained by the full model, and IEP indicates that 54.48% of the explanatory power of the full model is solely attributed to profabily-related news (uncorrelated wh other types of information). Factors related to the scale of operations (capal investment and growth opportuny shocks) are the second most important force driving returns. It has a REP of 33.39% and an IEP of 22.64%. Discount rate change ranks the last, having a REP of 9.66% and an IEP of 12.41%. This result is consistent wh the finding of Vuolteenaho (2002) that discount rate related news is less important in driving stock returns than cash flow news. Concerning the individual factors, Panel A shows that earnings yield and profabily change are the two most important factors, each alone capable of explaining nearly half of what is explained 21

23 by the model (REP=48.91% and 48.74% respectively). They are followed by the two scale-related factors, growth opportuny change (REP=20.06%) and capal investment (REP=15.0%). Discount rate change ranks the last (REP=9.66%). In terms of the uniqueness of the information conveyed (measured by IEP), earnings yield is the most important (IEP=16.44%), followed by profabily change (13.39%), growth opportuny change (12.7%), discount rate change (12.41%), and capal investment (9.25%). Panel B of Table VII reports the result by B/M-partions. The ranking in terms of the relative importance of three factor-groups in the pooled sample continues to hold in general (in eight of the deciles), that is, profabily-related information is the most important source of information, followed by scale-related information, and finally by discount rate change. One observation is that the explanatory power of discount rate change varies substantially across B/M partions. As the B/M ratio increases, discount rate change gradually becomes more important in driving returns. For the lowest B/M decile, the REP of the discount rate change is 1.62% and s IEP is 1.67%; they increase to 15.65% and 15.36% respectively in decile 9. However, the increasing trend reverses in decile 10 (highest B/M ratios). There is also evidence that the importance of profabily-related information increases slightly and that of scale-related information decreases slightly wh the B/M ratio. Panel C presents the result by size partions, which also confirms the rankings shown above in the pooled sample. In all size deciles except decile 9, profabily-related information dominates scale-related information, which in turn dominates discount rate change in explaining returns. In decile 9, scale-related information surpasses profabily-related information to become the most importance source of information, in terms of eher REP or IEP. Panel C also shows substantial variations in the importance of three factor-groups, especially of discount rate change, across size deciles. The explanatory power of discount rate change is 22

24 minimal in small size deciles (REP=2.23% and IEP=4.27 for the smallest decile). It gradually increases wh firm size. The REP of discount rate change reaches 20.95% and s IEP reaches 21.77% in the largest size decile. As shown above, in terms of the magnudes of regression coefficients, smaller firms have characteristics similar to high B/M firms. However, in terms of the importance of cash flow factors versus discount rate change in driving returns, small firms have characteristics similar to low B/M firms. This suggests that size and B/M effects are likely driven by different underlying forces. Panel D reports the result for growth partions. The general trends are as follows. Both profabily-related and scale-related factors become more important in driving returns as growth increases, whereas discount rate change becomes less important as growth increases. In all growth deciles, profabily-related information dominates scale-related information and discount rate change. While scale-related information explains more return variations than discount rate change among high-growth deciles, the oppose is true for low-growth deciles. VI. Summary and Concluding Remarks This study develops a theoretical model to explain stock price movements based on firmlevel fundamental information. The model shows that return is driven primarily by information related to scale and profabily of operations as captured by earnings yield, profabily change, capal investment, and growth opportuny change, and these cash flow related factors are complemented by discount rate change that affects the pricing of cash flows. Empirical analysis based on a comprehensive set of firm-level data shows that all five identified factors obtain highly significant coefficients wh predicted signs. The qualative properties of the model are confirmed not only in the pooled sample but also in annual samples and in subsamples partioned by size, book-to-market ratio and growth opportuny. On the other hand, 23

25 the magnudes of the effects of fundamental factors vary systematically wh size, book-to-market ratio, and growth. We find that profabily-related information (earnings yield and profabily change) is the most important source of information in driving stock price movements, followed by scale-related news, and finally by the discount rate change, and this ranking holds in both pooled sample and subsamples considered. However, the importance of fundamental factors also varies wh firm characteristics. The importance of cash flow factors in driving returns decreases wh size and bookto-market ratio and increase wh growth opportuny, whereas the importance of discount rate change moves in oppose directions. In particular, discount rate change has ltle importance in driving returns in smallest size deciles and in lowest growth deciles, whereas s explanatory power relative to that of the full model increases to over 20 percent in large size deciles and in high growth deciles. The theoretical and empirical results of this study enhance our understanding of the relation between stock return and firm-level information and how this relation differs for firms wh different characteristics. The analysis also uncovers the existence of size, book-to-market ratio and growth effects unrelated to cash flow factors and discount rate change. Furthermore, evidence suggests that these effects are driven by separate underlying forces, and one effect does not subsume another. Compared wh common-factor-based models, firm-level information holds greater promise in explaining cross-sectional returns. This suggests that may be more fruful for investors to search fundamental information than to devise trading strategies based on common-factor-based anomalies not explained by established asset pricing models. Our return model provides a useful structure for fundamental analysis. On the other hand, given our finding that size, book-to-market and growth effects are not subsumed by fundamental factors, is conceivably to design investment strategies that make use of signals from both firm-level fundamentals and common factors. 24

26 The study also leaves some puzzling empirical regularies for future research. For example, why does discount rate change play a greater role in driving the returns of low-growth firms than of high-growth firms? And given this, why does discount rate change also play a greater role in driving returns of lower B/M-firms? 25

27 References Berk, Jonathan, Richard Green, and Vassant Naik, 1999, Optimal investment, growth options, and secury returns, Journal of Finance 54, Berger, Philip, Eli Ofek, and Itzahk Swary, 1996, Investor valuation of the abandonment option. Journal of FinancialEeconomics 42, Balduzzi, Pierluigi, Edwin Elton, and Clifton Green, 2001, Economic news and the bond prices: Evidence from the US Treasury Market, Journal of Financial and Quantative Analysis 36, Boudoukh, Jacob, Mathew Richardson, Yuqing Shen, and Robert Whelaw, 2002, Do asset prices reflect fundamentals: Freshly squeezed evidence from the FCOJ Market, Working paper, Stern School of Business. Brealey, Richard, Stewart Myers, 2003, Principles of Corporate Finance 7 th Ed. Boston, Mass.: McGraw-Hill/Irwin. Brennan, Michael, Edwardo Schwartz, 1985, Evaluating natural resources investments. Journal of Business 58, Campbell, John, Robert Shiller, 1988, Stock prices, earnings, and expected dividends, Journal of Finance 43, Campbell, John, and Robert Shiller, 1989, The dividend-price ratio and expectations of future dividends and discount factors, Review of Financial Studies 1, Campbell, John, 2000, Asset pricing at the millennium, Journal of Finance 55, Chan, Louis, Jason Karceski, and Josef Lakonishok, 2002, The level and persistence of growth rates, Journal of finance 58, Chen, Naifu, Richard Roll, and Stephen Ross, 1986, Economic forces and the stock market, Journal of Business 59, Copeland, Tom, Aaron Dolgoff, and Alberto Moel, 2004, The role of expectations in explaining the cross-sectional of stock returns, Review of Accounting Studies 9, Cutler, David, James Poterba, and Lawrence Summers, 1989, What moves stock prices? Journal of Portfolio Management 15, Dix, Avinash, and Robert Pindyck, 1995, The options approach to capal investment, Harvard Business Review 73, Dix, Avinash, Robert Pindyck, 1994, Investment under Uncertainty (Princeton Universy Press, Princetion, N.J.) 26