Expected Stock Returns and Earnings Volatility

Transcription

1 Expected Stock Returns and Earnings Volatility Alan Guoming Huang December 15, 2004 Preliminary. Comments welcome. Department of Finance, Leeds School of Business, University of Colorado, Boulder, CO 80309, tel: I thank Boochun Jung, Kevin Sun, Sunny Yang, Jaime Zender, and in particular my advisors Eric Hughson and Chris Leach for many helpful discussions and comments. I am solely responsible for all errors.

2 Abstract In an economy with short-lived investors and a finite number of firms, firms with more volatile earnings are assigned lower prices in equilibrium. This finding suggests that earnings volatility should be a factor in determining expected stock returns, other things being equal. We investigate the way earnings volatility interacts with traditional factors for asset pricing. We use multi-factor models to test whether earnings volatility helps explain the cross section of stock returns. We find that earnings volatility, as measured by the coefficient of variation of earnings or cashflow, loads positively in panel and time-series regressions of size-sorted portfolio returns. However, it is not significant in crosssectional regressions of individual stock returns. At the portfolio level, earnings volatility is significant in combination with a market factor, and in combination with market, size, earnings yield, and book-to-market equity most of the time. The loadings of earning volatility are robust across proxies for size and earnings, windows for earnings volatility estimation, sub-samples, and sub-periods. We are able to disentangle the earnings volatility factor from the size effect, but not from return volatility. By constructing a mimicking portfolio for earnings volatility in addition to Fama and French s (1993) size and value mimicking portfolios, we find that the earnings volatility factor almost always loads positively in time-series regressions of stock returns. Depending on the proxy for earnings volatility, adding a return volatility factor to multi-factor regressions may or may not deplete the explanatory power of earnings volatility. At the individual firm level, we do not find significance in earnings volatility in Fama and French (1992) cross-sectional regressions of individual stock returns on beta, size, book-to-market, and earning volatility. To account for the difference of earnings volatility in explaining individual and portfolio returns, we conjecture that individual earning volatility might be measured with error, or that earnings volatility is diversifiable at the firm level but not at the portfolio level. 2

3 1 Introduction Large amount of empirical evidence has linked cross-sectional stock returns to firm characteristics, such as earning yield [e.g., Lamont (1998)], market equity, book-to-market ratio [e.g., Fama and French (1992), (1993)], dividend, and dividend payout ratio [e.g., Chen (1991), Lettau and Ludvigson (2001)]. These relationships are hard to explain in the traditional asset pricing paradigm; yet their loadings on returns are non-trivial. For example, Fama and French (1992) document that size and book-to-market ratio alone account for cross-sectional returns associated with the market beta. Despite the empirical success of these firm characteristics in explaining returns, these asset pricing anomalies typically focus on the direct relationship between the level of variables and stock returns. Much less attention has been paid to the possibility that the variability of firm characteristics might affect returns. Of particular interest is earnings volatility, which may have generic return implications given investors and managers apparent emphasis on earnings. For example, Berk (1995) reasons that the size effect (that returns on small stocks are higher than returns on large stocks) is due to firm cashflow riskiness, because the correlation of cashflows with the underlying risk factors will vary across firms in a one-period economy. There are also indirect evidence suggesting that earnings volatility may matter to returns. For example, Badrinath, Gay and Kale (1989) find that institutional investors are reluctant to invest companies with a history of large variations in earnings. Bricker et al. (1995) report that analysts tend to avoid firms with volatile earnings for the fear of forecast errors. This paper investigates the relationship between earnings volatility and expected stock returns. We first propose a parsimonious model with short-lived investors and limited number of securities to show that there exists a negative relationship between earnings volatility and price. In our multi-period, overlapping-generations (OLG) model, investors regard their investment problem as a tradeoff between immediate consumption and savings by investing in multiple assets that differ in dividend volatility. One advantage of using such a model is that the volatility of an asset s residual claims can be numerically linked to the certainty equivalent of consumer s utility for direct pricing purposes. Recent applications of OLG models by Constantinides, Donaldson and Mehra (2002) and Huang, Hughson and Leach (2004) in solving the equity premium puzzle show that asset returns can be expressed as the earnings yield in the stationary equilibrium. This is achieved without turning to additionally imposed 1

4 structures such as log-normality assumption between returns and aggregate consumption, which prior consumption-based CAPM models [e.g., Singleton and Hansen (1982), Campbell and Cochrane (1999)] typically feature. When calibrating the model to historical income and market data, we show that in equilibrium the cross-sectional variation in stocks earnings volatility can be used to explain the cross-sectional variation in prices. A firm with a more volatile cashflow stream is assigned lower price because of smaller certainty equivalent of its cashflow; therefore, its market value is comparatively smaller while its earnings yield, or return, is comparatively higher. The economy we use to show the negative relationship between price and earnings volatility is one that a finite number of firms have independently distributed earnings. Although not replicating the whole set of individual firms in the economy, it closely resembles the situation that firms are aggregated into a limited number of portfolios, a situation that numerous empirical asset pricing tests rest upon. Therefore, our results suggest that earnings volatility should be a factor in determining expected stock returns, other things being equal. Recent advancements in empirical asset pricing that idiosyncratic return volatility exhibits predictive power on stock returns [e.g., Malkiel and Xu (2001), Guo and Savichas (2003)] lend support to our thesis that earnings volatility might matter cross-sectionally. There are several reasons why idiosyncratic risk, whether from earnings or returns, may be priced. First, as argued by Malkiel and Xu (2001) and Levy (1978), many investors hold poorly diversified portfolios. Second, market may be inefficient in that earing volatility is firm-specific, fully diversifiable risk but investors incorrectly perceive it as priced, systematic risk. Third and most important, CAPM may be misspecified and does not correctly price all relevant factors, as it only holds under strict conditions, such as quadratic utility function and constant investment opportunities. Given that we argue for a story of earnings volatility, we next investigate the way earnings volatility interacts with traditional factors for asset pricing. In particular, we are interested in answering two empirical questions: (1) Can earnings volatility predict returns crosssectionally? And if the answer to (1) is positive, then (2) can earnings volatility serve as an independent factor? Specifically, will earnings volatility be driven out with the presence of return-informative variables such as size, book-to-market equity, earnings yield, and return volatility, or the other way around? To the best of our knowledge the empirical question of the volatility of corporate earnings 2

5 on returns hasn t been answered. Prior studies on return prediction using historical earnings focus on the level of earnings, such as earnings yield or dividend payout ratio [e.g., Fama and French (1988), Lamont (1998), Lettau and Ludvigson (2001)]. In recent accounting literature, Barnes (1999), and Allayannis and Weston (2003) both document that earnings (cashflow) volatility is negatively related with market value, and therefore, managers have incentives to smooth earnings over time. In light of these findings and our calibration results, answering the empirical question of earnings volatility on returns contributes to the identification of relevant pricing factors and motivates us to further refine asset pricing theories. We test the hypothesis that earnings volatility explains the cross section of stock returns at both the portfolio level and the individual firm level. We adopt standard methodologies of Fama and French (1993) to run time-series regressions on size-sorted portfolio returns, and of Fama and French (1992) to run cross-sectional regressions on individual stock returns. In addition to these standard regressions, we run panel regressions of returns based on the perception that returns of multiple assets across time consist exactly of a panel data. Running a panel regression is in line with the spirit of the two-pass regressions adopted in Fama and MacBeth (1973) and Fama and French (1992), where the authors test the significance of time-series coefficients of cross-sectional regressions. Directly applying a panel regression, however, not only enables us to derive the exact significance level of the coefficients, but also allows for different or unknown structures in the residuals, such as heteroscedascitiy and auto-correlation. At the portfolio level, to test the predictive power of earnings volatility on expected stock returns, we regress size-sorted portfolio returns on multiple variables including earnings volatility. We find that earnings volatility, as measured by the coefficient of variation of earnings or cashflow (the standard deviation divided by the absolute mean) loads positively in panel regressions of returns. Earnings volatility is significant at 1% in combination with a market factor, and at 5% in combination with market, size, earnings yield, and book-tomarket equity most of the time. The R 2 s of these regressions are generally in the range of 50-60%, which are comparable to those of Fama-French s (1993) three-factor time-series regressions. We use book equity sorted portfolios as the benchmark. However, the results are robust to portfolios sorted on different size proxies, including market equity, total assets and sales. The results are also robust across windows for earnings volatility estimation (e.g., using past twelve quarters of earnings vs. sixteen quarters to estimate earnings volatility), proxies 3

6 for earnings volatility (e.g., standard deviation of earnings scaled by sales), sub-samples (e.g., NYSE stocks only), and sub-periods. We are able to disentangle the earnings volatility factor at the portfolio level from the size and value effects, but not from return volatility. We construct a mimicking portfolio of earnings volatility in addition to Fama and French s (1993) size and value mimicking portfolios. We find that the earning volatility mimicking portfolio almost always loads positively in time-series regressions of stock returns. However, the earnings volatility factor drives out neither SMB, the size factor, nor HML, the value factor. Depending on the proxy for earnings volatility, adding return volatility to a multi-factor regression may or may not deplete the explanatory power of earnings volatility. We conclude that earnings volatility is a pricing factor independent of market, earnings yield, size, and book-to-market equity. The relationship between earnings volatility and return volatility seems worth further study. At the individual firm level, we follow Fama and French (1992) and run cross-sectional regressions of stock returns on β, size, book-to-market equity, and earning volatility. The results, however, do not show evidence that earnings volatility contains return relevant information. There are several possible reasons for the seemingly contradictory results between the portfolio level and the individual firm level. It might be errors-in-variable problem for earnings volatility at both the firm and portfolio levels, or that the portfolio level results are simply sampling luck. Given firm accounting distortions, firm-specific shocks, and our extensive robustness checks at the portfolio level, we are biased towards earnings volatility predicts portfolio returns. Another reason might be that earnings volatility is diversifiable at the firm level but not at the portfolio level. As shown in our calibration, when each portfolio contributes significantly to the market portfolio, changes in portfolio earnings volatility affect the market pricing kernel. If the market portfolio does not adjust fast enough or is measured with error, portfolio earnings volatility will be priced. That said, how to reconcile the difference in the explanatory power of earnings volatility between the portfolio level and the individual level merits further study. The rest of the paper is organized as follows. Section 2 presents and calibrates the model, and shows that there is a negative relationship between earnings volatility and price when the economy has a finite number of securities. Section 3 develops a factor representation for the model and specifies the empirical tests. Section 4 describes the data and variables. Section 5 details the empirical results at the portfolio level. Section 6 provides the results of individual return regressions in the fashion of Fama and French (1992). Section 7 concludes. 4

7 2 Motivation: A Modelling Perspective In this section we numerically show that in a parsimonious economy with a finite number of firms, the general equilibrium implies that earnings volatility is negatively priced. The economy used in the calibration closely resembles the one studied by Huang, Hughson and Leach (2004, HHL ). To foreshadow the results, other things being equal, in equilibrium firm prices decrease with volatile earnings, as measured by the coefficient of variation of earnings. The calibration results may appear somewhat unorthodox within the traditional asset pricing paradigm, where it is asserted that risk-adjusted returns should not include returns from idiosyncratic risks such as earnings volatility. We argue for the pricing of earnings volatility, for the reason that each asset in the economy contributes significantly to the market portfolio when the number of securities is limited. In the words of CAPM, each asset affects the market portfolio in a non-trivial way through (partially) independent earnings components, so that earnings volatility is priced. Due to computational constraints, we are not able to extend the calibration to a very large number of assets. Shall we be able to do so, where individual assets is consider marginal against the market portfolio, we conjecture that the traditional CAPM results will hold. 2.1 Short-lived investors and investment opportunities Consider short-lived investors with stochastic investment opportunities. For simplicity, investors live for two periods. A generation t investor (consumer) is born young at time t, grows old at time (t + 1), and ceases to exist at time (t + 2). The population consists of a sufficiently large measure of two generations. Agents within each cohort are homogeneous and rational. We can therefore construct a representative agent for each generation to study the equilibrium. A generation t agent receives sequential wealth endowments w 1 and w 2, and leaves no bequest or debt when he dies. w 1 and w 2 are assumed to be non-stochastic for simplicity. There is only one numeraire consumption good in the economy. Agents in generation-t choose security holdings to maximize a well-behaved, time-additive CRRA expected utility function: E[ 1 1 γ 1 j=0 βj (C t t+j) 1 γ ], where C t t+j denotes the consumption by generation t at time t+j, γ is the relative risk aversion coefficient (RRA), and β is the time preference factor. 5

8 In each period, there are N perfectly divisible securities indexed by 1, 2,..., N. The supply of each security is fixed at 1. A time-t investment in security i entitles the owner to the resell price and the residual claim d i (dividend/profit) at time t + 1. For illustrative purposes, we assume that the dividend (profit) distributions of securities are IID crosssectionally and intertemporally, and follow normal distribution characterized by mean E(d i ) and standard deviation σ(d i ) i. Let p i t be the ex-dividend price of security i at t. Constantanides, Donaldson and Mehra (2002), and HHL develop similar overlappinggenerations models to study the equity premium puzzle. The existence of a stationary equilibrium, like one in Lucas (1978), has been proved in those papers. The conditional equilibrium pricing equation for asset i is qualitatively identical with that in the standard intertemporal CAPM: E t [M t+1 R i t+1] = 1, (1) where M t+1 = Ct γ t+1 C, and R i t t t+1 = pi t+1 +di t+1. Note that C p i t+1 t and Ct t are derived consumptions t with budget conditions set at equality and market clearing conditions satisfied, i.e., C t t = w 1 i p i t, (2) and C t t+1 = w 2 + i (p i t+1 + d i t+1). (3) Also note that in stationary equilibrium, p i t+1 = p i t so that Rt+1 i = 1 + di t+1. p i t 2.2 Calibration Equations (1)-(3) establish a system which exactly identifies the solution for unknown price vector. However, for a reasonable positive value of γ, the pricing equations are highly nonlinear, for which an analytical solution is hard to solicit. To get around this, researchers since Hansen and Singleton (1982) typically assume joint lognormality between equilibrium consumption stream and returns, which conveniently transforms equation (1) to a linear combination of γ and the covariance between consumption growth and returns. However, given that consumption growth is too smooth to produce significant co-movements with asset returns, this linear transformation is well known for its inability to explain the equity 6

9 premium [e.g., Mehra and Prescott (1985)] and other pricing anomalies such as the size and value effects [e.g., Fama and French (1992)]. In the absence of analytical solution and the presence of potentially flawed transformation, we turn to numerical solution and calibrate the economy. One advantage of a such method is that each solution represents an equilibrium. We follow the line of HHL s parameterization of an OLG economy for calibration inputs. We need input values for length (number of years) of each model period, w 1, w 2, γ, β, securities number and their respective dividend distribution. In HHL, length of each model period is set to be 25 years, that is, investors live for 50 years of economic life. Due to the homogeneity property of the CRRA utility function [e.g., Constantnides, Donaldson and Mehra (2002)], the solutions for returns in equations (1)-(3) are scale invariant. This property enables us to conveniently normalize aggregate endowment to 1. The empirical humped-shape life-time income profile [e.g., Attanasio (1998)] leads Auerbach and Kotlikoff (1987) and others to adopt w(a) = exp( a a 2 ) for the representation of income profile, where a is the number of years into earnings. Using this income profile and assigning the first (second) half of lifetime income to w 1 (w 2 ) result in w 1 = and w 2 = We set γ to 6. Choosing a single-digit γ is consistent with the existing empirical evidence that the population-wide risk aversion coefficient is generally less than 10 [e.g., Barsky et al. (1997), Chetty (2003)] and avoids the equity premium puzzle problem. As for the rate of time preference, β, most economists agree that it should be less than 1. We use HHL s value of In unreported sensitivity analysis, both higher γ and lower β increase the price differentials between assets with different earnings volatilities; however, they don t change the nature of the model predictions. Model period returns are converted into annualized returns using simple annualization, as with HHL. Returns are then reported in the annual basis. In summary, we use the following inputs for the calibration: w 1 = 0.507, w 2 = 0.493, γ = 6, and β = 0.99, or a model-period time preference factor of , or Central to the calibration is the specification of asset number and their dividend distributions. Since in the model we implicitly treat corporate profits as residual claims, we will calibrate on aggregate corporate profit instead of actual dividend payout. Using the USA data from , HHL estimate that government debt interest payments and aggregate corporate profit account for about 2.5% and 7.5% of personal income respectively, and the standard deviation of aggregate profit is 2.5%. These estimates suggest that about 10% of 7

10 the per capita income is generated by residual claim payments with a volatility of about 3%. We will use these two moments as the benchmark for the asset dividend distributions. In particular, we calibrate asset dividends so that aggregate mean dividend equals For simplicity, we adopt 2-point distribution for dividends. We next present calibration results for two cases: when there are two assets in the economy and when there are multiple assets. 2.3 Earnings Volatility and Prices Two Assets Suppose the economy has two assets, asset 1 and 2. We analyze two scenarios of dividend distribution where assets may or may not have same mean dividend. In scenario 1, the two assets differ in both mean and standard deviation of dividend. Specifically, security 1 is larger in that E(d 1 t+1) = To maintain the 10% payout rate, E(d 2 t+1) = It is generally believed that small stocks have higher earnings volatility. To reflect this, we fix stock 1 s coefficient of variation of earnings at σ(d 1 t+1)/e(d 1 t+1) = 25%, and vary the coefficient of variation of stock 2 between 25% and 100% to compare the price and return differentials. Figure 1 details prices and returns as function of stock 2 s coefficient of variation of earnings. We make two observations. First, as shown in Panel A, when earnings volatility of small stock (stock 1) increases, its price decreases while the price of large stock (stock 2) increases. The reason is that the certainty equivalent of an asset with larger dividend dispersion is smaller. As the dispersion goes up, the value of the asset (in this case, stock 2) decreases. With stock 2 s earnings getting more volatile, the volatility of stock 1 s earnings becomes relatively less conspicuous even though its absolute level is fixed, making it relatively more attractive or valued higher. This valuation effect results in a lower price, or higher return for stock 2, and the inverse for stock 1. Second, as shown in Panel B, regardless of the size of earnings, stock returns are increasing in earnings volatility, as measured by the coefficient of variation of earnings. The return differential increases as the gap of earnings volatility between the two assets widens. When earnings volatility of the two stocks is identical, the premium is non-distinguishable from zero. The premium goes up significantly as the difference in earnings volatility becomes more pronounced. In the figure, the premium ranges in [-0.2%, 8.5%], representing 0-53% of stock 1 s return. 8

11 Figure 1-A: Prices as a function of earnings volatitility of stock σ(d 2 t )/E(d2 t ) Large stock-stock 1 Small stock-stock Figure 1-B: Returns as a function of earnings volatility of stock σ(d 2 t )/E(d2 t ) Large stock-stock 1 Small stock-stock 2 One may argue that Figure 1 is derived from specific parameter inputs to the calibration. The concern is that the return differential might be caused by differences in the dividend level rather than differences in dividend volatility. To address this concern, we consider scenario 2 where the two assets have same mean dividend but different earnings volatility. Specifically, we let E(d 1 t+1) = E(d 2 t+1) = 0.05, fix σ(d 1 t+1)/e(d 1 t+1) = 25%, and vary σ(d 2 t+1)/e(d 2 t+1) from 0 to 75%. That is, stock 2 at first has lower earnings volatility than stock 1, then rises to have higher volatility. Figure 2 depicts the price of these two assets. To save space, we do not report the return differentials. As shown in the figure, stock 2 s price is declining in its own volatility, while stock 1 s price is increasing in stock 1 s volatility. They are priced equally when the volatility is the same. Figure 2 illustrates that higher earnings volatility uniformly leads to lower price, confirming the findings in Figure Multiple Assets We extend the benchmark two-asset economy to a multiple-asset economy. Figure 3 shows asset prices when the economy has five assets. For the figure, all assets have same expected dividend of 2% but are ranked by the dividend coefficient of variation. Asset 1 is the riskfree asset. Asset 5 has the highest coefficient of variation. Asset 2 to asset 4 have evenly increasing dividend coefficient of variation in between the riskfree asset and asset 5. All of the assets have IID dividend distributions. The figure plots the cross section of asset prices when asset 5 s coefficient of variation varies between 100% and 200%. From Figure 3, we observe that the price pattern shown in Figures 1 and 2 is maintained in that prices are nicely negatively related with earnings volatility. We do the same exercise for up to ten assets and find the 9

12 Figure 2: Prices as a function of earnings volatitility of stock 2 Stock 1 Stock σ(d 2 t )/E(d2 t ) results sustain. Taken together, Figures 1 to 3 lead us to conclude that earnings volatility drives prices in a general-equilibrium economy where investors tradeoff immediate consumption and savings through a limited number of independent assets that differ in dividend volatility. In our parsimonious model, the limited number of assets can be thought of as representing a finite number of portfolios in the economy. In equilibrium, portfolios with more volatile cashflow streams are priced with comparatively smaller market values. It seems to us that the results arise due to the small number of assets in the economy, where each asset (portfolio) contributes significantly to the pricing kernel and the market portfolio. Any change in the residual claim property of an asset will result in changes in the risk characteristics of the market portfolio and the covariance between the asset and the market portfolio. In response to the comparative statics issue raised in HHL, who stress the importance of sensitivity analysis in calibrating asset pricing models, we perform various dimensions of sensitivity analysis, including single or multi-dimensional variations in relative distribution of lifetime income, risk aversion coefficient, and time preference factor, etc. Major results from the sensitivity analysis are that when earnings volatilities are fixed, (1) increases in γ or decreases in β drive up the price differentials; and (2) positive shocks to the first period income or to aggregate income decrease the price differentials. However, none of these experiments changes the prediction that earnings volatility is negatively priced when the 10

13 Figure 3: Prices with multiple assets Range of coefficient of variation economy consists of a limited number of securities. To save space, we do not report results from these sensitivity analyses. 3 Factor Representation and Empirical Specification The unconditional expected returns in equation (1) can be approximated by a factor model [e.g., Cochrane (1996), Yogo (2003)]. To show this, first taking the unconditional expectation of equation (1), we have E[M t R i t] = 1. (4) Assume that the stochastic discount factor, M t, is linear in F underlying factors denoted as a vector f t : M t = k + l f t, (5) where k is a constant and l is an F 1 vector of constants. Let µ f = E(f t ) and Σ fi = E[(f t µ f )Rt]. i Substitute (5) into (4), rearrange, and we can express the expected return in a linear factor model: E(Rt) i = a + b Σ fi, (6) 11

14 where 1 a = k + l µ f l b =. k + l µ f Interpret a as the riskfree rate, and b as the price of risk. Equation (6) then says that the expected return on asset i is the riskfree rate plus the risk-rewarding return, which is the price of risk times the quantity of risk. This is the familiar multi-factor representation [e.g., Ross (1976), Fama and French (1993)]. Our core calibration suggests that other things being equal, earnings volatility should be a factor in determing expected stock returns, at least when the asset number is limited. In addition, in the comparative statics we also observe that returns are closely related with investors lifetime wealth distribution and risk attitude, such as aggregate wealth, and risk aversion coefficient. These elements, however, may be related with each other; for example, it is well-known that wealth is inversely related with risk aversion. Therefore, the principal component of the additional factors may be represented by a common factor. A good proxy would be the market return, which might stand for investors perception of the general economic condition including variations in γ and wealth. Thus in a multifactor framework, we can test the following regression as a benchmark model to start with: R i t = α + β i mr m t + β i evev i t + ɛ i t, (7) where β is the risk price, m stands for the market, and EV stands for earnings volatility. Consistent with equation (6), α may be interpreted as abnormal return plus riskfree rate. The testable hypothesis is that α, β m and β ev are all significant. According to the calibration results which suggest that prices (returns) decrease (increase) with earnings volatility, β ev should be positive. In view of the traditional CAPM framework, the loadings on earning volatility in equation (7) should not be significant after controlling for the market return. Therefore, testing earnings volatility in combination with the market return seems a reasonable starting point. Contrary to predictions of the CAPM, plethora of research has identified numerous factors for empirical asset returns, among which the most recognized are size, book-to-market 12

15 ratio [e.g., Banz (1981), Fama and Frech (1992), (1993)], earnings yield [e.g., Lamont (1998)], dividend payout ratio [e.g., Lettau and Ludvigson (2001)], and own return volatility [e.g., Malkiel and Xu (2001)]. As a robustness check to equation (7), we study how earning volatility interacts with these known variables. A pickup of earnings volatility in the regressions, if any, can translate into yet another anomalous asset-pricing phenomenon. We adopt standard testing methodologies to test cross-sections and time-series of asset returns on equation (7) and its variations. Specifically, we follow Fama and French (1993) to run time-series regressions on sorted portfolio returns, and Fama and French (1992) to run cross-sectional regressions on individual stock returns. In addition to these standard regressions, we run panel regressions of returns based on the fact that returns of multiple assets across time consist exactly of a panel data. If any of the above mentioned variables is informative of returns in standard regressions, then in panel regressions the results should sustain. Running a panel regression is also in line with the spirit of the two-pass regressions in Fama and Macbeth (1973) and Fama and French (1992), where the authors test the significance of time-series coefficients of cross-sectional regressions. It can be proved that their resulting statistics are equivalent to those derived in OLS panel regressions. Directly applying a panel regression, however, not only enables us to derive the exact significance level, but also allows for different structures in the residuals. 4 Data and Variable Definition Our sample consists of all NYSE/NASDAQ/AMEX listed firms for which we find data on CRSP monthly returns and COMPUSTAT quarterly variables from 1962, which is the time that the farthest COMPUSTAT quarterly data go back to, to We select the survivalbias-free combined COMPUSTAT quarterly data, which include research quarterly files of extinct and acquired companies. We then merge the two data sets by matching current stock returns with latest fiscal quarter s accounting variables. We further eliminate financial services companies (SIC code between 6000 and 6999), and observations with negative or zero price, negative shares outstanding, missing return, missing earnings, and missing assets. The nature of our study requires the estimation of earnings volatility. The calibration suggests that expected returns are contingent on future earnings volatilities, which are obviously non-observable. The difficulty in empirical tests is to select an appropriate measure 13

16 for expected earnings volatility. To resolve this, we use historical earnings volatility as an instrumental variable. Historical earnings volatility is a good instrument as long as it is sufficiently correlated with expected volatility while sufficiently uncorrelated with other regressors and the residuals. If the estimation of earnings volatility involves historical earnings, the longer the volatility estimation window, the closer the volatility instruments will be to the real variable. Ideally, the sample should contain as many time-series observations as possible, in particular, for the estimation of earnings volatility. Unlike many previous studies which use annual COMPUSTAT data [e.g., Fama and French (1992), (1993)], we use quarterly data to increase the number of observations. Using quarterly COMPUSTAT data to match monthly returns also implies that the accounting information is passed to stock price more promptly than using annual data. In order to compute earnings volatility, we restrict the sample to only firms for which earning volatility can be computed with the past N-year quarterly observations. We call N the estimation window. We use estimation windows of 2 (8 quarters), 3 (12 quarters), and 4 (16 quarters) subsequently. To proxy for earnings, we use both earnings before extraordinary items (EI), which is defined as income before EI minus preferred dividends, and cashflow from operations, which is defined as earnings before EI plus depreciation and amortization plus change in working capital. Using cashflow as a proxy helps mitigate the frequently raised earnings management problem [e.g., Healy (1985)]. We then estimate earnings volatility using observations of earnings before EI or cashflow of the previous 2, 3 or 4 years. Since we regress a percentage (return) on the left hand side, it is desirable that the right hand side are also scaled measures. Therefor, we scale volatility by the absolute of its mean, i.e., use the (absolute) coefficient of variation to proxy for earnings volatility. 1 Using the coefficient of variation as earnings volatility measure is also consistent with our calibration process. Label the earnings (cashflow)-based volatility variables EV 2 (CFV 2), EV 3 (CFV 3) and EV 4 (CFV 4) for estimation windows of 2, 3 and 4 years respectively. In the robustness check, we also experiment with other measures of scaled volatility, such as standard deviation scaled by sales, and find results are consistent. For other variables, the value-weighted CRSP NYSE/AMEX/NASDAQ index return (including distribution) is used as a proxy for the market return, and book equity, lagged 1 Other studies use coefficient of variation as an earnings volatility measure includes Barnes(1999), Minton and Schrand (1999). 14

17 market equity, total assets or sales represents size. To a large extent, our variable definitions are consistent with those in Fama and French (1992). The only difference is that unlike them, we do not consider deferred taxes in book equity and earnings, because many of the observations for deferred taxes in quarterly files are missing. For the same reason, we do not directly use the cashflow from operations item from COMPUSTAT. Table I reports the summary statistics of major variables used in the regressions. Panel A provides descriptive statistics on measures of size (book equity, market equity, total assets, and sales), measures of earnings (earnings and cashflow), individual stock returns, and the market return. The sample has a total number of 1,661 thousand observations on monthly stock returns and 440 thousand observations on most quarterly operating variables. Due to missing values, the numbers of observations for operating variables are less than one third of observations for stock returns. By all of the four measures of size, the mean firm size in our sample is significantly higher than its median, implying that our sample consists of more small firms. This is consistent with other studies [e.g., Barnes(1999)]. The mean cashflow is twice as large as the mean earnings. This is because smaller firms tend to report quarterly earnings but not cashflow. Large scale of data availability for earnings starts from 1971, and for cashflow starts from Prior to these dates, there are only sporadic observations for both earnings and cashflow. For the rest of the paper, we restrict our sample to the period for operating earnings, and to for cashflow from operations. [Insert Table I here.] The estimation of earnings volatility requires sufficient observation of earnings measures in the estimation window. Enforcing this requirement results in a loss of about 8% of observations for both earnings volatility and cashflow volatility. In calculating earnings volatility, the standard deviation of earnings is scaled by the absolute value of its mean. This may create extremely large volatilities when mean returns are sufficiently close to zero. For example, the maximum of EV 3 can reach 4.64E+10. To mitigate the impact of extreme values, we winsorize the volatility measures at 1% and 99% percentiles. The winsorization greatly reduces the range of earnings volatility, especially the upper bound. For example, the maximum of winsorized EV 3 decreases to merely 49. In the rest of the paper, we do the same winsorization for all earnings volatility measures. From Table I, cashflows are more volatile than earnings. The means, as well as the standard deviations, of the three (scaled) cash flow volatility measures, are greater than 15

18 their earnings volatility counterparts. This speaks to a story of earnings management [e.g., Healy (1985)], i.e., managers tend to smooth earnings over time. In our regressions, we do not discriminate between both measures of earnings. Rather, we report results for regressions using earnings volatility estimated from both accounting earnings and cashflow. Table II presents the correlation matrix of two groups of variables: operating variables and earnings volatility variables. There is high degree of positive correlation within each group, while the inter-group correlation is low. All of the earnings volatility measures are negatively correlated with firm operating variables. The negative correlations, despite their small magnitude, are all significant at 5% level. This seems consistent with the conventional wisdom that large firms tend to have more stable earnings stream [see, e.g., Allayannis and Weston (2003)]. Between the two categories of earnings volatility measures, i.e., earnings-based and cashflow-based volatility, the correlation is higher within the same category. Volatility between the earnings and cashflow categories are less (but still significantly) correlated. [Insert Table II here.] Table II also reports the correlation between individual returns and other variables. Generally, returns are significantly correlated with earnings volatility measures based on cashflow (CFV 2-4), but are less so with earnings volatility measures based on net income. 5 Results with Portfolio Returns This section reports regression results from equation (7) and a number of its variations at the portfolio level. The primary objective is to determine whether earnings volatility explains stock returns in a traditional multi-factor framework, containing variables such as earnings yield, book-to-market ratio, and return volatility. We report results from panel regressions first, and then report Fama and French (1993) time-series regression results. We form portfolios sorted on size to test equation (7). Our calibration results suggest that market value is inversely related with earnings volatility, which is also argued by Barnes (1999) and Allayannis and Weston (2003). If this is the case, then sorting on size would create a wide range of variation in both the dependent variable (that is, returns) and the independent variable (that is, earnings volatility) so that regressions can produce sufficient 16

19 statistics. We select book equity (BE) as a proxy for size because it represents a non-risk adjusted value of investment to shareholders. Our prior analysis, as well as Berk (1995), raises the issue that market-based size measures, such as market value, are endogenously inversely related with returns. Returns are observed only when market value is observed, and vice versa. Forming portfolios on a contemporaneous variable of market value may therefore create the problem of errors-in-variable. An alternative is to use lagged market value or non-market-based operating measures, such as book equity, and as adopted in Berk (1996), book value of assets or sales. Using a non-risk adjusted measures such as book equity may also avoid the kind of data snooping bias raised by Lo and MacKinlay (1990). 2 As such, we select BE to sort portfolios and present primary results with BE-sorted decile portfolios. In robustness checks, we also test portfolios sorted on other size measures, such as lagged market equity and sales. To construct the BE-sorted portfolios, each month 10 portfolios are formed on ranked values of book equity of latest fiscal quarter using all stocks in the sample. Portfolio returns of each decile are weighted average returns of all firm returns of that decile, weighted by market equity. We use value-weighted returns rather than the traditional equal-weighted returns because value weighting is consistent with the market clearing conditions in our motivating model. The accounting measures of a portfolio, such as book equity, market equity, sales, operating earnings and cashflow, are simple aggregate of those variables of all of the firms of that portfolio. The earnings volatility of a decile portfolio is measured by the coefficient of variation of all earnings/cashflows of the decile firms traced by the length of the estimation window. By constructing portfolio this way, a firm s size decile is the only determinant of which portfolio the firm is in. A same firm may be placed in different portfolios over time because of changes in its decile position. Similarly, it is highly likely that each decile portfolio has different composition of firms month by month. Table III presents the properties of the 10 decile portfolios formed on BE from January 1971 to December On average, each decile has a firm number of about 432, which more than doubles the sample size of Fama and French (1992). Our first observation is that portfolio returns decrease notably with size, either measured by market equity or book equity. At first glance, these monthly returns may appear too high. But note that these are weighted average returns inside a portfolio, and it is possible that stocks with higher 2 Since a pattern between market value and return is known to exist, using a data that contains this information will lead to increased probability of rejecting the null in classical significance tests, as shown in Lo and MacKinlay (1990). 17

20 return inside each decile have larger market equity. Overall, the portfolio with the largest book equity (decile 10) swamps the others with regard to size: it weights more than 75% of all portfolios. The average value weighted return of the whole sample is about 1.4%, which is comparable to simple average returns of about 1% in other studies, for example, Fama and French (1992). Also observe that returns seem increasing with earnings volatility, in particular with those CF V measures. It also appears that mean returns decrease with book to market equity and earnings yield. In light of these portfolio properties, it is not possible to tell exactly how returns are driven by sample characteristics. We next run regressions to decide which variables are informative of returns. Of particular interest is to decide whether earnings volatility can survive traditional variables. [Insert Table III here.] 5.1 Primary Results Table IV reports results from panel regressions on our benchmark two-factor model of equation (7): R i t = α+β m R m t +β ev EV i t +ɛ i t with EV 3 or CFV 3 serving as the proxy for earnings volatility. The results are presented with a variety of regression methods, including OLS, White (1980) heteroscedasticity-correction, Newey-West (1987) autocorrelation-correction with a lag of 2, and generalized method of moments (GMM). The differences between these regression methods lie in the assumption about the residual structure. See, for example, Greene (1999) for a reference. [Insert Table IV here.] For our purposes, the most important observation from Table IV is that earning volatility loads positively. Whether we use EV 3 or CFV 3, earnings volatility is significant at 1% level for all types of regressions. A unit increase in EV 3 corresponds to a 0.02% increase in monthly return, and a unit increase in CFV 3 corresponds to a % increase in monthly return. These numbers, if applied to individual stocks and using the range of EV 3 between 0.08 and and the range of CFV 3 between 0.17 and from Table I, can explain up to 1% and 0.5% of monthly return respectively. The loadings of CFV 3 are smaller, which is consistent with the observation that cashflows are more volatile. 18

21 The market return and the intercept are also significantly positive in Table IV. This is consistent with our hypothesis that the intercept includes risk free rate, and the market factor may be related to people s wealth and risk attitude. To put in the CAPM framework, the estimates of alpha and market beta are significant, but they appear somewhat large. This is because the value-weighted returns on smaller decile portfolios are much higher than the market return and the traditional simple average returns. The resulting R 2 s of our two-factor model are as high as 50% to 60%. This degree of fitness is comparable to other studies, such as Fama and French s (1993) three-factor model. The primary findings in Table IV are robust to measures of earning volatility based on other estimation windows. Table V runs the same regressions using EV 2, EV 4, CFV 2 and CFV 4 as proxies for earnings volatility. In all cases where we run OLS and GMM regressions, earnings volatility, as well as the intercept and the market return, loads significantly at 1%. The results in Tables IV and V indicate that earning volatility is informative of size-sorted portfolio returns in combination with the market return alone. In what follows, we study the interaction of earnings volatility with other traditional return-informative variables. [Insert Table V here.] 5.2 Relevant Informative Firm Characteristics This section studies earnings volatility in combination with traditional informative variables in explaining the cross section of returns. It presents the core results of this paper. We consider several variables, including earnings yield (EY ), book to market equity (BM), size, and own return volatility. We add earnings yield to the regression to accommodate the possibility that the level and sign of earnings may affect returns. The way we define earnings volatility measures treats positive and negative earnings equally because the standard deviation of earnings is scaled by the absolute value of earnings. However, there is evidence that the level of earnings affects stock returns [e.g., Lamont (1998)]. In that investors may price the first moment of earnings, we include earnings yield, defined as the preceding quarter s earnings divided by lagged market equity, as an additional factor. The famous Fama-French three-factor model includes HM L, which is the zero-investment return from longing stocks with high book-to-market ratios and shorting stocks with low 19

22 book-to-market ratios, and SM B, which is the the zero-investment return from longing small stocks and shorting large stocks. Their results, among others [e.g., Banz (1981), Pontiff and Schall (1998)], suggest that book-to-market ratio and size also explain the cross section of stock returns. Therefore, we also include in the regressions book to market ratio (BM), proxied by the portfolio aggregate book equity divided by lagged one aggregate market equity, and size (ln(me)), proxied by logarithm of lagged one market equity. In addition, recent empirical evidence shows that return volatility, whether aggregate or idiosyncratic, is priced [e.g., Malkiel and Xu (2002), Ang et al. (2004)]. The core findings in this segment of literature are that own return volatility positively explains stock returns. Furthermore, it can be verified that earnings volatility is positively associated with return volatility in our calibration. So, if own return volatility is informative, and if earnings volatility is related with return volatility, will the factor of earnings volatility be driven out by return volatility in return regressions? It seems necessary to include the return volatility variable also. We define the portfolio s return volatility, RV, as the standard deviation of returns on the same decile portfolio over the past 36 months. Using different estimation window, such as 4 or 5 years, will not change the results. To sum up, our most extensive regression takes the following form: R i t = α + β m R m t + β ev EV i t + β ey EY i t + β bm BM i t + +β size ln(me) i t + β rv RV i t + ɛ i t (8) Table VI presents results from panel regressions using EV 3 and CFV 3 in combinations with one or more of the above mentioned variables. We start the regression with R m, EV 3 or CFV 3, and EY, then add BM, ln(me), and RV in sequence. There are four regressions in each case. Panels A1 and A2 provide respectively the OLS and GMM results with EV 3 as the earnings volatility measure, and Panels B1 and B2 provide results with CFV 3 as the earnings volatility measure. [Insert Table VI here.] The most significant observation from Table VI is that earnings volatility loads positively in combination with all these return-informative variables. This is particularly true in OLS regressions: among the eight OLS regressions, earnings volatility is significant at 1% in four of them, significant at 5% in another two, and significant at 10% in the rest two. It can be claimed from Table VI that earnings volatility is a pricing variable independent of earnings 20