Earnings Dispersion and Aggregate Stock Returns

Transcription

1 Earnings Dispersion and Aggregate Stock Returns Bjorn Jorgensen, Jing Li, and Gil Sadka y November 2, 2007 Abstract While aggregate earnings should a ect aggregate stock returns, the cross-sectional dispersion in rm-level earnings should not. Nonetheless, this paper demonstrates that cross-sectional earnings dispersion is positively correlated with contemporaneous stock returns and negatively correlated with lag stock returns. We o er two alternative interpretations for our results. First, higher earnings dispersion results in more uncertainty about aggregate earnings and less predictability. Consequently, investors demand higher (expected) rates of return during periods of uncertainty about future earnings, which results in a price decline. Second, high earnings dispersion results in short-run unemployment shocks, as workers migrate to better performing rms, suggesting that investors demand higher rates of returns when expected unemployment rises. JEL classi cation: E32, G12, G14, M41. Keywords: accounting valuation, earnings dispersion, expected-return variation, pro tability We would like to thank Nick Polson, Efraim Sadka, Ronnie Sadka, and Michael Staehr for valuable comments and suggestions. We would also like to thank the workshop participants in the Burton Workshop at Columbia University. Any errors are our own. y Bjorn, Jing, and Gil are from Columbia University, bnj2101@columbia.edu, jl2491@columbia.edu, and gs2235@columbia.edu.

2 1 Introduction While earlier studies investigate the rm-level relation between earnings and stock returns, recent studies investigate whether this relation also holds between aggregate earnings and aggregate market returns. 1 In this vein, the literature documents that, all else equal, higher expected earnings are associated with higher stock prices because higher earnings signal higher expected cash ows. For example, Ball and Brown (1968) document a positive contemporaneous relation between rm-level earnings changes and stock returns, where earnings changes represent earnings surprises. result should hold for the aggregate-level (market-level) as well. However, Sadka and Sadka (2007) nd that aggregate-level earnings changes are more predictable than rm-level earnings changes. Therefore, aggregate stock returns are positively related to the one-period-ahead aggregate earnings changes, i.e., current periods earnings were mostly predictable and contemporaneous cash ow news are re ected mostly in future earnings. While aggregate-level stock prices incorporate earnings news in a more timely fashion than rm-level stock prices, higher expected earnings imply higher expected cash ows and result in higher prices. While one would expect aggregate earnings to a ect aggregate stock prices, standard theory does not suggest that the cross-sectional dispersion in earnings a ects aggregate prices. Consider an economy with two assets. In the rst state of the world, each asset is expected to distribute $100 at the end of the period. In the second state of the world, one of the assets will distribute $50 and the other asset will distribute $150. A fully diversi ed investor holding both assets is indi erent between these two states. In both cases, the diversi ed investor will receive an overall payment of $200. In sum, investors should focus on the expected aggregate pro ts of their portfolio of assets regardless of how these pro ts are distributed among the di erent assets in the portfolio. This is, of course, simply a consequence of traditional asset pricing results, including two-fund separation, Capital Asset Pricing Model (CAPM), Intertemporal Capital Asset Pricing Model (ICAPM), and Arbitrage Pricing Theory (APT). 2 For this reason, apart from a few studies (e.g., Campbell and Lettau, 1999; Park, 2005; and Jiang, 2007), the literature mostly ignores the e ects of cross-sectional dispersion on aggregate stock returns. 1 See Kothari, Lewellen, and Warner (2006), Anilowski, Feng, and Skinner (2007), Ball, Sadka, and Sadka (2007), Sadka (2007), and Sadka and Sadka (2007), among others. 2 See Sharpe (1964), Lintner (1965), Merton (1973), and Ross (1976). This 2

3 While from a standard theoretical stand point, the cross-sectional dispersion in earnings should not a ect aggregate stock returns, this paper provides evidence to the contrary. Particularly, this paper nds that the cross-sectional dispersion in earnings changes is positively correlated with contemporaneous aggregate stock returns. 3 Since both returns and earnings are predictable (e.g., Fama and French, 1988, 1989; Campbell and Shiller, 1989a, 1989b; Lamont, 1998; and Ball, Sadka, and Sadka, 2007), this result suggests that when investors anticipate high dispersion in earnings changes, they demand higher rates of return, i.e., expected returns are positively correlated with expected cross-sectional earnings dispersion (henceforth, earnings dispersion). In addition to the contemporaneous relation between earnings dispersion and aggregate stock returns, the crosssectional dispersion in earnings changes is negatively correlated with prior year aggregate stock returns. This lagged relation suggests that dispersion in rm-level earnings changes is predictable. Furthermore, the contemporaneous and lagged relation together suggest that investors react negatively to expected future earnings dispersion, lowering aggregate stock prices, because investors demand higher (expected) rates of return. In contrast, we have no reason to expect that earnings dispersion relates to future (lead) aggregate stock returns because earnings are not a timely source of information (see Basu, 1997, among others). As expected, we nd no evidence relating earnings dispersion to future (lead) stock returns. We provide two alternative interpretations for our ndings. It is possible that either one of these interpretations, or both, explain our ndings. The rst interpretation suggests that higher future earnings dispersion results in more uncertainty about future aggregate earnings changes, and consequently, less predictability. This paper provides evidence consistent with this hypothesis insofar as aggregate stock returns contain less information about future aggregate earnings changes in periods with higher expected cross-sectional dispersion. This interpretation implies that investors demand higher rates of return during periods of higher uncertainty about future earnings changes. The second interpretation of our ndings is based on Lilien (1982) who studies the e ects of dispersion on unemployment. This theory suggests that high dispersion in performance will result in employees migrating from one employer, who performed poorly, to another employer, who is performing well. However, since the labor market is not frictionless, employees take time to relocate. Therefore, high earnings dispersion may result in short-term uctuations in employment. Our results are also 3 We use a common measure for earnings changes consistent with prior studies such as Collins, Kothari, and Rayburn (1987), Collins and Kothari (1989), and Kothari and Sloan (1992). Speci cally, earnings changes are de ned as earnings at period t minus earnings at period t 1, scaled by the stock price at t 1. 3

4 consistent with the second hypothesis. We nd that earnings dispersion is positively correlated with shocks to unemployment. Predictability of earnings dispersion implies that the shocks to unemployment are predictable as well. Therefore, our results suggest that high expected earnings dispersion is associated with high expected unemployment, which a ects some households incomes, wealth, risk aversion, and intertemporal rate of substitution. Therefore, investors demand higher rates of return (e.g., Jagannathan and Wang, 1996; and Santos and Veronesi, 2006). 4 Based on Lilien (1982), we test whether our earnings dispersion results are driven by withinindustry or across-industry variation. Speci cally, we generate two measures of earnings dispersion representing intra-industry and inter-industry earnings dispersion. We nd that intra-industry, rather than inter-industry, earnings dispersion has higher relative explanatory power of earnings predictability, i.e., intra-industry dispersion has a larger impact on predictability. Further, we nd that both inter-industry and intra-industry earnings dispersion are positively associated with short-term unemployment shocks. Our ndings suggest that per unit of dispersion, inter-industry dispersion has a larger impact on unemployment. However, the intra-industry variation is much larger. Consequently, both measures of dispersion signi cantly a ect unemployment. Consistent with our second interpretation, our results suggest that earnings dispersion (both inter-industry and intra-industry) and unemployment are substitute e ects on contemporaneous and lagged stock returns. We conducted several robustness tests. First, due to the lack of power in our test, we also test the predictability explanation based on repeated random sorted portfolios. For each year, we randomly sort the cross-section of rms into three groups, and then we calculate portfolio level timeseries returns and earnings changes. This random sorting procedure is repeated 100 times. Our results suggest that predictability declines with the cross-sectional earnings dispersion of the rms in the portfolio. Second, since Jiang (2007) documents that aggregate stock returns are correlated with the dispersion in book-to-market ratios and other fundamentals, we test whether our results are driven by similar factors. Our results are robust to including the cross-sectional dispersion in the book-to-market ratio. This result also suggests that the numerator - earnings changes - drive our results rather than the denominator - stock prices. Third, in order to further corroborate that our results are not induced by the scaling variable, we used dispersion in return-on-assets and nd 4 Boyd, Hu, and Jaganathan (2006) nd that the market response to unanticipated unemployment news depends on the market conditions. 4

5 similar results. Fourth, our results are robust to including other macro-economic indicators such as real-gdp growth and industrial production (e.g., Fama, 1990; and Schwert, 1990). Finally, the relation between earnings dispersion and lagged stock returns holds after controlling for the dispersion in stock returns as well. 5 The remainder of the paper is organized as follows. Section 2 motivates our study. Section 3 describes the data and its sources. Section 4 tests for the relation between earnings dispersion and aggregate stock returns. Section 5 describes the empirical tests used in testing the hypotheses laid out in Section 2. Section 6 describes our robustness tests. Section 7 concludes. 2 Motivation As noted above, from a standard theoretical stand point, the cross-sectional dispersion in earnings should not a ect aggregate stock returns. In this section, we develop two hypotheses in support of the link between cross-sectional dispersion in earnings and contemporaneous and lagged stock returns. The rst argument is based on how investor uncertainty or ambiguity manifests itself in nancial markets. The second argument is based on macroeconomic conditions and unemployment in particular. For our rst argument, we rely on two branches of the nance research. First, an extensive literature in nance investigates the e ect of estimation uncertainty on equilibrium stock returns, including Barry and Brown (1985), Clarkson, Guedes, and Thompson (1996), Coles and Loewenstein (1988), and Coles, Loewenstein, and Suay (1995). In these single period horizon models, investors are a priori uncertain about parameters that determine the level of future cash ows or the variance of future cash ows. When investors have higher degree of estimation uncertainty, they require compensation in the form of a higher risk premium. Thus, as estimation uncertainty changes, time varying risk premia are predicted to result. This estimation uncertainty likely has both a rm-speci c component and an economy-wide component. While the initial literature focused on the former e ect, recent papers such as Barberis, Vishny, and Shleifer (1998) could be viewed as incorporating the latter e ect as regime shifts which 5 We cannot include the contemporaneous return dispersion due to the high correlation with average stock returns. Consider the case where the spread in market betas is constant over time; the average market returns will determine the cross-sectional dispersion in returns. For the same reason, we included both earnings dispersion and average earnings changes as independent variables. 5

6 could explain investor sentiment. In a similar vein, Easley and O Hara (2006) deviate from expected utility and use prospect theory to argue that some investors refrain from participating in the stock market when there is too much ambiguity about the future payo s. One way in which estimation uncertainty may manifest itself is through cross-sectional dispersion in earnings (see Appendix). Consider, for example, the US energy market where di erent rms are investing in di erent production technologies such as coal, gas, nuclear, wind farms, solar, etc. This market is characterized by high uncertainty about future demands, future regulation, and future cost of alternative energy sources. This leads investors to have estimation uncertainty regarding the future pro tability of the sector and the economy as a whole and at the same time, we expect future dispersion in performance as technology evolves. To the extent that periods with high dispersion are predictable in the previous period, we would expect the following. In anticipation of higher dispersion in future earnings, i.e., higher estimation uncertainty concerning the next period, investors require a higher expected return in the next period which in turn depresses current stock prices resulting in lower current period stock return. Similarly, dispersion in earnings may lead to increased heterogeneity in investors beliefs which in turn may a ect stock prices (see Varian, 1985, among others). Our second argument that links cross-sectional earnings dispersion and aggregate stock returns is based on real e ects through the labor market. Lilien (1982) advances the theory that dispersion in performances or sectoral shifts can result in short-run unemployment shocks as employees migrate between employers/sectors. 6 Lilien further documents that sectoral shifts contribute to unemployment uctuations in the US during the period Speci cally, the share of total employment in manufacturing decreases while the share of total employment in retail trade, nance, insurance, real estate, and service industries increases. Based on Lilien s theory, we hypothesize that earnings dispersion, which proxies for dispersion in the demand for employees, results in short-term unemployment shocks. These short-term unemployment shocks directly a ect some household incomes, wealth, risk aversion, and intertemporal rate of substitution. Since the trade-o between current consumption and saving for future consumption is a ected by unemployment shocks, so is the overall aggregate stock market returns. The hypothesized link between earnings dispersion and aggregate stock returns depends on the 6 For more on the relation between unemployment and sectoral shifts, see Abraham and Katz (1986), Hamilton (1988), Loungani, Rush, and Tave (1990), and Hosios (1994). 6

7 time at which investors receive information. Since earnings dispersion is predictable from prior stock returns, we expect that as investors anticipate higher future dispersion, they also anticipate higher future unemployment. Consequently, investors demand higher aggregate returns. In sum, our hypothesis suggests that expected earnings dispersion is positively associated with expected rates of returns. 7 To reiterate, this e ect should arise due to a ected households response to unemployment in their consumption and investment behavior. This, in turn, results in a contemporaneous decline in stock prices, and lower returns, in response to higher earnings dispersion. 3 Data Our sample consists of all rms with December scal year-end from 1951 to 2005, with available return data in the CRSP monthly le and accounting data in the COMPUSTAT annual database. The December scal year-end requirement avoids misspeci cations due to di erent reporting periods. The annual return is measured by cumulative return from April of year t until March of year t + 1. We calculate the equal-weighted and value-weighted return of all individual stocks in our sample in each year. We measure earnings as income before extraordinary items, scaled by market value at the beginning of the scal period. We use equal-weighted and value-weighted mean and standard deviation measures of cross-sectional individual stock s earnings changes. Our value weights are the market capitalizations at the beginning of the period. For each year, we exclude stocks with the beginning-of-period prices below $1 and the top and bottom 5% of rms ranked by earnings changes used in the tests. We also exclude rms in top and bottom 5% ranked by value weights since extreme value weights can cause inaccurate calculations of second moment weighted variables (suggested by SAS). Finally, we exclude rms with negative book value. The average number of stocks per year is about 1,320 in our sample, increasing from 220 in 1951 to 2,865 in Table 1 reports summary statistics for our sample. Both market returns (equal-weighted and value-weighted) are approximately 15% annually in our sample. These gures are consistent with prior studies such as Sadka (2007). The equal-weighted and value-weighted aggregate earnings 7 Note that the positive relation between expected earnings dispersion and expected aggregate stock returns imply the predictability of stock returns as well (see Fama and French, 1988, 1989; Campbell and Shiller, 1988a, 1988b; Campbell, 1991; Lamont, 1998; Lettau and Ludvigson, 2001; and Ang and Bekaert, 2007). 7

8 change results in similar statistics. For example, the mean equal-weighed and value-weighted earnings changes are and 0.004, respectively. In contrast, the standard deviation of equal-weighted dispersion in earnings changes (0.010) is signi cantly larger than the value-weighted dispersion (0.161). The di erence in the variation in equal-weighted and value-weighted dispersion may explain the di erences in the results using the di erent measures. We extract data on Unemployment, real GDP and industrial production from the Federal Reserve Economic Data (FRED). Unemployment rates are available monthly. To obtain annual measures, we use the average of 12 months beginning April of year t until March of year t + 1. Since unemployment rates exhibit autocorrelation, we use an AR(2) model to estimate shocks to unemployment. The time-series of these shocks are denoted by U t. Summary statistics are reported in Table 1. Note that, by construction, the average of these shocks is zero. 3.1 The Time-Series of Earnings and Returns Figure 1 plots the time-series of aggregate earnings changes scaled by beginning period price. The gure plots both the equal-weighted (Figure 1a) and value-weighted (Figure 1b) earnings changes. Each gure also plots the corresponding equal-weighted and value-weighted market returns. These gures are consistent with those reported in Kothari, Lewellen, and Warner (2006). Note that both earnings and returns do not exhibit a trend or any particular serial correlation. Figure 1 also reveals some interesting patterns regarding the relation between earnings changes and stock returns, previously documented in Kothari, Lewellen, and Warner (2006) and Sadka and Sadka (2007). In particular, earnings changes appear to lag stock returns, i.e., stock returns are positively correlated with the one-period ahead earnings changes. This result is consistent with accounting conservatism insofar as accounting income lags economic income as re ected in stock returns. In addition, earnings changes appear to be negatively correlated with contemporaneous stock returns. These apparent relations between earnings changes and contemporaneous and lagged stock returns are consistent with the correlations reported in Table 2. For example, equal-weighted stock returns have a correlation with contemporaneous equal-weighted earnings changes and a correlation with the one-period ahead equal-weighted earnings changes. 8

9 3.2 Our Dispersion Measure Our equal-weighted and value-weighted earnings dispersion measures ( t _ew and t _vw) are de- ned as the equal-weighted and value-weighted standard deviation of rm-level changes in earnings scaled by beginning period stock price. 8 While earnings changes and returns do not appear to have a trend, the cross-sectional rm-level dispersion in earnings changes is increasing over time (Figure 2). The trend in dispersion is apparent for both equal-weighted and value-weighted measures of cross-sectional dispersion. This trend in dispersion is probably not due to the increase over time in the number of rms in our sample. If the earnings distribution remains unchanged, sampling more observations should not change its standard deviation. A larger sample should increase the accuracy of our measures for both average earnings change and for dispersion, but a larger sample should not generate a trend. 9 The trend in earnings dispersion is most likely due to changes in the distribution of earnings. In particular, Basu (1997) and Givoly and Hayn (2000) suggest that accounting conservatism has increased over time, which should increase the dispersion in earnings changes. Note that the time trend, apparent in Figure 2, is similar to the trend in the earnings response to bad news reported in Basu (1997). Figure 3 presents the evolution of the Basu (1997) measure of conservatism as bad news coe cient, ( ), from the following cross-sectional regression equation: X j;t P j;t 1 = DR j;t + 0 R j;t + 1 DR j;t R j;t + j;t (1) where X j;t and R j;t denote net income before extraordinary items and stock returns for rm j in period t. P j;t 1 denotes market value for rm j at the beginning of period t. DR j;t is a dummy variable that equals 1 if R j;t < 0 and zero otherwise. Figure 3 presents the sensitivity of earnings to negative returns (bad news), 0 + 1, along with t _ew. The gure is consistent with the hypothesis that earnings dispersion has increased due to an increase in conservatism. For example, both dispersion and asymmetric timeliness increase signi cantly after 1973, the year the Financial Accounting Standard Board (FASB) was formed. 8 Formally, we de ne dispersion for a cross-sectional variation in fx j;tg J j=1 as: t = q PJ j=1 wj;t (xj;t xt)2 where x t = 1=J P J j=1 xj;t and P J j=1 wj;t = 1. 9 Since the opening of the Nasdaq exchange signi cantly increases our sample, we excluded the Nasdaq rms and found the same trend in earnings dispersion. In addition, our remaining ndings are not sensitive to the exclusion of Nasdaq rms. These results are not tabulated. 9

10 In addition to the trend, the cross-sectional dispersion in earnings changes are serially correlated. Therefore, in order to estimate shocks in the cross-sectional dispersion, we use the following regression models to obtain equal-weighted and value-weighted shocks to the cross-sectional dispersion in earnings changes: 3X t _w = + 0 t + 1 D n t n _w + " t _w (2) where w = few, vwg, ew and vw denote equal-weighted and value-weighted, respectively, t is a time variable, D 1973 is a dummy variable, which equals one if the year is after 1973, and 0 otherwise. We added this time dummy to control for the spike in conservatism reported in Basu (1997). The shocks to dispersion are de ned as the residual of these regression models. For example, the timeseries of value-weighted shocks to earnings dispersion, DISP t _vw, is the time-series estimate of the regression residuals, " t _vw. Since the results are highly sensitive to the de nition of shocks, it is important to note that the relation between the cross-sectional dispersion of earnings changes and aggregate stock returns holds for several di erent models. In particular, the results hold when excluding the time variables and the dummy variable. Our results are also robust to excluding the third lag cross-sectional standard deviation ( t 3 _w). In addition, one can add t 2 to the regression model in Equation (2), with no signi cant change to the results. In sum, we believe our results to be robust to di erent estimates of shocks in dispersion. Table 1 reports summary statistics for our time-series shocks to earnings dispersion (henceforth, earnings dispersion). By construction, the mean shock is zero. In addition, the medians of both the equal-weighted (-0.002) and value-weighted (-0.017) series are very low in absolute value. The value-weighted earnings change has a much higher variance than that of the equal-weighted series. The standard deviation of the value-weighted series is approximately 16 times higher than that of the equal-weighted series. Furthermore, the minimum and maximum values are much higher for the value-weighted series. While the value-weighted series DISP t _vw has a much higher variance than that of DISP t _ew, the two series are highly correlated. The correlation, reported in Table 2, is and is highly statistically signi cant. This high correlation is not surprising because the two time-series are meant to capture the same underling dispersion in rm-level earnings changes. n=1 10

11 3.3 Earnings Dispersion and Aggregate Earnings The results reported in Table 2 suggest that the cross-sectional dispersion in rm-level earnings changes is higher during period of low aggregate earnings changes, i.e., dispersions is higher during bad times. The contemporaneous correlation between earnings dispersion (DISP t _w) and the average earnings change varies from (for equal-weighted dispersion and equal-weighted average) to (for value-weighted dispersion and value-weighted average). These correlations are statistically signi cant as well. This high correlation may be in part attributed to accounting conservatism. The conservatism principle does not allow the full recognition of economic gains until they are realized, but requires the full recognition of an economic loss as soon as it s anticipated. 10 Therefore, accounting earnings are more sensitive to bad news than they are to good news and, hence, the cross-sectional dispersion in earnings is likely to be higher during periods of lower aggregate pro ts. 4 The Intertemporal Relation Between Earnings Dispersion and Aggregate Stock Returns This sections tests the relation between the cross-sectional rm-level dispersion in earnings changes and aggregate stock returns. We test the contemporaneous, the lead (the relation between contemporaneous dispersion and future returns), and lag (the relation between contemporaneous dispersion and one-period prior returns). Since our dispersion measure is correlated with the average earnings change, it is important to control for the latter. This section utilizes the following regression model: R t+ = X t =P t 1 _w + 2 DISP t _w + t+ (3) where = f 1; 0; 1g and w = few, vwg. The time-series of shocks to the cross-sectional dispersion in earnings changes appears to have some signi cant spikes. Note that the results in this section holds when we exclude these observations. Speci cally, our results are robust to excluding years 1975, 1991, 2001, and 2003 for equal-weighted earnings dispersion and excluding the years 1991 and 2001 for our value-weighted earnings dispersion. 10 See for example, Basu (1997), Ball, Kothari, and Robin (2000), and Ball, Robin, and Sadka (2007). 11

12 4.1 The Contemporaneous Relation Table 2 reports the correlation between equal-weighted and value-weighted shocks to dispersion (DISP t _ew and DISP t _vw, respectively) and both equal-weighted market returns (R t _ew) and value-weighted market returns (R t _vw). The results indicate a positive association between the cross-sectional earnings dispersion and contemporaneous aggregate stock returns. The correlation varies from to Apart from value-weighted dispersion and value-weighted returns, the correlation is statistically signi cant as well. Table 3 reports OLS results for estimating the regression presented in Equation (3). The results in Table 3 are consistent with the correlations reported in Table 2: DISP t _w is positively related to R t _w. This result holds true for both equal-weighted and value-weighted measures of dispersion and returns. The coe cient of equal-weighted dispersion varies from to and the coe cient of value-weighted dispersion varies from to The t-statistic varies from to The results are generally stronger for the equal-weighted measure of shocks to dispersion, where the lowest t-statistic is corresponding to a coe cient of The relation between dispersion and contemporaneous stock returns is also re ected in the adjusted-r 2 of the regression. For example, when adding DISP t _ew and DISP t _vw compared to running Equation (3) with only X t =P t 1 _w, the adjusted-r 2 more than doubles. In addition to the results regarding the relation between dispersion and stock returns, Table 3 rea rms previously documented results regarding the relation between aggregate earnings changes and aggregate stock returns. Consistent with Kothari, Lewellen, and Warner (2006), Sadka (2007), and Sadka and Sadka (2007), Table 3 documents a negative association between contemporaneous earnings changes and contemporaneous stock returns. The coe cient varies from to with a t-statistic varying from to The Relation between Earnings Dispersion and Lagged Stock Returns It is well documented in the accounting literature that earnings are not timely (e.g., Ball and Brown, 1968; and Basu, 1997). Therefore, earnings lag stock returns and are predictable. In fact, Sadka and Sadka (2007) nd that contemporaneous aggregate earnings changes provide little or no new information, and that cash- ow news are re ected mostly in future earnings. Therefore, it is possible that earnings dispersion is predictable as well. To investigate this, we test the relation 12

13 between earnings dispersion and lagged (period t 1) stock returns. Table 4 reports OLS results for estimating Equation (3) above for lagged aggregate stock returns, = 1. The results are consistent with prior studies, suggesting the earnings lack timeliness and are predictable. High contemporaneous dispersion is preceded by lower aggregate stock returns. The coe cient of equal-weighted dispersion varies from to and the coe cient of valueweighted dispersion varies from to The t-statistic varies from to , i.e., the relation is statistically signi cant in all models. This result is consistent with the correlations reported in Panel B of Table 2. The correlations between DISP t _w and R t _w (where w = few, vwg) vary from to and are statistically signi cant as well. The results in Table 4 suggest that expected earnings dispersion explains a signi cant portion of the time-series variation in lagged aggregate stock returns. When earnings dispersion is added as an independent variable in Equation (3), the explanatory power more than doubles. For example, when regressing value-weighted returns on value-weighted earnings changes, the adjusted-r 2 is 2.7%. When value-weighted dispersion is added, the adjusted-r 2 increases signi cantly to 11.3%. The combined results in Tables 2-4 suggest that the cross-sectional earnings dispersion is positively correlated with contemporaneous stock returns and negatively correlated with lag stock returns. Therefore, the results are consistent with investors demanding higher (expected) rates of return during periods of high expected earnings dispersion, which results in price declines overall. 4.3 The Relation between Earnings Dispersion and Lead Stock Returns Another possible reason for the positive association between contemporaneous earnings dispersion and stock returns is that high contemporaneous dispersion is associated with declines in the expected rates of returns (e.g., Kothari, Lewellen, and Warner, 2006). The Campbell (1991) return decomposition is useful for demonstrating the intuition. Campbell decomposes stock returns into three components: expected returns, cash- ow news, and returns news as follows: r t = E t 1 (r t ) + N cf N r (4) where r t denotes stock returns (lower case letters denotes logs here). News about cash ow, N cf, is de ned as N cf = (E t E t 1 ) P 1 n=0 n d t+n, i.e., changes in expected cash ows. Consistently, returns news (changes in expected returns), N r, is de ned as N r = (E t E t 1 ) P 1 n=1 n 1 r t+n. 13

14 The relation between contemporaneous dispersion and contemporaneous and lagged returns results suggest that corr (r t ; DISP t _w) > 0, because dispersion is predictable and corr (E t 1 (r t ) ; DISP t _w) > 0. However, it is also possible that corr (r t ; DISP t _w) > 0, because corr (N r ; DISP t _w) < 0. To test the latter hypothesis, we estimate Equation (3) above for future returns, = 1. The results are reported in Table 5. The results in Table 5 are not consistent with the hypothesis that corr (N r ; DISP t _w) < 0. The coe cient changes signs in the di erent regression models. In addition, the coe cient is statistically insigni cant in all models. Panel C of Table 2 rea rms this conclusion. While the correlation between contemporaneous dispersion and lead stock returns is negative (the correlation varies from to ), it is statistically insigni cant. Equation (4) states that the positive relation between earnings dispersion and aggregate stock returns may be due to a positive relation between dispersion and future cash ows, corr (N cf ; DISP t _w) > 0. In unreported results, we nd some evidence consistent with a positive relation between contemporaneous earnings dispersion and lead aggregate earnings changes. However, this relation is apparent only for equal-weighted dispersion, corr (N cf ; DISP t _ew) ' 0:4. The value-weighted dispersion is not related to future pro ts. In sum, while we nd some evidence that earnings dispersion may provide a signal for future aggregate earnings, we do not believe this to be the main reason for the observed relation between aggregate stock returns and earnings dispersion. The reason is that if high earnings dispersion suggests higher future pro ts, then high expected dispersion should result in high stock returns. Nevertheless, our ndings suggest that the relation between earnings dispersion and lagged stock returns is negative. 5 Dispersion, Predictability, and Unemployment In section 2, we provide two alternative interpretations for our results: First, earnings dispersion a ects the predictability of aggregate earnings. Second, earnings dispersion is related to unemployment. It is plausible that both interpretations contribute to our results. This section empirically tests each interpretation. 14

15 5.1 Dispersion and Uncertainty about Future Earnings As noted above, predictability of aggregate earnings is well documented. However, the extent of predictability may vary over time. In this section, we test whether earnings dispersion a ects the ability of investors to predict aggregate pro ts. To proxy for expected earnings changes, we use the following property under market e ciency: E t 1 [X t ] = X t + t, where t (0; ). This assumption simply states that the realized value is an unbiased estimate of its expected value. Indeed, suppose one were assume, in contrast, that E t 1 [X t ] = a + bx t + t. Then, a 6= 0 and/or b 6= 1 would mean that investors consistently under or over forecast earnings growth, which contradicts market e ciency. Thus, actual realizations proxy for expectations under the e cient market hypothesis. We run the following regression to test for predictability: R t 1 = + X t + " t : (5) As predictability improves, declines because X t proxies for E t 1 [X t ] with less error. If investors perfectly predict earnings changes then = 0. Due to the errors-in-variables problem, is biased towards zero, and which is positive increases as declines. Notice that the goal here is to test whether earnings changes are predicted by current returns. The natural regression would be the reverse of Regression (5), where earnings changes are used as the dependent variable. However, the coe cient obtained in the reverse regression would not be in uenced by the errors-in-variables due to > 0, an e ect that is of interest to us (see Brown, Gri n, Hagerman, and Zmijewski, 1987). We hypothesize that earnings dispersion is positively correlated with. In other words, when investors are expecting dispersion in rm-level performance, they are less capable of predicting the aggregate (or average) performance. Therefore, we expect in Equation (5) to decline with dispersion. To test our hypothesis, we interact aggregate earnings changes with the rank of dispersion, X t R_DISP t. The coe cient on the interaction term represents the change in in Equation (5), when we increase the rank of dispersion. We expect the coe cient on the interaction term to be negative. The results are reported in Table 6. Our tests suggest that aggregate earnings are less predictable during periods of high dispersion. The coe cient on our interaction term, X t R_DISP t, is negative in all model speci cations. 15

16 The coe cient varies from to The coe cients are statistically signi cant for equalweighted dispersion measure with the t-statistic varying from to But, the coe cients for value-weighted dispersion measure are weaker, with t-statistic varying from to Nevertheless, our results are consistent with the hypothesis that aggregate earnings are less predictable during periods of high dispersion. To illustrate the economic signi cance of our results, note that the coe cient on X t R_DISP t suggest that in Equation (5) declines by , which is about 12% (=1.119/9.294), for a unit increase in rank of earnings dispersion. We also test the predictability explanation based on repeated random sorted portfolios. For each year, we randomly sort the cross-section of rms into three groups, and then we calculate portfolio level time-series returns and earnings changes. For each portfolio, we estimate the predictability regression as in Table 6. This random sorting procedure is repeated 100 times, and Table 7 reports the median, 25 percentile, and 75 percentile values of estimated coe cients for the 100 portfolio groups. The results are consistent with our hypothesis. For all portfolios, the coe cients of the interaction term, X t R_DISP t, are all negative with small variation among the 100 randomly sorted subsamples. The cross-sectional earnings dispersion could be driven either by the dispersion of average earnings changes across industry or by the dispersion among earnings changes within industry. It is worthwhile to examine which dispersion drives our results. To perform the industry analysis, we follow the Fama and French (1997) industry classi cations to classify the SIC codes into 48 industries. Within our data sample after deleting extreme observations for each year, we rst take the median value of change in earnings of each Fama and French industry in each year and calculate the standard deviation of industry median earnings. 11 Then a time series model with time and three lagged variables is used to get the time-series shocks to the dispersion of cross-industry earnings changes, DISP _IND t. Next we use the rm speci c change in earnings adjusted for industry median to get the measure of earnings dispersion within industry. The cross-sectional standard deviation of industry-median adjusted earnings is rst calculated, and then similar time series model is used to obtain the time-series shock to the industry adjusted earnings dispersion measure. This is our intra-industry earnings dispersion DISP _IntraIND t. These two industry 11 Since the number of rms per industry can be relatively low, the industry mean of earnings is sensitive to extreme observations. Instead of removing outliers for each industry, which would further reduce the number of observations, we use industry medians instead of industry means for calculating intra- and inter-industry dispersions. 16

17 dispersion measures are highly correlated with correlation about We then test the predictability of cross-industry and intra-industry earnings dispersions by running the lagged return regression similar to that in Table 6, replacing the earnings variables with industry median earnings changes and two di erent dispersion measures. Rank 1;t is the rank of cross-industry earnings dispersion (DISP _IND t ) and Rank 2;t is the rank of intra-industry earnings dispersion (DISP _IntraIND t ). Table 8 reports the results of our industry analysis. We nd no evidence that cross-industry earnings dispersion a ects the predictability of aggregated earnings since the coe cient of interaction term X t =P t 1 _IND Rank 1;t is statistically insigni cant and positive. However, the coe cients of interaction term X t =P t 1 _IND Rank 2;t are negative with values of and and with t-statistics of and in the equal-weighted and valueweighted return regressions, respectively. This suggests that intra-industry earnings dispersion does a ect earnings predictability. In sum, the results are consistent with the hypothesis that higher earnings dispersion results in more uncertainty about aggregate earnings and less predictability. Consequently, investors demand higher (expected) rates of return during periods of uncertainty about future accounting pro ts, which results in a contemporaneous price decline. 5.2 Earnings Dispersion and Unemployment Our second interpretation of the results suggest that high earnings dispersion results in unemployment, as employees transfer from the poorly performing to the well performing employers. Since the job market is not frictionless, this shift in employment should result in short-run unemployment (Lilien, 1982). Table 2 provides some initial univariate evidence consistent with the hypothesis that earnings dispersion is associated with shocks to employment. U t is positively correlated with DISP t _w. The correlation is for DISP t _ew and for DISP t _vw. These correlations are statistically signi cant as well. Note also that U t is positively correlated with contemporaneous returns. The correlations are above 40% for both equal-weighted returns (0.421) and value-weighted returns (0.405) and are statistically signi cant. In addition, contemporaneous shocks to unemployment are negatively correlated with lagged stock returns. The correlation is above 27% in absolute value and is statistically signi cant. 17

18 To test the relation between unemployment and earnings, we use the following regression: U t = X t =P t 1 _w + 2 DISP t _w + t (6) where w = few, vwg. The results are reported in Panel A of Table 9. The results suggest that unemployment rises during periods of low average earnings changes. This is not surprising because when rms are performing poorly, they are likely to employ less. The coe cient varies from to and is statistically signi cant (the t-statistic is above 4 in all models). In addition, the results suggest that unemployment rises during periods of high equal-weighted earnings dispersion. In contrast, controlling for average earnings changes, there is no statistical relation between the value-weighted earnings dispersion and unemployment. Panel B of Table 9 reports results for estimating Equation (3) including unemployment shocks, U t, as an independent variable. The results are consistent with the hypothesis that the relation between earnings dispersion and stock returns is due in part to expected unemployment. Panel B reports results for contemporaneous stock returns, = 0, in Equation (3). The coe cient on unemployment is positive and statistically signi cant. The coe cient varies from to and is statistically signi cant. The t-statistics vary from to The results are consistent with the hypothesis that the relation between earnings dispersion and aggregate stock returns may be due to unemployment. Not only is the coe cient on unemployment positive and statistically signi cant, but also the coe cient on earnings dispersion reduces signi cantly. Recall that the coe cient on DISP t _ew, reported in Table 3, varies from to 7.181, with the highest t- statistics of When unemployment is added, the coe cient and its signi cance decline; The coe cient varies from to 5.639, with the highest t-statistic of In addition, the coe cient on unemployment reduces signi cantly when earnings dispersion is included as does its statistical signi cance. Panel C of Table 9 reports results for lagged stock returns, = 1, in Equation (3), including unemployment shocks, U t, as an independent variable. The results indicate that unemployment shock is consistently negatively related with lagged stock returns and statistically signi cant. The coe cient varies from to and the t-statistics vary from to Similar to contemporaneous results, the adjusted-r 2 also increases in all regressions when unemployment is included in the lagged return regression results reported in Table 4. The magnitude of coe cients 18

19 and t-statistics of earnings dispersions also decrease compared to those in Table 4, though the reduction is not as large as in contemporaneous results. In Table 4, the coe cient on DISP t _ew varies from to , with highest t-statistic of When unemployment is added, the coe cient varies from to , with the highest t-statistic of Consistent with the relation between unemployment and contemporaneous returns, the coe cient on unemployment reduces signi cantly when earnings dispersion is included. Furthermore, the explanatory power of the model does not increase substantially when unemployment is included, compared with the results reported in Table 4. We also perform the industry analysis using cross-industry and intra-industry earnings dispersions for the unemployment hypothesis and the results are reported in Table 10. Panel A provides the relation between two dispersion measures and unemployment shock. Consistent with Panel A of Table 9, unemployment rises during periods of low average industry median earnings changes. In Equation (6) when both DISP _IND t and DISP _IntraIND t are included in the regression, both coe cients are not statistically signi cant due to the high correlation between these two measures. The other two models regress the unemployment on each dispersion measure separately and the results show that both cross-industry and intra-industry dispersions are signi cantly and positively related to unemployment. Our ndings suggest that per unit of dispersion, inter-industry dispersion has a larger impact on unemployment. This result is intuitive because reassignment of labor across industries is likely to take longer time than reassignment within industries. However, DISP _IND t has much smaller standard deviation (0.001) than DISP _IntraIND t (0.018). Consequently, both measures of dispersion signi cantly a ect unemployment. Panel B of Table 10 reports the results for estimating contemporaneous returns, = 0, in Equation (3), using industry earnings changes (X t _IND) and dispersions (DISP _IND t and DISP _IntraIND t ) with or without unemployment. Similar to the results in Table 9, when unemployment is added into the regression model, its coe cient is positive and statistically signi cant (at the 10% level). In multivariate regressions, the coe cient of unemployment varies from to and t-statistics vary from to Also, the results show that the coe cients of both DISP _IND t and DISP _IntraIND t decline and their t-statistics reduce after including the unemployment in the regression. Compared to the regression model with unemployment alone, the coe cient and signi cance of unemployment with earnings dispersion variables also reduce. 19

20 Panel C reports the results for estimating lagged returns, = 1, in Equation (3), with industry earnings changes and two dispersion measures, also with and without unemployment. The results show that intra-industry earnings dispersion, rather than inter-industry earnings dispersion, is signi cantly negatively correlated with the lagged stock returns, con rming our results in Table 8. The coe cient on unemployment is negative and statistically signi cant (at the 10% level) in all regressions. In multivariate regressions, the coe cient on unemployment varies from to and t-statistics vary from to Again, after unemployment is added into the regression, the magnitude of coe cients and t-statistics of DISP _IND t and DISP _IntraIND t declines. This suggests that unemployment explains part of the relation between the earnings dispersion and lagged stock returns. In sum, the results are consistent with the hypothesis that earnings dispersion is predictable and is indicative of unemployment. Therefore, investors demand higher expected rates of returns during periods of high expected earnings dispersion. The resulting unemployment generates contemporaneous price declines. 6 Robustness Tests Our results using price-de ated earnings dispersion might be driven purely by the denominator, i.e., the dispersion of stock prices. To address this concern, we perform additional robustness tests. First, we redo the contemporaneous and lagged return regressions in Tables 3 and 4 while controlling for the dispersion in book-to-market. Second, we use di erent dispersion measures, such as earnings changes de ated by total assets. Third, we test whether our results hold for returns excess of the risk-free rate. Finally, we also control for some macro-economic variables. Our results are robust to all these additional tests. 6.1 Controlling for Book-to-Market The data on book value is available only after year 1962 in COMPUSTAT. Therefore, our rst robustness test covers the period from 1963 to We further delete the up and bottom 5% of rms ranked by book-to-market ratio each year. Similar to earnings dispersion, we rst obtain the time-series shocks to cross-sectional dispersion in book-to-market ratio, DISP t _btm, as the 20