Predictability of Aggregate Earnings

Predictability of Aggregate Earnings Aydin Uysal November 2011 Abstract In this study, I provide evidence that aggregate earnings are predictable based on the cointegration relation between earnings and cash flows implied by the accounting identity that earnings is the sum of the cash flows and the accruals. I first show that earnings and cash flows follow random walks with drifts while accruals is stationary with zero mean. I then show that earnings and cash flows are cointegrated and the cointegration error is the accruals. I finally show that earnings is the error correction term in this cointegration relation, hence predictable. My results which are robust to various financial statement frequencies, earnings measures, universes, and periods may help to answer some of the questions which were raised regarding to the contemporaneous relationship between aggregate earnings surprises and stock returns in the recent literature. 1 Introduction The recent finding by Kothari et al. (2006) that aggregate earnings surprises are negatively associated with contemporaneous stock returns is in contrast to the earlier evidence by Ball and Brown (1968) that firm level earnings surprises are positively associated with the contemporaneous stock returns. This finding has initiated a new line of research that examines the associations between aggregate earnings, cash flows, accruals, expected inflation, expected real returns, and risk free rates. Since the expected excess returns must be explained either by cash flows news or by discount rate news based on Campbell and Shiller (1988) decomposition of returns, and since earnings surprises are positively associated with cash flows news, the negative association between earnings surprises and expected excess returns may be driven by higher discount rates expected for the future. In order to test this, Kothari et al. (2006) examine the association between earnings surprises and changes in several discount rate proxies, which were initially proposed by Fama and French (1989), and find that while earnings surprises are positively associated with changes in treasury bill rates, they are negatively associated with changes in term and default spreads. Hence, Kothari et al. (2006) conclude that: These results provide strong, albeit indirect, evidence that earnings and discount rates move together. (p. 539) Following Kothari et al. (2006), while Hirshleifer et al. (2009), and Cready and Gurun (2010) mainly attribute the negative association between earnings, cash flows, and accruals surprises to discount rate news, Sadka and Sadka (2009) suggest that if earnings are predictable then this negative association may be due to a negative association between expected returns and expected changes in earnings. As the authors provide evidence that earnings are predictable they conclude that: Intuitively, the results suggest that either (1) investors become more risk averse when aggregate earnings change is high, and demand a sufficiently high risk premium that more than offsets the good news contained in the high earnings change; and/or (2) investors are able to predict aggregate earnings change and as they predict higher future earnings they demand lower risk premia. (p. 99) My objective in this study is to further examine the predictability of aggregate earnings. In summary, I show that aggregate earnings are predictable based on the accounting identity that aggregate earnings (hereafter earnings) is the sum of the aggregate cash flows (hereafter cash flows) and aggregate accruals 1

(hereafter accruals). I show this by first providing evidence that while earnings and cash flows follow random walks with drifts, accruals are stationary with zero mean. I then provide evidence that earnings and cash flows are cointegrated and the cointegration error is the accruals. I finally provide evidence that earnings is the error correction term in this cointegration relation hence predictable. My results are robust to various financial statement frequencies, earnings measures, universes, and periods. The remainder of this paper is organized as follows. In section 2 I review the literature related to my study. In section 3 I detail out the research design by stating my assumptions, deriving the model, and explaining the implementation. In section 4 I provide the empirical results. In section 5 I conclude. 2 Literature Review In order to show the predictability of earnings I build on three lines of literature that I briefly summarize below. In the first line of literature, Ball and Watts (1972) provide evidence that earnings follow a random walk with drift and conclude that:...in general, measured annual accounting incomes for U.S. corporations follow either a submartingale [random walk is a specific case of a submartingale] or some very similar process. (p. 663) Consistent with Ball and Watts (1972), I provide evidence that aggregate earnings follow a random walk with drift too. Moreover I provide evidence that aggregate cash flows follow a random walk with drift as well. I establish these by augmented Dickey-Fuller tests following Dickey and Fuller (1979). In the second line of literature, Dechow and Dichev (2002) use working capital accruals under the assumption that these will reverse within a fiscal year and provide evidence to support that:...our assumption that most working capital accruals reverse within one year seems reasonable for this sample. (p. 47). Following Dechow and Dichev (2002), I also use working capital accruals as a measure of accruals and provide evidence that aggregate accruals are stationary with zero mean in my sample as well. I establish these by augmented Dickey-Fuller tests following Dickey and Fuller (1979) too. Finally, in the third line of literature, following Johansen (1988), I first establish that earnings and cash flows are cointegrated and the cointegration error is the accruals. Then, following Engle and Granger (1987), I provide evidence that earnings is the error correction term in this cointegration relation and hence it is predictable. To my knowledge the cointegration of earnings and cash flows were first examined by Martikainen and Puttonen (1993) and Finger (1994). However, while the focus of Martikainen and Puttonen (1993) was the predictability of future returns, the focus of Finger (1994) was the predictability of future cash flows. So that, I believe this is the first study to examine the predictability of future earnings within a cointegration framework. 2

3 Research Design 3.1 Model Following Ball and Watts (1972) many researchers assumed that accounting incomes follow random walk hence they are unpredictable. However, in their seminal work Engle and Granger (1987) point that An individual economic variable, viewed as a time series, can wander extensively and yet some pairs of series may be expected to move so that they do not drift too far apart. Typically economic theory will propose forces which tend to keep such series together. (p. 82). In other words, if each element of a set of variables which are in an equilibrium relationship achieves stationarity after differencing, yet a linear combination of them is already stationary, the set of variables in the equilibrium relationship is said to be cointegrated. The accounting identity that earnings, E t, is the sum of cash flows, C t, and accruals, A t, E t = C t + A t (1) is one equilibrium relationship. Furthermore, from Ball and Watts (1972) it is known that earnings follow a random walk hence achieves stationarity after first differencing and from Dechow and Dichew (2002) it is known that accruals which is a linear combination of earnings and cash flows is stationary. If I can also show that cash flows follow random walk hence achieves stationarity after differencing I can establish that earnings and cash flows are cointegrated which I will formally do in section 4. More formally, I re-write accounting identity (1) as A t = E t C t. (2) I define the variable vector X t as [E t, C t ], the cointegration vector α as [1, 1] and finally re-write accounting identity (2) as A t = α X t. (3) That is, if earnings and cash flows follow random walks and achieve stationarity after first differencing and accruals are stationarity with zero mean, then earnings and cash flows are cointegrated with cointegration vector α = [1, 1]. Moreover, following Engle and Granger (1987), there exist a vector error-correction representation (VECM) of this cointegrated system which is X t = ν + γα X t 1 + Γ(L) X t 1 + ɛ t (4) where X t is the vector of first differences, ν and γ are (2x1) vectors, and Γ(L) is a finite-order distributed lag operator. This VECM (4) implies the following system of equations E t = ν E + γ E (α E E t 1 + α C C t 1 ) + Γ 111 E t 1 + Γ 112 C t 1 +... + ɛ t C t = ν C + γ C (α E E t 1 + α C C t 1 ) + Γ 121 E t 1 + Γ 122 C t 1 +... + ɛ t. (5) and after substituting (3) in (5) E t = ν E + γ E A t 1 + Γ 111 E t 1 + Γ 112 C t 1 +... + ɛ t C t = ν C + γ C A t 1 + Γ 121 E t 1 + Γ 122 C t 1 +... + ɛ t (6) 3

In this VECM (4) the term α X t 1 is the last period s equilibrium error and the vector γ is the vector of adjustment coefficients. While α X t 1 measures how much the cointegrated variables are deviated from their equilibrium levels, the vector γ controls which of these variables will subsequently adjust trying to restore the equilibrium and the Granger Representation Theorem states that if the variables in vector X t 1 are cointegrated, then at least one of the adjustment coefficients in γ must be non-zero. That is if earnings and cash flows are cointegrated, the accruals measures how much the earnings and cash flows are deviated from their equilibrium levels and the vector γ = [γ E, γ C ] controls whether earnings or cash flows will adjust in the subsequent period to restore the equilibrium. Finally, the Granger Representation Theorem states that either γ E or γ C must be non-zero that is either earnings or cash flows must be predictable. Hence following the Granger Representation Theorem I hypothesize that: Hypothesis: If earnings and cash flows are cointegrated and if the error correction term is the earnings then future earnings must be predictable. 3.2 Implementation In order to test the above hypothesis that either earnings or cash flows are predictable, I closely follow the methodology by Lettau and Ludvigson (2004) and estimate the parameters of the system of equations in (6) implied by the VECM (4) in a VAR framework in the next section. However, before doing so I first establish that earnings and cash flows follow random walks with drifts and accruals are stationary with zero mean using augmented Dicker-Fuller unit root tests. I then establish earnings and cash flows are cointegrated using Johansen L-max and Trace tests. Finally I decide how many lags to use for the VECM (6) using Akaike and Bayesian information criterion. 4 Empirical Results 4.1 Data I retrieve financial statement data from Compustat. Following Richardson et al. (2005), I measure earnings, E t, as operating income after depreciation (Compustat item OIADP), accruals, A t, as change in working capital accruals which is defined as the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item STI) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC). I measure cash flows, C t, as the difference between the earnings and the working capital accruals. 4.1.1 Sample I use annual data for the 50 year period from 1959 to 2008 for my empirical tests. Following Kothari et al. (2006), Hirshleifer et al. (2009), and Sadka and Sadka (2009), I include all firms in Compustat sample with December 31 st fiscal period end dates and sum up earnings, cash flows and accruals for all. 4.1.2 Descriptive Statistics Figure (1) plots the historical aggregate earnings, cash flows, and accruals. It is immediately clear from this figure that while aggregate earnings and cash flows tend to move together, aggregate accruals seem to behave stationary around mean zero as it would be expected. 1 Although I will be using earnings, cash flows, and accruals at levels in the following sections because of the econometric model I am using, I report the descriptive statistics of these variables after scaling them by lagged aggregate total asset values in order to obtain comparable statistics to the prior literature. 1 The exact time series mean and standard deviation of accruals are 0.0065 and 0.0096. 4

Figure 1: Historical Aggregate Earnings, Cash Flows, and Accruals Table (1) reports the means, standard deviations, medians, quartiles, and the correlations of aggregate earnings, cash flows, and accruals. While the sample statistics for earnings are consistent with Hirshleifer et al. (2009), the sample statistics for cash flows and accruals statistics are not. This is mainly because of the depreciation expense that Hirshleifer et al. (2009) take into consideration in calculation of accruals whereas following Richardson et al. (2005) I don t. The last three columns of Table (1) report the Pearson correlations above diagonal, the Spearman correlations below diagonal, and the serial correlations on diagonal. Consistent with prior literature while aggregate earnings are positively correlated with aggregate cash flows and accruals, aggregate cash flows are negatively correlated with aggregate accruals, however, similar to Hirshleifer et al. (2009) sample this negative correlation at aggregate accruals is lower than the firm level negative correlations in my sample too. Furthermore all three variables are serially correlated. Earnings have the strongest serial correlation and accruals have the weakest serial correlation. 4.2 Test Results In this subsection I report the results for unit root and cointegration tests that I use to establish that earnings and cash flows follow random walks with drifts, accruals are stationary with zero mean, and earnings and cash flows are cointegrated with a cointegrating vector α = [1, 1]. 4.2.1 Unit Root Tests Table (2) reports the augmented Dickey-Fuller unit root test results for earnings, cash flows, and accruals together with the 95% critical values for lags 0 through 5. Consistent with Ball and Watts (1972) it cannot 5

Table 1: Descriptive Statistics of Aggregate Earnings, Cash Flows, and Accruals, 1959-2008 This table reports the descriptive statistics for aggregate earnings, cash flows, and accruals. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database and scaled by aggregate total assets, (Compustat item AT). Columns 6 through 8 report the Pearson correlations above diagonal, the Spearman correlations below diagonal, and the serial correlations on diagonal for E t, C t, and A t. Mean Std Q1 Median Q3 E t C t A t N E t 0.0971 0.0151 0.0883 0.0972 0.1085 0.8473 0.7715 0.5692 50 C t 0.0906 0.0124 0.0804 0.0932 0.0976 0.7495 0.5897-0.0839 50 A t 0.0065 0.0096 0.0002 0.0039 0.0117 0.6108 0.0080 0.4255 50 be rejected that earnings follow a random walk with a drift for lags 0 through 5 with 95% confidence. Again consistent with Dechow and Dichev (2002) it can be rejected with 95% confidence that accruals follow a random walk in favor of accruals follow a stationary process with zero mean which is reported in table (1). Moreover similar to earnings it cannot be rejected that cash flows follow a random walk with a drift for lags 0 through 5 with 95% confidence. Table 2: Augmented Dickey-Fuller Tests for Unit Roots in Aggregate Earnings, Cash Flows, and Accruals, 1959-2008 This table reports the augmented Dickey-Fuller test statistics for unit roots in aggregate earnings, cash flows, and accruals together with the 95% critical values for lags 1 through 5. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. Lags 0 1 2 3 4 5 E t 4.5457 1.9771 2.4782 2.2333 2.4671 2.8270 C t 5.0555 2.6099 3.1583 3.1294 2.4507 2.4475 A t -7.1869-6.1003-4.2057-3.2428-3.3783-4.0246 95% CV -2.9235-2.9250-2.9266-2.9282-2.9298-2.9313 4.2.2 Cointegration Tests Table (3) reports the Johansen L-max and Trace test results for cointegration of earnings and cash flows together with 95% critical values. No cointegration can be rejected in both tests and for all lags just with the exception of lag 5 of L-max test. Moreover, the existence of a single cointegration vector cannot be rejected in favor of 2 cointegration vectors for lags 1 and 2 with 95% confidence for both tests. Although the existence of single cointegration vector can be rejected in favor of 2 cointegration vector for lags 3 through 5 with 95% confidence for both tests, this cannot be rejected for lags 4 and 5 with 99% confidence from the unreported results. This means that at least for lag 2 with 99% confidence we can accept that not only earnings and cash flows are cointegrated, but earnings, cash flows, and net 6

operating assets are cointegrated. In the unreported results I verify this following Engle and Yoo (1987), however, I leave this interesting finding for future research and for this study accept the existence of a single cointegrating vector. Table 3: Johansen Cointegration Test for Aggregate Earnings and, Cash Flows, 1959-2008 This table reports the Johansen cointegration test statistics for aggregate earnings and cash flows together with the 95% critical values for lags 1 through 5. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. L-max Test Trace Test Test Statistic 95% CV Test Statistic 95% CV r 0 1 0 1 0 1 0 1 Lags 1 27.5970 1.5710 14.2640 3.8410 29.1680 1.5710 15.4940 3.8410 2 22.1200 2.1330 14.2640 3.8410 24.2540 2.1330 15.4940 3.8410 3 18.4340 8.7190 14.2640 3.8410 27.1540 8.7190 15.4940 3.8410 4 20.4280 4.9480 14.2640 3.8410 25.3760 4.9480 15.4940 3.8410 5 10.4780 5.3730 14.2640 3.8410 15.8510 5.3730 15.4940 3.8410 4.2.3 Akaike and Bayesian Information Criterion Tests Table (4) reports the Akaike and Bayesian information criterion test results for VECM (4) for lags 0 through 5. The values for Akaike information criterion are corrected for unbiasedness. Both Akaike and Bayesian information criterion are minimized at lag 1 implying that a single lag for VECM (4) will provide the best fit for identifying the parameters of the cointegration relationship between earnings and cash flows. This result is also consistent with Dechow et al. (1998) firm level results in the sense that in order to remove the serial correlation in earnings changes that the authors reported an additional lag of earnings change is required. Table 4: Akaike and Bayesian Information Criterion This table reports the Akaike and Bayesian information criterion for VECM representation of E t and C t for lags 0 through 5. Akaike information criterion is corrected for unbiasedness. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. Lags 0 1 2 3 4 5 AIC -13.9359-14.7087-14.7042-14.6164-14.5929-14.5797 BIC -13.8348-14.5123-14.4205-14.2566-14.1726-14.1205 7

4.3 Estimation Results 4.3.1 Cointegration Vector Estimates Although the accounting identity (2) implies that the cointegrating vector α is [1, 1], for completeness I estimate this vector following Johansen (1987). Table (5) reports the cointegrating vector estimates for lags 1 though 5 after normalizing α E to 1. The results provides further support that the data is very consistent with the accounting identity (2). The cointegrating vector is very close to [1, 1] for all 5 lags and closest at lag 1. Table 5: Johansen Cointegration Vector for Aggregate Earnings and, Cash Flows, 1959-2008 This table reports the Johansen cointegration vector for aggregate earnings and cash flows together with the 95% critical values. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. Lags 1 2 3 4 5 α E 1.0000 1.0000 1.0000 1.0000 1.0000 α C -1.0061-1.0070-0.9910-0.9654-0.9723 4.3.2 VECM Parameter Estimates Now that I established that earnings and cash flows follow random walks with drifts, accruals are stationary with zero mean, and earnings and cash flows are cointegrated with a cointegrating vector α = [1, 1], I estimate the parameters of the VECM (6) with one lag based on the Akaike and Bayesian criterion. Table (6) reports the parameter estimates together with the t-statistics and R 2 s for this system. With the exception of the adjustment parameter γ C of cash flows all parameters are statistically and economically significant and consistent with the Granger Representation Theorem although the adjustment parameter γ C of cash flows is statistically not different from zero, the adjustment parameter γ E of earnings is highly significant with a coefficient -1.6905 and t-statistic -4.3861. That is when earnings and cash flows deviate from their equilibrium levels and the the equilibrium error accruals manifests itself, subsequently earnings adjust trying to restore the equilibrium relationship. Furthermore the sign of the adjustment parameter γ E of earnings is consistent with Sloan (1996) and negative, that is relatively high (low) accruals in this period leads to relatively low (high) earnings the next period. This can also visually observed in figure (1) for years 2001 and 2002. 4.4 Earnings Forecasts In this subsection I forecast earnings changes based on the parameters that I estimated above. For the in sample forecasts I use the final set of parameters that I estimated using the complete data set and for the out sample forecasts I use the set of parameters that I re-estimated every fiscal period in order not to introduce any look ahead bias in my estimates. 4.4.1 In Sample Results Table (7) reports the correlation between realized and forecasted changes in earnings based on the final set of parameters that I estimated using the full data set above. I lose one observation since I 8

Table 6: Parameters Estimates from the Cointegrated VAR This table reports the parameter estimates of the cointegrated VAR for E t and C t with one lag. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. Equation Dependent Variable Parameter E t C t Intercept ν 0.0252 0.0145 (2.8514) (2.0616) A t 1 γ -1.6905-0.3953 (-4.3861) (-1.2837) E t 1 Γ 1.4239 1.1872 (5.1458) (5.3696) C t 1 Γ -0.7005-0.4712 (-2.7875) (-2.3466) R 2 0.4977 0.6493 N 50 50 forecast one period ahead, so that I have 49 observations for the calculations. Future changes in earnings are highly predictable with a correlation coefficient between realized and forecasted earnings changes 70.63% which is statistically significant at 99% level. Table 7: In Sample Forecasts This table reports the correlation between the realized E t and the forecasted E t based on the final set of parameters estimated with the cointegrated VAR for E t and C t with one lag. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. E t, E t N Correlation 0.7063 49 p-value (0.0001) 4.4.2 Out Sample Results Table (8) reports the correlations between realized and forecasted changes in earnings based on the set of parameters that I re-estimated each fiscal period in order not introduce any look ahead bias in my estimates. I lose 6 observations since I need at least 4 observations to be able to estimate the parameters of the VECM (6), 1 observation for calculating the changes for the previous period, and 1 oberservation for forecasting the next period ahead, so that I have 44 observations for the calculations. Changes in earnings are still highly predictable with a correlation coefficient between realized and forecasted earnings changes 50.83% which is statistically significant at 99% level. 9

Table 8: Out Sample Forecasts This table reports the correlation between the realized E t and the forecasted E t based on the annual set of parameters estimated with the cointegrated VAR for E t and C t with one lag. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. E t, E t N Correlation 0.5083 44 p-value (0.0004) In summary, future changes in earnings are highly predictable based on the both in sample and out sample forecast results, although correlation between realized and predicted changes in earnings decrease by 20% from in sample results to out sample results. 4.5 Robustness Tests In this subsection, I test the robustness of my above results to various financial statement frequencies, earnings measures, universes, and periods. 4.5.1 Financial Statement Frequency In order to increase the number of observations in my sample, I use quarterly financial statements and measure earnings, E t, as operating income after depreciation (Compustat item OIADPQ), accruals, A t, as change in working capital accruals which is defined as the difference between current assets (Compustat item ACTQ) minus cash and short term investments (Compustat item STIQ) and the current liabilities (Compustat item LCTQ) minus debt in current liabilities (Compustat item DLCQ), and cash flows, C t, as the difference between the earnings and the working capital accruals. I obtain the annualized values by aggregating all variables for the past four quarters. Although, because of the limited quarterly financial statements prior to 1963, my sample period only extends from 1963 to 2008, my data points increase from 50 to 184. Figure (2) plots these historical trailing four quarter aggregate earnings, cash flows, and accruals. Similar to figure (1), it is clear from this figure that while aggregate earnings and cash flows tend to move together, aggregate accruals seem to behave stationary around mean zero. I re-estimate the parameters of the VECM (6) with one lag based on the Akaike and Bayesian criterion using the trailing four quarter aggregate values. Table (9) reports the parameter estimates together with the t-statistics and R 2 s for this system. With this new sample that is almost quadrupled in size, consistent with the Granger Representation Theorem both adjustment parameters γ E of earnings and the adjustment parameter γ C of cash flows are highly significant. That is when earnings and cash flows deviate from their equilibrium levels and the equilibrium error accruals manifests itself, subsequently both earnings and cash flows adjust trying to restore the equilibrium relationship. The sign of the adjustment parameter γ E of earnings is still consistent with Sloan (1996) and negative, that is relatively high (low) accruals in this period leads to relatively low (high) earnings the next period. Furthermore the sign of the adjustment parameter γ C of cash flows is consistent with Barth et al. (2001) and positive, that is current accruals predict future cash flows after controlling for current cash flows. Table (10) reports the in sample and out sample correlations between realized and forecasted changes in trailing four quarter earnings. Next four trailing-four-quarter earnings are all highly predictable using both in sample and out sample parameter estimates, implying the predictability of aggregate annual earnings. 10

Table 9: Parameters Estimates from the Cointegrated VAR This table reports the parameter estimates of the cointegrated VAR for E t and C t with one lag. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADPQ), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACTQ) minus cash and short term investments (Compustat item CHEQ) and the current liabilities (Compustat item LCTQ) minus debt in current liabilities (Compustat item DLCQ), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are trailing four quarter aggregates for all firms. Equation Dependent Variable Parameter E t C t Intercept ν -0.0034-0.1209 (-0.916) (2.0616) A t 1 γ -0.0717 0.3206 (-3.4218) (4.5775) E t 1 Γ 1.0524 0.6165 (13.8901) (2.4344) C t 1 Γ 0.0686-0.2086 (2.9774) (-2.707) R 2 0.5837 0.2478 N 184 184 Table 10: Robustness Checks for the Frequency of Financial Statements This table reports the correlation between the realized E t and the forecasted E t based on the final and annual set of parameters estimated with the cointegrated VAR for E t and C t with one lag for different earnings measures. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADPQ), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACTQ) minus cash and short term investments (Compustat item CHEQ) and the current liabilities (Compustat item LCTQ) minus debt in current liabilities (Compustat item DLCQ), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are trailing four quarter aggregates for all firms. In Sample E t, E t Out Sample First Quarter (t=1) Correlation 0.7139 0.7002 p-value (0.0000) (0.0000) Second Quarter (t=2) Correlation 0.7439 0.7200 p-value (0.0000) (0.0000) Third Quarter (t=3) Correlation 0.6869 0.6468 p-value (0.0000) (0.0000) Fourth Quarter (t=4) Correlation 0.5599 0.5133 p-value (0.0000) (0.0000) N 183 178 11

Figure 2: Historical Trailing Four Quarter Aggregate Earnings, Cash Flows, and Accruals 4.5.2 Earnings Measures Table (11) reports the in sample and out sample correlations between realized and forecasted changes in earnings using the earnings measure earnings before extraordinary items (Compustat item IB), Et IB, versus the operating income after depreciation (Compustat item OIADP), Et OIADP. The last two columns of table (11) repeat the results from table (7) and (8) for Et OIADP. Although results for Et IB are weaker based on in sample parameter estimates, they are stronger based on out sample parameter estimates and both are still very strong and statistically significant at 99% level. 4.5.3 Universes Table (12) reports the in sample and out sample correlations between realized and forecasted changes in earnings for both S&P 500 and Compustat universes. The last two columns of table (12) repeat the results from table (7) and (8) for Compustat universe. Although results for the S&P 500 index are weaker than the Compustat universe, they are still very strong and statistically significant at 99% level. One possible reason for this could be the fact that firms are actively added and removed from the S&P 500 index which induces relatively more noise to aggregate earnings, cash flows, and accruals resulting less precise parameter estimates. 4.5.4 Periods Table (13) reports the in sample and out sample correlations between realized and forecasted changes in earnings for periods ending 2000 and 2005 which were sample periods in recent studies. Although 12

Table 11: Robustness Checks for the Earnings Measure This table reports the correlation between the realized E t and the forecasted E t based on the final and annual set of parameters estimated with the cointegrated VAR for E t and C t with one lag for different earnings measures. Earnings, E t, is measured by earnings before extraordinary items (Compustat item IB), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. IB E t, E t OIADP In Sample Out Sample In Sample Out Sample Correlation 0.6806 0.5722 0.7063 0.5083 p-value (0.0007) (0.0000) (0.0001) (0.0004) N 49 44 49 44 Table 12: Robustness Checks for the Universe This table reports the correlation between the realized E t and the forecasted E t based on the final and annual set of parameters estimated with the cointegrated VAR for E t and C t with one lag for S&P 500 and Compustat universes. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. S&P 500 E t, E t Compustat In Sample Out Sample In Sample Out Sample Correlation 0.6158 0.3309 0.7063 0.5083 p-value (0.0001) (0.0264) (0.0001) (0.0004) N 49 44 49 44 13

the sample periods in these studies were not started with fiscal year 1959, in order to make full use of the limited times series data I go as far back as possible. The last two columns of table (13) repeat the results from table (7) and (8) for period ending 2008. Not surprisingly predictability of both earnings and cash flows deteriorate as the sample period decreases as a result of the significant sampling error induced in the parameter estimates during the early estimation periods. Nevertheless significant in sample predicatability and some out sample predictability exist even in very short periods. In fact given that investors are not limited to time series data that is available for researchers from Compustat only for starting 1959, they could potentially have made better prediction for earnings changes based on more accurate out sample parameters using the extended time series data that they would have access to. For example, one source of historical data is Moody s Industrial Manuals which Davis et al. (2000) used to construct a dataset going back to 1929. I am currently in process of collecting the historical financial statement data for at least S&P 500 universe too. Table 13: Robustness Checks for the Period This table reports the correlation between the realized E t and the forecasted E t based on the final and annual set of parameters estimated with the cointegrated VAR for E t and C t with one lag for different periods. Earnings, E t, is measured by operating income after depreciation (Compustat item OIADP), accruals, A t, is measured as the change in working capital accruals which is the difference between current assets (Compustat item ACT) minus cash and short term investments (Compustat item CHE) and the current liabilities (Compustat item LCT) minus debt in current liabilities (Compustat item DLC), and cash flows, C t, measured as the difference between the earnings and the accruals. Earnings, cash flows, and accruals are aggregated for all firms with December 31st fiscal period ends in Compustat database. E t, E t 1959-2000 1959-2005 1959-2008 In Sample Out Sample In Sample Out Sample In Sample Out Sample Correlation 0.4145 0.0416 0.6140 0.3198 0.7063 0.5083 p-value (0.0071) (0.8067) (0.0057) (0.0390) (0.0001) (0.0004) N 41 36 46 41 49 44 In summary, my results are robust for different measures of earnings, robust for different universes, and getting stronger as more data points become available each year. 5 Conclusion In this study I provided evidence that aggregate earnings are predictable based on the accounting identity that earnings is the sum of the cash flows and the accruals. In this accounting identity earnings and cash flows follow random walks with drifts while accruals is stationary with zero mean and earnings and cash flows are cointegrated with the cointegration vector α = [1, 1] and the cointegration error is the accruals. My results are robust for various financial statement frequencies, earnings measures, robust for universes, and getting stronger as more time series data become available. 14

References Ball, R. and P. Brown (1968). An empirical evaluation of accounting income numbers. Journal of Accounting Research 6, 159 178. Ball, R. and R. L. Watts (1972). Some time-series properties of accounting income. Journal of Accounting Research 27, 663 682. Barth, M. E., D. P. Cram, and K. K. Nelson (2001). Accruals and the prediction of future cash flows. The Accounting Review 76, 27 58. Campbell, J. and R. Shiller (1988). Stock prices, earnings, and expected dividends. Journal of Finance 43, 661 676. Cready, W. M. and U. Gurun (2010). Aggregate market reaction to earnings announcements. Journal of Accounting Research 48, 289 334. Davis, J. L., E. F. Fama, and K. R. French (2000). Characteristics, covariances, and average returns: 1929 to 1997. The Journal of Finance 1, 289 406. Dechow, P. M. and I. D. Dichev (2002). The quality of accruals and earnings: The role of accrual estimation errors. The Accounting Review 77, 35 59. Dechow, P. M., S. P. Kothari, and R. L. Watts (1998). The relation between earnings and cash flows. Journal of Accounting and Economics 25, 133 168. Dickey, D. A. and W. A. Fuller (1979). Distribution of the estimators for autoregressive time weries with a unit root. Journal of the American Statistical Association 74, 427 431. Engle, R. F. and C. W. Granger (1987). Cointegration and error correction: Representation, estimation, and testing. Econometrica 55, 251 276. Fama, E. and K. French (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics 25, 23 49. Finger, C. A. (1994). The ability of earnings to predict future earnigns and cash flow. The Journal of Accounting Research 32, 210 223. Hirshleifer, D., K. Hou, and S. H. Teoh (2009). Accruals and aggregate stock market returns. Journal of Financial Economics 91, 389 406. Johansen, S. (1988). Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control 12, 231 254. Kothari, S. P., J. Lewellen, and J. B. Warner (2006). Stock returns, aggregate earnings surprises, and behavioral finance. Journal of Financial Economics 79, 537 568. Lettau, M. and S. C. Ludvigson (2004). Understanding trend and cycle in asset values: Reevaluating the wealth effect on consumption. American Economic Review 94, 276 299. Martikainen, T. and V. Puttonen (1993). Dynamic linkages between stock prices, accrual earnings and cash flows: A cointegration analysis. Annals of Operations Research 45, 319 332. Richardson, S., R. G. Sloan, M. Soliman, and I. Tuna (2005). Accrual reliability, earnings persistence and stock prices. Journal of Accounting and Economics 39, 437 485. Sadka, G. and R. Sadka (2009). Predictability and the earnings-returns relation. Journal of Accounting Research 94, 87 106. Sloan, R. G. (1996). Do stock prices fully reflect information in accruals and cash flows about future earnings? The Accounting Review 71, 289 315. 15