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ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES

A principal-components analysis demonstrates that common earnings factors explain a substantial portion of firm-level earnings variation, implying earnings shocks have substantial systematic components and are not almost fully diversifiable as prior literature has concluded. Furthermore, the principal components of earnings and returns are highly correlated, implying aggregate earnings risks and return risks are related. In contrast to previous studies, the correlation we report between the systematic components of earnings and returns is stable over time. We also show that the earnings factors are priced, in the sense that the sensitivities of securities' returns to the earnings factors explain a significant portion of the cross-sectional variation in returns, even controlling for return risk. This suggests earnings performance is an underlying source of priced risk. Our evidence that the information sets of returns and earnings are jointly determined implies cash flow risk and return risk are not fully separable, and raises the possibility that it is the common variation of earnings and returns that is priced.


1. Introduction

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES

The accounting literature following Ball and Brown [1968] documents a positive relation between earnings and returns at the firm level. In contrast, the literature in finance and economics generally follows Shiller [1981] in studying the relation at the aggregate (i.e., market index) level, and typically concludes that measures of aggregate profitability or cash flow (we define these terms more precisely in section 2) are not important contributors to aggregate price variation. For example, Campbell [1991] concludes that cash flow news explains only 15% of the variation in market return over 1952–1988, and Campbell and Vuolteenaho [2004] conclude that cash flow news explains only 20% of the variation. This literature generally attributes aggregate price changes primarily to variation in aggregate discount rates, or “expected returns” (e.g., Campbell and Shiller [1988a, 1988b], Campbell [1991], and Campbell and Ammer [1993]). To resolve these seemingly conflicting results, the literature generally has inferred that firm-level news about profitability—unlike returns—must be primarily idiosyncratic and hence almost entirely diversifiable. If earnings news is largely diversifiable but return news is not, then aggregate profitability likely would have only a minor effect on aggregate stock prices.

The conclusion that aggregate earnings news does not contribute substantially to asset price variation seems counter-intuitive for a variety of reasons. First, the existence of a substantial market factor in firms' earnings (Brown and Ball [1967]) implies that earnings variability is not in fact largely diversifiable. Second, variation in aggregate economic output is a plausible contributor to asset risk, and corporate profits not only comprise approximately 10% of GDP, but also are correlated with other GDP components.1 Third, it is counter-intuitive that variation in the aggregate stock market index is independent of variation in the underlying earnings stream of the firms that comprise it. Thus, Cochrane[2001, p. 398] concludes: “It is nonetheless an uncomfortable fact that almost all variation in [aggregate] price/dividend ratios is due to variation in [aggregate] expected excess returns. How nice it would be if high prices reflected expectations of higher future cash flows.”

We argue that earnings provides a superior cash flow news variable, and report strong and consistent evidence that aggregate prices and earnings are in fact closely related. We contribute three main results. Using a principal-components analysis, we first demonstrate that common earnings factors do explain a substantial portion of firm-level variation in earnings, which implies earnings shocks have substantial systematic components and thus are not largely diversifiable. Indeed, the systematic components of earnings and returns are similar in magnitude, seemingly inconsistent with the conclusion in prior literature that much of cash flow news (but not expected-return news) is idiosyncratic.2 Second, we show that the principal components of earnings and returns display canonical correlations of up to 0.70, which means earnings risk and return risk are closely related.3 It therefore might not be possible to separately identify earnings/cash flow risks and return risks, or more specifically to conclude that most undiversifiable risk is due to changes in expected returns, as in the substantial literature on excess volatility following Shiller [1981]. Similarly, estimating separate cash flow betas and discount-rate betas, as in Campbell and Vuolteenaho [2004], may not suffice because the covariance of stock returns with the interaction/correlation of cash flow news and expected-return news may be what is important for pricing. Our third major result is that systematic earnings risk is priced, in the sense that the sensitivities of securities' returns to the earnings factors explain a significant portion of the cross-sectional variation in returns, even when controlling for systematic return risk. This result is important because it suggests that earnings performance, as well as being substantially undiversifiable, is an important underlying source of priced asset risk. Overall, our results indicate that accounting earnings has substantial undiversifiable variation, that systematic earnings risk is correlated with return risk, and that systematic earnings risk is priced.

We contribute several other findings. Our pricing tests are conducted on portfolios formed by sorting on well-known asset-pricing anomalies, which implies the premium we observe on systematic earnings risk is a source of the returns from trading on these anomalies. In particular, the results for portfolios formed on earnings momentum are consistent with Ball's [1978] risk-based explanation of “post earnings announcement drift.”4 We also report that aggregate earnings, while negatively correlated with contemporaneous aggregate returns (consistent with Kothari, Lewellen, and Warner, [2006]), is positively correlated with lagged aggregate returns. This result is consistent with the firm-level literature (e.g., Beaver, Lambert, and Morse [1980], Collins and Kothari [1989], Kothari and Sloan [1992], and Collins, Kothari, Shanken, and Sloan [1994]), which shows that the market anticipates most of the variation in earnings. The result also is consistent with accounting rules and practices, under which economic income (return news) is not “recognized” as accounting income until it is “realized” in later periods.

One reason we obtain different results from prior literature is the aggregate cash flow “news” variable used. Shiller [1981] uses dividends, which we argue in section 2 is inferior to accounting earnings as a news variable. Much of the finance and economics literature following Campbell [1991] does not derive the cash flow variable from firms' financial statement data, for example by basing it on dividends, earnings or operating cash flow, but indirectly infers cash flow news from stock returns. The standard procedure decomposes returns into three components: expected returns, changes in expectations of future cash flows (cash flow news) and changes in expected returns (discount-rate news). Returns models are used to estimate the first and last components (expected returns and changes in expected returns), and cash flow news then is backed out as the residual variation in returns—that is, as the component of returns that is not explained by the model. Campbell [1991, 1993, 1996] observes that this procedure relies on a well-specified expectation model for returns; that is, it suffers from the “bad model” problem (Fama [1998]). Model error introduces a structural relation between the estimates of return news and cash flow news, because error in one generates offsetting error in the other. This makes research on the relative importance of return news and cash flow news difficult to interpret. Not surprisingly, the results from this procedure also are sensitive to the model used and the sample period studied. Campbell [1991] reports a correlation between cash flow news and discount rate news that varies from −0.664 to 0.097, depending on the time period and model. Campbell and Vuolteenaho [2004], using a different expectation model, find a correlation of 0.114 for 1929–2001.5 In addition, inverting the procedure, by first modeling expected cash flows and then backing out expected returns, could reverse the results and lead to the opposite conclusion, that discount rate news does not explain much price volatility (see Chen and Zhao [2008]). The approach we take avoids the “bad model” problem by studying the relation between stock returns and accounting earnings. These variables are observed directly and independently of each other, which avoids imposing the structure of a returns model on the earnings or cash flow variable.

We note several caveats. First, our study identifies the systematic factors in both earnings and returns using principal-components analysis, which identifies factors only up to a sign. We believe we can correctly sign the first principal component, by signing it to obtain a positive correlation with average earnings, with which it most likely is highly correlated. For robustness, we also conduct pricing tests for aggregate growth in earnings, a measure that does not utilize principal-components analysis, and find similar results. Second, our analysis utilizes annual returns and earnings, which limits the time series to approximately 55 observations at best and limits the power of our tests. Finally, since our focus is on earnings risk we do not explicitly model expected returns. Despite these caveats, our results generally indicate that systematic earnings have an effect on the cross-section of stock returns in a fashion that is consistent with expectations.6

The remainder of the paper is as follows. Section 2 outlines our reasons for believing dividends are a poor proxy relative to earnings for expected cash flows. Section 3 describes the data used for this study. Section 4 discusses the principal-components analyses of earnings and returns. In section 5, we conduct asset-pricing tests showing aggregate earnings are priced. Conclusions are offered in section 6.

2. Dividends, Earnings, and Expected Cash Flows

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES

Campbell [1991] provides a useful framework for understanding the relation between earnings and returns, by decomposing returns rt into three components: expected returns Et−1(rt), return news Nr, and cash flow news Ncf:

  • image(1)

where E(·) is the expectation operator and lower case denotes logs. A central research design choice involves measuring news about cash flow, Ncf.

One approach is to indirectly estimate news about cash flow, as the residual component of stock returns that is not explained by the estimated values of the other two components, expected returns Et−1(rt) and return news Nr. This approach requires a well-specified expectation model for returns (Campbell [1991, 1993, 1996]), because model error leads to structurally related errors in estimates of returns and cash flow news. Not surprisingly, results from this procedure are sensitive to the model used and the sample period studied. Chen and Zhao [2008] argue that reversing the procedure, by first modeling expected cash flows and then backing out expected returns, can lead to very different results and perhaps even the conclusion that discount rate news does not explain price volatility. Overall, the indirect procedure suffers from the “bad model” problem (Fama [1998]).

An alternative approach is to observe the cash flow news variable more directly (i.e., not as a residual). Here, the finance literature typically bases the news variable on dividends. News about cash flow then is defined as inline image, where Δdt denotes dividend growth (in logs) at time t and ρ is the inverse of 1 plus the dividend yield. Return news (changes in expected returns), Nr, is defined as inline image. The primary reason for constructing the cash flow variable from dividends appears to be that, in the absence of frictions, asset prices are well-known to be discounted expected cash flows, and therefore unexpected variation in asset prices (i.e., stock return) is due to changes in either expected returns (discount rates) or expected future cash flows. This “dividend-discount model” has provided a theoretical justification for using dividends as the independent variable.

We use earnings growth to construct our proxy for shocks to expected cash flows.7 One reason for preferring earnings over dividends is the Miller and Modigliani [1961] proof that, given earnings and investment, dividends are irrelevant for asset prices (ignoring effects such as taxes and contracting costs). Consistent with this insight, the “discounted residual income” model of Preinreich [1936], Peasnell [1982], Ohlson [1995] and others specifically derives the relation between price, book value and earnings. This model provides a specific framework for relating earnings and returns. Another reason for preferring earnings to dividends is the legal requirement that dividends can only be paid from realized earnings. The above reasons share the common view that earnings are the primitive variable from which dividends and other distributions are derived. A related reason for preferring earnings is that dividends is a substantially lower-frequency variable. Dividends are a smoothed and lagged function of earnings (Lintner [1956] and Fama and Babiak [1968]), and hence contain less information and exhibit lower volatility than earnings. Dividends are subject to low-frequency structural changes, such as changes in tax regime. A fourth reason for preferring earnings is the fact that a large proportion of firms pay little or no dividends (Fama and French [2001] and DeAngelo, DeAngelo, and Skinner [2004]), which severely limits the informativeness of dividends as a cash flow variable in cross-sectional commonality tests. Fifth, the firm-level literature contains ample evidence that returns are more highly correlated with earnings than with cash flows and dividends, particularly when these variables are measured over horizons as short as a quarter or a year.8 Sixth, research has shown that only a small percentage of equity analysts use cash flow measures to justify their recommendations.9 Finally, the much misunderstood objective of accrual accounting is to make earnings a better predictor of future cash flow than cash flow itself. The Financial Accounting Standards Board (FASB, the U.S. standard-setter) states this as follows:

Information about enterprise earnings based on accrual accounting generally provides a better indication of an enterprise's present and continuing ability to generate favorable cash flows than information limited to the financial effects of cash receipts and payments. (FASB [1978], p. 2)

Their [investors creditors, and others] interest in an enterprise's future cash flows and its ability to generate favorable cash flows leads primarily to an interest in information about its earnings rather than information directly about its cash flows.” (FASB[1978, p. 13], para. 43)

For the above reasons, we use earnings growth as our proxy for changes in expected future cash flows. In this regard, our approach is similar to that in Vuolteenaho [2000, 2002].

3. Data

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES

Returns and earnings are measured with the same frequency, annually. We do not use quarterly data to avoid imposing a seasonal model on earnings. Returns are annual cumulative returns from the beginning of April to the end of March of the following year, and earnings are measured as earnings in year t scaled by the average asset values at the end of years t − 1 and t, here designated as return-on-assets (ROA). The data consist of 71,622 firm-year observations over 1950–2005 for NYSE- and AMEX-listed stocks with December fiscal year-ends, from the Center for Research in Security Prices (CRSP) and Compustat databases. The number of firms each year ranges from 230 to 2,393; overall, there are 2,594 different firms in the sample.

We specify ROA rather than return-on-equity as our earnings measure for several reasons. Unlike return-on-equity, ROA avoids having to exclude observations with negative values of the denominator (assets are strictly nonnegative, but book values of equity are not). In addition, the earnings distribution is left-skewed, that is has many large negative values. Negative earnings also are associated with low book values of equity, inducing greater left skew in return-on-equity. Nevertheless, repeating the analyses presented below using return-on-equity yields similar—yet somewhat weaker—results, due in part to the smaller sample. Moreover, our findings are similar if operating income is used instead of earnings.

4. The Systematic Components of Earnings and Returns

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES

Prior studies typically examine the joint hypotheses that cash flow or profitability news is systematic and that it is priced. We separate the two questions. In this section, we first show that cash flow variation as reflected in accounting earnings has substantial systematic components of approximately the same relative importance as the systematic components in returns. We then examine two pricing questions. In this section, we examine the relation between systematic earnings variation and systematic return variation (i.e., between earnings and returns risk factors). In the following section, we examine whether the systematic components of earnings are priced in the cross-section of stock returns (i.e., whether earnings can be viewed as a source of priced risk).

When investigating the systematic components of earnings and returns, it is important to note that the variables are fundamentally different. Stock returns reflect all information that revises expectations of future cash flows, symmetrically including revisions that increase and revisions that decrease firm value. Information arrives almost continuously and in high frequency, so the Central Limit Theorem implies that stock returns are approximately symmetrically distributed, particularly when expressed as growth rates. In contrast, accounting earnings are based on accounting “recognition” rules, which have two salient properties. First, accountants are reluctant to base earnings calculations on revisions in expectations that they cannot verify independently of managers. Relative to returns, earnings therefore more closely resemble realized cash flow outcomes than revisions in expected cash flows. This implies that accountings earnings are persistent and hence prewhitening is required when estimating an earnings news variable. Second, accountants are conservative, in the sense (Basu [1997, p. 4]) that they adopt a lower verification standard for losses (downward revisions in expected cash flows) than for gains (upward revisions). Earnings therefore incorporate a higher frequency of unrealized capital losses than unrealized capital gains, which causes an asymmetrically high frequency of large negative earnings observations and implies that accounting earnings are left-skewed relative to returns. We exclude extreme observations from the principal-component analysis because large negative earnings shocks are due primarily to firm-specific accounting effects, and the objective is to efficiently extract the systematic components of earnings and returns, not firm-specific factors. For returns, we exclude the top 5% and bottom 1% of the distribution each year to obtain the distribution plotted in figure 1, panel A. The resulting earnings distribution still has a considerably larger left tail, and therefore we exclude the top 1% and bottom 5% of observations each year to obtain the distribution plotted in figure 1, panel B.

image

Figure 1—. The distribution of stock return and ROA. This figure presents histograms of stock returns and ROA of individual firms. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Panels A and B include observations pooled across the sample period. In panel A, the bottom 1% and top 5% of the distribution of returns each year are truncated, while in panel B, the bottom 5% and top 1% of ROAs are truncated. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

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4.1 extracting principal components

We use principal-component analysis to estimate the systematic components of returns and earnings, extracting five principal components (PCs), separately for each variable. We follow the methodology implemented in (Connor and Korajczyk [1986, 1987]), which allows the extraction of principal components of an unbalanced panel (i.e., incomplete data).

Define X to be the n × T matrix of observations for the variable considered (either returns or earnings). We assume that the data-generating process for Xj,t is an approximate factor model:

  • image(2)

where F is a k × T matrix of shocks to the variable that are common across the set of n assets, B is an n × k vector of factor sensitivities to the common shocks, and ɛ is an n × T matrix of asset-specific shocks. Systematic, or undiversifiable, shocks are those affecting most assets, while diversifiable shocks are those with weak commonality across assets. Define V = E(ɛɛ′). Chamberlain and Rothschild [1983] characterize an approximate factor model with k systematic factors as one for which the minimum eigenvalue of B′ B approaches infinity and the maximum eigenvalue of V remains bounded as n approaches infinity.

In an approximate factor-model setting for a balanced panel, Connor and Korajczyk [1986] show that n-consistent estimates (up to a linear transformation) of the latent factors, F, are obtained by calculating the eigenvectors corresponding to the k largest eigenvalues of

  • image(3)

They refer to these estimates as Asymptotic Principal Components. Note that Ω is a T × T matrix, so the computational burden of the eigenvector decomposition is independent of the cross-sectional sample size, n. This implies that factor estimates can be obtained for large cross-sectional samples. Standard approaches to principal-component or factor analysis often are unimplementable on large cross-sections because they require eigenvector decompositions of n × n matrices.

To accommodate missing data we follow the approach in Connor and Korajczyk [1987], estimating each element of Ω by averaging over the observed data. Let X be a variable with missing data replaced by zeros, and define N to be an n × T matrix for which Nj,t is equal to one if Xj,t is observed and is equal to zero if Xj,t is missing. Define

  • image(4)

Ωu is the unbalanced panel equivalent of Ω in which the (t, τ) element is defined over the cross-sectional averages of the observed data only. While Ω in a balanced panel is guaranteed to be positive semi-definite, Ωu is not. However, in large cross-sections we have not encountered cases in which Ωu is not positive definite. The estimates of the latent factors, inline image, are obtained by calculating the eigenvectors for the k largest eigenvalues of Ωu.

Using the above procedure, we extract the first five principal components for both returns and earnings. To illustrate the amount of commonality across assets, for both earnings and returns we estimate time-series regressions for each stock on the five extracted factors, and record the p-values of the factor loadings, the R2 values, and the adjusted-R2 values. The regression estimated is:

  • image(5)

where inline image is the k × 1 vector of factor estimates for year t.

Figure 2 plots cross-sectional averages of the R2 of the firm-level regressions. The R2 represents the percent of the variation in firm-level returns and earnings that can be attributed to systematic variation in returns and earnings, respectively. Figure 2 shows that a substantial component of the firm-level variation in both earnings and returns can be attributed to systematic variation. The first PCs of earnings and of returns explain 17% and 33% of firm-level earnings and returns, respectively; the first and second PCs together explain 28% and 42%, respectively; and the systematic components of earnings and returns captured by the first three PCs contribute as much as 42% and 48% of their variation, respectively. Five PCs together explain about 60% of the firm-level variation in both earnings and returns. These results show that both earnings and returns have significant systematic components, and that the structures of their communalities are similar. The results are consistent with the early single-factor CAPM-based results of Ball and Brown [1969] and Beaver, Kettler, and Scholes [1970].

image

Figure 2—. Commonality diagnostics of stock returns and ROA. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. Then, for each variable (return and ROA) and each stock, a time-series regression of the variable on its common factors is executed. The figure reports the average R2 of these regressions using one, two, three, four, and five factors. Each year, the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

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Table 1 reports the proportion of firms whose returns and earnings exhibit statistically significant variation with the corresponding principal component. For example, the returns and earnings of approximately 65% and 39% of the sample firms have a statistically significant relation (at the 20% level) with their respective principal components. These results are consistent with the hypothesis that both returns and earnings have significant systematic components.

Table 1.  Diagnostics of Commonality in Stock Returns and Returns-on-Assets
Panel A: Stock ReturnsPanel B: Returns-on-Assets
Significance1 Factor2 Factors3 Factors4 Factors5 FactorsSignificance1 Factor2 Factors3 Factors4 Factors5 Factors
  1. This table reports distribution statistics of time-series regressions. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. The principal components are orthogonalized in the following fashion: The second component is orthogonalized to the first, the third is orthogonalized to the first and second, and so on. Then, for each variable (return and ROA) and each stock, a time-series regression of the variable on its (orthogonalized) common factors is executed. The table reports the percentage of firms in the sample that exhibit significant coefficients at the 1%, 2%, 5%, 10%, and 20% statistical significance levels. The average R2 and the average adjusted-R2 of these regressions are also reported below. Prior to the extraction of principal components, each year the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

2065.3024.2522.9415.0324.632039.4223.1024.7924.1425.35
1057.5619.4316.429.7517.851030.4717.8618.9818.8219.43
549.4215.4211.106.4413.11523.9413.5415.1613.9115.03
240.0511.376.783.979.14216.898.6710.9610.1611.49
134.439.414.932.586.36112.986.658.957.869.27
Avg R20.330.420.480.530.59Avg R20.170.280.420.500.58
Avg Adj R20.280.340.360.370.41Avg Adj R20.120.180.290.340.40

An interesting question is the number of factors that determine the commonality in earnings and returns, although the focus of this paper is on the existence of commonality as distinct from the exact number of underlying factors. Unreported analysis of the eigenvalue structures of returns and earnings shows that the first principal component of both returns and earnings exhibits a significant effect, as expected. The remaining eigenvalues decline sharply, leveling off at about 15% of the value of the first eigenvalue. Although the exact number of factors remains unclear, the evidence indicates that returns and earnings share a similar number of significant factors. The criteria suggested in Bai and Ng [2002] result in five factors for both returns and earnings. These results using annual data complement previous studies, which typically focus on monthly return observations (e.g., Trzcinka [1986], Brown [1989], and Connor and Korajczyk [1993]).

The literature provides conflicting evidence on whether cash flows are diversifiable. On the one hand, some studies find evidence suggesting that cash flow variation is mostly idiosyncratic and diversifiable (e.g., Campbell and Shiller [1988a, 1988b], Campbell [1991], and Vuolteenaho [2002]). On the other hand, other studies (e.g., Brown and Ball [1967], Fama [1990], Schwert [1990], Kothari and Shanken [1992], Lettau and Ludvigson [2005], Sadka [2007], and Ang and Bekaert [2007]) find that variation in aggregate measures of profitability and cash flow exists, and causes variation in aggregate prices. The results presented in figure 2 support the conclusions of the latter studies because they suggest that both cash flows (earnings) and returns have significant systematic components and, therefore, neither is fully diversifiable.

4.2 from principal components to risk factors

Principal components analysis requires two adjustments: rotation and prewhitening. Rotation includes both signing the factors (because principal components analysis does not extract a sign) and orthogonalizing them. The first principal component of each variable is signed to have a positive correlation with the variable's cross-sectional equal-weighted average. The remaining components are signed to have positive correlation with the macroeconomic indicators (for brevity, these correlations are not tabulated), real GDP growth and growth in industrial production (each PC typically exhibits the same correlation sign with both indicators).

The correlations between the different principal components reported in table 2 incorporate our signing approach. The table also reports the time-series correlations between the principal components and the equal-weighted cross-sectional averages. There is a high correlation (0.99) in our annual data between the first principal component of returns and the equal-weighted average, consistent with prior results for monthly returns (e.g., Connor and Korajczyk [1988]). Similarly, the first earnings PC is highly positively correlated with aggregate earnings (0.96). In light of these high correlations, we believe that the first PC of earnings captures average profitability and the first return component represents the market factor. Since the economic interpretation of the remaining factors is unclear, they are mainly used for demonstrating commonalities.

Table 2.  Correlation of Principal Components of Stock Returns and Returns-on-Assets
 PC1 RETPC2 RETPC3 RETPC4 RETPC5 RETPC1 ROAPC2 ROAPC3 ROAPC4 ROAPC5 ROAAvg RETAvg ROA
  1. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. Panel A presented the time-series correlation matrix of the first five principal components and returns and ROAs, as well as the cross-sectional average of returns and ROAs. For panel B, the principal components are orthogonalized in the following fashion: The second component is orthogonalized to the first, the third is orthogonalized to the first and second, and so on. Prior to the extraction of principal components, each year, the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

Panel A: Before orthogonalization
PC1 RET1           
PC2 RET0.281          
PC3 RET0.09−0.051         
PC4 RET0.02−0.010.001        
PC5 RET0.18−0.09−0.03−0.011       
PC1 ROA0.080.21−0.100.39−0.051      
PC2 ROA−0.020.08−0.230.330.010.761     
PC3 ROA−0.090.090.270.160.100.16−0.011    
PC4 ROA−0.02−0.26−0.270.240.20−0.090.000.001   
PC5 ROA−0.09−0.02−0.010.01−0.06−0.090.000.000.001  
Avg RET0.990.370.110.000.160.130.01−0.08−0.07−0.101 
Avg ROA0.090.19−0.060.370.050.960.750.30−0.11−0.110.141
Panel B: After orthogonalization
PC1 RET1           
PC2 RET01          
PC3 RET001         
PC4 RET0001        
PC5 RET00001       
PC1 ROA0.080.20−0.090.39−0.041      
PC2 ROA−0.13−0.10−0.230.050.0701     
PC3 ROA−0.140.070.260.120.18001    
PC4 ROA0.00−0.24−0.290.260.130001   
PC5 ROA−0.060.020.000.05−0.0600001  
Avg RET0.990.090.02−0.02−0.010.13−0.14−0.13−0.04−0.071 
Avg ROA0.090.17−0.050.370.070.960.020.16−0.04−0.030.141

Panel A of table 2 reports a substantial correlation between the first and second principal components (0.28 for returns and 0.76 for earnings). Although the PCs span the same space regardless of whether they are correlated, it is important for interpretation purposes to obtain uncorrelated components. We therefore orthogonalize the components of both returns and earnings as follows: The second component is orthogonalized to the first, the third is orthogonalized to the first and second, and so on. The correlations between the orthogonalized returns and earnings components are reported in table 2, panel B.

The persistence of the earnings components makes their direct use unreasonable in the context of our asset-pricing tests below. From an economic standpoint, it is appropriate to study innovations to the time series because in theory only unanticipated changes are priced. We therefore prewhiten the earnings components by applying an AR(2) model to each, and use the estimated shocks from this model to proxy for the innovations to the earnings risk factors. In our sample, this model generates approximately serially uncorrelated shocks.10 Unreported tests confirm that returns do not exhibit significant serial correlation, so the return risk factors do not need equivalent prewhitening. The first two factors of returns and earnings are plotted in figure 3.

imageimage

Figure 3—. Time series of return principal components and ROA AR(2)-adjusted principal components. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. The first two panels plot the time series of the first two principal components of returns. The second principal component is orthogonalized with respect to the first component. For ROAs, shocks to both time series are proxied by the residuals of a second order autocorrelation model applied to each component. The second two figures plot the time-series shocks for the first two principal components of ROAs (orthogonalized). Each year, the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

4.3 the relation between earnings and returns factors

Table 3 reports the correlation between the first five prewhitened earnings factors, the lead earnings factors, and the return factors. The first return and earnings factors are contemporaneously negatively correlated (−0.21), consistent with Kothari, Lewellen, and Warner [2006]. The negative contemporaneous relation between earnings and returns also is apparent in figure 3. In contrast, returns are positively correlated (0.34) with future profitability, indicating the market is able to predict future accounting earnings, as expected. The negative contemporaneous correlation between aggregate earnings and returns may indicate that expected returns and expected earnings are negatively correlated (Sadka and Sadka [2009]), for example because expected returns are high in recessions when investors demand high risk premiums, but expected profitability in recessions is low.

Table 3.  Correlation of Principal Components of Stock Returns and AR(2)-Adjusted Principal Components of Returns-on-Assets
 PC1 RETPC2 RETPC3 RETPC4 RETPC5 RETPC1 ROAPC2 ROAPC3 ROAPC4 ROAPC5 ROALPC1 ROALPC2 ROALPC3 ROALPC4 ROALPC5 ROA
  1. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. The principal components of returns and ROAs are separately orthogonalized in the following fashion: The second component is orthogonalized to the first, the third is orthogonalized to the first and second, and so on. A second order autocorrelation model is applied to each principal component of ROAs whose time-series shocks are used to proxy for factor innovations. The table reports the time-series correlation matrix of five components of returns and five components of ROAs (contemporaneous and lead). Prior to the extraction of principal components, each year the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

PC1 RET1              
PC2 RET−0.021             
PC3 RET0.030.031            
PC4 RET−0.07−0.010.041           
PC5 RET0.010.02−0.02−0.011          
PC1 ROA−0.210.28−0.290.20−0.271         
PC2 ROA0.13−0.07−0.280.110.07−0.101        
PC3 ROA−0.120.25−0.100.200.100.170.141       
PC4 ROA−0.12−0.13−0.030.170.320.05−0.220.141      
PC5 ROA−0.10−0.02−0.130.03−0.070.17−0.400.160.031     
LPC1 ROA0.340.39−0.100.380.150.020.040.300.07−0.021    
LPC2 ROA−0.20−0.16−0.130.09−0.130.34−0.060.040.120.23−0.101   
LPC3 ROA−0.020.14−0.130.100.330.060.140.06−0.010.040.170.161  
LPC4 ROA0.13−0.300.160.230.21−0.190.19−0.040.01−0.120.05−0.200.151 
LPC5 ROA0.130.14−0.24−0.090.14−0.190.220.05−0.200.040.17−0.420.180.021

In addition to the pairwise factor correlations, we also compute canonical correlations between earnings and returns. In particular, we compute the first canonical correlation between the first two factors of earnings and the first two factors of returns; the first canonical correlation between the first three factors of earnings and the first three factors of returns; and so on. Table 4 reports the results for both contemporaneous and lead-lag canonical correlations. The contemporaneous canonical correlations between earnings and returns are 0.36, 0.51, 0.58, and 0.62 with 2, 3, 4, and 5 factors, respectively. These results suggest that the return space contains some information about earnings of the same period. Returns are even more strongly correlated with lead earnings factors. For the first lead of earnings factors with contemporaneous return factors, the correlations increase to 0.57–0.72. This result suggests that contemporaneous returns are more correlated with future profitability than with contemporaneous profitability, consistent with accounting recognition rules and with the efficiency of markets in foreseeing earnings. The correlations between lead earnings and returns decrease to 0.19–0.55, and are mostly statistically insignificant. In general, when two or three factors are considered, it seems that returns are correlated with contemporaneous and lead earnings, but not with lag earnings, consistent with expectations.

Table 4.  Canonical Correlations: Stock Returns and Returns-on-Assets
ROA in Period 2 Factors 3 Factors 4 Factors 5 Factors
  1. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. The principal components of returns and ROAs are separately orthogonalized in the following fashion: The second component is orthogonalized to the first, the third is orthogonalized to the first and second, and so on. A second order autocorrelation model is applied to each principal component of ROAs whose time-series shocks are used to proxy for factor innovations. The table reports the first canonical correlation between each two groups of common factors for different lags and for different number of factors in each group. The first column on the left indicates the number of lags that ROA components lead return components. For example, lead 0 is contemporaneous, lead 1 is the correlation of return at time t with ROA at time t + 1, and lead −1 is the correlation of return at time t with ROA at time t − 1. The P-values (using a Wilks's Lambda distribution) are reported in square brackets. Prior to the extraction of principal components, each year the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

−30.190.450.500.56
[0.792][0.221][0.271][0.131]
−20.200.400.500.54
[0.748][0.211][0.123][0.143]
−10.350.410.580.59
[0.184][0.272][0.006][0.009]
00.360.510.580.62
[0.127][0.015][0.020][0.006]
10.570.570.690.72
[0.001][0.010][0.000][0.000]
20.380.470.490.59
[0.098][0.123][0.077][0.039]
30.410.550.640.68
[0.075][0.040][0.010][0.046]

The canonical correlations reported in table 4 are quite robust. Similar results are obtained when the correlations are computed separately for the first and second half of the sample period, as well as using separately odd and even years. This finding contrasts with the results from using the residual procedure to estimate cash flow news, which are sensitive to the chosen sample period and expectation model for returns. For example, Campbell [1991], table 2, reports a correlation between cash flow news and discount-rate news that varies from −0.664 to 0.097, depending on the time period and model used to estimate news. Campbell and Vuolteenaho [2004], using a different expectation model, estimate a correlation of 0.114 (table 3) for the period 1929–2001. One possibility is that the residual estimation procedure adds a relatively large amount of noise to the estimated cash flow variable.

Further evidence of an economically substantial correlation between returns and earnings risks is reported in figure 4, which shows the average fraction of firm-level return volatility that is explained by systematic earnings variation. Specifically, the figure reports two statistics: (1) the R2 of a time-series regression of firm return on the earnings risk factors (these are the prewhitened PCs of earnings); and (2) the ratio of the latter R2 to the R2 computed from a regression of firm return on the five return risk factors. The figure reports the average of (1) and (2) across the sample firms for different lags: Panel A uses the five contemporaneous earnings factors, panel B uses their lead values, and panel C uses both contemporaneous and lead factors. All panels show that five PCs of earnings can explain, on average, over 50% of individual-firm systematic return variation. In panel C, the six contemporaneous and lead earnings factors explain more than 75% of the variation in the average firm's stock returns. Coupled with the canonical correlations computed above, these results suggest that systematic earnings variation accounts for a substantial amount of the variation in stock returns.

image

Figure 4—. Stock returns and principal components of ROA. Stock returns are compounded annually from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted for ROAs using the asymptotic principal components (APC) method. The principal components are orthogonalized in the following fashion: The second component is orthogonalized to the first, the third is orthogonalized to the first and second, and so on. A second order autocorrelation model is applied to each principal component of ROAs whose time-series shocks are used to proxy for factor innovations. For each stock, a time-series regression of its returns on the ROA factors is executed. The bars plotted in panel A represent the average R2 of these regressions using one, two, three, four, and five factors of ROAs (contemporaneous), while the symbols are the average of the ratio of R2 using five return factors and those plotted as bars. Similarly, panel B uses the lead series of ROA factors for the regressions. Panel C uses the first three ROA factors (contemporaneous and lead). Each year, the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The sample includes NYSE- and AMEX-listed stocks, with December fiscal year-end, over the period April 1950 to March 2006.

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The substantial correlation between systematic earnings and systematic returns has important implications. Theoretically, if cash flow news and return news are distinct, one can identify two different types of risk: return risk, as measured by the sensitivity of a firm's stock returns to Nr, and cash-flow risk, as measured by the sensitivity of a firm's stock returns to Ncf. Thus, Campbell and Vuolteenaho [2004] use a vector-autoregression (VAR) model to infer Nr and Ncf as separate variables. The model is used to estimate Et−1(rt) and Nr; then, the cash flow news variable Ncf is estimated as a “residual” term, that is, the remaining return variation that is not attributed by this procedure to expected returns and return news. However, if Nr and Ncf are highly correlated, it is not meaningful to distinguish between cash flow risk and return risk as economically separate variables. Yet the results in tables 2–4 imply that cash flow risk and return risk are highly correlated, and hence not economically separable. In particular, we document that expected earnings are negatively correlated with stock returns, which suggests that Nr and Ncf are negatively correlated (see also Campbell [1991]). The substantial correlation between systematic earnings and systematic returns suggests four things. First, the two components of price, returns and cash flows, may be jointly driven by common economic factors. Second, it may not be feasible to identify separate effects of cash flow news and returns news. Third, the priced risk may well be the variation that is common to earnings and returns. Fourth, the VAR procedure arbitrarily attributes the joint cash flow and return effects to returns alone, which potentially explains the weak effects Campbell and Vuolteenaho [2004] report for cash flows.

The common factors extracted in principal components analysis lack obvious economic intuition. To provide some assurance the estimated principal components of earnings are economically meaningful, we test whether they are correlated with well-known macroeconomic variables (these correlations are not reported for brevity).11 Specifically, the earnings and returns factors are related to growth in industrial production, real GDP growth, the unemployment rate, and inflation. We also examine the canonical correlations of three groups (returns, earnings, and lead earnings) of five factors with the group of the four macroeconomic variables. The canonical correlations are all quite high, suggesting that the space spanned by returns, earnings, and lead earnings are all correlated with the space spanned by macroeconomic variables.

5. Pricing Systematic Earnings

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES

5.1 contemporaneous versus lead earnings factors

This section reports robust evidence that lead earnings risk factors are priced. That is, they contribute to the explanation of cross-sectional differences in portfolio returns. The pricing tests specify lead as well as contemporaneous earnings factors as independent variables because previous sections show that returns factors lead earnings factors, consistent with firm-level studies including Collins and Kothari [1989] and Beaver, Lambert, and Morse [1980], and that macroeconomic variables also lead earnings.12 The substantial decline in profits in 2001 is likely due to Statement of Financial Accounting Standards (SFAS) 142, which changed the accounting treatment of goodwill arising from acquisitions. When the standard was adopted in 2001, many firms wrote off a substantial portion of their goodwill against reported earnings. This resulted in a transitory negative shock to aggregate 2001 earnings that had no implications for current aggregate returns (see Sadka and Sadka [2009] and Jorgensen, Li, and Sadka [2009]). We therefore exclude 2001 from the pricing tests, which requires the exclusion of the contemporaneous factors for year 2000 and the lead earnings factors for 2001.

5.2 test portfolios

Three sets of 25 portfolios are constructed on the basis of variables likely to induce cross-sectional variation in expected returns. These portfolios then are used to test whether earnings risk factors are priced. The first two sets are equal-weighted and value-weighted book-to-market-sorted portfolios. It is well documented that stocks with high book-to-market on average outperform stocks with low book-to-market, so sorting on this variable is a natural way of inducing cross-sectional variation in expected returns for the pricing model to explain.13 The portfolios are rebalanced in the beginning of April of each year, and the weights for the value-weighted portfolios are firms' relative market values at that time. Portfolio returns are calculated for the period April 1963 to March 2006.

The third set of portfolios is based on post-earnings-announcement drift, or earnings momentum. In this earnings-based anomaly, current earnings predict future abnormal returns (Ball [1978]), so it too is a natural variable for inducing cross-sectional variation in expected returns when testing the pricing of systematic earnings risk. Based on (Bernard and Thomas [1989, 1990]), we sort stocks into portfolios according to their standardized unexpected earnings (SUE) from a seasonal random walk earnings expectation with a drift (i.e., trend). Specifically, SUE for stock i in month t is defined as:

  • image(6)

where Ei,q is the most recent quarterly earnings announced prior to month t for stock i (not including announcements in month t), Ei,q−4 is earnings four quarters previously, and σi,t and Ci,t are the standard deviation and average, respectively, of (Ei,q− Ei,q−4) over the preceding eight quarters.14 Quarterly data are available for the period April 1974 to March 2006. The portfolios are rebalanced every month and stocks are held until four months after their earnings announcement date. We then calculate their cumulative annual returns.

5.3 cross-sectional regressions

The portfolios are used to test linear asset-pricing models of the form:

  • image(7)

where E[Ri] denotes the expected return of portfolio i (in excess of the risk-free rate), βi are factor loadings, and γ is a vector of premiums. Factor loadings are estimated from a multiple time-series regression:

  • image(8)

where ft is a vector of factors. First, the regression in (8) is estimated using the full sample. Because the factors are extracted using principal-components analysis, they are identified up to a scale. Thus, prior to running the regression in (7), we normalize the cross-section of β by scaling each βi by its respective cross-sectional standard deviation. This has no impact on the calculated standard errors, but allows us to interpret each estimated factor premium as the percent return per unit standard deviation of sensitivity to that factor, and zero to all other factors. Then, (7) is estimated every year, using the consistent cross-sectional regression proposed by Black, Jensen, and Scholes [1972], and Fama and MacBeth [1973], resulting in a time series of estimated premia γt. The time-series means and standard errors of the premia then are calculated. Last, the adjusted R2 of the cross-sectional regression is calculated as an intuitive measure that expresses the fraction of the cross-sectional variation of average excess returns captured by the model.

This research design tests whether the extracted factors can explain the cross-section of returns on the market-to-book and SUE portfolios. That is, it tests whether the first earnings and first returns factors are priced, in the sense that they carry a positive premium.15 The economic significance of the factor premia we report below is highlighted by the fact that the cross-sectional range in portfolio premia is 4.06, 2.92, and 7.83% annually for the equal- and value-weighted book-to-market portfolios, and the SUE portfolios, respectively.

5.4 the pricing of earnings risk: results

Before presenting the cross-sectional analyses of the pricing of earnings factors, we show that the sensitivities of portfolio returns to the earnings factors indeed are significant, to alleviate potential concerns of spurious results from our pricing tests. Table 5 reports the factor loadings of each portfolio using a model that includes both contemporaneous and lead earnings factors. Overall, the results for all three portfolio sets indicate that very few loadings on contemporaneous earnings are statistically significant, while most loadings on lead earnings are significant. This is consistent with our prior conclusion that lead earnings is more important than contemporaneous earnings in asset pricing.

Table 5.  Earnings Factor Loadings
Portfolio RankingBook-to-Market (Equal-Weighted)Book-to-Market (Value-Weighted)SUE (Equal-Weighted)
ROAt-statisticLead ROAt-statisticROAt-statisticLead ROAt-statisticROAt-statisticLead ROAt-statistic
  1. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. A second order autocorrelation model is applied to each principal component of ROAs whose time-series shocks are used to proxy for factor innovations. Three different sets of portfolios are analyzed: 25 book-to-market portfolios (both equal- and value-weighted) and 25 portfolios sorted by standardized unexpected earnings (SUE). The variable SUE for stock i in month t is defined as [(Ei,q− Ei,q−4) − ci,t]/σi,t, where Ei,q is the quarterly earnings most recently announced as of month t for firm i (not including announcements in month t); Ei,q − 4 is earnings four quarters ago; and σi,t and ci,t are the standard deviation and average, respectively, of (Ei,q− Ei,q−4) over the preceding eight quarters. The book-to-market portfolios are rebalanced at the beginning of April of each year (and held for one year); the portfolio weights for the value-weighted portfolios are the market values at the beginning of April. The SUE portfolios are rebalanced every month while holding each stock up to four months after the announcement date. The returns of all portfolios are the cumulative annual return from April of a given year through March of the following year. The table reports factor loadings, which are calculated using time-series regressions of portfolio returns (excess of the risk-free rate) on the innovations of the first principal component of ROA and their lead values (t-statistics in square brackets). Prior to the extraction of principal components, each year the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The year 2001 was excluded because a new accounting rule (SFAS 142) caused a large price-irrelevant shock to aggregate earnings. The sample includes NYSE- and AMEX-listed stocks with December fiscal year-end over the period April 1963 to March 2006 (SUE portfolio returns are available from March 1974).

1−4.01[−1.14]10.54[2.76]−5.49[−2.10]6.58[2.32]−1.81[−0.67]7.46[2.54]
2−3.84[−1.20]8.69[2.49]−6.13[−2.53]3.44[1.31]−2.30[−0.85]7.08[2.38]
3−2.98[−0.89]6.34[1.74]−3.82[−1.93]3.11[1.44]−2.00[−0.73]5.56[1.87]
4−4.23[−1.44]5.98[1.87]−3.91[−1.84]1.70[0.74]−2.38[−0.83]5.75[1.83]
5−5.25[−1.93]7.07[2.39]−3.02[−1.52]5.64[2.61]−3.47[−1.23]6.37[2.07]
6−4.23[−1.42]5.71[1.76]−3.40[−1.55]3.71[1.56]−3.43[−1.16]6.15[1.91]
7−4.61[−1.77]6.46[2.28]−3.17[−1.55]4.06[1.83]−3.68[−1.10]6.82[1.86]
8−3.09[−1.01]5.00[1.50]−2.29[−1.17]1.80[0.85]−3.70[−1.23]6.00[1.83]
9−3.99[−1.57]6.03[2.18]−2.90[−1.37]1.02[0.44]−2.37[−0.76]7.04[2.06]
10−3.97[−1.60]5.04[1.88]−2.87[−1.48]1.96[0.93]−3.56[−1.20]7.44[2.31]
11−4.36[−1.87]4.92[1.94]−3.12[−1.48]3.80[1.66]−2.80[−0.83]8.17[2.21]
12−2.51[−1.06]4.27[1.66]−0.81[−0.39]3.88[1.71]−3.00[−0.92]7.12[1.99]
13−2.59[−1.05]6.83[2.56]−0.28[−0.15]1.74[0.85]−3.20[−1.05]7.58[2.27]
14−5.13[−2.09]6.62[2.48]−1.20[−0.59]3.91[1.77]−3.34[−1.00]8.25[2.26]
15−2.50[−1.04]6.25[2.39]−2.66[−1.27]4.32[1.90]−3.66[−1.09]8.31[2.26]
16−4.27[−1.52]6.64[2.18]−3.02[−1.55]4.78[2.25]−3.83[−1.13]8.17[2.21]
17−3.29[−1.17]6.40[2.08]−3.12[−1.67]3.99[1.96]−4.80[−1.62]7.74[2.40]
18−1.97[−0.67]6.75[2.12]−2.90[−1.26]4.07[1.63]−3.62[−0.99]7.75[1.95]
19−3.32[−1.12]7.21[2.23]−1.11[−0.48]3.51[1.39]−5.11[−1.59]8.68[2.47]
20−3.44[−1.22]7.78[2.54]−0.16[−0.06]5.37[1.98]−4.63[−1.32]7.43[1.95]
21−2.19[−0.65]7.30[1.98]−3.37[−1.32]3.07[1.10]−3.78[−1.08]8.04[2.11]
22−1.83[−0.51]8.89[2.28]−0.74[−0.30]3.75[1.42]−6.39[−1.77]8.43[2.15]
23−1.53[−0.39]10.40[2.45]−0.44[−0.16]7.00[2.40]−5.07[−1.34]8.44[2.05]
24−3.76[−1.06]10.34[2.69]−0.98[−0.37]8.12[2.78]−5.61[−1.53]8.75[2.19]
25−2.57[−0.98]10.46[3.68]−1.14[−0.51]6.56[2.72]−4.62[−1.25]8.47[2.10]

For the equal-weighted 25 book-to-market portfolios, the evidence in table 6, panel A, indicates that both earnings and return risks are priced. A comparison of the first two rows in panel A shows that, considered individually, the first principal component of returns explains 53% of the variation in the portfolio returns, whereas the first principal component of earnings explains 39%. Their respective premia are estimated at 3.00 and 2.62%, with t-statistics of 3.36 and 3.63.

Table 6.  Pricing Systematic Earnings Using Cross-sectional Regressions
Int.RET PC1ROA PC1ROA LPC1RET PC2ROA PC2ROA LPC2Adj. R2
  1. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. The second principal components of returns and ROAs are orthogonalized to the first components, respectively. A second order autocorrelation model is applied to each principal component of ROAs whose time-series shocks are used to proxy for factor innovations. Three different sets of portfolios are analyzed: 25 book-to-market portfolios (both equal- and value-weighted) and 25 portfolios sorted by standardized unexpected earnings (SUE). The variable SUE for stock i in month t is defined as [(Ei,q− Ei,q−4) − ci,t]/σi,t, where Ei,q is the quarterly earnings most recently announced as of month t for firm i (not including announcements in month t); Ei,q−4 is earnings four quarters ago; and σi,t and ci,t are the standard deviation and average, respectively, of (Ei,q− Ei,q−4) over the preceding eight quarters. The book-to-market portfolios are rebalanced at the beginning of April of each year (and held for one year); the portfolio weights for the value-weighted portfolios are the market values at the beginning of April. The SUE portfolios are rebalanced every month while holding each stock up to four months after the announcement date. The returns of all portfolios are the cumulative annual return from April of a given year through March of the following year. Factor loadings are calculated using time-series regressions of portfolio returns (excess of the risk-free rate) on various risk factors. The factors considered are the first two principal components of returns (orthogonalized) and the innovations to the first two principal components of ROAs (contemporaneous and lead). The table reports the results of Fama and MacBeth [1973] regressions of portfolio returns (excess of the risk-free rate) on the (normalized) factor loadings for different models (premiums are reported in percent; t-statistics in square brackets). For each model, the adjusted R2 computed from a single cross-sectional regression of average excess portfolio returns on their factor loadings is reported. Prior to the extraction of principal components, each year the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The year 2001 was excluded because a new accounting rule (SFAS 142) caused a large price-irrelevant shock to aggregate earnings. The sample includes NYSE- and AMEX-listed stocks with December fiscal year-end over the period April 1963 to March 2006 (SUE portfolio returns are available from March 1974).

Panel A: 25 book-to-market portfolios (equal-weighted)
−17.313.00     0.53
[−2.36][3.36]      
17.78 2.62    0.39
[3.72] [3.63]     
2.08  2.44   0.33
[0.65]  [3.74]    
10.12 1.921.86   0.50
[2.64] [3.08][3.31]    
−5.941.671.381.17   0.62
[−1.08][2.18][2.80][2.43]    
−18.833.17  −0.26  0.52
[−2.16][2.93]  [−0.32]   
19.26 2.95  −0.70 0.39
[4.23] [3.68]  [−1.10]  
7.32  2.43  1.180.38
[2.06]  [3.73]  [2.09] 
13.83 2.542.28 −0.961.320.52
[3.09] [3.18][3.90] [−1.74][2.25] 
−8.982.191.671.811.32−1.030.360.77
[−1.35][2.43][3.06][3.96][1.87][−2.03][1.28] 
 
Panel B: 25 book-to-market portfolios (value-weighted)
−9.052.33     0.62
[−1.67][2.99]      
10.10 1.62    0.28
[3.44] [2.09]     
4.08  1.85   0.38
[1.62]  [3.11]    
6.35 1.191.53   0.48
[2.20] [1.57][2.77]    
−4.711.840.360.84   0.65
[−1.08][2.57][0.51][1.68]    
−2.611.41  1.23  0.68
[−0.42][1.71]  [1.84]   
11.33 1.28  −1.02 0.36
[3.55] [1.87]  [−2.01]  
4.13  2.00  0.380.35
[1.65]  [3.10]  [1.06] 
8.11 1.051.30 −0.84−0.200.52
[2.33] [1.41][2.10] [−1.82][−0.51] 
0.951.220.250.511.26−0.470.050.65
[0.17][1.43][0.34][1.01][1.82][−1.08][0.14] 
 
Panel C: 25 SUE portfolios (equal-weighted)
−50.986.92     0.77
[−13.49][11.35]      
−4.72 −6.39    0.65
[−1.25] [−10.81]     
−33.25  6.22   0.61
[−9.15]  [10.87]    
−26.40 −4.133.67   0.78
[−7.62] [−9.13][8.97]    
−42.214.80−2.871.68   0.86
[−13.02][10.02][−7.60][5.20]    
−51.724.92  3.16  0.86
[−13.59][9.29]  [6.80]   
−8.42 −6.47  0.85 0.65
[−2.51] [−10.89]  [2.68]  
−39.49  4.55  −3.130.78
[−10.47]  [9.18]  [−8.02] 
−33.37 −2.983.74 0.05−1.820.80
[−10.49] [−7.66][8.59] [0.16][−5.78] 
−40.953.83−2.812.023.92−0.51−1.000.92
[−12.38][8.24][−5.36][3.80][5.30][−1.54][−3.12] 

The premium on the first return factor (which in essence is the market factor) varies from 1.67 to 3.00% annually, depending on which earnings and return factors are in the pricing model, with a t-statistic that varies from 2.18 to 3.36. Thus, the premium is statistically significant for all pricing model specifications. This result differs from many other studies that do not find the market return to be priced. Our results may stem from the use of annual betas versus the commonly used monthly betas, consistent with the results in Handa, Kothari, and Wasley [1989]. Unreported results also show that the value-weighted market factor of Fama and French [1993] is significantly priced when it is used alone to explain the cross-section of the annual returns of their 25 size and book-to-market portfolios. The pricing of the market factor also is apparent from the high adjusted-R2 (53%) when the first returns factor is included on its own. The second returns factor, which is the second principal component, does not appear to be priced.

The first earnings factor (which in essence is aggregate, market-wide earnings) attracts a premium that varies from 1.38 to 2.95% annually across the pricing models. The risk premium is statistically significant in all models, with t-statistics varying from 2.80 to 3.68. The lead earnings factor is priced as well: Its premium varies from 1.17 to 2.44% and is statistically significant in all models, with t-statistics varying from 2.43 to 3.96.

The first two rows in panel A indicate that both return and earnings risk factors explain a substantial amount of the pricing of the equal-weighted book-to-market-sorted portfolios. Subsequent rows report regression models with various combinations of return and earnings risk factors. When the earnings factors are included in the pricing model, the contemporaneous and lead first earnings factors are priced, and the premium on the returns factors declines substantially. For example, the premium on the first returns factor declines from 3.00% when included alone to 1.67% when the contemporaneous and lead first earnings factors are added. Both the contemporaneous and lead first earnings factors are statistically significant. These results support the hypothesis that systematic earnings variation is priced.

Figure 5, panel A, plots the excess returns and the loadings, βi, for the shocks to the lead of the first principal component of earnings. The figure shows that the loading on the first earnings risk factor is increasing with expected returns. These results suggest that high book-to-market portfolios earn higher returns because they are more sensitive to undiversifiable variation in aggregate earnings (i.e., earnings risk). As shown in the figure, this result holds consistently across portfolios with the exception of the two bottom book-to-market portfolios, which earn low returns but have high loadings on the earnings risk factor.16

image

Figure 5—. Excess returns and lead earnings loadings of book-to-market and earnings-momentum portfolios. Three different sets of portfolios are analyzed: 25 book-to-market portfolios (both equal- and value-weighted) and 25 portfolios sorted by standardized unexpected earnings (SUE). The variable SUE for stock i in month t is defined as [(Ei,q− Ei,q−4) − ci,t]/σi,t, where Ei,q is the quarterly earnings most recently announced as of month t for firm i (not including announcements in month t); Ei,q−4 is earnings four quarters ago; and σi,t and ci,t are the standard deviation and average, respectively, of (Ei,qEi,q−4) over the preceding eight quarters. The book-to-market portfolios are rebalanced at the beginning of April of each year (and held for one year); the portfolio weights for the value-weighted portfolios are the market values at the beginning of April. The SUE portfolios are rebalanced every month while holding each stock up to four months after the announcement date. The returns of all portfolios are the cumulative annual return from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted for ROAs using the asymptotic principal components (APC) method. Shocks to the first principal component of ROAs are proxied by the residuals of a second order autocorrelation model. The earnings loadings (points on the graphs) are calculated using time-series regressions of portfolio returns on the lead shock to the first principal component of ROAs. The time-series average of annual portfolio returns (excess of the risk-free rate) are shown as bars on the graphs. Prior to the extraction of principal components, each year the ROA sample is truncated at the bottom 5% and the top 1%. The year 2001 was excluded because a new accounting rule (SFAS 142) caused a large price-irrelevant shock to aggregate earnings. The sample includes NYSE- and AMEX-listed stocks with December fiscal year-end over the period April 1963 to March 2006 (SUE portfolio returns are available from March 1974).

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Figure 6 reports complementary results, plotting realized average returns against the fitted expected returns. The fitted values are calculated using Equation (7), where the loadings are computed through a time-series regression of portfolio excess returns on the lead shock to the first principal component of earnings. Apart from the bottom book-to-market portfolios, the realized returns are similar to the model's fitted returns.

image

Figure 6—. The cross-section of book-to-market and earnings-momentum portfolio returns and aggregate earnings. Three different sets of portfolios are analyzed: 25 book-to-market portfolios (both equal- and value-weighted) and 25 portfolios sorted by standardized unexpected earnings (SUE). The variable SUE for stock i in month t is defined as [(Ei,q− Ei,q−4) − ci,t]/σi,t, where Ei,q is the quarterly earnings most recently announced as of month t for firm i (not including announcements in month t); Ei,q−4 is earnings four quarters ago; and σi,t and ci,t are the standard deviation and average, respectively, of (Ei,q− Ei,q−4) over the preceding eight quarters. The book-to-market portfolios are rebalanced at the beginning of April of each year (and held for one year); the portfolio weights for the value-weighted portfolios are the market values at the beginning of April. The SUE portfolios are rebalanced every month while holding each stock up to four months after the announcement date. The returns of all portfolios are the cumulative annual return from April of a given year through March of the following year. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted for ROAs using the asymptotic principal components (APC) method. Shocks to the first principal component of ROAs are proxied by the residuals of a second order autocorrelation model. Each scatter point in each of the graphs represents one of the 25 portfolios, with the realized average return (excess of risk-free rate) on the horizontal axis and the fitted expected return on the vertical axis. The realized average return is the time-series average return, and the fitted expected return is calculated as the fitted value from E(Ri, t) =γ0+γ′βi, where Ri,t are the returns of portfolio i, βi is a factor loading, and γ is the estimated risk premium. The loadings are computed through a time-series regression of portfolio excess returns on the lead shock to the first principal component of ROAs over the entire sample period. The straight line in each graph is the 45 line from the origin. Prior to the extraction of principal components, each year the ROA sample is truncated at the bottom 5% and the top 1%. The year 2001 was excluded because a new accounting rule (SFAS 142) caused a large price-irrelevant shock to aggregate earnings. The sample includes NYSE- and AMEX-listed stocks with December fiscal year-end over the period April 1963 to March 2006 (SUE portfolio returns are available from March 1974).

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Panel B of table 6 reports similar results from pricing tests on value-weighted book-to-market-sorted portfolios. The first return factor appears to be priced, as are the contemporaneous and lead first earnings factors. However, the statistical significance of the results declines relative to panel A, particularly when the earnings and returns factors are included together. When included together, the risk premiums for returns and earnings decline as well. These results support not only the hypothesis that systematic earnings variation is priced, but also that it is difficult to distinguish between earnings risk and returns risk.

The results for the SUE-sorted portfolios are reported in panel C of table 6. The results indicate that earnings risk, and in particular the lead of the shocks to the first principal component of earnings, is priced and is significant. The premium varies from 1.68 to 6.22% annually. The t-statistic varies from 3.80 to 10.87. When included on its own, the lead of the shocks to the first principal component of earnings explains as much as 61% of the cross-section of expected portfolio returns. This high explanatory power is not due to a small spread in excess returns, as figure 5, panel C, shows that the post-earnings-announcement-drift portfolios generate high excess returns.

The plots in figure 5 illustrate the pricing of earnings risk. The figure plots loadings on the shocks to the lead earnings factor (the first principal component of earnings) and the average excess return for each of the 25 portfolios. The loadings on the lead earnings factor are increasing with excess returns in all panels. Panels A and B of figure 5 help explain the weaker results for the value-weighted book-to-market portfolios in panel B of table 6 since the portfolios generate less spread in excess returns than the equal-weighted portfolios. The lower spread in excess returns also is observable in panel B of figure 6. Panel C of figure 5 shows strong results for the SUE portfolios. The figure clearly demonstrates that expected returns increase with the loading. This suggest the excess returns to earnings momentum strategies can be explained in part by earnings risk, consistent with the hypothesis in Ball [1978]. Figure 6, panel C, provides complementary evidence, in that the realized returns align quite well with the fitted (expected) returns generated by an asset pricing model using only the lead of the shocks to the first principal component of earnings.

Overall, the results reported in table 6 and figures 5 and 6 are consistent with our hypothesis that earnings risk is priced. More specifically, it seems that since aggregate earnings shocks are highly predictable, the lead earnings factor is a more substantial risk factor in terms of pricing than the contemporaneous earnings factor.

The high correlation between earnings and returns factors implies it is not possible to clearly identify whether earnings risk or return risk is priced, or alternatively whether an unobservable factor, such as investor confidence or business conditions, is driving both the pricing of returns and earnings. To investigate whether the common variation in returns and earnings contains pricing information, we repeat our pricing analysis above while adding the interaction term between the first principal component of returns and the first principal component of earnings (lead, prewhitened). The results of these cross-sectional regressions are reported in table 7. In all cases, the interaction term is significantly priced, while the premia on return and lead earnings factors are significantly reduced. For both sets of book-to-market portfolios, the return and lead earnings factors contribute no additional explanatory power relative to the interaction between them. These results further emphasize the importance of considering the joint variation of cash-flows and returns, and the possibility of nonlinearity in the pricing of aggregate earnings and returns.

Table 7.  Pricing the Interaction of Return and Lead Earnings Factors
Int.RET PC1ROA LPC1RET × ROA PC1 × LPC1Adj. R2
  1. ROA is defined as earnings in a given year scaled by the average of asset value during that year and the previous year. Common factors are extracted separately for returns and ROAs using the asymptotic principal components (APC) method. The second principal components of returns and ROAs are orthogonalized to the first components, respectively. A second order autocorrelation model is applied to each principal component of ROAs whose time-series shocks are used to proxy for factor innovations. Three different sets of portfolios are analyzed: 25 book-to-market portfolios (both equal- and value-weighted) and 25 portfolios sorted by standardized unexpected earnings (SUE). The variable SUE for stock i in month t is defined as [(Ei,q− Ei,q−4) − ci,t]/σi,t, where Ei,q is the quarterly earnings most recently announced as of month t for firm i (not including announcements in month t); Ei,q−4 is earnings four quarters ago; and σi,t and ci,t are the standard deviation and average, respectively, of (Ei,q− Ei,q−4) over the preceding eight quarters. The book-to-market portfolios are rebalanced at the beginning of April of each year (and held for one year); the portfolio weights for the value-weighted portfolios are the market values at the beginning of April. The SUE portfolios are rebalanced every month while holding each stock up to four months after the announcement date. The returns of all portfolios are the cumulative annual return from April of a given year through March of the following year. Factor loadings are calculated using time-series regressions of portfolio returns (excess of the risk-free rate) on various risk factors. The factors considered are the first principal component of returns, the innovations to the first principal component of ROAs (lead), and the interaction of the two. The table reports the results of Fama and MacBeth [1973] regressions of portfolio returns (excess of the risk-free rate) on the (normalized) factor loadings for different models (premiums are reported in percent; t-statistics in square brackets). For each model, the adjusted R2 computed from a single cross-sectional regression of average excess portfolio returns on their factor loadings is reported. Prior to the extraction of principal components, each year the return sample is truncated at the bottom 1% and the top 5%, while the ROA sample is truncated at the bottom 5% and the top 1%. The year 2001 was excluded because a new accounting rule (SFAS 142) caused a large price-irrelevant shock to aggregate earnings. The sample includes NYSE- and AMEX-listed stocks with December fiscal year-end over the period April 1963 to March 2006 (SUE portfolio returns are available from March 1974).

Panel A: 25 book-to-market portfolios (equal-weighted)
 2.45  3.480.72
 [0.71]  [3.70] 
 10.25−0.350.913.940.71
 [1.91][−0.57][1.78][3.90] 
Panel B: 25 book-to-market portfolios (value-weighted)
 [2.30]  [3.14] 
 2.370.680.862.180.75
 [0.49][1.18][1.68][2.76] 
Panel C: 25 SUE portfolios (equal-weighted)
 −18.32  6.140.60
 [−5.59]  [10.63] 
 −50.925.372.402.950.79
 [−12.93][10.36][6.11][5.83] 

Our cross-sectional regression results are robust to several tests (for brevity they are not tabulated here, but are available from the authors on request). First, we study aggregate growth in earnings and aggregate growth in free cash flow, calculated as growth in the sum of free cash flow over all firms in the market (and hence equivalent to growth in a value-weighted market portfolio).17 Second, we apply the stochastic discount factor (SDF) approach as an alternative to the cross-sectional regressions methodology. This method utilizes the General Method of Moments (GMM) of Hansen [1982] and Hansen and Jagannathan [1997]. Overall, the evidence supports the conclusion that lead earnings represents a priced risk factor, that it is highly correlated with the return factor, and that it is priced in that it explains in part the cross-sectional variation in portfolio returns.

6. Conclusions

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES

This paper shows that there exists a significant systematic component to earnings variation and that this systematic component affects asset prices. We extract three aggregate factors of earnings and of returns and show that these factors explain approximately 60% of firm-level volatility in earnings and returns, respectively. In contrast to several prior studies that suggest that cash flows are almost entirely diversifiable, these results suggest the variation in earnings is largely systematic and not almost completely diversifiable. We also find that the common factors of earnings and returns are highly correlated, which implies that the information sets of returns and earnings are jointly determined and that it may not be possible to separately identify earnings/cash flow risk and return risk. The covariance of stock returns with the interaction/correlation of cash flow news and expected-return news may be what is important for pricing.

We then employ covariance-risk models to show that sensitivity to the earnings factors can explain a substantial portion of the cross-sectional variation in expected returns induced by sorting on the well-known asset-pricing anomalies of book-to-market and post-earnings-announcement drift. The pricing of the earnings factors is mostly apparent when lead earnings factors are employed, consistent with the notion that earnings are anticipated by investors.

These results have important implications since they imply that firm profitability is a substantial source of aggregate, undiversifiable risk. Furthermore, they are inconsistent with the Shiller [1981] theory that almost all aggregate market risk is due to shifts in discount rates. Because our test portfolios are formed by sorting on well-known asset-pricing anomalies, the results also imply that a source of the apparent excess returns to trading on these anomalies is undiversifiable earnings-performance risk that is priced.

Footnotes
  • 1

    Blanchard and Perotti [2002] estimate that the contemporaneous elasticity of changes in profits to changes in GDP is 2.15 for annual data and 4.50 for quarterly data.

  • 2

    For example see Campbell and Shiller [1988a, 1988b], Campbell [1991], and Campbell and Ammer [1993]. Vuolteenaho ([2002, p. 233]) interprets his results as showing that “expected-return-news series are highly correlated across firms, while cash-flow news can largely be diversified away in aggregate portfolios.”Cochrane ([2001, p. 399]) concludes: “Much of the expected cash-flow variation is idiosyncratic, while the expected return variation is common, which is why variation in the index book/market ratio, like variation in the index dividend/price ratio, is almost all due to varying expected excess returns.”

  • 3

    In contrast to previous studies, the correlation we report between the systematic components of earnings and the systematic components of returns is stable over the time period studied, 1951–2005.

  • 4

    The possibility that earnings momentum may reflect compensation for bearing systematic risk is also raised in Sadka [2006].

  • 5

    This difference could be due to the different sample periods, but we find that the earnings-returns relation is stable over time, which suggests it is due to the expectation models.

  • 6

    Throughout this paper, we address returns and earnings observed over periods with the same length (chiefly, annual returns and earnings). In particular, we do not refer to “event window” returns over short periods around earnings announcements. The accounting literature on earnings and returns is surveyed in Kothari [2001].

  • 7

    The term “cash flow” is used in the finance and economics literature because prices are present values of cash flows to investors (i.e., dividends). We argue below that as an informational variable related to stock returns (i.e., revisions in expectations of cash flows), earnings is a superior measure of the firm's free cash flow and hence of its capacity to pay future dividends.

  • 8

    Kleidon [1986] points out that assessing the volatility of cash flows using dividends is especially difficult in the presence of dividend smoothing. Kleidon further suggests that other measures, such as accounting earnings, may be more appropriate.

  • 9

    From an analysis of 976 equity analyst reports, Govindajaran [1980] found that an overwhelming majority of analysts focus on earnings rather than cash flow measures. Bradshaw [2002] found that 76% of equity analysts use P/E multiples in making investment recommendations, and only 5 use cash-flow-based multiples.

  • 10

    We also apply a time-series model similar to the one used by Basu [1997] at the firm level, where earnings changes are regressed on their lag value with a dummy variable for negative lag values. Basu finds that positive earnings changes are primarily persistent, but negative earnings changes are substantially more transitory. The earnings shocks we extract using this model are highly correlated with the AR(2)-generated shocks (correlation above 0.90).

  • 11

    Correlation between the return factors and macroeconomic variables supports the hypothesis that returns vary with business conditions (e.g., Fama and French [1989]). A similar observation applies to correlation with the earnings factors.

  • 12

    Similarly, Vassalou [2003] finds that a factor that includes information about future GDP growth explains some of the cross-sectional variation in stock returns. We interpret the positive correlation between returns and future profits as evidence of earnings predictability. Dow and Gorton [1997] and Hirshleifer, Subrahmanyam, and Titman [2006] provide alternative interpretations, though even then it would be appropriate to view lead earnings factors as risk factors.

  • 13

    Further, Kothari and Shanken [1997] and Vuolteenaho [2002], among others, document that book-to-market ratios have two major components, expected returns and expected profitability.

  • 14

    This SUE variable has been used by Chan, Jegadeesh, and Lakonishok [1996], Chordia and Shivakumar [2002], and Chordia et al. [2008], though those studies do not include a drift term (i.e., they assume Ci,t= 0). Bernard and Thomas ([1989, 1990]) and Ball and Bartov [1996] incorporate a drift.

  • 15

    Note that our goal is not to offer the “best” model for expected returns, but rather to estimate the role of earnings risk. Nevertheless, our research design, based on 25 portfolios separately sorted by book-to-market and SUE rather than the commonly used 25 portfolios double sorted by size and book-to-market, alleviates some of the concerns outlined in Daniel and Titman [2006], Phalippou [2007], and Lewellen, Nagel, and Shanken [2008].

  • 16

    Over-prediction of returns on the low book-to-market portfolios is not unique to our pricing model. Notably, the Fama-French model over-predicts its lowest portfolio by a statistically significant 0.34% (Fama and French [1993], model (iv), table 9a). Because this is a quintile portfolio, it corresponds to the bottom 5 of our 25 book-to-market portfolios.

  • 17

    To obtain fairly accurate data on free cash flow, it is necessary to have some data from the statement of cash flows. Unfortunately these are not available until 1971. Therefore, we employ a measure of free cash flow used by Lehn and Poulsen [1989] and by Lang, Stulz, and Walking [1991], where free cash flow is defined as operating income before depreciation minus interest expenses and taxes. Lehn and Poulsen [1989] also exclude dividends in the calculation of free cash flow. Our results are robust to this definition of free cash flow as well.

REFERENCES

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Dividends, Earnings, and Expected Cash Flows
  5. 3. Data
  6. 4. The Systematic Components of Earnings and Returns
  7. 5. Pricing Systematic Earnings
  8. 6. Conclusions
  9. REFERENCES
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