The Earnings Term Structure of Analyst Forecasts and Return Anomalies

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1 The Earnings Term Structure of Analyst Forecasts and Return Anomalies Zhi Da and Mitch Warachka Preliminary and Incomplete: All Comments Welcome Abstract We construct term structures for expected earnings growth by indexing analyst forecasts according to their maturity. Growth stocks, large stocks, and past losers have relatively steep convex earnings term structures in comparison to value stocks, small stocks, and past winners respectively. These initial earnings term structures overestimate (underestimate) the expected earnings growth of growth stocks, large stocks, and past losers (value stocks, small stocks, and past winners) in the future. However, the market appears to account for these systematic biases in expected earnings growth when pricing assets since cross-sectional variation across the earnings term structures cannot produce abnormal trading profits. Instead, cashflow betas derived from earnings term structures are higher for value stocks, small stocks, and past winners than growth stocks, large stocks, and past losers respectively. These differences in cashflow sensitivity are consistent with risk-based explanations for the size and value premium as well as momentum. We thank Michael Brennan, Phil Dybvig, Bing Han, David Hirshliefer, Inmoo Lee, Steve Orpurt, Mungo Wilson, and Tracey Zhang for their helpful comments and suggestions. University of Notre Dame, 239 Mendoza College of Business, Notre Dame, IN., 46556, USA. Singapore Management University, L.K.C. School of Business, 50 Stamford Road, , Singapore. 1

2 Over the past several decades, finance academics and professionals have documented considerable cross-sectional variation across the returns of different stock portfolios. However, the interpretation of this cross-sectional return variation remains controversial. Indeed, the value premium (value stocks with high book-to-market ratios earn higher returns than growth stocks with low book-to-market ratios) is central to the debate regarding market efficiency. Fama and French (1996) argue this premium is compensation for risk. Bansal, Dittmar, and Lundbald (2005), Cohen, Polk, and Vuolteenaho (2006) as well as Campbell, Polk, and Vuolteenaho (2006) conclude that value stocks are riskier than growth stocks since the cashflow innovations of value stocks have a higher covariance with market-wide cashflow fluctuations than the cashflow innovations of growth stocks. In contrast, Lakonishok, Shleifer, and Vishny (1994), Dechow and Sloan (1997), and LaPorta, Lakonishok, Shleifer, and Vishny (1997) argue the value premium reflects biased initial expectations of future earnings growth. Analyst forecasts are an important source of expectations regarding future earnings, with numerous empirical studies documenting a strong relationship between forecast revisions and stock returns. However, the prior literature usually focuses on a single forecast maturity. For example, LaPorta, Lakonishok, Shleifer, and Vishny (1997) investigate quarterly earnings forecasts while LaPorta (1996) and Dechow and Sloan (1997) investigate long term forecasts. Our contribution is the introduction of an earnings term structure which indexes analyst forecasts according to their maturity. Earnings term structures are a parsimonious but complete summary of earnings growth expectations, and offer three procedures for analyzing return anomalies. First, forward rates for earnings growth derived from earnings term structures can be compared with future earnings growth expectations (realizations). This comparison examines whether biases in these forward rates are systematically related to the stock characteristics underlying return anomalies. Second, conditioning on the slope and curvature of earnings term structures provides trading strategies capable of determining if biased expectations generate anomalous returns. Third, cashflow betas can be estimated from earnings term structures to explore this risk-based explanation for anomalies. We empirically implement these three procedures to study the value and size premium as well as momentum. A total of three analyst forecasts define the level, slope, and curvature of a firm s earnings term structure. Forecasts along the earnings term structure range from the current year until five 2

3 years into the future. The level of a firm s earnings term structure equals its long term forecast. 1 The earnings term structure s slope then gauges the extent to which current earnings growth is expected to expand, while its curvature reflects the rate of this expansion. 2 With regards to curvature, convex earnings term structures predict an acceleration in earnings growth, while concave earnings term structures indicate that analysts expect earnings growth to slow in the future. Slope and curvature are time-varying whenever different forecasts along an earnings term structure have revisions that differ in magnitude or direction. Focusing on a single analyst forecast implicitly assumes that earnings term structures can only experience parallel shifts, and further assumes stock returns induced by cashflow innovations are attributable entirely to fluctuations in this single forecast. Our empirical implementation reveals considerable time-variation in the slope and curvature of earnings term structures as different forecast maturities often have revisions in opposite directions. Stock returns are sensitive to revisions in each forecast along the earnings term structure, with these sensitivities varying across different book-to-market, size, and momentum portfolios. For example, the returns of value (growth) stocks are more responsive to revisions in short (long) term forecast maturities. Thus, when evaluating return anomalies, earnings term structures are necessary to extract the conditional information in analyst forecasts. 3 Our first application of the earnings term structure is conducted after sorting stocks into portfolios according to their book-to-market ratio, size, and past one-year return. Growth stocks, large stocks, and past losers have steeper more convex earnings term structures than value stocks, small stocks, and past winners respectively. Mean-reversion towards a horizontal earnings term 1 Long term forecasts for earnings growth are issued by analysts, while short term growth rates are inferred using prior earnings realizations and subject to measurement error. Long term analyst forecasts are also more stable over time than their short term counterparts. Our definition for level does not impose any assumptions on the relative accuracy of different forecast maturities. Moreover, the slope and curvature of an earnings term structure are independent of this definition. 2 For a given long term forecast, firms with slower forecasted earnings growth in the short term have steeper earnings term structures. This steepness reflects the greater optimism surrounding their future earnings prospects. 3 Analysts also issue stock recommendations and price targets. Womack (1996) reports that stock prices react to the announcement of analyst recommendations, while Brav and Lehavy (2003) document the influence of price targets on stock prices. 3

4 structure also occurs, with earnings growth declining to a lower rate which is similar across the various forecast maturities. However, these mean-reverting dynamics are consistent with earnings growth converging to a steady-state level, and are not necessarily indicative of biased forecasts. To circumvent the problem of consecutive analyst forecasts pertaining to different future timeperiods, we compute forward rates for earnings growth. 4 These forward rates serve as initial expectations of future earnings growth, and confirm the presence of systematic biases in analyst forecasts related to the value and size premium. 5 The relatively steep convex (flat concave) earnings term structures of large growth (small value) stocks generate upward (downward) biases in forward rates for earnings growth relative to expected earnings growth in the future. Forward rates for earnings growth are also biased when compared with realized earnings growth. Although growth stocks and large stocks have high forward earnings growth rates, they experience lower realized earnings growth than value stocks and small stocks respectively. Nonetheless, the market may be aware of the systematic biases in analyst forecasts and mitigate their impact on prices. To study the return implications of analyst forecasts, we examine trading strategies designed to exploit these biases by conditioning on the level and slope of earnings term structures. Stocks with high long term forecasts and low short term forecasts have steep earnings term structures, implying their forward rates for earnings growth are likely to be biased upward. 6 Therefore, we implement a level/slope trading strategy which begins by sorting stocks into portfolios according to their long term forecasts, and then their expected earnings growth over the short term. 7 However, this strategy yields insignificant risk-adjusted 4 For example, consecutive two-year earnings forecasts only have one year in common if the second forecast is issued one year after the original forecast. Therefore, the initial two-year forecast cannot be compared with the second forecast. 5 Unlike forward rates inferred from traded bond prices in the interest rate literature, forward rates for earnings growth are not defined by the assumption of no-arbitrage since analysts are not obligated to trade stocks at prices implied their forecasts. However, testing whether forward rates for earnings growth are biased predictors of future earnings growth does not require the assumption of no arbitrage. 6 Short term refers to the time interval between the first and second year, while long term refers to the subsequent two to four year timeperiod. 7 We also sort stocks in portfolios according to their slope and buy (sell) stocks with the flattest (steepest) earnings term structures. The performance of this strategy is similar to the level/slope strategy. In addition, an augmented value strategy which conditions on book-to-market and slope characteristics marginally outperforms the standard value strategy. 4

5 returns after controlling for book-to-market, size, and momentum characteristics as well as the market. For comparative purposes, we implement the trading strategy in LaPorta (1996) which buys (sells) stocks with low (high) long term forecasts. This strategy ignores short term earnings growth and focuses exclusively on the level of earnings term structures. We find LaPorta (1996) s trading strategy underperforms our level/slope strategy. The failure of biases in analyst forecasts to generate abnormal trading profits does not necessarily imply that book-to-market, size, and momentum characteristics proxy for sources of systematic risk. 8 Fortunately, besides formulating trading strategies, the earnings term structure allows analyst forecast revisions to proxy for innovations in expected earnings. Motivated by our earlier findings that stock returns respond to forecast revisions along the entire earnings term structure, we derive and estimate cashflow betas that incorporate time-varying earnings term structures at the portfolio level. Vuolteenaho (2002) demonstrates that the cashflow component of Campbell and Shiller (1988) s decomposition can be measured using earnings data. To our knowledge, we are the first to compute cashflow betas from revisions in analyst earnings forecasts as the prior literature computes cashflow innovations from realized earnings. An important advantage of the cashflow beta methodology is its independence from stock price (return) data. Cashflow betas relate risk premiums directly to fundamentals. Biases in analyst forecasts are mitigated in our cashflow beta implementation. Cashflow betas represent covariances which are computed from cashflow innovations. These innovations can be defined relative to biased expectations without introducing similar biases into the covariances. The innovations underlying our cashflow beta estimates are also computed over monthly horizons. These innovations eliminate biases that persist over this horizon. Richardson, Teoh, and Wysocki (2004) document a walkdown in analyst forecasts as they approach their maturity. This phenomena corresponds to a gradual reduction in optimism over horizons longer than one month. Furthermore, unlike prior cashflow betas, our estimates are not conditioned on an assumed process for expected returns. The cashflow betas in Campbell and Vuolteenaho (2004) assume an expected return premium for small stocks and value stocks, while those in Bansal, Dittmar, and Lundbald (2005) involve assumptions on consumption growth. 8 More precisely, the returns generated by the trading strategies cannot reject the four-factor model. However, from a behavioral perspective, our trading strategies may simply be unable to detect mispricings beyond those already incorporated into the benchmarking procedure. 5

6 We obtain strong evidence linking return anomalies with cashflow risk. Cashflow betas derived from analyst forecasts are higher for value stocks, small stocks, and past winners than growth stocks, large stocks, and past losers respectively. In particular, the value (small stock) portfolio has a cashflow beta that is 50% larger than the growth (large stock) portfolio, while the cashflow beta of the past winner portfolio is 24% higher than the past loser portfolio. These cashflow betas imply the value and size premium as well as momentum are more likely the result of cashflow risk than biased expectations for earnings growth. Specifically, the cashflows of growth stocks, small stocks, and past winners are more sensitive to market-wide cashflow fluctuations. The cashflow betas explain almost half of the cross-sectional variation in expected returns for bookto-market and size sorted portfolios. Therefore, our empirical evidence supports a risk-based explanation of these return anomalies. Moreover, analyst forecasts are an important source of information regarding future earnings, despite exhibiting systematic biases related to firm-level characteristics. Our earnings term structures contribute to a growing literature that recognizes the need for incorporating multiple analyst forecasts into studies of expected returns. This literature includes Frankel and Lee (1998), Lee, Myers, and Swaminathan (1999), Claus and Thomas (2001), Easton, Taylor, Shroff, and Sougiannis (2002), Ali, Hwang, and Trombley (2003), as well as Easton and Sommers (2006). By offering a parsimonious summary of the earnings growth expectations inherent in analyst forecasts, earnings term structures facilitate comprehensive studies into the origins of expected returns. The remainder of this paper is organized as follows. Section I describes our data and the forecast maturities which comprise the earnings term structure. Section II details the slope and curvature of our earnings term structure along with their importance, while evidence linking biased analyst forecasts with return anomalies is presented in Section III. Section IV then investigates the return implications of these biases using trading strategies derived from crosssectional variation across the earnings term structures of individual firms. The cashflow betas of book-to-market, size, and momentum portfolios are estimated using portfolio-specific earnings term structures in Section V. Section VI concludes and offers suggestions for future research. 6

7 I Data Our sample of analyst earnings forecasts is obtained from the Institutional Brokers Estimate System (IBES) Summary unadjusted file. We initially include all unadjusted consensus earnings forecasts starting in 1984 through Consensus earnings forecasts are produced monthly by IBES, typically on the third Thursday of every month. Our conclusions are robust to defining the concensus forecast as the median or the mean forecast, with the median being less sensitive to changes in analyst coverage. 9 We retain 545,165 firm-month observations for which the firm s earnings in the previous year (A0 t ), consensus earnings forecasts for the current fiscal year (A1 t ), the subsequent fiscal year (A2 t ), and long term growth (LT G t ) are available. 10 The t subscripts denote when analyst forecasts are employed to construct an earnings term structure. On average, there are approximately 2,000 stocks in our sample each month, comprising 72.2% of the entire US stock universe in terms of market capitalization as reported in Panel A of Table 1. NYSE stocks and NASDAQ account for 52.0% and 43.9% of these stocks respectively. The sample contains relatively large stocks whose average market capitalization is about 2,600 million dollars. The resulting dataset is then merged with the COMPUSTAT/CRSP merged dataset whenever price and/or accounting variables are needed. Observations with negative book values are eliminated before constructing the book-to-market ratios. Stock returns are obtained from CRSP after adjusting for delistings. Shares splits are also accounted for using the split factor in CRSP. Analyst forecasts are denominated in dollars per share except for the long term forecasts which are expressed as annualized percentage growth rates. The long term forecasts also have no fixed maturity date. Instead, they apply over the next three to five years, while annual forecasts have fixed maturity dates. Thus, to create our earnings term structure, dollar-denominated annual forecasts are converted into annualized percentage growth rates. As discussed in the next section, our earnings term structure consists of annualized percentage growth rates for the current year (A1 t,% ), the next two years (A2 t,% ), and the subsequent three to five years (LT G t ). These earnings growth rates parallel the spot interest rates along interest rate term structures. 9 Uninformed analysts are likely to herd and adopt the consensus forecast without inducing a revision that influences returns (Clement and Tse (2005)). 10 Quarterly forecasts are not utilized due to seasonality. A minimum analyst coverage filter is not imposed. However, we obtain qualitatively similar results in a smaller sub-sample which requires at least two analysts for each consensus forecast. 7

8 II Slope and Curvature Measures The slope and curvature of the earnings term structure are defined using two and three forecast maturities respectively which enables us to measure the evolution of expected earnings growth. This section confirms that by incorporating multiple analyst forecasts, these earnings term structure properties are more informative than individual forecasts. A. Slope To evaluate the forecasted earnings dynamics of individual firms across time, the relationship between their long and short term forecasts is studied. We convert the current year s dollardenominated A1 t forecast into an annualized percentage growth rate A1 t,% as follows A1 t,% = A1 t A0 t A0 t, (1) where A0 t denotes the firm s earnings in the previous year. This A1 t,% growth rate defines the slope of an earnings term structure Slope t = LT G t A1 t,%. (2) This slope metric summarizes the extrapolation of a firm s forecasted long term earnings growth relative to the current year. The difference in equation (2) parallels the term premium defined by long term minus short term bond yields. A negative slope indicates earnings growth is forecasted to decline, while a positive slope predicts faster earnings growth. For a given LT G t forecast, firms with lower A1 t,% implied growth rates have steeper earnings term structures. The variation in A1 t,% reported in Panel A of Table I attests to the importance of computing the slope of a firm s earnings term structure instead of only considering its LT G t forecast. Indeed, the large slope increase between 2000 and 2001 is attributable to a decrease in A1 t,%, with the opposite occuring in the subsequent year. Therefore, current earnings growth cannot be ignored when examining analyst optimism. For consistency, all the earnings term structure properties in Table I are computed once a year at the end of June. The market-wide entries in Table 1 aggregate across stocks by summing over their individual earnings forecasts. This aggregation is performed using earnings forecasts at the firm level rather than on a per share basis. 8

9 The slope of a firm s earnings term structure contains information which is not present in its book-to-market ratio. For example, consider two growth stocks with identical book and market values. A large market value can result from high current earnings combined with low forecasted growth, or a combination of low current earnings and high forecasted growth. Despite identical book-to-market ratios, the second stock has a steeper earnings term structure due to the greater optimism surrounding its future earnings growth. B. Curvature The earnings term structure s curvature summarizes the rate at which analysts predict earnings growth will accelerate or decline. In other words, curvature represents the second derivative of earnings growth along an earnings term structure. The curvature measure divides the first four years of the earnings term structure in half, starting with the following implied two-year growth rate A2 t,% = 1+ A2 t A0 t A0 t 1. (3) This percentage represents an annualized earnings growth rate for the next two years. The earnings term structure s curvature is then defined as Curvature t = LT G t +2A1 t,% 3 A2 t,%, (4) since A2 t is situated two years before LT G t s four year average horizon and one year after A1 t. 11 High long term forecasts relative to A2 t,% tend to produce convex earnings term structures which imply accelerating earnings growth. In contrast, relatively low long term forecasts lead to concave earnings term structures which are consistent with analysts anticipating a reduction in earnings growth after two years. According to Panel A of Table I, the average earnings term structure is upward sloping and concave. Panel B of Table I reports that the A1 t,% and A2 t,% short term growth rates are highly positively correlated, while A1 t,% and LT G t are negatively correlated. The negative correlation between the extreme ends of earnings term structure attests to the importance of 11 Equation (4) can also be derived from the difference between the expected earning growth during the second and fourth year versus the first and second year, LT G A2 % 2 A2 % A1 % 1. This difference equals LT G+2A1 % 2 3A2 % 2 which is equivalent to equation (4) after multiplying by 2/3. 9

10 studying their slope and curvature rather than relying on a single analyst forecast. The negative correlation between the slope and curvature measures emphasizes their distinct nature, although both properties gauge the extrapolation of current earnings growth. Note that price-earnings (P/E) multiples fail to explicitly incorporate the collection of analyst forecasts underlying our earnings term structure. Although price-earnings multiples are based on the extrapolation of current earnings, they cannot capture the curvature of a firm s earnings term structure since they assume future earnings growth is linear. Furthermore, residual income models such as Frankel and Lee (1998) and Lee, Myers, and Swaminathan (1999) require estimates for a firm s cost of equity and dividend payout rate under the assumption of clean surplus accounting. Dechow, Sloan, and Soliman (2004) s duration measure also requires estimates for the cost and growth rate of a firm s equity. More importantly, their duration measure does not incorporate analyst earnings forecasts. C. Stock Characteristics and Earnings Term Structures Table I documents significant time-variation in the aggregate earnings term structure at the market level. This time series property is complemented by the considerable cross-sectional variation between the earning term structures of different book-to-market, size, and momentum portfolios reported in Table II. Growth stocks have steep convex earnings term structures relative to value stocks since the long term forecasts of growth stocks are nearly double their counterparts for value stocks. Large stocks have steeper more convex earnings term structures than small stocks due to their lower forecasted earnings growth in the short term. Consequently, unlike the disparity between growth and value stocks, the relatively flat concave earnings term structures of small stocks reflects their high implied earnings growth rates across all forecast maturities. Past winners have flatter earnings term structures than past losers as high past returns portend stronger current earnings growth. Beyond the current year, past winners and losers have similar rates of forecasted earnings growth. Figure 1 plots the earnings term structures of growth stocks, large stocks, and past losers against value stocks, small stocks, and past winners respectively. The earnings term structures are plotted in the year of each portfolio s formation as well as three and five years afterwards. Mean- 10

11 reversion is detected in the earnings term structures of book-to-market and size portfolios. In particular, they converge towards horizontal earnings term structures as earnings growth declines to a lower rate which is similar across the various forecast maturities. These mean-reverting dynamics indicate that earnings term structures are not limited to parallel shifts. Consequently, this mean-reversion highlights the need to study multiple forecasts revisions when examining the market s reaction to expected earnings growth. D. Importance of Slope and Curvature To examine the importance of slope and curvature, we determine whether stock returns can be summarized by revisions in a single forecast maturity. Forecast revisions are computed for several forecasts along the earnings term structure until their eventual maturity. Revisions are denoted R T,H with T being the forecast maturity (in years) and H the horizon (in years) over which these revisions are computed with H T. Long term forecast revisions are denoted by T =4,withH = 3 being the maximum horizon over which revisions in long term forecasts are computed. These revisions are defined by consecutive forecasts and represent the dynamics of earnings term structures across time. We avoid dividing forecast revisions by price, as conducted in Doukas, Kim and Pantzalis (2002), since this normalization can induce systematically smaller revisions for higher priced stocks. However, a downward revision of 2% in a stock s long term forecast, from 22% to 20% is less drastic than a revision from 4% to 2%. To account for this base rate effect, we form normalized revision ratios which divide long term revisions by their original forecasts. 12 R 1,1 NR 4,H = R 4,H LT G, (5) Similarly, NR 1,1 is defined as and NR A1 2,1 as R 2,1, with these normalized revisions both representing a percentage change in A2 forecasted earnings over a one-year horizon. The following cross-sectional regression is conducted on individual stocks to determine the sensitivity of their returns to these normalized revisions r p = β 0 + β 1 NR 1,1 + β 2 NR 2,1 + β 3 NR 4,1 + ɛ, (6) 12 The normalized revision from 22% to 20% equals ( ) = 1 10, while ( ) = 1 2 is assigned to a revision from 4% to 2%, which is five times larger in absolute value. 11

12 where r p denotes the contemporaneous annual return of a portfolio and ɛ is a mean zero error term. The Fama-MacBeth (1973) procedure estimates the β parameters. The β estimates from equation (6) are reported in Table III. For the returns of growth stocks, revisions in long term forecasts are more influential than those in short term forecasts. The opposite pattern is recorded for value stocks. These inequalities provide further evidence linking earnings term structure dynamics with book-to-market characteristics. Although this link is less salient for size and momentum characteristics, past winners and losers are slightly more sensitive to fluctuations in long term forecasts than earnings forecasts for the current year. Thus, suspicions over the quality of long term forecasts are insufficient to prevent their revisions from influencing stock returns. More importantly, Table III provides strong evidence that the return implications of the earnings term structure cannot be reduced to fluctuations in a single forecast. The results from the regression in equation (6) cannot be ascertained from a residual income model or the Gordon growth model. Evidence in the next two sections reveals that the market is aware of biases in analyst forecasts and mitigates their impact on asset prices. Furthermore, earnings term structures allow expected earnings growth to vary over time while the Gordon growth model assumes constant earnings growth. Finally, observe that the implied growth rates underlying our slope and curvature measures are non-linear functions of analyst forecasts. Consequently, there does not exist a set of linear regression coefficients capable of replicating these properties of the earnings term structure. Moreover, regression coefficients are subject to estimation error which is not present in our slope and curvature definitions. III Return Anomalies and Forward Rate Biases This section analyzes the value and size anomalies as well as the Jegadeesh and Titman (1993) momentum strategy with twelve-month formation and holding periods. Our investigation of these anomalies is motivated by the results in Table II which suggest a link between stock characteristics and the extrapolation of current earnings growth. Book-to-market, size, and momentum portfolios are rebalanced annually at the end of June. We then study whether their resulting cross-sectional returns are related to biases in forward earnings growth rates. These forward 12

13 growth rates are inferred from our earnings term structures and represent the initial earnings growth expectations of analysts. Analysts are not required to trade stocks at prices implied by their forecasts. This situation contrasts with forward rates in the fixed income literature which are inferred from the market prices of bonds under the assumption of no-arbitrage. However, one can evaluate whether forward rates are biased predictors of future expectations and realizations without this assumption. 13 Lakonishok, Shleifer, and Vishny (1994) s assert that the value premium arises from incorrect initial earnings expectations. Using price targets issued by analysts, Brav, Lehavy, and Michaely (2005) report that growth stocks have higher implied expected returns than value stocks. This evidence suggests the value premium may be caused by excess optimism surrounding the future prospects of growth stocks. However, Doukas, Kim, and Pantzalis (2002) explicitly test and reject the hypothesis that errors-in-expectations are responsible for the value premium after finding that value stocks, not growth stocks, have more negative annual forecast errors. 14 the opposite end of the earnings term structure, Dechow and Sloan (1997) report that naive long term growth expectations explain a large percentage of the value premium. However, along with Chan, Karceski, and Lakonishok (2003), they highlight several difficulties associated with computing long term realized growth rates. Unlike revisions in long term forecasts, forward rates for earnings growth avoid inappropriate comparisons between two long term forecasts issued on different dates. Instead, the long term forecast s maturity is fixed at four years to circumvent the problem of consecutive long term forecasts pertaining to different future timeperiods. 15 The forward earnings growth rate denoted f(t, 2, 4) is defined as f(t, 2, 4) = (1 + LT G t) 4 On (1 + A2 t,% ) 2 1, (7) 13 Information arriving after forward rates are calculated can be incorporated into updated expectations of earnings growth. However, systematic biases in forward rates related to firm characteristics imply that analyst forecasts violate the law of iterated expectations. 14 LaPorta, Lakonishok, Shleifer, and Vishny (1997) examine forecast errors computed from the last quarterly forecast before an earnings announcement. However, initial earnings expectations correspond to the original forecasts issued by analysts, not those closest to an earnings announcement. 15 Recall from Table III that long term forecasts are crucial for understanding the stock returns of growth stocks and large stocks. 13

14 between year two and four. To investigate whether forward growth rates are biased predictors of expected growth rates in the future, we compute the following expectation of earnings growth A % (2, 4) = (1 + A2 t,% ) 2 1 (8) two years after the f(t, 2, 4) forward rates are inferred. Hence, A % (2, 4) denotes the expected earnings growth rate at the beginning of the [2,4] interval. The realized earnings growth rate at the end of this interval is also computed. In addition, we compute f(t, 1, 2) forward rates for earnings growth defined as (1+A2 t,%) 2 1+A1 t,% 1 using the first two maturities along the earnings term structure. These forward rates are then compared with A % (1, 2) at the beginning of the [1,2] interval as well as realized earnings growth at the end of this one-year period. The A % (1, 2) growth rates are computed as A1 t,% in equation (1) one year after their f(t,1, 2) counterparts are inferred. As reported in Panel A of Table IV, systematic biases across different portfolios are manifested in forward rates for earnings growth. Relative to value stocks, growth stocks have an upward bias in their forward rates for earnings growth. In particular, future expectations and realizations of earnings growth are both lower than their corresponding forward rates for growth stocks. Likewise, relative to small stocks, large stocks have an upward bias in their forward rates. These upward (downward) biases suggest optimism (pessimism) surrounds the initial earnings growth expectations of growth stocks and large stocks (value stocks and small stocks). Moreover, these biases are consistent with errors-in-expectations causing the value and size premium. Forward rate biases in the past winner and loser portfolios are similar, especially for the short term f(t, 1, 2) rates. Relative to past winners, past losers have much larger upward biases in their f(t, 1, 2) forward rates. This result is again consistent with the errors-in-expectations hypothesis, although it is not observed for the f(t,2, 4) forward rates. The weaker relationship between momentum and forward rate biases may arise from momentum being a short-term phenomenon while forward rates are defined over horizons beyond one year. Furthermore, the IBES database is orientated towards large firms, with each stock in our sample also required to have A1 t, A2 t, and LT G t forecasts. These limitations on the cross-section of stocks are known to reduce the strength of momentum (Hong and Stein (1999)). In addition, our momentum strategy s twelvemonth formation and holding period is less profitable than strategies with shorter formation and holding periods. 14

15 As reported in Panel B of Table IV, cross-sectional regression results involving individual stocks confirm the forward rate biases. We regress revisions in expected growth rates for earnings as well as their forecast errors on firm-level characteristics as follows Bias = β 0 + β 1 BM + β 2 Size + β 3 Mom + ɛ, (9) using the Fama-MacBeth (1973) methodology. The four bias variables we examine are defined as A % (1, 2) f(t, 1, 2) and A % (2, 4) f(t, 2, 4), to assess revisions in expected earnings growth, as well as two realized forecast errors over the [1,2] and [2,4] timeperiods. The firm-level characteristics include book-to-market ratios (BM), size, and past returns (Mom). 16 These independent variables in equation (9) are cross-sectionally demeaned and standardized every year. Consequently, the regression intercept β 0 can be interpreted as the average bias across all stocks, while the other β coefficients represent the impact of a one standard deviation change in their respective characteristic. Forward rates are unbiased predictors of expected and realized earnings growth in the future provided β 0 equals zero. If biases in the forward rates of earnings growth are unrelated to firm characteristics, then the β i coefficients for i =1, 2, 3 are zero. Consequently, the above regression tests the relationship between biased initial expectations of earnings growth and the value, size, and momentum anomalies. For the regressions involving f(t,1, 2), the intercept terms are significantly negative. This finding suggests that earnings forecasts are generally optimistic over the short term. However, for the f(t,2, 4) regressions, the intercept terms are significantly positive, indicating pessimism surrounds these initial forecasts of longer term earnings growth. 17 More importantly, consistent with our earlier results, Panel A of Table IV reports the slope coefficients are significantly positive for the book-to-market ratios and significantly negative for size. These coefficients support the errors-in-expectations hypothesis for the value and size premium. Indeed, relative to value 16 Size is defined as the log of a firm s market capitalization. We filter out any forward rate revisions and forward rate errors outside the [-1,1] interval. This procedure removes outliers which constitute less than 5% of the total observations. 17 Dividing the LT G t expectation for earnings growth by the expected growth rate A2 t,%,asinequation(7), causes the f(t, 2, 4) forward rates to slightly underestimate future earnings growth. A corresponding convexity adjustment can explain a portion of their pessimism relative to realized earnings growth. However, the convexity adjustment for f(t, 1, 2) only reinforces the optimism of short term forward rates for earnings growth. 15

16 and small stocks, growth and large stocks have upward biases in their forward rates for earnings growth. The slope coefficients for momentum are positive but insignificant, except for the regression involving f(t, 1, 2) s forecast errors. These coefficients suggest a weaker link between biased initial expectations of earnings growth and momentum. To summarize, forward rates for earnings growth implied from analyst forecasts have biases which are systematically related to stock characteristics underlying return anomalies. These forward earnings growth rates are computed from two spot rates for earnings growth along an earnings term structure. Thus, forward rate biases are related to biased spot rates. For instance, Doukas, Kim, and Pantzalis (2002) report that analysts initially underestimate (overestimate) A1 t for growth (value) stocks. This regularity results in higher (lower) realized annual earnings and smaller (larger) subsequent A1 t,% growth rates, a property which could potentially explain the upward (downward) bias in the f(t,1, 2) forward rates of value (growth) stocks. However, biased spot rates for earnings growth are not necessarily responsible for biased forward rates since two biased spot rates can yield an unbiased forward rate. Therefore, forward rates for earnings growth may be interpreted as capturing the relative optimism or pessimism associated with the growth rate forecasts along an earnings term structure. The next section examines if such relative optimism or pessimism distorts market prices and causes return anomalies. IV Trading Strategies The previous section indicates that biases in forward earnings growth rates are related to return anomalies. As recorded in Table II, stocks with relatively flat earnings term structures are generally value stocks, small stocks, and past winners, while relatively steep earnings term structures are associated with growth stocks, large stocks, and past losers. However, this empirical evidence is only circumstantial since the market can adjust for biases in analyst forecasts when incorporating these expectations into stock prices. Therefore, in the next two sections, we study the asset pricing implications of analyst forecasts. We incorporate cross-sectional differences across the level and slope of earnings term structures into a trading strategy. Stocks with high long term forecasts and low short term forecasts have steep earnings term structures, along with forward rates for earnings growth which overestimate future earnings growth. Conversely, stocks with low long term forecasts and high short 16

17 term forecasts have flat earnings term structures whose forward rates underestimate earnings growth in the future. For emphasis, these properties of our earnings term structures cannot be ascertained from a single analyst forecast. Each month from January 1984 to December 2004, we conduct a 3 by 3 double-sort. This procedure classifies stocks into nine portfolios according to their long term growth forecasts (LT G t ) and short term growth forecasts (STG t ). The short term growth forecast (STG t )is defined as the average of A1 t,% and A2 t,%. Our level/slope trading strategy then purchases the portfolio of stocks with the lowest LT G t and highest STG t, while selling the portfolio consisting of stocks with the highest LT G t and lowest STG t. 18 For comparison, a trading strategy similar to the one in LaPorta (1996) is implemented. Specifically, stocks are sorted into nine portfolios according to their LT G t. We then buy stocks with the lowest LT G t and sell those with the highest LT G t. Observe that this strategy only conditions on the current level of a firm s earnings term structure. Panel A of Table V reports the equally-weighted and value-weighted returns from both trading strategies across several holding periods. We first attempt to replicate the results in LaPorta (1996). Although the equally-weighted portfolio return on the lowest LT G t portfolio (portfolio 9) consistently exceeds the return of the highest LT G t portfolio (portfolio 1), the return spread between these two portfolios almost disappears after value-weighting. In contrast, the level/slope strategy s long portfolio consisting of stocks with the lowest LT G t and highest STG t (portfolio 31) consistently outperforms the short portfolio whose stocks have the highest LT G t and lowest STG t (portfolio 13) under both equal-weighting and value-weighting. In addition, the return spread from the level/slope strategy is generally higher than the return spread from LaPorta (1996) s trading strategy. In unreported results, we verify that the performance of both strategies is similar across two non-overlapping subperiods. The first subperiod is from 1984 to 1995 while the second is from 1996 to The LT G t and STG t earnings growth rates are correlated with stock characteristics as documented in Table II. Therefore the profit to the trading strategies could be due to exposure to systematic risks associated with these characteristics. We control for these systematic risks using the four-factor model. Panel B of Table V presents the risk-adjusted return and factor loadings 18 A strategy that buys (sells) stocks with the flattest (steepest) earnings term structures produces qualitatively similar results which are unreported. 17

18 to the monthly balanced trading strategies. As expected, our trading strategies load negatively on the size factor (SMB) and positively on the book-to-market factor (HML). Compared to LaPorta s (1996) strategy, the level/slope strategy loads more on the momentum factor UMD. After the four-factor risk adjustment, none of the trading strategies produce a significant abnormal return, although our level/slope strategy slightly outperforms LaPorta s (1996) strategy. Jagannathan, Ma, and Baldaque da Silva (2005) also report that analyst optimism cannot be exploited to produce abnormal returns. Therefore, despite systematic biases in analyst forecasts related to firm-level characteristics and the importance of revisions in these forecasts to stock returns, biased expectations of earnings growth cannot be exploited to produce abnormal trading profits. Observe that trading strategies derived from cross-sectional variation across earnings term structures differ from those defined by book-to-market characteristics. 19 Moreover, existing proxies for analyst optimism such as forecast revisions and forecast errors are only available ex-post which excludes them from being incorporated into trading strategies. Additional advantages of conditioning on the earnings term structure are its independence from book values, which can manifest industry-specific capital structure characteristics, and its monthly availability which allows for frequent rebalancings. In addition, a firm s earnings term structure is independent of its stock price. Consequently, conditioning on properties of the earnings term structure avoids Berk (1995) s critique regarding sorts that condition on variables explicitly normalized by stock price. V Cashflow Betas The inability of biases in analyst forecasts to generate abnormal trading profits does not necessarily that book-to-market, size, and momentum characteristics are proxies for risk. For example, Griffin and Lemmon (2002) challenge the distress risk explanation of the value premium. Instead, under an alternative behavioral hypothesis, our level/slope trading strategy may simply be unable 19 An augmented value strategy which sorts stocks according to their book-to-market ratios and then the slope of their earnings term structures is also implemented. This augmented value strategy buys value stocks with flat earnings term structures and sells growth stocks with steep earnings term structures. In unreported results, this strategy s return exceeds the standard value premium. 18

19 to detect mispricings beyond those already incorporated into the benchmarking procedure. Therefore, we examine whether the earnings term structure can provide a risk-based explanation for return anomalies using cashflow betas. This methodology decomposes deviations between expected and realized returns into cashflow and discount rate innovations, each with their own beta coefficient. However, discount rate fluctuations have offsetting affects on capital gains and reinvestment opportunities for intermediate cashflows such as dividends. Therefore, cashflow betas alone are sufficient to determine risk (expected returns). Prior implementations of Campbell and Shiller (1988) s decomposition usually begin with a VAR procedure to estimate expected return innovations. Cashflow innovations are then computed as a residual. Consequently, cashflow innovations are derived from an assumed process for expected return dynamics as well as a chosen conditional information set. For example, Campbell and Vuolteenaho (2004) infer cashflow innovations after specifying a first-order VAR model for expected return dynamics which conditions on the premium earned by small value stocks as well as other market variables. An alternative methodology in Bansal, Dittmar, and Lundbald (2005) examines the cashflow implications of consumption. Their approach assumes an AR(1) process for consumption and a moving-average relationship between cashflow and consumption growth whose joint-dynamics are combined into a VAR estimation. Our earnings term structure enables analyst forecast revisions to proxy for future cashflow innovations. Recall from Table III that analyst forecast revisions exert a significant influence on stock returns. We begin with the decomposition of Campbell and Shiller (1988) r t E t 1 [r t ] = N CF,t N DR,t (10) involving cashflow and discount rate innovations respectively. We focus on the cashflow component defined as N CF,t = (E t E t 1 ) ρ j Δd t+j (11) where d t+j denotes the log cashflow during the [t + j 1,t+ j) timeperiod. This innovation can be further analyzed using the clean-surplus accounting identity B t+j = B t+j 1 + X t+j D t+j, (12) where B t+j, X t+j,andd t+j denote a firm s book value, earnings, and cashflow respectively, with d t+j in equation (11) being the log of D t+j. Vuolteenaho (2002) utilizes the clean-surplus identity 19 j=0

20 and defines the log return on book-equity as ( ) Bt+j+1 + D t+j+1 e t+j = log B t+j ( =log 1+ X ) t+j+1. (13) B t+j This identity allows Vuolteenaho (2002) to replace the Δd t+j terms in equation (11) with log returns involving contemporaneous earnings N CF,t = (E t E t 1 ) ρ j e t+j. (14) As in Cohen, Polk, and Vuolteenaho (2006) along with Campbell, Polk, and Vuolteenaho (2006), cashflow betas are estimated using the following regression 20 j=0 N i CF,t = α CF + β i CF N M CF,t + εi t, (15) where the i and M superscripts on the monthly cashflow innovations N k CF,t denote the ith portfolio and the market respectively. Expectations of the e t+j log returns are inferred from analyst forecasts using a three-stage growth model as detailed in Appendix A. These aggregate expectations involve summing across the individual earnings forecasts and book values of firms within a portfolio, with earnings aggregated at the firm level rather than on a per share basis. For emphasis, analyst forecasts have not previously been incorporated into the estimation of cashflow betas. Instead, prior research has relied on fluctuations in realized earnings. Although analyst forecasts are biased, our estimation of the cashflow betas involves cashflow innovations which are computed over monthly horizons. These innovations eliminate biases that persist over this short horizon. Cashflow betas also represent covariances between cashflow innovations rather than expectations of future earnings. Biased analyst forecasts exert little influence on these covariances provided biases in their forecasts for the market portfolio and the i th portfolio are not highly correlated. 21 Panel A of Table VI reports that value stocks have higher cashflow betas than growth stocks. In particular, the average cashflow beta for value stocks is considerably higher than the cashflow 20 Campbell and Vuolteenaho (2004) estimate the covariances between returns and cashflow fluctuations rather than the sensitivity between two cashflow innovations, while Lettau and Wachter (2006) investigate time-varying cashflow dynamics instead of their covariances. 21 Easton and Sommers (2006) document that optimistic analyst forecasts can overestimate costs of capital. The inability of trading strategies derived from biases in analyst forecasts to generate abnormal returns implies the market mitigates these biases when forming its earnings expectations. 20