Inflation, earnings forecasts, and post-earnings announcement drift

Transcription

1 Inflation, earnings forecasts, and post-earnings announcement drift Sudipta Basu Fox School of Business Temple University 108 Speakman Hall 1810 N. 13 th St. Philadelphia, PA Tel. (215) Stanimir Markov The University of Texas at Dallas School of Management 800 West Campbell Road Richardson, TX Tel: Lakshmanan Shivakumar London Business School Regent s Park, London NW1 4SA United Kingdom Tel. (44) Lshivakumar@london.edu Date: January 13, 2008 We thank Stephen Ryan, Devin Shantikumar, Ramgopal Venkataraman, an anonymous referee and workshop participants at London Business School, Emory University, Pennsylvania State University, Columbia University, Tilburg University, RSM Erasmus University, the 2006 Financial Management Association European Conference, 2006 American Accounting Association annual meetings and 2007 Indian School of Business Conference for their helpful suggestions. We also thank IBES for making available data on analysts forecasts.

2 Abstract We examine whether financial analysts fully incorporate expected inflation in their earnings forecasts for individual stocks. We find that expected inflation proxies, such as lagged inflation and forecasts from the Michigan Survey of Consumers, predict future earnings growth of a portfolio long in high SUE firms and short in low SUE firms, but that analysts do not fully adjust for this relation. Analysts earnings forecast errors can be predicted using expected inflation proxies, and these systematic forecast errors are related to future abnormal stock returns. Overall, our evidence is consistent with the Chordia and Shivakumar (2005) hypothesis that the postearnings announcement drift is related to investor underestimation of the impact of expected inflation on future earnings growth.

3 1. Introduction The post-earnings announcement drift is a market anomaly that has been both robust and extensively studied over a period of more than forty years (Ball and Brown, 1968; Bernard and Thomas, 1990, among others). One explanation for this phenomenon is that investors under-react to earnings surprises (Bernard and Thomas, 1990; Ball and Bartov, 1996). Chordia and Shivakumar (2005) argue that this under-reaction reflects in part investors underestimation of the impact of expected inflation on future earnings growth because various expected inflation proxies predict future earnings growth, future quarterly returns, and future 3-day earnings announcement returns for SUE (standardized unexpected earnings)-sorted stocks. In this study, we examine whether analysts underestimate the impact of inflation on future earnings. The motivations for our analysis are twofold. First, Chordia and Shivakumar (2005) hypothesize that investors underestimate the impact of expected inflation when forming earnings expectations, which are not directly observable. A direct examination of analysts' earnings expectations, viewed in the literature as a good proxy for investors expectations, can therefore help preclude alternative (i) rational risk-based explanations or (ii) irrational discount rate-based explanations for the evidence in Chordia and Shivakumar (2005). These alternative explanations are especially important as most asset-pricing theories suggest that discount rates are determined by systematic factors. Second, given the resources expended on investment research and our institutional evidence that analysts actively seek and analyze inflation information, an examination of whether analyst expectations fully incorporate inflation information is of interest independent of the issue of how prices are set (i.e., how a marginal investor s earnings expectations incorporate inflation information). Such an examination would yield novel evidence on the extent to which earnings forecasts, an important element of analysts research reports, fully incorporate macroeconomic information in their forecasts. 1

4 Empirically, we examine how well proxies for expected inflation predict analysts earnings forecast errors for a portfolio that is long in stocks with high standardized unexpected earnings (SUE) and short in stocks with low SUE. We call this portfolio the PMN portfolio. We find that common proxies for expected inflation, such as lagged inflation and inflation forecasts from the Michigan Survey of Consumers, predict the future earnings growth of the PMN portfolio, but we also find that analysts do not fully use this earnings-predictive ability of inflation when forecasting future earnings. The proxies for expected inflation can predict analysts earnings forecast errors of the PMN portfolio for up to two quarters ahead. These results hold after controlling for the ability of current and lagged SUE to predict future earnings growth or future forecast errors. The results are also robust across sub-periods as well as to either firm-level or portfolio-level data analyses. Finally, these results are observed for inflation but not for other macroeconomic variables, such as real output growth or real interest rates. We conclude that analysts do not fully incorporate expected inflation information in their earnings forecasts. To further establish a link between the documented inefficient use of inflation information by financial analysts and the inefficient use of inflation information by investors as implied by prior evidence of stock returns predictability, we examine whether inflation s ability to predict stock returns is diminished after including analysts forecast errors. We find that the ability of expected-inflation proxies to predict returns is diminished by about 30% upon the inclusion of analysts earnings forecast errors. This evidence suggests that the inflation-related market inefficiency is partly due to investors reliance on analysts inefficient forecasts. Overall, we make several contributions to the literature. First, our analysis of analysts forecast errors and stock returns provides new evidence in support of the role of inflation-related errors in causing post-earnings announcement drift. Second, we provide new evidence on how well analysts incorporate macroeconomic information in their forecasts. Although half of the variation in firms earnings is driven by macro-economic factors (e.g., Brown and Ball, 1967) 2

5 and analysts often discuss the relation between inflation and future earnings in their research reports, prior literature on analysts forecasts has largely ignored these issues, severely limiting our understanding of how earnings expectations are formed. Although we document that financial analysts do not fully incorporate inflation in their earnings forecasts, we urge caution in drawing inferences about the irrationality of financial analysts from this evidence, as we do not know the optimization problem facing the analysts (Basu and Markov, 2004). For example, due to frequent shifts in the inflation exposure of individual firms earnings, changes in monetary policy regimes, and large infrequent price shocks, the costs of detecting the exact relation between macro-economic information, such as inflation and individual firms earnings, may be too high relative to its benefits in improving accuracy. In addition, though some research shows that analysts earnings forecast accuracy is rewarded (Mikhail et al., 1999; Hong and Kubik, 2003), the importance of these rewards to analysts is still an open question. We next discuss our paper s background and motivation, and then describe institutional evidence on how analysts use information about inflation when forecasting earnings. Section 3 reports our analyses of analysts forecasts. Section 4 studies the relation between inflationrelated forecast errors and post-earnings-announcement stock returns, and Section 5 concludes. 2. Background and motivation 2.1. Inflation and investors earnings expectations Several studies have shown that macroeconomic variables are key determinants of corporate earnings (Brown and Ball, 1967; Gonedes, 1973; Magee, 1974) and that macroeconomic news explains a significant portion of the time variation in corporate earnings (O Brien, 1994). More recently, Kothari, Lewellen and Warner (2006) and Shivakumar (2007) provide evidence that corporate earnings contain information about inflation. The evidence in 3

6 these studies suggests that earnings expectations should incorporate inflation expectations a relation that has largely remained unexplored. We try to fill this void by examining if analysts earnings forecasts fully incorporate the information contained in inflation expectations. To better understand the relationship between earnings and inflation, we consider the following simple decomposition of a firm s earnings growth: E it = β it INF t + ε it (1) where β it is the objective earnings exposure to inflation for firm i in period t, INF t is inflation in period t, and ε it captures the change in earnings caused by sources other than inflation. The above equation states that changes in a firm s earnings are proportional to inflation. Thus, for example, with other factors held constant, if inflation in a given period is 2.5%, a firm with earnings exposure to inflation of 2.0 will see its earnings increase by 5%, whereas a firm with earnings exposure of 2.0 will see its earnings decline by 5%. Chordia and Shivakumar (2005) conjecture that, during periods of high inflation, investors under-predict (over-predict) earnings growth for firms with positive (negative) earnings exposure and that systematic variation in earnings exposure to inflation across SUE-sorted portfolio causes inflation-induced mispricing to vary monotonically across SUE-portfolios, causing the post-earnings-announcement drift. One reason why earnings exposure to inflation is expected to vary across SUE-sorted portfolios is that earnings growth is the numerator in SUE and, since inflation is a determinant of earnings growth, sorting stocks on SUE to some extent sorts stocks on their earnings exposure to inflation. Firms with high earnings exposure to inflation are likely to have larger increases in earnings and thus tend to be included in high-sue portfolios, while firms with negative or less positive earnings exposure to inflation are likely to be included in low-sue portfolios. Thus, sorting stocks on SUE should yield portfolios that have different earnings exposure to inflation. 4

7 Chordia and Shivakumar (2005) provide evidence in support of their conjecture by analyzing stock returns of SUE-sorted portfolios. However, they cannot entirely eliminate riskbased explanations for their findings. More generally, stock return analyses cannot distinguish mispricing due to cash-flow-forecast errors from those that are due to discount-rate errors. This alternative explanation, although a concern for all studies of market efficiency, is particularly troubling for the evidence in Chordia and Shivakumar (2005), as most asset pricing theories predict expected returns or discount rates to be determined by systematic factors, such as inflation and other aggregate variables. Hence, to provide clearer evidence on the conjecture in Chordia and Shivakumar (2005) we directly examine whether inflation expectations are fully incorporated in earnings forecasts. Our empirical tests examine financial analysts earnings forecasts as investors earnings expectations are unobservable. Since analysts are more sophisticated than the average investor, the study of analysts forecasts could bias against our finding inflation-induced forecast errors Relation to studies on inflation illusion The economics literature has long recognized that inflation likely impacts economic behavior, and that behavior in high inflation environments likely differs significantly from low inflation environments. Several studies have recently re-examined Modigliani and Cohn s (1979) conjecture that high inflation leads to lower market values at the aggregate level due to investor s inappropriate use of nominal discount rates to discount real cash flows. For example, Campbell and Vuolteenaho (2004) claim that inflation illusion explains almost 80% of the time-series variation in mispricing of the S&P 500. However, Thomas and Zhang (2007) point out that the evidence in Campbell and Vuolteenaho (2004) is sensitive to the choice of inflation measure as well as to the choice of dividends or earnings as a growth measure. 5

8 While the inflation illusion hypothesis focuses on aggregate market forecasts in an inflationary environment, we study analyst forecasts at the firm level. The distinction between forecasts at the aggregate market level and forecasts at the firm level is important. Inefficiencies at the firm level, as documented in this study, do not necessarily imply inefficient use of inflation information by analysts at the aggregate level. For instance, Kothari et al. (2006) show that the under-reaction to earnings news observed in firm-level analysis is not observed at the aggregate market level. Conversely, evidence of forecast efficiency at the aggregate market level does not imply forecast efficiency at the firm level. Thus, even though Thomas and Zhang (2007) find that analysts growth forecasts for the aggregate market are efficient with respect to inflation information, this does not imply that analysts incorporate inflation efficiently in firm-specific forecasts. In addition, the inflation illusion hypothesis studies the relation between inflation and long-term growth forecasts, which is either the growth forecast for dividends that can be maintained in perpetuity or equivalently, the growth forecast for earnings in perpetuity under a full-payout dividend policy. In contrast, our study examines how analysts incorporate inflation in short-horizon (less than one year) earnings per share estimates. Thus, our analyses have little to say on whether analysts ignore inflation in long-term growth forecasts. In sum, while our paper is similar to the inflation illusion literature in examining the relation between inflation and earnings forecasts, it differs in examining disaggregated short-term forecasts, which may produce results that are considerably different from those previously documented Inflation and analyst earnings forecasts Surprisingly little is known about the relation between analysts earnings forecasts and inflation. Most prior studies that investigate the properties of analysts earnings forecasts focus 6

9 on firm-specific information, such as prior period earnings surprises and prior stock returns, and find that forecasts do not fully incorporate such information (Abarbanell, 1991; Abarbanell and Bernard, 1992, among others). Ignoring the role of macroeconomic variables in forecasting future earnings is unfortunate, especially in light of the evidence that macroeconomic and systematic variables account for nearly half the variation in firms earnings changes (Brown and Ball, 1967) and that the arrival of macroeconomic news explains a significant portion of the time variation in corporate earnings (O Brien, 1994). 1 What does the evidence that analysts do not efficiently use firm-specific information like past earnings imply for how analysts use macro-economic information such as inflation? Relative to firm-specific information, one could argue that incorporating macroeconomic information in earnings forecasts is much simpler, because macroeconomic forecasts are widely available and so, unlike firm-specific information, need not be gathered or forecast separately for each firm. On the other hand, to incorporate macroeconomic information in forecasts, analysts need to estimate a firm s exposure to macroeconomic variables that will vary across firms as well as over time for a given firm. Moreover, relative to the functioning of a single firm, the macro-economy is much more complex. The heavily intertwined actions of economic agents and of governmental and monetary authorities are arguably more difficult to forecast than the actions of managers in a firm. Thus, a priori, it is unclear whether analysts would be more or less efficient in utilizing macroeconomic information relative to firm-specific information. 1 Studies that examine the relation between expected inflation and analyst earnings forecasts (Ackert and Hunter, 1995; Sharpe, 2002; Thomas and Zhang, 2007) find little evidence of inefficiency. This is not entirely surprising as prior studies do not consider cross-sectional and time-variation in earnings exposure to inflation, which is an important economic phenomenon (Chordia and Shivakumar, 2005). 7

10 2.4. Institutional evidence To set the stage for our analyses, we initially examine institutional evidence on whether and how analysts use inflation information in their earnings forecasts. In particular, we examine a small sample of archival analysts reports in the Investext Plus database provided by Thomson Financial, with a focus on how analysts generally deal with inflation in their reports. Analysts often issue research reports with the sole purpose of projecting future industry prices and their effects on companies profitability. For example, a JP Morgan research report on three major pharmaceutical distributors entitled Healthcare Distribution: Drug Price Inflation Still Matters identifies drug-price inflation as a key near-term earnings driver. 2 The report analyzes historical price data, acquired by the analysts for a fee from a commercial vendor, representing the top 50 drugs by sales. The analysts project price increases for 15 drugs and a subsequent decline in distributors operating margin of 40 basis points on a year-to-year basis. A Credit Suisse First Boston research report entitled Food Retailers: Inflation Revisited jointly analyzes the inflation dynamics of input and output prices. 3 Shelf prices and wholesale prices do not move in lockstep The negative spread between growth in the CPI Food-At-Home and PPI Finished Consumer Foods widened to approximately 390 basis points in the fourth quarter 2003 and was 70 basis points in the first quarter The inflation data used in the report are available for free from the US Department of Labor. Finally, a Citigroup Smith Barney report on the restaurant industry analyzes the wage inflation expectations of 95 respondents to their regular Monthly Restaurant Industry Survey. 4 Based on the survey results, the analysts conclude that inflation will be more of a concern in 2005 than it was in 2004, but they do not change their "Buy" ratings on 4 of their 11 covered stocks. 2 The report was written by Lisa Gil, Atif Rahim, and Michael Minchak and was dated December 6, The report was written by Jack Murphy and Teresa Ging and was dated April 27, The report was written by Mark Kalinowski, Jeffrey Carnevale, and Kwame Aryeh and was dated November 9,

11 When we examined reports for individual firms, we found several instances in which inflation was mentioned in the report, but we could not identify any report in which analysts discussed firms earnings exposure to inflation or explicitly discussed how information about economy-wide prices was incorporated in their earnings forecasts. Although the lack of such discussions suggests the possibility that analysts ignore cross-sectional variation in earnings exposure to inflation, it is possible that their forecasts fully incorporate such information and that the reports simply do not discuss all the information used in arriving at a forecast. Based on an analysis of reports and a survey of individual analysts, Horngren (1955) found that analysts never explicitly adjusted financial statements for general price-level changes in their reports, but nevertheless survey evidence indicated that the analysts made such adjustments either mentally or indirectly (e.g., by comparing depreciation adequacy against cost-of-asset replacements). 3. Empirical analysis 3.1. Research design To test whether analysts fully incorporate inflation information in their earnings forecasts, our empirical investigation focuses on a portfolio PMN that is formed by sorting stocks on SUE. Chordia and Shivakumar (2005) document this portfolio to have significant exposure to inflation, which enables us to conduct more powerful tests. The focus on the PMN portfolio also enables us to simultaneously examine the other objective of this study, which is to test whether inflation-related pricing errors explain the post-earnings-announcement drift. Early studies that attempted to identify portfolios with significant inflation-exposure from regressions of security returns on inflation met with little success (Schipper and Thompson, 1981, and Gay and Manaster, 1982), a result attributed to the instability in firms exposures to 9

12 inflation (Schipper and Thompson, 1981, and Bernard, 1984). 5 Boudoukh et al. (1994) find that the correlation between industry returns and expected inflation is related to industry cyclicality, with procyclical industries being negatively correlated and noncyclical industries being positively correlated. However, Tufano (1998) finds that inflation exposure within the goldmining industry varies considerably both across quarters and cross-sectionally, suggesting that industry membership is a weak proxy for earnings exposure to inflation. Due to the limitations of the alternative approaches, our tests rely on the portfolio PMN. The logic behind the significant inflation-exposure observed for PMN is the following: since inflation is an important determinant of earnings changes in any given quarter, firms with higher (lower) earnings exposure to inflation are likely to have larger (smaller) increases in earnings growth, which is captured by SUE. Of course, earnings growth is also determined by factors other than inflation, making this relationship noisy. Chordia and Shivakumar (2005) show that this noise is mitigated by constructing portfolios based on SUE and that, since stocks in the lowest (highest) decile of SUE have significantly negative (positive) exposure to expected inflation, the zero-investment portfolio PMN, which is long on stocks in the highest SUE decile and short on stocks in the lowest SUE decile, maximizes earnings exposure. 6 This approach also finds support in Bernard (1984), who shows that accounting information is useful in the identification of portfolios with significant exposure to inflation. To form the PMN portfolio, we first compute SUE it for firm i in each month t as 5 This happens for many reasons: firms hedge their exposure to inflation risk, some of their contracts are on fixed prices, firms have international operations, accounting earnings as well as taxes are based on historical costs of goods sold and depreciation that is based on historical costs of assets, and so on (cf. French et al., 1983; Bernard, 1986; Ball et al., 1993). It is worth pointing out that the use of historical costs for inventory and assets in measurement of accounting earnings can by itself cause earnings exposure of firms to be negative in periods of declining inflation. This is because, while sales grow at current inflation levels, the cost of goods sold and depreciation expenses grow at lagged inflation rates, which, if higher than current rates, can cause earnings to decline. 6 The Chordia-Shivakumar approach assumes that inflation exposure is more stable at the SUE-portfolio level than at the individual firm level. If this assumption were invalid, then earnings exposure to inflation would be attenuated for these portfolios, as firms frequently jump from one portfolio to another. They report that the probability of a firm continuing with the same portfolio for more than a year is no different from that expected under a random walk. 10

13 SUE it Eiq Eiq 4 = (3) σ iq where E iq represents the most recently announced earnings for firm i corresponding to earnings for quarter q, E iq 4 represents the earnings four quarters ago, and σ iq is the standard deviation of (E iq E iq 4 ) over the prior eight quarters. 7 To avoid using stale earnings, we use only earnings announced within four months of the portfolio formation month (i.e., month t). In each month, sample firms are sorted into deciles based on SUE iq, using the distribution of SUE from the prior three months to determine the decile cut-offs. To avoid biases that might be introduced by limiting the SUE distribution to firms with an analyst following, the decile cut-offs are based on all firms in the merged CRSP and COMPUSTAT database irrespective of whether IBES has data available on analysts forecasts. Finally, we construct portfolio PMN by going long (short) in stocks in the highest (lowest) SUE portfolio Sample Our initial sample consists of all NYSE, AMEX, and NASDAQ firms with data on the monthly CRSP, quarterly COMPUSTAT, and detailed IBES databases. We focus only on common stocks and eliminate ADRs, REITs, Americus Trust Components, units, and closed-end funds from the sample. Further, we restrict our sample to firms with their individual analysts forecast errors available between July 1984 and December For each firm and each quarter, we construct our own analysts consensus forecasts as the mean of IBES individual analysts earnings forecasts issued in the same month as the earnings announcement or in the immediately previous month. 8 Forecast errors (FERR iq ) are then calculated as the actual earnings reported in 7 Standardizing earnings change (E iq E iq 4 ) by price at end of month t, instead of σ iq, leaves our results qualitatively unchanged. 8 IBES-provided consensus forecasts often include stale forecasts. O Brien (1988) shows that a consensus forecast constructed from recent individual forecasts is more accurate than the IBES consensus forecast. Brown (1991) 11

14 IBES, less our consensus forecast, divided by the stock price at the end of the portfolio formation month. 9 To obtain PMN portfolio-level data, FERR PMN,q+j, we subtract the average FERR i,q+j for the lowest SUE portfolio from the average FERR i,q+j for the highest SUE portfolio. Our analyses use SUE for the four quarters prior to portfolio formation (i.e., SUE iq 3 to SUE iq ) and both SUE and forecast errors for the four quarters subsequent to the portfolio formation month t (i.e., SUE iq+1 to SUE iq+4 and FERR iq+1 to FERR iq+4 ). We delete the extreme 1% of observations on either side for SUE i,q+j (j = 3 to +4) and FERR i,q+j (j = +1 to +4) in each portfolio formation month to reduce the impact of outliers on the regression parameters. Our conclusions are unaffected by this exclusion criterion. Finally, for all regressions using observations on individual firms, we report t-statistics based on Huber-White standard errors clustered at the firm level. Our analyses focus on the predictability of SUE and forecast errors for quarters q + 1 to q + 4, where quarter q corresponds to the quarter whose earnings are used to sort stocks into SUE portfolios. For analysis of forward-looking SUE (SUE iq+j, j = 1 to 4), we include only firmquarters that also have data on FERR i,q+j for the same quarter. Similarly, for analysis of forwardlooking forecast errors, we include only firm-quarters that have data on SUE for the corresponding quarter. These sampling restrictions enable direct comparison of results across analyses of SUE and forecast errors, although the results are robust to not imposing the sampling restrictions. In addition, we also require our sample firms to have SUE data for quarters q 3 to q (i.e., SUE iq 3 to SUE iq ), as these are included in the analyses as control variables. After the above exclusions, the PMN portfolio consists of 168 stocks in each month, on average. shows that timely composite earnings forecasts are more accurate than both the mean of all outstanding forecasts and the most recent forecast. Our results are robust to using IBES-provided consensus forecasts. Also, we have replicated our results using split-unadjusted data from IBES. 9 Our results are qualitatively unaffected when stocks with prices less than $1 are deleted from the analysis. 12

15 Table 1, Panel A reports descriptive statistics for the SUE and analysts forecast errors for quarters subsequent to the PMN portfolio formation month. We multiply the average subsequent SUE and FERR for the low SUE portfolio by -1 before combining it with the corresponding average SUE and FERR for the high SUE portfolio. The mean and median SUE for stocks in the PMN portfolio are significantly positive in the three quarters subsequent to the portfolio formation month (i.e., quarters q + 1 to q + 3). The mean and median SUE decline monotonically in these quarters and turn negative in quarter q + 4. A similar pattern emerges in the forecast errors as well. The mean and median forecast errors for the PMN portfolio decrease monotonically over quarters q + 1 to q + 4. Both mean SUE and mean forecast error are statistically different from zero for quarters q to q Earnings exposure to inflation in earnings growth deciles To estimate the earnings exposure to inflation of each earnings growth decile, we estimate a pooled regression of SUE iq+1, our earnings growth measure, on actual inflation in the contemporaneous year (INF q-2,q+1 ), where q corresponds to the quarter whose earnings growth is used in forming portfolios. The dependent and independent variables are not measured in quarter q (i.e., SUE iq and INF q,q ), as such a regression would involve estimating regressions separately for portfolios sorted on the dependent variable, and would therefore be misspecified. The results are presented in Table 1 Panel B. Earnings growth is significantly related to contemporaneous annual inflation for the two extreme deciles, P 1 and P 10, and is marginally related for the next most extreme deciles, P 2 and P 9. The lack of significance for the middle six earnings growth portfolios is likely due to the low power of the regressions. Given that inflation was low and relatively stable during our sample period, its effects on contemporaneous earnings growth would be difficult to identify empirically for portfolios with relatively small exposures to 13

16 inflation. 10 Compared with our results, Chordia and Shivakumar (2005) find significant earnings exposure for eight of the ten earnings growth portfolios using a sample from 1972 to Their sample period is longer than ours and includes the high-inflation period of the 1970s. More importantly for the current study, significant differences in the earnings exposure are observed across the earnings growth deciles. We reject the hypothesis that the earnings exposure to inflation is the same across all earnings growth deciles at less than the 1% level using an F-test. The earnings exposure of the lowest earnings growth portfolio is a significantly negative 0.06, whereas the corresponding value for the highest earnings growth portfolio is These coefficients imply that one standard deviation increase in annual inflation (1.06) decreases SUE iq+1 for portfolio P 1 by 0.064, while increasing the SUE iq+1 for portfolio P 10 by These represent approximately 10% of the average SUE iq+1 for portfolios P 1 and P 10. In order to maximize the power of our tests, subsequent analyses focus primarily on a zero-investment portfolio that is long on the highest SUE portfolio and short on the lowest SUE portfolio. The power of tests is critical for our study, because our analyses are predictive in nature and our sample period is characterized by relatively low and stable inflation. Thus, unless the earnings exposure to inflation is sufficiently large, it would be difficult to identify empirically any relation between inflation and future earnings growth or future forecast errors. The findings in Panel B suggest that the zero-investment portfolio, PMN, has a significantly positive exposure to inflation. Apart from maximizing earnings exposure, the use of a zero investment portfolio also controls for spurious correlations that might arise from inflation being related to potential biases in earnings growth or forecast errors that equally affect all stocks. 11 Moreover, our focus on a zero-investment portfolio accommodates time variation in earnings exposure even at the SUE portfolio level since time variation could occur if managers of all firms 10 We did not find a significant coefficient on inflation in unreported regressions at the aggregate market level. 11 Chopra (1998) shows that, at the aggregate market level, analysts optimism varies across business cycles. 14

17 systematically adjust their earnings exposure to inflation across business cycles. Analyses of the PMN portfolio, however, assume any time variation in the earnings exposures to be similar across extreme deciles so that the relationship between inflation and earnings is stationary for the hedge portfolio, PMN. 3.4 Earnings exposure to inflation for PMN portfolio First, we verify that in our sample the PMN portfolio has significant positive exposure to inflation. Towards this, we regress earnings growth in quarter q + 1 (SUE i,q+ 1) for stocks in the PMN portfolio on contemporaneous realized inflation INF q-2,q+1, where q corresponds to the quarter whose SUE is used in forming the PMN portfolio. In this regression, the dependent variable is measured one quarter subsequent to the quarter whose SUE is used in PMN formation, as a regression of PMN s SUE in quarter q would essentially involve estimating a regression for stocks sorted on the dependent variable. The findings in Table 1, Panel C suggest that the zero-investment portfolio, PMN, has a statistically significant exposure to inflation of However, this coefficient is smaller than the exposure of 0.14 implied by Table 7 in Chordia and Shivakumar (2005). The lower coefficient in our sample likely results from our requirement that sample firms have analysts forecast data, biasing our sample towards larger firms. Nance, Smith, and Smithson (1993) show that larger firms hedge more of their inflation risk, both through real decisions such as geographic diversification and through financial instruments, and so they are likely to have a lower inflation exposure. The lagged SUEs are significantly positive in the first three quarters and negative in the fourth quarter, as shown by Bernard and Thomas (1990). 12 The adjusted R 2 s in these regressions are relatively low, mainly due to the use of firm-level data. Moreover, 12 Unlike Bernard and Thomas (1990), we estimate the regression using stocks in the extreme deciles that are formed by sorting stocks on SUE iq. This approach includes the extreme values of SUE iq in the regression, causing the coefficient on SUE iq to be attenuated in our regressions relative to those reported in the Bernard and Thomas (1990). 15

18 inflation is relatively stable during our sample period, as a result of which a smaller fraction of the variation in SUE of individual firms is explained by inflation. 13 Since earnings changes for a firm are affected by both price changes (i.e., inflation) as well by changes in quantity (i.e., real output growth), we check whether the above relationship between earnings and inflation is robust to controls for real output growth. We obtain data on industrial production growth data from the St. Louis Federal Reserve website at: Regressions in columns II and IV of Table 1, Panel C, show that the coefficient on industrial production growth is insignificant. More importantly, the inclusion of this variable has little impact on the inflation exposure for the PMN portfolio. From columns III and IV, which control for four lags of SUE, we observe that the inflation exposure of the PMN portfolio is robust to these controls as well. Overall, our findings confirm that the inflation exposure of the PMN portfolio is significantly positive. We next examine whether the contemporaneous earnings exposure observed in Table 1, Panel C enables the prediction of future earnings growth, measured as SUE, for the PMN portfolio based on current expectations of inflation. We use two different proxies for expected inflation in our analyses, one based on time-series estimates and the other based on survey data. Our time-series estimate for future inflation is lagged annual inflation, INF q 3,q, chosen in view of the high persistence of inflation. 14 The survey-based proxy for inflation expectations is the one-year-ahead inflation forecasts reported by the Michigan Survey of Consumers, EINF q. 15 We chose the Michigan Survey of Consumers over other surveys for inflation forecasts (such as the Livingstone survey) because of its monthly availability. Throughout the paper, expected inflation 13 The average annual inflation was 3.02% during our sample period, with a standard deviation of 1.06%. The low and relatively stable inflation is a well-known characteristic of the late 1980s and the 1990s. 14 A more sophisticated time-series model would require parameter estimation and would introduce an unknown amount of noise into the expected inflation proxy. In any case, the loss of power from using lagged inflation as a proxy for expected inflation is not a concern because we find significant results even with this proxy. 15 The survey data are available monthly from 1978 and are based on a random sample of at least 500 households. The Survey Research Centre at the University of Michigan conducted the telephone interviews. 16

19 is measured in the month prior to the portfolio formation month to ensure that these data would have been publicly available before portfolio formation. Table 2 reports results from predictive regressions for SUE in the four quarters following the portfolio formation quarter (i.e., SUE iq+1 to SUE iq+4). The regressions use pooled time-series cross-sectional data for individual stocks in portfolios P 1 and P 10 with variables signs being reversed for stocks in P 1 to account for their short position in portfolio PMN. Consistent with prior studies (e.g., Bernard and Thomas, 1990), the coefficients on lagged SUE in the regression of quarter-ahead SUE are significantly positive for the first three lags and significantly negative for the fourth lag. The adjusted R 2 is 4.96% for this predictive regression. Including expected inflation as an additional explanatory variable marginally increases the adjusted R 2 s. The coefficient on expected inflation is significantly positive for regressions of SUE in all four quarters q + 1 to q + 4, irrespective of whether we measure this variable using lagged inflation or the forecast from the Michigan Survey. This indicates that expected inflation has significant predictive power for future earnings growth even after controlling for the information in lagged earnings growth. The coefficient on expected inflation measured as lagged inflation, reported in Panel A, is 0.05 for the quarter-ahead SUE. It decreases to 0.02 as the prediction horizon is extended to quarter q + 4. The coefficients for expected inflation measured using the Michigan Survey in Panel B are generally higher in magnitude, with values around 0.09 one quarter ahead, and decline to 0.05 for quarter q + 4. Although the slope coefficients are about twice as large when survey data are used, the adjusted R 2 s are slightly higher for the time-series proxy, indicating that the two proxies are equally effective in predicting future earnings growth. 17

20 3.5 Forecast errors and expected inflation The results in Table 2 indicate that expected inflation information is useful for predicting earnings up to four quarters ahead. If analysts use all publicly available information, including inflation expectations, and efficiently forecast future earnings, then their future forecast errors should be orthogonal to expected inflation data. However, if analysts underutilize inflation information or fail to consider the impact of expected inflation on future earnings, then expected inflation will predict future forecast errors. We first plot the relationship between forecast errors for PMN and actual monthly inflation in Figure 1. This figure indicates a positive relationship between lagged monthly inflation and forecast errors for PMN in the future months. In general, periods with higher inflation are followed by periods with higher forecast errors for PMN. We more formally test the relationship between analysts forecasts errors and inflation by estimating a predictive regression, as in Table 2, but we do so after replacing future SUE with future forecast errors (FERR PMN ) as the dependent variable. Table 3 reports the results from this analysis. Panel A reports results when lagged annual inflation serves as the measure for inflation expectations, and Panel B reports results when the Michigan Survey inflation forecast serves in the same capacity. Because we selected firm-quarters with data on both SUE and forecast error in constructing the sample, our analyses in Tables 2 and 3 are based on identical observations, with only the dependent variable differing between the two tables. Regressing one-quarter-ahead earnings forecast errors (FERR i,q+1 ) on SUE in the prior three quarters (i.e., SUE iq 3 to SUE iq ), we find that the coefficients on the first two lags are significantly positive. This result is consistent with the findings of Abarbanell and Bernard (1992), which show that analysts do not fully use the information in lagged earnings growth. When we extend the regression to include expected inflation as an additional explanatory variable, we find that the coefficients on expected inflation are significantly positive for forecast 18

21 errors in the subsequent four quarters (except for the Michigan Survey proxy for quarter q + 4). 16 For both expected inflation measures, the coefficient on expected inflation as well as its statistical significance monotonically decrease as one moves from one-quarter-ahead forecast errors to four-quarter-ahead forecast errors. This is consistent with analysts slowly incorporating the effects of inflation in their forecasts. Comparing coefficients on expected inflation across Tables 2 and 3 also provides interesting insights into the delayed response of analysts to earnings information in inflation expectations. The inflation coefficients from regressions of SUE (Table 2) are very similar in size to those from regressions of forecast errors (Table 3), suggesting that analysts ignore most of the predictive ability of inflation with regard to future earnings growth. The adjusted R 2 s in these predictive regressions are generally small, suggesting that the variation in forecast errors due to analysts ignoring inflation for individual firms is small. Given the relatively stable inflation in our sample period, and also that firm-specific shocks are likely to be major determinants of the forecast errors for individual firms, this is not surprising. In a later section, we show that aggregating forecast errors to portfolios significantly reduces firm-specific noise, causing substantial improvement in the adjusted R 2 s. 3.6 Robustness checks Generalizability to full sample The analyses in Tables 2 and 3 use only the firms in the extreme SUE deciles. To test the generalizability of these results to all firms, we repeated the analyses in Tables 2 and 3 after redefining PMN as long on portfolios P 6 to P 10 and short on portfolios P 1 to P 5. Qualitatively, the use of all stocks in the analyses does not change our results (untabulated for brevity). Inflation 16 This result is robust to including lagged forecast errors (i.e., FERR iq 3 to FERR iq ) as additional explanatory variables. 19

22 expectation is found to have significant predictive power for both earnings growth and forecast errors of the redefined PMN portfolio. For instance, in regressions of one-quarter-ahead forecast errors (i.e., FERR q+ 1) the coefficient on lagged inflation (INF q-3,q ) is 0.03 (t-statistic=8.94), while that on Michigan survey expectations of inflation (EINF q ) is 0.10 (t-statistic=6.41) Sub-period analyses The previous analyses pool data for the last 21 years, which assumes that the relations we examine have been stationary over time. However, Fama (1998) emphasizes that many apparent stock-market anomalies were significantly reduced after they were first documented, suggesting either that the original phenomena were period-specific or that rational investors arbitraged them away once they had been pointed out. This viewpoint suggests the possibility that the effects of inflation misvaluation have abated over time and that our pooled analyses might overstate the extent to which any anomaly persists in the most recent data. To explore whether the predictive ability of inflation for forecast errors is period-specific, we split our sample into roughly equal halves and repeat the main regressions in each sub-period. We report results for both SUE and forecast error for the next two quarters for each expected inflation proxy. Table 4, Panel A, which reports results from analyses using lagged annual inflation, indicates that in both sub-periods the coefficient on lagged inflation is significantly positive in both periods for the SUE regressions and for the forecast error regressions, although the statistical significance is weaker in both sub-periods than that in Tables 2 and 3 due to fewer observations in the sub-period analyses. Also, the marginal significance of the inflation coefficient and the lower adjusted R 2 in the forecast error regressions for the post-1994 period are partly due to the inclusion of new economy firms in this sub-period. Earnings of these firms are more volatile and more difficult to forecast, leading to greater noise in the regressions. 20

23 Overall, our conclusion that analysts underutilize inflation information is robust across subperiods Portfolio-level analyses To be consistent with prior studies on analysts rationality and on the post-earningsannouncement drift, (e.g., Ball and Brown, 1968; Bernard and Thomas, 1990; Abarbanell and Bernard, 1992; Ball and Bartov, 1996; Easterwood and Nutt, 1999), all our analysis thus far is based on pooled firm-level data. Even though we use robust clustered standard errors to control for potential correlation problems in the pooled regressions, we still check the sensitivity of our results with regard to potential cross-correlation concerns by repeating the regressions using portfolio-level data. 17 In addition to addressing the correlation concerns, the portfolio-level analysis will also reduce firm-specific noise in the regressions, and thereby improve the explanatory power of the models relative to firm-level analyses. To be consistent with the previous tables, we construct the PMN portfolio using only the two extreme deciles, P 1 and P 10. However, our results are qualitatively similar if we redefine PMN using all SUE deciles (i.e., long in the top 5 SUE deciles, P 6 through P 10 and short in the bottom 5 SUE deciles, P 1 through P 5 ). We construct portfolio-level SUE (SUE PMN,q+j, j = 3 to +4) and forecast errors (FERR PMN,q+j, j = 3 to +4) for PMN by averaging the variables of interest within the SUE deciles and then subtracting the average of the lowest SUE decile from that of the highest SUE decile. We compute these averages every month since the composition of the SUE decile portfolios changes every month. However, this procedure is likely to induce serial correlation in the variables since SUE and forecast errors are available only on a quarterly basis. To account 17 We cannot control for cross-sectional dependence using the Fama Macbeth approach, as values for inflation would be identical across portfolio observations in the monthly cross-sectional regressions. 21

24 for the serial correlation, we use Newey West standard errors. We have alternatively computed the portfolio-level variables at a quarterly rather than monthly frequency and obtained qualitatively similar results. Table 5 reports results from a time-series regression of SUE PMN,q+j and FERR PMN,q+j (j = +1 to +4) on the two measures for expected inflation. Panel A reports results for SUE PMN,q+j (j = +1 to +4), and Panel B reports results for FERR PMN,q+j (j = +1 to +4). While the coefficient on Michigan Survey expected inflation is significantly positive in all regressions of SUE PMN,q+j (j = +1 to +4), the coefficient on lagged inflation is significantly positive only in quarters q+1 and q+2. The coefficients on lagged SUE are generally insignificant in these regressions and the coefficient signs do not follow any clear pattern, a phenomenon very different from that observed in earlier firm-level analyses in which the first three lags tend to be positively correlated and the fourth lag tends to be negatively correlated with current period SUE. This difference across the portfolio-level and firm-level analyses is, however, consistent with Kothari et al. (2006), who show that the return predictive ability of lagged SUE varies substantially across portfolio-level and firm-level analyses. The average adjusted R 2 s in models II and IV for one-quarter-ahead SUE are about 20%, a substantial improvement over the corresponding adjusted R 2 s of about 5% observed for the firm-level analysis in Table 2. Focusing on regressions of FERR PMN,q+j (j = +1 to +4), we find that the coefficient on expected inflation is significantly positive for all four quarters subsequent to portfolio formation. This result holds both for lagged inflation and for the Michigan Survey forecasts of inflation. The coefficient of 0.59 on the Michigan inflation forecasts in regression of FERR PMN,q+1 suggests that a one-standard deviation increase in inflation forecasts of 0.55% increases the quarter-ahead forecast errors (expressed as a percentage of lagged stock price) for PMN by 0.09, corresponding to an economically significant 2.5 cents for the average firm. For comparison purposes, the average of actual earnings per share reported by firms in our sample is 24 cents. The coefficients 22