Investor Uncertainty and the Earnings-Return Relation Dissertation Proposal Defended: December 3, 2004 Kenneth J. Reichelt Ph.D. Candidate School of Accountancy University of Missouri Columbia Columbia, MO 65211 Tel: (573)884-2488 Email: ken.reichelt@missouri.edu Current Version: February 16, 2005 I wish to thank the dissertation committee members, Jere Francis, John Howe, Ken Shaw and especially Dr. Inder Khurana (chairman) and Raynolde Pereira, for their generous support. I also benefited from comments by Tina Xu and other workshop participants at the University of Missouri-Columbia. I also wish to thank Ron Howren for his technical support including programming and databases. I gratefully acknowledge I/B/E/S International, Inc. for providing data on earnings forecasts and other data. All errors are my own.
Investor Uncertainty and the Earnings-Return Relation Abstract This paper examines the role of investor uncertainty on the earnings-return relation. In the absence of perfect knowledge about the true state of the economy, investors form beliefs about this state variable. Recent theory proposes that uncertainty in their belief about the true state of the economy varies across time and influences investors response to information. Specifically, theory asserts that investors response to information will be more muted during times of investor uncertainty. This study empirically evaluates this prediction. In particular, I examine whether changes in expectations of future earnings are more heavily weighted in current stock returns when investor uncertainty is low. The theory also anticipates that unexpected current earnings will be more heavily weighted when investor uncertainty is low. The evidence supports both predictions.
1. Introduction This paper focuses on the role of investor uncertainty on the earnings-return relation. Within the context of this study, investors uncertainty pertains to their beliefs about the true state of the economy. The earnings-return relation is a relation between current stock returns and current and future earnings components. A rich literature has examined the accounting earnings-return relation and also the factors that influence this relation. This paper examines how investor uncertainty affects the relation between current returns and current and future earnings components. A starting point for this study is recent studies which point out that investors do not have perfect knowledge of the true state of the economy (David 1997; Veronesi 1999; Veldkamp 2004). In the absence of perfect knowledge, investors form beliefs based on current and past information. Investor uncertainty then arises when investors are uncertain about their beliefs about the true state of the economy. This investor uncertainty varies across time. This has been used as the underlying explanation for several observed economic phenomena. For instance variations in stock volatility (Schwert 1989; Campbell and Cochrane 1999) has been inferred as evidence of time varying investor uncertainty. More recently, Ozoguz (2003) finds that investors require a risk premium that is positively associated with their uncertainty of the state of the economy suggesting that the market prices this risk. Investor uncertainty also has implications on how investors will react to accounting information. During times of greater investor uncertainty, Veronesi (1999) argues that investors expectations about future cash flows will be more sensitive to new information, resulting in greater stock price volatility. In response to this higher stock 1
volatility, individual investors in turn will discount new information at a higher rate. Given that earnings represent an important source of information, the upshot from this line of inquiry is that prevailing investor uncertainty will influence the earnings-return relation. In particular, theory anticipates investor uncertainty will negatively influence the weights placed on the earnings components. The earnings-return relation has received considerable academic attention (Kothari (2001) provides an excellent survey). The basis for the earnings-return relation is that accounting earnings are posited to reflect value relevant information. In particular, current stock returns are viewed to incorporate unexpected current earnings, as well as the changes in expectations about future earnings (Collins et al. 1994; Lundholm and Myers 2002) (Hereafter, I interchangeably refer to unexpected current earnings as current earnings and changes in expectations of future earnings as future earnings). One line of enquiry has been to understand factors that influence the sensitivity of the earnings-return relation. For example, Collins and Kothari (1989) find that earnings persistence, systematic risk, and growth opportunities explain the cross-sectional variation in the earnings-return relation. Recent research has commenced to examine factors that have differential effects on the current and future earnings components. For example, Lundholm and Myers (2002) and Gelb and Zarowin (2002) find that the weight of the future earnings component is increasing in the level of firm disclosure. In this paper, I examine the influence of investor uncertainty on the extent to which current earnings and future earnings are reflected in current returns. The basic testable hypothesis pursued in this study is whether investor uncertainty negatively affects the weighting of the earnings components incorporated in current stock returns. Based on Veronesi (1999), higher investor uncertainty will cause investors to 2
more heavily discount information contained in accounting earnings. As a consequence, higher investor uncertainty is expected to reduce the weights of earnings components. I evaluate the influence of investor uncertainty on both current as well as future earnings components. The data for this study are collected from multiple publicly available sources. Returns and earnings data are obtained from CRSP, IBES, and Compustat databases yielding a sample size of 43,899 firm-year observations for the 13 year period from 1990 to 2003. Based on extant research, I use two measures of ex ante investor uncertainty. One measure, DIFFPE, follows Conrad et al. (2002) and measures investor uncertainty from changing discount rates, as reflected in changes in the price-to-forecasted earnings ratio. DIFFPE is defined as the difference between the monthly market price-earnings ratio and the average of the prior 12 months. By construction, DIFFPE is expected to increase when investor uncertainty is lower and decrease when investor uncertainty is higher. Following Strivers and Sun (2002), I also use implied stock volatility as a second measure of investor uncertainty. ANN_CHG_VIX measures the change in implied stock market volatility over the stock return period. It is based on the annual change in the Chicago Board Options Exchange (CBOE) volatility index. Figure 1 shows the implied volatility for the 1990-2003 period and is based on daily CBOE volatility index data. As anticipated, investor uncertainty, as reflected in implied stock volatility, is shown to be higher in recessions such as 1990-91 and 2001, and during national crises around the 1991 Gulf War and the 9/11 WTC. Empirical tests based on current stock returns support the basic hypotheses. Consistent with theory, the weight on the future earnings and current earnings components is decreasing with investor uncertainty. I find the evidence holds for both 3
measures of investor uncertainty - DIFFPE and ANN_CHG_VIX. As well, a component of current earnings, the markets prior expectation of current earnings, is decreasing with investor uncertainty. I also find these results hold after controlling for losses, growth, size, persistence and risk. The above findings suggest that the weightings of current earnings and future earnings components of current stock returns, are decreasing with investor uncertainty. The findings of this paper contribute to the extant literature on the earningsreturns relation. Lev (1989) pointed out that there is considerable variation in the earnings-return relation across time, and he conjectured that this is partly due to macroeconomic factors. On the other hand, recent theory suggests it is the investor uncertainty about the true state of the economy that may be relevant in explaining variation. I find evidence consistent with this prediction. This paper, by focusing on investor uncertainty of macroeconomic conditions, sheds light on the time series variation of the earnings-return relation. This paper also contributes to explaining how investor uncertainty affects the information content of current and future earnings weighting in current stock values. Johnson (1999) distinguishes between business cycle stages (expansionary and recessionary periods) and found that earnings news is more heavily weighted in current stock values in expansionary periods when earnings are more persistent and growth rates are higher. In contrast to Johnson (1999), this paper does not distinguish between expansionary and recessionary periods. Rather, this study examines variation in investor uncertainty about the true state of the economy and how it affects investors response to earnings information. While related, Conrad et al. (2002) differs from the present study in that they examine whether investor reactions to good and bad earnings announcements differs 4
between economic regimes. In contrast, this paper examines whether the relative weights on the earnings components differ by investor uncertainty. The remainder of the paper is organized into three sections. Section two provides a brief review of the literature. Section three develops the testable hypotheses. Section four describes the data and the empirical methodology. The last section summarizes and concludes the paper. 2. Literature Review Beginning with the seminal work of Ball and Brown (1968), a rich literature in accounting has examined the earnings-return relation. In general, these studies have found that current stock returns reflect information incorporated in accounting earnings. Subsequent research by Collins et al. (1994) modeled current stock returns as reflecting both unexpected current earnings as well as changes in expectations about future earnings. 1 An important question pursued by prior research is why the responsiveness of current stock returns to earnings varies across firms as well as time. Collins and Kothari (1989) directly address this question by examining the factors that influence the earnings response coefficient. They find that a higher level of growth opportunities, more earnings persistent, and lower systematic risk contribute to a higher earnings response coefficient. In addition, they find the risk free rate influences the time-series variation in the earning response coefficient. 2 Despite the importance of these findings, Lev (1989) points to the 1 They also empirically find by adding changes in future earnings expectations as an explanatory variable to the earnings-return relationship, there is a significant improvement in explanatory power by 3 to 6 times. 2 Despite the clear statistical association between security returns and contemporaneous earnings, the explanatory power has been low with respect to stock returns, and the regression coefficients have been unstable over time, according to Lev (1989). 5
instability of the earnings-return relation over time. He conjectured that macroeconomic conditions may be a contributing factor to this observed instability. Johnson (1999) examines Lev s (1989) conjecture by investigating whether the weighting of earnings in current returns varies across macroeconomic regimes. She begins her analysis by distinguishing between recessionary and expansionary periods. In examining firm-level ERCs 3, she finds that during expansionary periods that current earnings are more heavily weighted in current stock returns. Her explanation is that ERCs are positively associated with earnings persistence (Kormendi and Lipe 1987; Collins and Kothari 1989; Easton and Zmijewski 1989), and earnings persistence is higher in expansionary periods when growth opportunities are greater. Conrad et al. (2002) also examines the influence of macro level factors on the returns-earnings relation. In particular, they focus on the differential response to good news (earnings announcements that exceed consensus analyst forecasts) and bad news (earnings announcements that do not exceed consensus analyst forecasts) across relative stock market levels. They find that bad news ERCs in relatively higher market levels are greater than bad news ERCs in relatively lower market levels. Conversely, they find that good news ERCs in relatively higher market levels are no different than good news ERCs in relatively lower market levels. Their basic finding is consistent with the argument that negative shocks in periods of relatively high market levels is significant because it lowers the market s estimate of future cash flows as well as increasing the uncertainty of future cash flows. In contrast, positive shocks in periods of relatively low 3 An earnings response coefficient (ERC) measures the relative stock price response to an earnings surprise (actual earnings less analysts forecasted earnings) around the time of the firm s earnings announcement. It is the coefficient term b 1, that results from regressing abnormal (excess) returns around the time of the earnings announcement (AR it ) on earnings surprises, scaled by price (UE it ) such as in the following regression equation: AR it = b 0 + b 1 UE it.+ e it. 6
market levels are relatively muted. The explanation here is that while the news increases the markets expectation of future cash flows, the market discounts this information at a higher rate given the general uncertainty of a low relative market level. Conrad et al. (2002) find a similar reaction to good news even during relatively higher market levels. They argue that the market response is relatively small since the positive shock was anticipated (Conrad et al. 2002, pp. 2507-2508). I extend prior literature by examining the influence of investor uncertainty about the state of the economy on the earnings-return relation. In contrast to prior studies, I focus on the impact of investor uncertainty on the weighting of the earnings components in the earnings-return relation. The idea is that investors do not observe the true state of the economy, and investor uncertainty is not constant but varies over time. One possible explanation, offered by Chamley and Gale (1994) and Veldkamp (2004), is that uncertainty varies over time due to changes in economic activity. Investor uncertainty is higher when less information is revealed by lower economic activity, while investor uncertainty is lower when more information is revealed by higher economic activity. A second explanation, offered by Veronesi (1999), is that investor uncertainty increases when investors change their prior belief about the true state of the economy. This occurs when new information is learned that is contrary to their prior belief. Consequently, stock prices become more volatile and risk-averse investors compensate for the higher uncertainty by demanding a greater risk premium. Recent evidence by Ozoguz (2003) suggests that this risk is systematic and hence investors require a positive risk premium. In this paper, I test another implication of investor uncertainty. Specifically, I examine the theoretical prediction, whether investor uncertainty will result in investors discounting information, contained in accounting earnings, at a higher rate. Empirically, I 7
anticipate investor uncertainty to reduce the weightings of both the current and future earnings components. The focus of investor uncertainty on the earnings components is similar in spirit to recent research which has focused on the impact of disclosure on the earnings components. For example, Lundholm and Myers (2002) examine whether the earnings content (unexpected earnings and changes in future earnings expectations) of current stock returns increases for firms with expanded disclosure policies. They find in the presence of higher firm-level disclosure 4, that the market places more weight on future earnings in current stock returns. However, they do not find evidence that disclosure rankings affect the current earnings content of current stock returns. Similarly, Gelb and Zarowin (2002) find similar results for future earnings, but they do not specifically test for current earnings content. In contrast to the focus on disclosure, this paper examines whether investor uncertainty affects the current and future earnings content of current stock returns. 3. Hypothesis Development 3.1 Future Earnings and Investor Uncertainty A number of prior studies have noted that current stock returns reflects both news on current as well as future earnings (Warfield and Wild 1992; Collins et al. 1994). The underlying explanation is that accounting lacks timeliness and as a consequence generally lags stock returns in measuring value creation. (Lundholm and Myers 2002). As such, the inclusion of future earnings should improve the explanatory power over models that just include current earnings. Testing this prediction, Collins et al. (1994) 8
find the explanatory power of models with future earnings to be about three to six greater than that of models with just current earnings. 5 The conclusion that emerged from this inquiry and relevant for this study is that current period stock returns contain information about current as well as future earnings. Lundholm and Myers (2002) extend the aforementioned research by examining how the level of firm disclosure affects the significance of current and future earnings in the returns-earnings regression. This is similar in spirit to the analysis adopted in this paper. In this paper, I focus on the role of investor uncertainty and how it affects the current and future earnings component in the earnings-return relation. As noted earlier, by investor uncertainty I mean investors uncertainty in their beliefs about the true state of the economy. Investors do not have perfect knowledge about the true state of the economy because they do not know the true processes underlying macro level variables (Veronesi 1999). In the absence of this perfect knowledge, investors form beliefs on the state variable using existing information. However, several factors can contribute to investor uncertainty in their beliefs about the true state of the economy. For example, prior research contends that when the level of information available in the economy is low, investor uncertainty will increase (Veldkamp 2004). For instance, when economic activity is low such as in recessions, less information is generated because there is a low level of economic activity. This low level of information in turn contributes to investor uncertainty of the true state of the 4 They measure firm-level disclosure by American Investment Management Research (AIMR) disclosure rankings. 5 Extending this inquiry further, Warfield and Wild (1992) find the significance of future earnings in the returns-earnings relation increases with shorter reporting periods. 9
economy. Empirically, the higher level of stock volatility during periods of low economic activity has been pointed out as evidence of higher investor uncertainty. A consequence of higher uncertainty is that investors will hedge against this uncertainty by discounting information at a higher discount rate (Veronesi (1999). The underlying idea here is that when investors are more uncertain, the sensitivity of their beliefs to new information increases thus contributing to greater asset price volatility. With the resulting greater stock price volatility, risk-averse investors require to be compensated for bearing greater risk. In turn, this hedging behavior results in investors discounting new information they receive at a higher rate. This effectively reduces the weight of the information contained in stock (asset) prices. Put differently, stock prices will become less sensitive to news when investor uncertainty is greater. As referenced above, current stock returns are posited to contain information about current and future earnings. As Lundholm and Myers (2002) point out, current stock returns incorporate three components: unexpected current earnings, changes in expectations of future earnings, and random error, represented in the following equation (1): R t 0 + β1uxt + β 2i Et ( X t+ i ) + i= 1 = β ε (1). t In this equation, Rt is the annual stock return of the current period t, UX t is the unexpected earnings, defined as the annual earnings X t less the prior period s expectation E t-1 (X t ), ) is the change in the expectations about future earnings in year t+i, and E t ( X t + i εt is the disturbance term. 6 (For brevity, unexpected earnings will be interchangeably 6 This model is derived from the assumption that stock prices are equal to discounted value of expected future cash flows to shareholders. Collins et al. (1994) base this on the assumption that revisions in 10
referred to as current earnings, and changes in expectations of future earnings will be referred to as future earnings.) With respect to the future earnings component, Veronesi s (1999) model implies that investors will impound less future earnings information into current stock returns when they are more uncertain about the true state of the economy. With respect to equation (1), I expect investor uncertainty to negatively affect the coefficient on future earnings, ß 2. This provides the first testable hypothesis pursued in this paper. H1: The weight of future earnings, incorporated in current stock returns, decreases with investor uncertainty. 3.2 Current Earnings and Investor Uncertainty As referred to in equation (1), current stock returns are expected to contain information about current earnings. The second hypothesis predicts that the weight of current earnings, incorporated in current stock returns, is expected to decrease with investor uncertainty. When investors are more uncertain about the true state of the economy, theory predicts that their beliefs are more sensitive to new information thus contributing to greater asset price volatility. To compensate for greater volatility, riskaverse investors demand a greater risk premium. This hedging behavior results in investors discounting new information they receive at a higher rate. Current earnings news becomes discounted at a higher rate such that its value to investors is muted. For instance, information pertaining to current earnings, such as earnings announcements and earnings expectations are correlated with revisions in earnings expectations, following Kormendi and Lipe (1987). Lundholm and Myers (2002) derive the same from Ohlson s (1995) residual income valuation model by using a two period numerical example. 11
prior expectations, becomes less value relevant. Consequently, current earnings news is incorporated in current stock returns at a lower weight. The opposite prediction is made when investors are less uncertain about the true state of the economy. When investors are less uncertain, their beliefs are less sensitive to new information thus contributing to less asset price volatility. To compensate, riskaverse investors hedge at a lower risk premium which results in new information being discounted at a lesser rate. Current earnings news then becomes less muted by investors. Consequently, current earnings news is incorporated in current stock returns at a greater weight. Since current earnings news is less weighted in current stock returns when investor uncertainty is greater while the opposite holds when investor uncertainty is lesser, the second hypothesis is as follows. H2: The weight of current earnings, incorporated in current stock returns, decreases with investor uncertainty. 4. Research Design 4.1 Data and sample selection The sample used in this study consists of 43,899 firm-year observations covering fiscal year-ends from October 1990 to July 2003. The data used in this paper are from publicly available archival sources such as the Center for Research of Security Prices (CRSP), Standard and Poor s Compustat Industrial Annual, Institutional Brokers Estimates System (IBES), and Chicago Board Options Exchange (CBOE) Volatility Index data. The sample period covers fiscal year-ends from 1990 to 2003, since CBOE Volatility Index data is available for 1990 and afterwards, and earnings forecasts are available up to July 2004. The sample is constructed from intersecting 53,860 IBES 12
earnings forecasts (October 1990 to July 2004) with CRSP monthly returns and pricing files 7. Firm-year observations without a matching CRSP permno (3,377) and without complete current returns data (4,515) are removed. Compustat annual industrial data are then added, after removing unmatched Compustat cusips (1,157) and missing earnings data (912). The final sample size consists of 43,899 firm-year observations covering the October 1990 to July 2003 fiscal year-ends. 4.2 Models and variable definitions Investor Uncertainty Two variables are employed to compute ex ante investor uncertainty: the difference in market price-earnings ratio (DIFFPE t ), and the annual change in CBOE Volatility Index (ANN_CHG_VIX t ). DIFFPE t is a monthly time series variable, based on Conrad et al. (2002), to measure relative stock market level. Investor uncertainty is higher when stock market level is lower and vice versa, as suggested in regime shifting models such as Veronesi (1999). This variable is defined as the difference between the current monthly market price-earnings ratio and the average of the prior 12 months. Since the variable captures the relative change in market price-earnings ratio, it also captures variations in investor discount rates that reflect variations in investor uncertainty. To measure ex ante earnings in the market PE ratio, IBES analyst forecasted earnings are used. The first step in computing the monthly DIFFPE t is to compute the monthly market price/earnings ratio. The market price/earnings ratio for a particular month, t, is calculated by the following equation: 7 Eventus software (v 7.6) is used to compute stock returns from CRSP monthly returns files. 13
P/E(mkt) t = 1/ wit( Et [ EPSiτ ]/ Pit) (2) i= {1, Nt} where w it is the value of the firm i relative to the total market value of firms available in the sample for month t, P it is the share price of firm i in month t, and E t [EPS it ]is the median analysts forecast in month t for annual earnings reported in month t. After the monthly market price/earnings ratios is constructed, DIFFPE t, the difference between each month s market price/earnings ratio and the average of the market s monthly price/earnings ratio over the previous 12 months period is calculated. To be included in the computation of the DIFFPE t, a firm must have: 1) a price available on the earnings announcement date, 2) an earnings shock (actual earnings less consensus forecasts, scaled by stock price 6 days prior to earnings announcement date) between [-0.5 and 0.5], 3) a stock price of $5.00 or greater, 6 days before the earnings announcement date, 4) positive announced earnings, 5) and an actual earnings to market capitalization ratio less than or equal to one. According to Conrad et al. (2002), analyst forecasted earnings are used in the P/E calculation, because they better measure the market s valuation of expected future cash flows than a ratio constructed from current earnings. After the DIFFPE t variable is computed for each month of each year, each firm s fiscal year-end is mapped by the month in which the fourth-quarter earnings was announced, using IBES earnings announcement dates. For example, if a firm announces it earnings on January 1994, then the DIFFPE t for January 1994 is assigned. This estimates investors belief in the market s relative level when annual earnings were announced. Figure 2 presents a historical graph of DIFFPE t from January 1990 to December 2003. Note that DIFFPE t is generally positive prior to March 2000 when stock 14
market levels were relatively high, and are generally negative afterwards until mid 2003 when they were lower. ANN_CHG_VIX t is a monthly time-series variable that measures the direction (rate of change) of implied stock market volatility, based on the annual percentage change in the Chicago Board Options Exchange Volatility Index (VIX). Investor uncertainty is higher when stock market volatility is increasing and is lower when it is declining. The variable is computed over a one year period that begins three months after a firm s fiscal year starts until three months after the fiscal year ends to coincide with the stock return period. For instance, for a firm with a December 31, 2002 fiscal year-end, the ANN_CHG_VIX t variable is computed as: (VIX t VIX t-1 )/VIX t-1 where VIX t is the CBOE volatility index at the end of March 2003. The VIX is computed by the Chicago Board Options Exchange to measure market expectations of near term volatility conveyed by stock index option prices (CBOE 2004). It is computed by a formula that averages the weighted prices of out-ofthe-money S&P 500 index options. The S&P 500 index is used since it approximates the US stock market level and represents a significant portion of the total US stock market value (Standard & Poor's 2004). Strivers and Sun (2002) use VIX as a measure of implied volatility and find that the change in VIX is negatively associated with stock returns. Stock market volatility tends to increase during times of greater uncertainty when stock market returns are lower. Figure 1 presents a historical graph of the daily VIX indices from January 1990 to December 2003 8. Note that CBOE VIX is higher in the 1990-91 period when the 8 The data for Figure 1 were obtained from the Chicago Board Options Exchange website: http://www.cboe.com/micro/vix/historical.aspx. 15
economy was in a recession, and in the 2000 to 2003 period when stock market levels declined, suggesting that increases in volatility are associated with investor uncertainty. Models the two hypotheses examine whether the weights of earnings (current unexpected earnings and changes in future earnings expectations), incorporated in current stock returns, decrease with investor uncertainty. To test these hypotheses, equation (1) is expanded to include a main effect variable for investor uncertainty and interaction terms for current unexpected earnings and changes in future earnings expectations. The following equations (3) and (4) are shown below with predicted signs, and are derived from Lundholm and Myers (2002): R t = (-) (+) (+) (+) (-) b 0 + b 1 X t-1 + b 2 X t + b 3 AF t+1 + b 4 DIFFPE t + b 5 X t-1 *DIFFPE t (+) (+) + b 6 X t *DIFFPE t + b 7 AF t+1 *DIFFPE t + k ij * X i * Z j 3 i= 1 5 j= 1 + e t (3) R t = (-) (+) (+) (-) c 0 + c 1 X t-1 + c 2 X t + c 3 AF t+1 + c 4 ANN_CHG_VIX t (+) (-) + c 5 X t-1 *ANN_CHG_VIX t +c 6 X t *ANN_CHG_VIX t (-) 3 + c 7 AF t+1 *ANN_CHG_VIX t + k ij * X i * Z j + e t (4) i= 1 5 j= 1 where, R t is the buy and hold return, including dividends, starting three months after the beginning of the current fiscal year (t) until three months after the end of the fiscal year (t+1), 16
X t-1 is income available to common stockholders before extraordinary items (Compustat #237) in the prior fiscal year (t-1) scaled by market value three months after the beginning of the current fiscal year (t), X t is income available to common stockholders before extraordinary items (Compustat #237) in the current fiscal year (t) scaled by market value three months after the beginning of the current fiscal year (t), AF t+1 is the most recent annual earnings forecast for the following fiscal year, t+1, made three days prior to the announcement of the current year s earnings for period t, scaled by market value three months after the beginning of the current fiscal year (t), DIFFPE t and ANN_CHG_VIX t, are as previously defined, and 3 i= 1 5 j= 1 k * X * Z ij i j (where i=1 to 3 and j=1 to 5) is the interaction of three earnings variables (where X 1 is X t-1, X 2 is X t, and X 3 is AF t+1 ) with five control variables, Z j, resulting in a total of 15 coefficients, k ij. The five control variables are LOSS t, GROW t, SIZE t, PERS, and BETA t, and are defined as follows: LOSS t is an indicator variable =1 if current period earnings, X t, is negative, and equal to = 0 otherwise. GROW t is asset growth, measured as the annual percentage change in total assets, computed as (TA t TA t-1 )/TA t-1, where TA t is total assets (Compustat #6) at the end of fiscal year t. SIZE t is the natural log of market value of equity (number of shares outstanding times share price), measured three months after the end of fiscal year t-1. 17
PERS is earnings persistence, measured for each firm as the coefficient from regressing X t on X t-1 in the sample. BETA t is measured for each firm-year observation as the coefficient from regressing CRSP daily returns in year t on CRSP value-weighted returns. A brief discussion of the variables and their predicted coefficient signs follows. Consistent with Collins et al. (1994), proxies for unexpected current earnings are X t-1 and X t. The signs of the coefficients are expected to be negative for X t-1 and positive for X t, assuming prior year s earnings are permanent. Change in expectations of future earnings are measured by analyst forecasts for earnings in the next year, AF t+1. Analyst forecasts are used instead of actual future earnings and actual future returns, since this approximates expected future earnings in period t. Changes in expectations of future earnings, E X ), is measured by the variable, AF t+1, since the regression model t ( t+ 1 includes X t-1 as the prior expectations of future earnings, E X ). The signs of the t 1 ( t+ 1 coefficient is expected to be positive for AF t+1, consistent with proxies used by Collins et al. (1994) and Lundholm and Myers (2002). Analyst forecasts are based on the most recent available IBES detailed earnings estimate 9, three trading days prior to the earnings announcement of period t. One future year is chosen because estimates for the second and following years are very infrequent. The sign of the coefficient DIFFPE t is expected to be positive since higher current stock returns are expected when relative stock market levels are higher. The sign of the coefficient of ANN_CHG_VIX t is expected to be negative since lower stock returns are expected in more volatile periods. 9 Consensus analyst forecasts are not used since they are less accurate and less associated with stock prices, according to Brown (2001). 18
It is possible that the earnings coefficients may be affected by other time variant factors that prior research has found to be significant. Prior research has found that earnings coefficients are affected by earnings persistence (Kormendi and Lipe 1987; Collins and Kothari 1989; Easton and Zmijewski 1989), systematic risk (Collins and Kothari 1989; Easton and Zmijewski 1989), firm growth opportunities (Collins and Kothari 1989), the presence of losses (Hayn 1995), and firm size (Easton and Zmijewski 1989). To control for these factors, the five control variables, as previously defined, are interacted with each of the three earnings variables, X t-1, X t, and AF t+1. This results in a total of 15 control variables in the regression model. Hypothesis one predicts that the weight of future earnings, incorporated in current stock returns, decreases with investor uncertainty. As mentioned earlier, DIFFPE t is negatively associated with investor uncertainty while ANN_CHG_VIX t is positively associated with investor uncertainty. To test hypothesis one, the coefficient (b 7 ) of the interaction term, AF t+1 *DIFFPE t in equation (3), should be positive and the coefficient (c 7 ) of the interaction term, AF t+1 *ANN_CHG_VIX t in equation (4), should be negative. Hypothesis two predicts that the weight of current earnings, incorporated in current stock returns, decreases with investor uncertainty. To test hypothesis two, the coefficient (b 6 ) of the interaction term, X t *DIFFPE t in equation (3) should be positive and the coefficient (c 6 ) of the interaction term, X t *ANN_CHG_VIX t in equation (4), should be negative. A t-test is used to test for statistical significance of hypotheses one and two. In addition, since X t-1 and X t together proxy for unexpected current earnings, then hypothesis two is tested by the joint significance of X t-1 *DIFFPE t and X t *DIFFPE t in equation (3) and X t- 1*ANN_CHG_VIX t and X t *ANN_CHG_VIX t in equation (4). A partial F-test is employed to test for joint significance of these two interaction variable coefficients. 19
A test for the trend of the earnings variable coefficients, by sub-sample, is employed as a sensitivity test. Decile ranking sub-samples of the variables, DIFFPE t and ANN_CHG_VIX t, are separately constructed and current returns are regressed on X t-1, X t and AF t+1 for each sub-sample. The linearity of the trend is tested by regressing the coefficients on decile ranking, using a t-test. The coefficients of X t and AF t+1 should exhibit a positive trend as the DIFFPE t decile increases. This is because the earnings coefficients, which measure the weight of earnings information in current returns, are predicted to increase over the DIFFPE t deciles as investor uncertainty decreases. However, since X t-1 is negatively associated with current returns, the coefficient should exhibit a negative trend. The opposite predictions hold for the ANN_CHG_VIX t decile rankings, since ANN_CHG_VIX t is positively associated with investor uncertainty. A negative trend is predicted for the X t and AF t+1 coefficients over the ANN_CHG_VIX t deciles, since the hypotheses predict that less earnings information is weighted in current stock returns as investor uncertainty increases. However, a positive trend is predicted for X t-1, since it is negatively associated with current returns. Appendix A discusses additional robustness tests that are planned. 5. Results The results are discussed in three sections the sample data, tests based on difference in market PE, and tests based on Annual Change in Volatility. 5.1 Sample Data Table 1 presents descriptive statistics for variables used in equations 3 and 4 in the final sample of 43,899 firm year observations. Variables are windsorized at the 1 st 20
and 99 th percentile to minimize the effect of extreme outliers in the regression tests. The descriptive statistics appear to be comparable to other studies that used similar variables. Mean and median current returns are 0.146 and 0.059, respectively, and mean (median) current earnings are 0.077 (0.054), while mean (median) analyst future earnings are 0.143 (0.073). Median DIFFPE t (0.450) is comparable to mean DIFFPE t reported by Conrad et al. (2002) for quarterly results covering the 1988 to 1998 period of 0.445, however, I report a lower mean DIFFPE t of 0.174. The difference is possibly due to the uneven dispersion of month-ends in a sample based on annual fiscal periods, since December is a predominant month-end, while Conrad et al. (2001) reports quarterly results that are more evenly dispersed among all month-ends 10. To ensure the accuracy of the DIFFPE t measure, I compare the mean and standard deviation of the market PE ratio computed by Conrad et al. (2002) for the sample of firm quarter observations from 1988 to 1998(16.842, 3.064) to the time-series I computed for the same period (15.360, 3.066), and they appear comparable in magnitude and dispersion. The remaining variable descriptive statistics are reasonable. The mean ANN_CHG_VIX t indicates a 7.6% annual increase in implied stock volatility for the firm-year observations in the 1990-2003 period examined. This is reasonable since this period experienced financial turmoil such as the two recessions (1990-91 and 2001), 9/11 WTC, and two Gulf Wars. The LOSS t variable indicates that 23.5 percent of the firm- 10 In untabulated results, the mean DIFFPE t time-series from 1988 to 1998 (weighting each monthly DIFFPE t equally) is 0.374, which is closer to the quarterly based results obtained by Conrad et al. (2002). This suggests that an uneven distribution of fiscal year-end months may result in the mean DIFFPE t being less comparable. 21
year observations have a loss. The mean (median) persistence parameter for each firm is 0.357 (0.307) and the mean (median) beta is 0.810 (0.705). Correlation matrix results from Table 2 reveal expected associations. Current returns are significantly correlated with prior year s earnings, current year s earnings, future earnings, DIFFPE t and ANN_CHG_VIX t. This is evident since all p-values are <0.001for both Pearson (r p ) and Spearman (r s ) coefficients. Current returns are negatively associated with prior year s earnings (X t-1 ), since it proxies for prior expectations of current earnings. DIFFPE t is positively associated with current returns (r p =0.167, r s =0.159) since higher stock returns are realized when the stock market level is increasing. ANN_CHG_VIX t has a negative association with current returns (r p =-0.101, r s =0.102) since volatility tends to increase in weaker stock market conditions where returns are lower. 5.2 Tests based on Difference in Market PE Tables 3 reports the regression results from equation (3) where the difference in the market PE ratio (DIFFPE t ) is the measure of investor uncertainty. All main effect earnings variables: prior year s earnings, current year s earnings, and future year s earnings, are highly significant (p <0.001) and in the predicted direction. The prior year s earnings (X t-1 ) coefficient is significantly negative (p<0.001), as expected, suggesting that X t-1 is the market s prior expectation of current earnings. DIFFPE t is significantly positive (p<0.001) suggesting that current returns are higher when relative stock market levels are higher. Table 3 also reports the regression results from adding variables to control for losses, growth, size, persistence and risk (beta). Based on the regression model results 22
with control variables, loss significantly interacts with prior year s earnings, growth and persistence significantly interacts with current year s earnings, size significantly interacts with current and future year s earnings, and beta significantly interacts with all earnings variables. Multicollineary is high with X t-1, X t, AF t-1 and the interaction terms with SIZE t, since VIF values are in excess of 10. However, the test variables that interact DIFFPE t with the earnings variables are not affected. This means that the test results are still valid for the regression model with control variables. Evidence of the first hypothesis, whether the weight of future earnings (reflected in current stock returns) decreases with investor uncertainty, is supportive. As predicted, Table 3 reports for the regression model without control variables, that the interaction test variable, AF t+1 *DIFFPE t, is significantly positive (p<0.001) with a coefficient of 0.035. Since DIFFPE t is negatively associated with investor uncertainty, this suggests that the weight of future earnings, reflected in current stock returns, decreases with investor uncertainty. With control variables in the regression model, the results are similar, AF t+1 *DIFFPE t is significantly positive (p = 0.005) with a coefficient of 0.029. In another test, the sample was divided into 10 deciles of DIFFPE t and separate regressions of current returns on X t-1, X t and AF t+1 were performed. Untabled results reveal a nonmonotonic increasing trend of future earnings coefficients over the 10 DIFFPE t deciles, significant at 0.091 (one-tailed), suggesting that future earnings are more heavily weighted in current returns as investor uncertainty declines. Together these results suggest that the weight of future earnings, incorporated in current stock returns, decreases with investor uncertainty. Evidence of hypothesis two, whether the weight of current earnings (reflected in current stock returns) decreases with investor uncertainty, is supportive. Table 3 reports 23
the interaction test variable, X t *DIFFPE t, is negative and insignificant for both regression models, contrary to the predicted hypothesis. The regression model without control variables reports a coefficient of -0.011 (p=0.336) and the regression model with control variables reports a coefficient of -0.002 (p=0.808). However, since unexpected current earnings consists of actual earnings, X t less prior period expectations, proxied by X t-1, then a test of joint significance of the interaction terms is necessary. As predicted, the significance of the incremental effect of DIFFPE t on unexpected current earnings, X t *DIFFPE t and X t-1 *DIFFPE t, is jointly significant (p<0.001) in both regression models. Further evidence for hypothesis two is found in tests based on deciles of DIFFPE t. Untabled results reveal no significant trend of the coefficient of X t over the 10 deciles of DIFFPE t (p=0.376). However, as predicted, there is a negative non-monotonic trend in the coefficient of X t-1 (p=0.091), suggesting that the relative weight of prior year s earnings decreases with investor uncertainty. More about this result is discussed in the next paragraph. Together these test results suggest that the weight of unexpected current earnings, incorporated in current stock returns, decreases with investor uncertainty. Further analysis reveals that X t-1, the weight of the market s prior expectation of current period earnings decreases with investor uncertainty. If earnings are autoregressive, then the market s assessment of unexpected earnings is equal to Xt γ X t 1. Using the Table 3 results (without control variables) to illustrate, unexpected earnings are equal to 0.249(X t 1.490X t-1 ) when DIFFPE t = 1, such as when investor uncertainty is lower. Here 1.490 times 0.249 is equal to the sum of the coefficient of X t-1 (-0.321) and the interaction term coefficient of X t-1 *DIFFPE t (-0.050). When DIFFPE t = -1, such as when investor uncertainty is higher, unexpected earnings are 24
equal to 0.249(X t 1.089X t-1 ), where -1.089 times 0.249 is equal to -0.321 plus 0.050. To summarize, when investor uncertainty is lower, the autoregressive coefficient ( γ ) is greater (1.490 when DIFFPE t =1) than when investor uncertainty is higher (1.089 when DIFFPE t =-1). This suggests that the weight of the market s prior expectation of current earnings (X t-1 ) decreases with investor uncertainty. The results for both hypotheses are robust for the possibility of cross-sectional correlation. Since firms may have several years of observations there may not be independence of the error terms and the explanatory variables. Hubert-White sandwich estimators of variance are computed using Stata software (robust cluster option) to relax the assumption of independence among 8,303 firm clusters. The future earnings interaction term, AF t+1 *DIFFPE t, is significantly positive (p<0.001) in the model without control variables and with control variables (p=0.006). The current earnings interaction terms, unexpected current earnings, X t *DIFFPE t and X t-1 *DIFFPE t, are jointly significant (p<0.001) in both regression models. All coefficient values are the same as reported in table 3. 5.3 Tests based on Annual Change in Implied Volatility Index Table 4 reports the regression results from equation (4) where the annual change in volatility (ANN_CHG_VIX t ) is the measure of stock market condition. Since volatility tends to increase during weaker stock market periods, ANN_CHG_VIX t is negatively correlated with current returns. Consequently the interaction coefficient signs of the test variable should be the opposite from those reported in table 3 results involving DIFFPE t. All main effect earnings variables in the regression model without control variables: prior year s earnings, current year s earnings, and future year s earnings, are 25
highly significant (p <0.001) and are in the predicted direction. Prior year s earnings coefficients are significantly negative (p<0.001) and roughly of similar magnitude (- 0.329) to those of current earnings (0.267) suggesting that the market seems to treat current earnings as if it follows a random walk. In the regression model with control variables, all main effect earnings variables, except current earnings, X t, are significant. Prior year s earnings and future earnings are highly significant (p <0.001) while current earnings are not (p=0.181). Because of significant multicollinearity among the earnings main effect variables, it is not clear whether current earnings follow a random walk. Table 4 also reports the regression results from adding variables to control for losses, growth, size, persistence and risk (beta). Beta and size significantly interact with all earnings variables, loss only significantly interacts with prior and current year s earnings, growth only significantly interacts with prior and future year s earnings, and persistence only significantly interacts with current year s earnings. Evidence of the first hypothesis, whether the weights of future earnings (reflected in current stock returns) decreases with investor uncertainty, is supportive. As predicted, the interaction test variable, AF t+1 *ANN_CHG_VIX t, is significantly negative (p=0.002) with a coefficient of -0.136 in the regression model without control variables. This suggests that the weight of future earnings decreases with investor uncertainty. Similarly, in the regression model with control variables, the interaction test variable is significantly negative (p=0.007) with a coefficient of -0.129. Further evidence is found in tests based on deciles of ANN_CHG_VIX t. Untabled results reveal a significant non-monotonic negative trend in the coefficient of AF t+1 over the 10 deciles of ANN_CHG_VIX t (p=0.051), suggesting that less future earnings are weighted in current stock returns as 26