1. Introduction
Analysts are key financial market participants. Researchers often use analysts’ earnings forecasts as proxies for market expectations and differences in opinions. In addition, analysts’ earnings forecasts are one of the rare settings for which researchers have a large natural data set of individual analysts’ actual decisions, and for which the biases in decision making can be observed and verified ex-post. Not surprisingly, the activities of analysts have been a fertile ground for behavioral research. Prior studies have shown that analysts often suffer from a number of biases. However, the implications of these potential cognitive biases for investors and, even more so for managers, are less understood.
This study considers the behavior of financial market participants from a perspective different from that of previous research. It focuses on anchoring bias, a topic that has been characterized by Hirshleifer (2001) as an important part of “dynamic psychology-based assetpricing theory in its infancy” (p. 1535). “Anchoring” describes the fact that, in forming numerical estimates of uncertain quantities, adjustments in assessments away from some initial value are often insufficient. One of the first studies of this cognitive bias is the seminal experiment by Kahneman and Tversky (1974). These authors report that estimates of an uncertain proportion (the percentage of African nations in the United Nations) were affected by a number between 0 and 100 that was determined by spinning a wheel of fortune in the subjects’ presence. Subsequent research (reviewed in Section 2) has confirmed the generality and the robustness of this cognitive bias.
We hypothesize that market participants such as sell-side analysts and investors may also be affected by such anchoring bias when they estimate the future profitability of a firm. This estimation is a complex task that involves a high degree of uncertainty. This suggests that market
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participants may anchor on salient but irrelevant information. In particular, our discussions with financial analysts suggest that earnings forecasts of a specific firm are likely to be affected by the levels of forecasted EPS of its industry peers. One analyst pointed out in an interview that analysts “are reluctant to make earnings forecasts that further deviate from the current industry
‘norm’ (i.e., a historically stable range of forecasted EPS within the industry).” Specifically, when a company’s current forecasted EPS level has already been much higher (lower) than those of its industry peers, analysts appear to make insufficient upward (downward) adjustments even if the forecast revisions are well supported by fundamental information. We describe this observation as the analysts’ anchoring bias towards its industry norm. To capture this intuition, we construct a measure of cross-sectional anchoring in forecasted EPS (FEPS) as the difference between the firm’s FEPS (F-FEPS) and the industry median FEPS (I-FEPS), scaled by the absolute value of the latter. With this measure of cross-sectional anchoring (named CAF hereafter), we generate the following hypotheses.
First, if analysts anchor on the industry norm, their forecasts should be too close to this number. As a consequence, analysts are likely to underestimate (overestimate) the future earnings of firms with their forecast earnings per share (F-FEPS) above (below) the I-FEPS. In other words, analysts give more pessimistic earnings forecasts for firms with a high FEPS (i.e., firms with F-FEPS above I-FEPS) than for similar firms in the same industry with a low FEPS
(i.e.; firms with F-FEPS below I-FEPS). Therefore, earnings forecast errors should be lower for high FEPS firms than for low FEPS firms in the same industry.1
If investors are affected by biased analysts’ earnings forecasts, investors’ expectations of a firm’s future profitability should be similarly biased. Firms with a high FEPS compared to their
1 We define forecast errors as (Forecasted EPS – Actual EPS) / |Actual EPS|. All our results hold if the forecast errors are alternatively defined as (Forecasted EPS – Actual EPS) / Price.
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industry peers should suffer from low expectations regarding their future profits. Conversely, firms with a low FEPS relative to their industry peers should enjoy unduly high expectations regarding their future profits. If this is the case, stocks with high levels of EPS forecasts should significantly outperform similar stocks in the same industry with low levels of EPS forecasts when the firm’s true profitability is subsequently revealed, for example, around subsequent earnings announcement dates.
We generate empirical results consistent with all the hypotheses suggested by crosssectional anchoring. Using U.S. data from 1983 to 2005, we find that analysts’ earnings forecasts for firms with a high CAF are more pessimistic than the forecasts on similar firms with a low
CAF. This result is consistent with analysts anchoring their forecasts on the industry median. We further find that stock returns are significantly higher for firms with a high CAF than for similar firms in the same industry with a low CAF. The positive relationship between firm CAF and future stock returns cannot be explained by known risk factors, book-to-market ratios, earningsto- price ratios, fundamental value-to-price ratios, accounting accruals, price momentum, earnings momentum, or the nominal price per share. Moreover, earnings surprises are relatively more positive for firms with a high CAF than for firms with a low CAF. These results are consistent with the notion that investors are also affected by the cross-sectional anchoring bias.
All these results are stronger when the industry norm is more stable and when market participants are less sophisticated. Finally, firms with a low CAF experience more positive revisions in earnings forecasts and more positive forecast errors after a stock split relative to nosplit firms than do firms with a high CAF. Consequently, firms with a low CAF experience more negative changes in earnings surprises relative to no-split firms after a stock split than do firms with a high CAF. Results are robust to controlling for alternative anchors. For example, in
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addition to anchoring on the industry norm, it is also possible that analysts and investors may anchor on the most recently announced earnings. Although we find that analysts and investors also anchor on the most recently announced earnings, our key results hold even after controlling for this effect. In fact, we find that both cross-sectional and time-series anchoring biases affect financial markets; but the former is more influential than the latter.
These results confirm that anchoring, an important cognitive bias in the psychology literature, affects decision making by individuals in an important economic setting. This large sample test complements the previous research that was largely based on small sample experimental work. To the best of our knowledge, this study is the first one to use a large sample archival approach to understand the implications of the cross-sectional anchoring effect in a finance setting. Although we focus on analysts’ earnings forecasts and price behavior in order to take advantage of a particularly rich data set, we expect that our results can be generalized in other settings as well. The results of this study also enhance our understanding of the financial markets by providing new understanding of analyst and investor behavior. Of particular importance, the results suggest that understanding this cognitive bias may yield a trading strategy that generates abnormal returns. Specifically, our results suggest that a hedge portfolio that goes long on firms with a high CAF and short on firms with a low CAF could, over the period studied, have generated a monthly risk-adjusted return (alpha) of 0.76%, or 9.12% per year. 2 The profitability of such a trading strategy remains significant for investment horizons that extend to at least 12 months. Finally, our results suggest a corporate strategy based on stock splits for managers of firms with a high level of FEPS. Such a strategy can mitigate under-valuation and sometimes generate over-valuation by influencing analysts’ earnings forecasts or revisions.
2 A similar trading strategy based on time-series anchoring generates trading profits that are only one-third of those generated from cross-sectional anchoring.
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In addition, our study complements previous studies on nominal stock prices. Benartzi et al. (2007) find that the cross-sectional distribution of nominal stock prices per share in the United
States has been very stable with the median hovering around $30 since early in the last century.
We show that a similar effect exists for forecasted EPS: the median nominal FEPS has been hovering between $1.50 and $2.00 (shown in Figure 2) since analysts’ earnings forecasts became available in 1978. Baker, Greenwood, and Wurgler (2009) suggest that managers split shares to cater to investors’ preference driven by “small-cap premiums.” However, the source of this higher valuation for low-price firms remains unclear. We consider the possibility that these firms are overvalued because of the anchoring bias of market participants. Consistent with this view, our results suggest that low FEPS stocks (relative to their industry peers) are indeed overpriced.
The remainder of this study is organized as follows. In Sections 2, we review the previous studies on anchoring bias. In Section 3, we develop our research hypotheses. In Section
4, we describe our research design. Section 5 discusses our sample and descriptive statistics, while Section 6 presents our empirical results. Finally, we conclude the study in Section 7.
2. Prior Research on Anchoring
The results of prior research (Kahneman and Tversky (1974)) suggest that individuals use cognitively tractable decision strategies, known as heuristics, to cope with complex and uncertain situations. These heuristics reduce complex inference tasks to relatively simple cognitive operations. Although these “mental short-cuts” help individuals in dealing with complex and uncertain situations, they may also lead to systematically skewed outcomes. The anchoring effect is one of the most studied cognitive biases that lead individuals to make sub-optimal decisions.
In their classic study, Kahneman and Tvesky (1974) explore the idea that individuals frequently
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form estimates by starting with an easily available reference value and then adjusting from this value. Although this approach may not be problematic per se, research has shown that individuals typically fail to properly adjust their final estimates away from the salient but overemphasized starting point (the “anchor”).
Kahneman and Tversky’s (1974) seminal example involves spinning a wheel-of-fortune in front of the subjects and thus generating a number between 0 and 100. They asked the subjects for their best estimates of the percentage of African nations in the United Nations. The obviously irrelevant random number generated from the wheel-of-fortune generates systematic bias in the estimations. For example, the average estimate from subjects who observed the number 10 was
25%. In contrast, the average estimate from subjects who observed the number 65 was 45%. This result has been replicated in many other experimental settings. For example, Kahneman and
Tversky (1974) asked half of their subjects to estimate the value of 1x2x3x4x5x6x7x8 and asked the other half to estimate the value of 8x7x6x5x4x3x2x1. The average answers from the two groups were 512 and 2,250, respectively. Russo and Shoemaker (1989) provide an anchor based on a constant (varying from 400 to 1,200) plus the last three digits of the subject’s phone number. The two researchers then asked for an estimate of the year in which the Attila the Hun was finally defeated. Estimates were positively and significantly correlated with the anchor.
More recently, Qu, Zhou, and Luo (2008) provide physiological evidence of the anchoring process based on event-related potential techniques (i.e., techniques that measure the brain responses stimulated by a thought or a perception).
Research has shown that anchoring influences various types of decisions in many different contexts. These include judicial sentencing decisions (Englich and Mussweiler, (2001)), personal injury verdicts (Chapman and Bornstein (1996)), estimation of the likelihood of
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diseases (Brewer, Chapman, Schwartz, and Bergus (2007)), job performance evaluation
(Latham, Budworth, Yanar, and Whyte (2008)), judges’ rankings in competitions (Ginsburgh and van Ours (2003)), and real estate acquisitions (Northcraft and Neale (1987)).3
Previous research has also suggested that it is particularly difficult to correct anchoring bias. Consistent with this view, Northcraft and Neale (1987) conclude (p. 95) that “(1) experts are susceptible to decision bias, even in the confines of their ‘home’ decision setting, and (2) experts are less likely than amateurs to admit to (or perhaps understand) their use of heuristics in producing biased judgments.” Plous (1989) shows that task familiarity is not sufficient to avoid anchoring bias and that the effects of anchoring bias are not significantly influenced by the ease with which respondents can imagine the outcome (outcome availability), by the instructions to list the most likely path to the outcome (path availability), or by casting the problem in terms of avoidance (rather than occurrence). Plous (1989) also mentions that anchoring bias exists even after correcting for various social demand biases (i.e., the existence of expert opinion running against the initial anchor). Wright and Anderson (1989) consider the effect of situation familiarity on anchoring. They conclude (p. 68) that, “The anchoring effect is so dominant that increasing situational familiarity did not result in decreased anchoring.” They find that monetary incentives can reduce anchoring, but the effect is only marginal in its statistical significance. In contrast, Tversky and Kahneman (1974) find that payoffs for accuracy do not reduce the anchoring effect. Further, Brewer, Chapman, Schwartz, and Bergus (2007) report that
3 In addition, anchoring has been shown to influence intuitive numerical estimations (Wilson, Houston, Etling, and
Brekke (1996)), probability estimates (Plous (1989)), estimations of sample means and standard deviations (Lovie
(1985)) and estimates of confidence intervals (Block and Harper (1991)), sales predictions (Hogarth (1980)),
Bayesian updating tasks (Lopes (1981)), utility assessments (Johnson and Schkade (1989)), risk assessments
(Lichtenstein, Slovic, Fischhoff, Layman, and Combs (1978)), preferences of gambles (Lichtenstein and Slovic
(1971)), perception of deception and information leakage (Zuckerman, Koetsner, Colella, and Alton (1984)), negotiation outcomes (Ritov (1996)), and choices between product categories (Davis, Hoch and Ragsdale (1986)).
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accountability does not reduce anchoring bias in doctors’ predictions of infection. Whyte and
Sebenius (1997) provide results suggesting that groups do not de-bias individual judgments.
The amount of research on the anchoring bias in financial markets is very limited.
DeGeorge, Patel, and Zeckhauser (1999) suggest that executives aim to exceed salient EPS thresholds. George and Hwang (2004) propose that investors are reluctant to bid the price high enough when a stock price is at or near its highest historical value. Consistent with this intuition, they find that a stock price near its 52-week high has predictive power for future stock returns.
Campbell and Sharpe (2009) show that professional forecasters anchor their predictions of macroeconomic data such as the consumer price index or non-farm payroll employment on previous values, which leads to systematic and sizeable forecast errors. Baker, Pan, and Wurgler
(2009) suggest that anchoring bias also affects corporate acquisitions. However, these studies focus on time-series (i.e., historical information of the firm itself) anchoring bias. In contrast, we focus on the effect of cross-sectional (i.e., contemporaneous information of other firms) anchoring, a topic that has not been explored by the prior research, although we also consider time-series anchoring of most recent announced earnings.
3. Hypotheses Development
Given the documented robustness of anchoring bias, we hypothesize that market participants such as sell-side analysts and investors should also be affected by anchoring heuristics when they estimate the future profitability of a firm. This estimation is a complex task that involves a high degree of uncertainty, which makes market participants naturally anchor on salient information in their decision making. Prior research (Chapman and Johnson (2002)) suggests that anchors are most influential if they are expressed on the same response scale as the
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items being estimated (i.e., dollars for dollars rather than dollars when estimating percentage) and if they represent the same underlying dimension (width for width rather than width when estimating length). The popular financial website, Investopedia.com, notes that, “Earnings per share is generally considered to be the single most important variable in determining a share’s price.”4 Tversky and Kahneman (1974) show in an experimental setting that subjects priced with the median of other subjects’ estimates anchor on this median. A natural candidate for possible anchors in our setting is thus the industry median forecast earnings per share.5 Since an analyst usually covers a group of firms within the same industry, this number is readily available and is naturally associated with the task at hand. For example, Zacks Investment Research states in the first line of a recent analyst report that, “Median EPS is projected to drop 21.2%.”6
To validate the plausibility of industry median forecasted EPS as an anchor, we interviewed six stock analysts from leading investment banks. First, we described two hypothetical stocks, stock A and stock B, with identical business and firm characteristics (such as firm size, firm performance, market power, corporate governance structure, and so forth).
Second, we told our interviewees that the only differences between stock A and stock B were the level of earnings per share (EPS) and the number of shares outstanding: stock A has an EPS of
$0.1 with 100,000 shares outstanding and stock B has an EPS of $10 with 1,000 shares outstanding. Third, we showed our interviewees a hypothetical figure of the industry crosssectional distribution of forecast EPS (similar to Figure 2 in our study) with the industry median forecasted EPS hovering around $1.5. Finally, we asked them which of the stocks is more likely to double its earnings per share next year (i.e., from $0.1 to $0.2 per share for stock A, and from
4 http://www.investopedia.com/terms/e/eps.asp.
5 We do not argue here that the industry median FEPS is the only possible anchor that leads to behavioral bias.
Instead, we argue that it is an important one, particularly in explaining the empirical patterns documented in this study. We will discuss alternative anchors including time-series anchoring in Section 7.2.
6 http://www.reuters.com/article/pressRelease/idUS213655+25-Jun-2009+BW20090625.
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$10 to $20 per share for stock B). Five out of six interviewed analysts picked Stock A. When we asked them which stock is more likely to halve its earnings per share next year (i.e., from $0.1 to
$0.05 per share for stock A, and from $10 to $5 per share for stock B), these five analysts chose stock B instead. In a follow-up discussion, analysts suggested that their estimations were obviously affected by the industry ‘norm’ of the forecast EPS, especially when it is stable over time. If participants indeed anchor on the industry median FEPS (i.e., cross-sectional anchoring), this should have important implications for the behavior of analysts, investors and the managers of publicly traded companies. First, if analysts anchor on the industry median forecasted EPS (I-FEPS), their forecasts should be too close to this number. As a consequence, they would underestimate the future earnings growth of firms with high FEPS (relative to the industry median). In other words, analysts should give more optimistic earnings forecasts for firms with low FEPS (relative to the industry median) than for similar firms in the same industry with high FEPS (relative to the industry median). Thus, signed earnings forecast errors would be larger for low FEPS firms than for high FEPS firms in the same industry. This motivates our first hypothesis: H1: Analyst forecasts are more optimistic (indicated by a higher signed forecast errors in our study) for firms with a low FEPS relative to their industry median FEPS than for firms with a high FEPS relative to their industry median FEPS.
If investors are affected by biased analysts’ earnings forecasts, their expectations of future profitability should also be biased. Firms with high FEPS relative to their industry median
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should suffer from low expectations regarding their future profits. Conversely, firms with low
FEPS relative to their industry median should enjoy unduly high expectations regarding their future profits. If this is the case, stocks with high FEPS should significantly outperform similar stocks in the same industry with low FEPS once the true profitability is revealed. This motivates our second hypothesis:
H2: Controlling for risk factors, future stock returns for firms with high FEPS relative to their industry median FEPS are higher than for firms with low FEPS relative to their industry median FEPS.
This prediction should be particularly true around subsequent earnings announcement dates.
4. The Research Design
We apply two basic approaches to test our hypotheses: regression analyses and portfolio sorts. The regression approach allows us to control easily for a host of potentially confounding effects. The portfolio approach allows us to address econometric issues such as overlapping observations and non-linearities more easily than in a regression framework. The portfolio approach also allows us to deal more easily with the “bad model issue” discussed by Fama
(1998) and Mitchell and Stafford (2000).
4.1 Regression analysis
The following cross-sectional and time-series model is used to test our hypotheses:
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DepVar α βCAF γ X ε , i,t
K
i,t
K
i,t i,t     1 1 (1) where DepVari,t represents the value of the dependent variable for firm i in period t. To test our first hypothesis, analysts’ forecast error (FE) is the dependent variable. FE is the difference between the consensus EPS forecast and the actual EPS announced after the end of the fiscal year, scaled by the absolute value of the latter. The consensus EPS forecast is the mean of oneyear- ahead EPS forecast in the previous month from the Institutional Brokers’ Estimate System
(I/B/E/S) unadjusted summary historical file. The actual EPS is reported in the I/B/E/S actual file. To test the second hypothesis, two dependent variables are evaluated at the end of each calendar month, t. The first is BHAR0:1, defined as the cumulative buy-and-hold raw return for firm i in the current month, t.7 The second is ECAR, defined as the sum of the three-day, riskadjusted, cumulative abnormal returns around the earnings announcements over the next twelve months after the end of calendar month t-1.
The main treatment variable, CAF, measures cross-sectional anchoring bias. CAFi,t-1 is defined as the difference between the FEPS for firm i (F-FEPS) in month t-1 and the industry median FEPS (I-FEPS) in the same month, scaled by the absolute value of the latter. We define
48 industries following the approach of Fama and French (1997). Various other CAF specifications and industry definitions are tested, but the results remain quantitatively and qualitatively similar.8 These results are not presented here but are available upon request. Two interesting features of this variable is that the firm can choose its preferred value of CAF through stock split (and reverse stock splits) but also that a firm can affect the value of CAF for other
7 We focus on a one-month horizon to minimize the bad model problem discussed by Fama (1998) and Mitchell and
Strafford (2000). As discussed in Section 6, the results hold if we extend the horizon to twelve months.
8 For example, we define CAFi,t-1 as the difference between firm i’s FEPS and I-FEPS, scaled by the standard deviation of the former within each industry. We also try defining the industries using 2-digit SIC codes.
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firms in the same industry by engaging in a stock split.9 The fact that economically irrelevant decisions affect the value of CAF and make it an arbitrary number mitigates the risk that CAF proxies for some omitted constructs such as a risk factor.
Aside from including an (untabulated) constant, a vector of K control variables (XK) is included in the regression. Specifically, K
Xit1 includes the logarithm of firm i’s market capitalization (Size) at the end of month t-1, the logarithm of its book-to-market ratio (BTM), its accounting accruals (Accruals), and the three-day abnormal return around firm i’s most recent earnings announcement before the beginning of month t (ESrecent). The lagged information is used for all of the control variables to ensure that the values of these variables have been known by investors at the beginning of month t to avoid any look-ahead bias. We also control for past returns in our specifications. When FE or ECAR is the dependent variable, we simply use the six-month buy-and-hold return in the prior six months (Ret-6:0). However, when BHAR0,1 is the dependent variable, we control for a one-month lag of past six-month buy-and-hold return (Ret-7:-
1) and the past one-month return (Ret-1:0), because previous research has shown the importance of intermediate-term momentum and short-term reversal (Jegadeesh and Titman (1993, 2001)). In addition, we control for the following three additional variables when FE is the dependent variable: Experience (the natural logarithm of one plus the average number of months current analysts have been following the firm), Breadth (the natural logarithm of the average number of stocks followed by current analysts) and Horizon (the natural logarithm of one plus the number
9 Suppose that Firm X (the firm for which the analyst is forecasting) has an EPS forecast of $2.00. Firm Y is the only other firm in the industry and its total forecasted earnings are $2,100 and it has 1,000 common shares outstanding. Thus, Firm Y’s forecasted EPS is $2.10. So, the industry median forecasted EPS is $2.05. CAF for firm
X is ($2.00-$2.05) ÷ |$2.05| = -0.02. Reconsider the above example but now Firm Y has 2,000 shares outstanding.
Firm Y’s forecasted EPS is $2,100 ÷ 2,000 = $1.05. The industry median is now $1.525 and CAF for firm X is
($2.00-$1.525) ÷ |$1.525| = 0.31. Note that the stability of the anchor (i.e., the industry median forecasted EPS) also significantly affects the anchoring bias. We provide more detailed discussions in section 7.1.
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of months before firm i’s next earnings announcement). The detailed definitions of these variables are described in Appendix 1.
If H1 is correct, the coefficient of CAF should be negative, when FE is the dependent variable. In essence, when F-FEPS is low relative to I-FEPS, analysts may anchor on I-FEPS and issue over-optimistic forecasts. This would lead to low subsequent stock returns as market participants gradually revise and correct their optimism. Then, we expect negative earnings surprises when the true earnings are announced. Therefore, if H2 is correct, we expect that the coefficient of CAF should be positive, when BHAR0,1 is the dependent variable. We also expect that the coefficient of CAF should be positive when ECAR is the dependent variable, as investors realize their initial mistake when subsequent earnings are released. We use the Fama-MacBeth
(1973) procedure to estimate equation (1), when the dependent variable is continuous (FE,
BHAR, or ECAR). The Newey–West (1997) heteroskedasticity and autocorrelation consistent estimates of standard errors are used to compute the t-statistics on the estimated coefficients.