2.1 Economic theories predicting analyst underreaction

Our description of a mechanism leading to market underreaction to complex 10-K information begins with a description of economic incentives for analysts to underreact to such information. Consistent with Raedy et al. (2006), we define analyst underreaction as the tendency to partially revise earnings forecasts in response to information relevant for valuing a firm's equity securities. Trueman (1990) provides the earliest economic theory for analyst underreaction. The theory predicts that, to avoid negative attention from investors, weak analysts only partially revise their forecasts in the direction of new information, thus giving the impression of greater accuracy in their prior forecasts. In that case, a weak analyst's individual forecast and the consensus forecast exhibit underreaction to new information.7

Raedy et al. (2006) empirically demonstrate analyst underreaction increasing with the forecast horizon, a proxy for uncertainty in the analyst's (unreported) unbiased earnings expectations.8 To guide future research, Raedy et al. (2006) develop a theoretical model that explains the paper's empirical results. The theoretical model hinges on the assumption that analysts have asymmetric loss functions, whereby the reputation cost of forecast inaccuracy due to overreaction to previously available information exceeds the cost of underreaction. That is, investors prefer to trade on information that continues in the same direction. If an investor buys (sells) stock after an analyst raises (lowers) her earnings forecast, the investor's trade becomes profitable if subsequent information confirms the direction of the previous forecast revision. To increase the likelihood of good (bad) news following good (bad) news forecast revisions, analysts underreact to the 10-K's implications for future earnings. Corollaries predict that underreaction increases with the amount of asymmetry in the analyst's loss function and the uncertainty associated with the analyst's (unreported) unbiased estimate of future earnings. With no uncertainty or no asymmetry in the analyst's loss function, the analyst simply reports her unbiased expectation of future earnings. Raedy et al. (2006) analytically derives an amount of analyst underreaction that optimally lowers the odds of a forecast revision reversal.

Linnainmaa et al. (2016) analytically derive three sources of analyst underreaction, manifesting as autocorrelation in analysts' forecast errors. Consistent with Raedy et al. (2006), Linnainmaa et al. (2016) estimate that about 60% of such autocorrelation stems from analysts knowingly underreacting to new information due to uncertainty about the model generating the firm's reported earnings. Linnainmaa et al. (2016) estimate that another 20% of the autocorrelation in analysts' forecast errors is a statistical artefact of pooling forecast error observations across firm or time-period groups, and the rest stems from analysts' (self-correcting) misestimation of earnings persistence.

Bernhardt et al. (2016) provides evidence consistent with analysts facing the type of asymmetry in reputation costs of inaccuracy described by Raedy et al. (2006). Specifically, Bernhardt et al. (2016) model underreaction in analysts' buy-sell-hold recommendations as a function of analyst reluctance to revise recommendations too frequently. Essentially, Bernhardt et al. (2016) assume too frequent recommendation revisions frustrate investors wanting to hold positions based on those recommendations and detract from the analyst's credibility. The analyst must balance investor demand for timely recommendation revisions that reflect changes in fundamental value on the one hand with the loss of credibility accompanying frequent recommendation revisions on the other hand. As in Raedy et al. (2006), the Bernhardt et al. (2016) model assumes each analyst determines her own degree of underreaction.

2.2 Analyst response to information in 10-K filings

While studies of financial analyst forecasting behaviour and the information content of their earnings forecast revisions have a long history, surprisingly few studies focus on the behaviour of financial analysts' forecasts following 10-K filings. Bradshaw et al. (2001) find that analysts' forecasts published up to 12 months after the previous earnings announcement, which is well-past the 10-K filing date, do not fully incorporate the negative implications of large positive accruals for a firm's future earnings. Li and Ramesh (2009, p. 1199) conclude that “(analysts do) not respond contemporaneously in a pervasive fashion to periodic SEC filings that follow earnings announcements”. The contemporaneous window includes the 11 trading days centred on the 10-K filing date, and the paper finds no evidence of elevated analyst forecast revision activity on any of these days. This is consistent with the forecast delay documented by Lehavy et al. (2011) and Li and Ramesh (2009).

Lehavy et al. (2011) present results consistent with the following inferences: (i) firms with more complex 10-Ks attract more analyst coverage; (ii) analysts work harder to understand more complex 10-Ks, as measured by the time delay from the 10-K filing date until the analyst's first forecast following that date; (iii) the information contained in analysts' forecasts following 10-K filings increases with the complexity of the firm's 10-K, with information content measured by the proportion of absolute one-day returns at the time of all forecasts between the 10-K filing date and the end of the fiscal year, to the total of all absolute daily returns from the 10-K filing date until the end of the subsequent fiscal year; and (iv) forecasts following more complex 10-K filings are more dispersed, less accurate, less timely, and reflect more overall analyst uncertainty.

Our paper extends Lehavy et al. (2011) by focusing on whether analysts' forecasts underreact to the earnings implications of 10-K information and, if so, whether the underreaction increases with 10-K complexity. The results of our investigation are not obvious, given the evidence in Lehavy et al. (2011) indicating that 10-K complexity attracts more analyst coverage, as well as greater analyst effort, and breeds forecast uncertainty. As described in subsection 2.1, Raedy et al. (2006) analytically shows that underreaction increases with the uncertainty of the earnings implications of the underlying information, and with the excess penalty for inaccuracy of analyst forecasts that overreacted versus those that underreacted to the information that prompted the forecast revision. Our extension of Lehavy et al. (2011) investigates whether the underreaction-increasing effect of increased forecast uncertainty significantly outweighs the underreaction-decreasing effect of better analyst coverage. Furthermore, we examine whether the impact of analyst underreaction on the efficiency with which market prices impound 10-K information increases with 10-K complexity.

2.3 Stock price response to information in 10-K filings

Griffin (2003) is the first paper to find a stock price reaction to 10-K filings. Li and Ramesh (2009) confirm the Griffin (2003) result only when the first news of the firm's earnings comes at the time of the 10-K filing. Both Li and Ramesh (2009) and Griffin (2003) concentrate their investigations on a narrow window surrounding the 10-K filing date. This may be problematic, since more recent papers find that analysts take some time to analyse the 10-K information before responding with a revised forecast of the firm's next year earnings. In fact, Livnat and Zhang (2012) find that the market responds more strongly to forecasts that do not appear immediately after the 10-K filing date, and Bae et al. (2023) find that a market-based measure of valuation uncertainty (return volatility) spikes immediately after the 10-K filing date and then declines to a place below the valuation uncertainty before the filing of the 10-K. Thus, it is hard to know when to measure the market's reaction to 10-K information. Our solution to this problem is to examine the market's reaction to analysts' 10-K-straddling forecast revisions.

You and Zhang (2009) use the three-day return around the 10-K filing date to represent information available from the 10-K and find that investors underreact to complex 10-K information, as measured by the number of words in the 10-K.9 Miller (2010) provides insight into a mechanism that explains the You and Zhang (2009) evidence of a complexity-driven price drift in the direction of the 10-K-straddling 3-day return. Specifically, Miller (2010) provides evidence of an inverse relation (no relation) between 10-K complexity and abnormal trading by small (large) investors. This evidence suggests that, due to trades by large investors immediately following complex 10-K filing dates, prices partially move in the direction of value-relevant 10-K information, and prices continue to drift in that direction due to delayed trades by smaller investors. Miller (2010) attributes the sluggish response by small investors to the high cost of quickly analysing complex 10-K information.

Instead of the three-day return centred on the 10-K filing date as the proxy for the information in the 10-K filing, our proxy is the analyst's 10-K-straddling earnings forecast revision, and we begin the post-10-K return accumulation period on the second day following the date of the analyst's revised forecast. Thus, the forecast revision window expands as needed to allow more time for investors and analysts to process more complex 10-K information. Any complexity-driven analyst underreaction and price drift observed in our study is not due to information processed between the 10-K filing date and the date of the revised forecast.10

Using individual analysts' 10-K-straddling earnings forecast revisions to proxy for the earnings implications of 10-K information, we find no evidence of market inefficiency with respect to the earnings implications of low-complexity 10-K information, and we find evidence of significant market underreaction to the earnings implications of high-complexity 10-K information. While these results are consistent with You and Zhang (2009), our paper extends You and Zhang (2009) in several ways. First, we rely on a 10-K information proxy that allows time for analysts to interpret the 10-K's earnings implications. Second, we invoke controls for analyst underreaction and find evidence suggesting that, left to its own devices, market prices would have overreacted to the earnings implications of high- and low-complexity 10-K information. Third, we uncover a mechanism leading to market underreaction to complex 10-K information. The next section describes this mechanism.

2.4 The impact of analyst underreaction on stock prices

Relatively few papers provide evidence regarding the impact of analysts' forecasts on market efficiency with respect to information in corporate financial reports. Abarbanell and Bernard (1992) and Shane and Brous (2001), respectively, find that analysts underreact to information reflected in their earnings forecast errors and to information underlying their forecast revisions. These papers find that this analyst underreaction can partially explain the market underreaction to the same information. Chang et al. (2017) find that analysts' earnings forecasts and market prices underreact to information about earnings seasonality. Chen et al. (2020) and Keskek and Tse (2024) find a positive relation between the drift in stock prices following analysts' earnings forecast revisions and the completeness with which the revised forecast incorporates the information underlying the forecast revision.

To investigate the impact of complexity-driven analyst underreaction to 10-K information on market efficiency, our study extends techniques developed in Abarbanell and Bernard (1992), Shane and Brous (2001), and Hollie et al. (2017). Hollie et al. (2017) is the first study to apply these techniques to studying the impact of analyst underreaction on market efficiency with respect to 10-K information. With reference to various cash and accrual components of operating earnings, Hollie et al. (2017) find that analyst underreaction to information in these earnings components mitigates what would otherwise be market overreaction to such 10-K information. The ability to simulate the market's response to 10-K information without the influence of analysts is a major feature of the analyses in Hollie et al. (2017) and in the present study.

Engelberg et al. (2020) find that analysts' stock price forecasts and actual stock prices fail to impound predictions of stock price changes based on various documented anomalies. The authors conclude by saying “we cannot measure the extent to which analysts may impact anomalies, so we do not know whether and to what extent the anomalies would persist if analysts ‘got it right’” (Engelberg et al., 2020, p. 12). This sets the stage for our investigation of the degree to which analyst forecasting behaviour explains market inefficiency with respect to information disseminated with firms' complex 10-K filings. The technique we use simulates the market's reaction while controlling for the analyst's reaction.

5.1 Measuring complexity

As described by Loughran and McDonald (2024, p. 2), “complexity is a broad and amorphous concept that is difficult to quantify”. The overall complexity of 10-K information increases with the firm's underlying operating complexity (Hoitash & Hoitash, 2022; Huang et al., 2018), efforts to comply with complex accounting policy promulgated by accounting regulators (Chychyla et al., 2019), and the complexity of discretionary disclosures associated with the application of accounting policies (Cazier & Pfeiffer, 2016). Prior studies measure overall 10-K complexity with reference to the Gunning Fog Index (Bushee et al., 2018; Gao et al., 2023; Lehavy et al., 2011; Li, 2008); the Bog Index (Bonsall et al., 2017); XBRL diversity (Hoitash & Hoitash, 2018); the intensity of complexity-related word usage with reference to a researcher-specified list of complexity-related words (Loughran & McDonald, 2024); word count (You & Zhang, 2009); gross file size (Loughran & McDonald, 2014); gross file size, net of space allocated to tables, charts, and figures (Bae et al., 2023; Loughran & McDonald, 2016); and scarcity of quantification within the 10-K's textual disclosures (Siano & Wysocki, 2018).

As described by Loughran and McDonald (2024), the Fog Index suffers from identifying as complex words, simple to understand frequently used multisyllable words like “including and agreement,” and both the Fog and Bog Indexes suffer from identification of generally accepted readability-enhancing financial jargon as complexity-increasing (Loughran & McDonald, 2014).18 Net file size suffers from broad-based elimination of charts, figures, and tables which can constitute a large component of complex information in many 10-Ks. Prior studies find high correlations between gross and net file size (Loughran & McDonald, 2014) and between net file size and word count (Loughran & McDonald, 2024). Given the high correlations among complexity measures and a desire to avoid subjectivity and other pitfalls associated with net file size, Fog Indexes, and Bog Indexes, we use gross file size to proxy for financial reporting complexity.19 Across three levels of gross 10-K file size, we examine the degree to which analyst and market efficiency with respect to 10-K information depends on financial reporting complexity.20

5.2 Evaluating H1

As shown in Table 1 Panel C, the variable ${\mathit{FE}2}_{\mathit{fy}}^a=\left(A_{\mathit{fy}}-{F2}_{\mathit{fy}}^a\right)/P_{\mathit{fy}}^a$ represents the price-deflated signed error in analyst a's first year y earnings forecast, ${F2}_{\mathit{fy}}^a$, following f's year y − 1 10-K filing date. $A_{\mathit{fy}}$ represents the target of ${F2}_{\mathit{fy}}^a$, and $P_{\mathit{fy}}^a$ represents f's closing stock price as of the second day prior to the date I/B/E/S associates with ${F2}_{\mathit{fy}}^a$. The variable ${\mathit{Rev}}_{\mathit{fy}}^a=\left({F2}_{\mathit{fy}}^a-{F1}_{\mathit{fy}}^a\right)/P_{\mathit{fy}}^a$ represents the analyst's forecast revision, where ${F1}_{\mathit{fy}}^a$ represents a's most recent forecast of f's year y earnings preceding the 10-K filing date, meaning the revision straddles the 10-K filing date. In Equation (1), our coefficient of interest is ${\alpha }_1^a$, which captures the extent of analyst underreaction to the information underlying the forecast revision.

Following Abarbanell and Bernard (1992), we transform ${\mathit{FE}2}_{\mathit{fy}}^a$ into percentiles on a scale of zero (smallest percentile) to one (largest percentile) before estimating models containing ${\mathit{FE}2}_{\mathit{fy}}^a$.21 We also transform ${\mathit{Rev}}_{\mathit{fy}}^a$ into percentiles placed on a scale of zero to one. As shown in(1), ${\mathit{FE}2}_{\mathit{fy}}^a$ has three earnings news components: predictable optimism/pessimism bias, captured by the intercept, ${\alpha }_0^a$; predictable underreaction, captured by analyst a's underreaction coefficient, ${\alpha }_1^a$, times the 10-K information variable, ${\mathit{Rev}}_{\mathit{fy}}^a$; and an unpredictable earnings shock represented by the residual, $u_{\mathit{fy}}^a$.

In regression models (1) and (2) above, the Controls vector includes year fixed effects to mitigate potential omitted variable bias caused by excluding unobserved variables that evolve over time but are constant across firms (e.g., macroeconomic or regulatory trends). It also includes analyst-firm fixed effects to mitigate unobservable time-invariant heterogeneity across analyst-firm pairs. To mitigate identification issues and control for the contemporaneous returns-revision relation, the Controls vector includes a variable indicating the quintile of the 3-day abnormal return (${\mathit{\text{RevCAR}}}_{\mathit{fy}}^a$) centered on the date of ${F2}_{\mathit{fy}}^a$ and interacted with S, M, and L, our 10-K file size indicator variables.

To control for the You and Zhang (2009) good/bad news signal (discussed below), the Controls vector includes $10K\_{\mathit{CAR}}_{\mathit{fy}}$, a variable indicating the quintile of the 3-day abnormal return around the filing date, interacted with S, M, and L, our 10-K file size indicator variables. To control for post-earnings announcement drift and analyst underreaction to news around the time of the annual earnings announcement (e.g., Abarbanell & Bernard, 1992), the Controls vector includes $\mathit{AEA}\_{\mathit{CAR}}_{\mathit{fy}}$, a variable indicating the quintile of the 3-day abnormal return around the most recent earnings announcement. The time between pre- and post-filing forecasts varies across analysts. We control for this variation by including the number of days from F₁ to the 10-K filing date ($\mathit{\text{Days}}\_F1\_{10K}_{\mathit{fy}}^a$) and the number of days from the 10-K filing date to F₂ ($\mathit{\text{Days}}\_10K\_{F2}_{\mathit{fy}}^a$). In addition, we control for the number of days from the annual earnings announcement to the 10-K filing (Days_AEA_10-K_fy) and the number of days from the 10-K filing to the upcoming first quarter earnings announcement ($\mathit{\text{Days}}\_10-K\_{Q1\mathit{EA}}_{\mathit{fy}}^a$).22

5.3 Evaluating H2

H2 examines market efficiency with respect to 10-K information and whether the impact of analyst underreaction on market efficiency increases with 10-K complexity. We measure analyst impact as the difference between market underreaction coefficients in regressions with and without controls for analyst underreaction. Our tests evaluate whether this difference increases with 10-K complexity.

As described in (1), ${\mathit{FE}2}_{\mathit{fy}}^a$ contains a predictable component that is correlated with the information underlying the analyst's forecast revision (${\mathit{Rev}}_{\mathit{fy}}^a$) and a shock ($u_{\mathit{fy}}^a$) that is uncorrelated to this information. Since ${\rho }_1$ captures the market's response to the predictable component of ${\mathit{FE}2}_{\mathit{fy}}^a$, ${\rho }_2$ estimates the ERC and should have approximately the same value as ${\lambda }_2$ in (6).23

As described by Shane and Brous (2001), including ${\mathit{FE}2}_{\mathit{fy}}^a$ in (7) controls for the relation between ${\mathit{FE}2}_{\mathit{fy}}^a$ and ${\mathit{Rev}}_{\mathit{fy}}^a$. Thus, ${\mathit{FE}2}_{\mathit{fy}}^a$ in (6) controls for analyst underreaction to the 10-K information reflected by ${\mathit{Rev}}_{\mathit{fy}}^a$. ${\rho }_1/{\rho }_2$ then simulates the market underreaction coefficient, without the influence of analyst underreaction, and ${\lambda }_1/{\lambda }_2$ in (6) minus ${\rho }_1/{\rho }_2$ in (7) estimates the impact of analyst underreaction on market efficiency with respect to 10-K information reflected by ${\mathit{Rev}}_{\mathit{fy}}^a$. Using a difference-in-differences research design and bootstrapping techniques described in MacKinnon et al. (2018) and Ng and Wilcox (2012), we estimate whether the difference between ${\lambda }_1/{\lambda }_2$ and ${\rho }_1/{\rho }_2$ significantly increases with 10-K complexity.

6.1 Does analyst underreaction increase with 10-K complexity (H1)?

Table 3 column (1) shows the results of estimating Model (2) to evaluate H1. Consistent with H1, estimates of Model (2) coefficients show that analysts underreact to the information underlying their own 10-K-straddling forecast revisions and the underreaction increases with 10-K complexity. The analyst's underreaction coefficient on the information variable, ${\mathit{Rev}}_{\mathit{fy}}^a$, increases monotonically from 0.0126 for earnings forecast revisions straddling 10-K filings in the lowest tercile of the file size distribution to 0.0155 for the middle file size tercile and 0.0191 for the largest file size tercile. Thus, the analyst underreaction coefficient on revisions straddling high-complexity 10-Ks is (an economically and statistically significant) 52% higher than the coefficient on revisions straddling low-complexity 10-Ks. This result is consistent with the inference that, due to greater uncertainty regarding the earnings implications of complex 10-K information, analysts' forecast revisions underreact to a greater extent with reference to high-complexity 10-Ks than they do with reference to low-complexity 10-Ks. The earnings uncertainty effect of complexity on analyst underreaction apparently outweighs any reduction in underreaction due to more able analysts following more complex firms.

6.2 Does analyst impact on market efficiency increase with 10-K complexity (H2)?

Table 3 columns (2) and (3) report the results of estimating Models (8) and (9) to evaluate H2. As described in subsection 5.3 above, Models (8) and (9) differ only because (8) includes the earnings shock, $u$, from Model (2); whereas, (9) includes the entire analyst forecast error, $\mathit{FE}2$. Both Models (8) and (9) regress future returns on $\mathit{Rev}$, but the coefficient on $\mathit{Rev}$ takes on different meanings depending on whether $u$ or $\mathit{FE}2$ is in the model.

As described in subsection 5.2, since $\mathit{Rev}$ and $u$ are uncorrelated, ${\lambda }_1$, the coefficient on $\mathit{Rev}$ in Model (8), measures the ERC times the market's underreaction coefficient, including the impact of analyst underreaction; that is, the relation between $\mathit{FE}2$ and $\mathit{Rev}$ is not controlled. Since the coefficient on $u$ measures the ERC, $\frac{{\lambda }_1}{{\lambda }_2}$ effectively estimates the market underreaction coefficient, including the impact of analyst underreaction. Including $\mathit{FE}2$ in Model (9) controls for the relation between $\mathit{FE}2$ and $\mathit{Rev}$, so the coefficient, ${\rho }_1$, on $\mathit{Rev}$ in Model (9) measures the ERC times the market's underreaction coefficient, excluding the impact of analyst underreaction, and the coefficient, ${\rho }_2$, on $\mathit{FE}2$ estimates the ERC. Thus, ${\rho }_2$ in (9) approximates ${\lambda }_2$ in (8); $\frac{{\rho }_1}{{\rho }_2}$ in (8) provides an estimate of the market underreaction coefficient, excluding the impact of analyst underreaction; and $\frac{{\lambda }_1}{{\lambda }_2}-\frac{{\rho }_1}{{\rho }_2}$ provides an estimate of the impact of analyst underreaction on market efficiency with respect to the information reflected by $\mathit{Rev}$.

Models (8) and (9) allow estimation of analyst impact within 10-K file size terciles, so $\left(\frac{{\lambda }_{1L}}{{\lambda }_{2L}}-\frac{{\rho }_{1L}}{{\rho }_{2L}}\right)-\left(\frac{{\lambda }_{1S}}{{\lambda }_{2S}}-\frac{{\rho }_{1S}}{{\rho }_{2S}}\right)$ estimates the difference in the impact of analyst underreaction on market efficiency with respect to 10-K information underlying $\mathit{Rev}$ for observations associated with large 10-K file sizes (proxying for high-complexity 10-K information) versus observations associated with small 10-K file sizes (proxying for low-complexity 10-K information). In our tests of H2, finding that $\left(\frac{{\lambda }_{1L}}{{\lambda }_{2L}}-\frac{{\rho }_{1L}}{{\rho }_{2L}}\right)-\left(\frac{{\lambda }_{1S}}{{\lambda }_{2S}}-\frac{{\rho }_{1S}}{{\rho }_{2S}}\right)$ is greater than zero is consistent with the impact of analyst underreaction on market efficiency increasing with 10-K complexity. Table 4 summarises the results of estimating Models (8) and (9) in Table 3.

While Table 4 shows that analyst underreaction significantly impacts the market response to information underlying analyst forecast revisions straddling both low- and high-complexity 10-K filings, the impact associated with large file size (high-complexity) 10-Ks is 45% higher than the impact associated with small file size (low-complexity) 10-Ks and the difference is statistically significant with a p-value less than 0.01 (estimated with bootstrapping techniques in Table 5).

An interesting implication that emerges from our evidence in Table 4 is that the impact of analyst underreaction on market efficiency with respect to 10-K information increases with 10-K complexity. We find that, controlling for the impact of analyst underreaction, the market overreacts to information underlying forecast revisions straddling both low- and high-complexity 10-Ks with statistically significant overreaction coefficients of −0.0150 and − 0.0108, respectively. Without controlling the impact of analyst underreaction: (i) the simulated market overreaction to low-complexity 10-K information disappears with an insignificant underreaction coefficient estimated at 0.0018; and (ii) the simulated market overreaction to high-complexity 10-K information has significant underreaction with an underreaction coefficient estimated at 0.0135. This evidence is consistent with analyst underreaction mitigating market overreaction to low-complexity 10-K information and fully explaining market underreaction to high-complexity 10-K information.

Overall, our tests of H1 and H2 produce evidence consistent with the following mechanism giving rise to market underreaction to the earnings implications of high-complexity 10-K filings. First, the underreaction-increasing uncertainty associated with the earnings implications of high-complexity 10-K information outweighs the underreaction-decreasing greater ability of analysts attracted to following firms with complex 10-Ks, leading to a positive relation between 10-K complexity and analyst underreaction. Second, investors rely more heavily on analysts for the interpretation of more complex 10-K information, investors do not effectively unravel the underreaction in analysts' earnings forecasts, and we observe an impact of analyst underreaction on market efficiency that increases with 10-K complexity. Third, this greater impact on stock prices fully explains price discovery-compromising market underreaction to the earnings implications of information underlying analysts' 10-K-straddling earnings forecast revisions.