مفاهیم بقا و پیرایش اطلاعات برای آزمون کارایی بازار

Predictability of future returns using ex ante information (e.g., analyst forecasts) violates market efficiency. We show that predictability can be due to non-random data deletion, especially in skewed distributions of long-horizon security returns. Passive deletion arises because some firms do not survive the post-event long horizon. Active deletion arises when extreme observations are truncated by the researcher. Simulations demonstrate that data deletion induces a negative relation between future returns and ex ante information variables. Analysis of actual data suggests a 30–50% bias in the estimated relations. We recommend specific robustness checks when testing return predictability using ex ante information.

To test market efficiency, prior research estimates cross-sectional regressions of ex post long-horizon stock price performance on ex ante variables (e.g., analysts’ forecasts, abnormal accruals).1 A significant cross-sectional relation implies returns are predictable, i.e., market inefficiency.2 One scenario that would generate such a significant relation assumes optimistic analysts’ forecasts (see Brown et al., 1985; Brown, 1997; Lim, 2001; Abarbanell, 1991; Stickel, 1990)3 and market's naive reliance on those forecasts in setting prices. Future actual financial performance reveals the optimism, leading to negative forecast errors. This bad “news” lowers prices and generates a negative association between ex post security price performance and ex ante analysts’ forecasts or proxies for the predictable biases in these forecasts (e.g., abnormal accruals). We show that survival and data trimming bias the relation between ex ante information variables and subsequent price performance. Data trimming means either deletion of extreme observations (i.e., data truncation) or winsorization (i.e., setting the values of extreme observations to 1% and 99% percentile values). The bias in the estimated regression relation stems from a combination of (i) the statistical properties of the variables, namely the (right) skewness of long-horizon stock returns,4 and (ii) research design features that are common and almost inevitable. In particular we discuss data availability (i.e., survival) requirements as well as winsorization or truncation of extreme observations.5

We show that the previously documented cross-sectional relation between ex ante information variables (e.g., analyst forecasts or management's optimistic financial reporting) and the subsequent price performance is likely to be biased. In the research setting we examine, the regression relation is biased by about 30–50%. The bias stems from a combination of (i) the right-skewness of long-horizon security returns and financial performance measures and (ii) non-random truncation of data, either because of non-survival (i.e., passive) or through the active removal of extreme observations. These are common research design features of previous studies and those involving passive truncation due to non-survival are beyond the control of a researcher. We show that if the sample firms’ survival and/or active data truncation are not random with respect to the ex post performance variables, statistical inferences are biased. We demonstrate this using both a simple model where the market rationally prices unbiased earnings forecasts as well as through simulations and analysis of actual data. The simulations demonstrate that both forecast optimism and negative abnormal returns are induced when “extreme” observations of ex post long-horizon performance are truncated from the sample. As a consequence of data truncation, a statistically and economically significant association between ex ante earnings growth forecast and ex post abnormal performance is induced. Examination of real data suggests that passive data truncation (i.e., non-survival) is not a random event. The non-random nature of passive data truncation arises because survival is correlated with measures of risk and thus associated with extreme performance. Regressions of future stock returns on forecasted earnings growth or other financial variables using samples of progressively surviving firms provide results consistent with survival magnifying the strength of the relation. The degree of magnification in the samples we examine is 30–50%. It is difficult to precisely assess the effects of non-survival on the results in past studies because the data needed to estimate the effect does not exist for non-surviving firms. Developing alternative tests faces similar obstacles. However, the evidence in this study suggests (i) the inference of predictable long-horizon performance based on ex ante information could be erroneous and (ii) need for additional sensitivity tests in future research. In this respect, we believe researchers should provide the following information. First, we encourage researchers to report the actual effects of passive truncation (i.e., non-survival) on sample composition. This will facilitate a preliminary evaluation of whether survival is an important issue in the specific context at hand. Second, we recommend conducting an analysis similar to the one we perform in Table 8 and Table 9. That is, while holding fixed the horizon for the dependent variable, eliminate observations based on their future non-survival and report results for progressively smaller, surviving samples. While such analysis is not a perfect diagnosis, it can shed light on the potential effect and direction of passive truncation.