The Foster Model: Wall Street’s Method for Precisely Forecasting Corporate Earnings [Original]

The market indices have performed well recently—everything that was expected to rise has indeed risen. There may still be some consolidation ahead. Captain Boat is temporarily not issuing new stock recommendations, and he reminds everyone that the recent gains have been concentrated in stocks tied to price-increase themes; other stocks have offered little profit opportunity. Fellow investors who sit before their computers watching the indices climb while their own holdings stagnate—don’t get frustrated! Many others are in exactly the same situation. Today we’ll discuss how to forecast corporate earnings—a rather technical topic, so some readers may find it difficult to follow; feel free to skip this article if it seems too advanced. On various financial software platforms, you’ll find a section titled ‘Earnings Forecasts,’ which displays analysts’ projections for a given stock’s earnings over the coming years. How do they achieve such forecasts? Naturally, Chinese analysts’ accuracy tends to be lower, whereas Wall Street analysts achieve significantly higher precision. For instance, one Wall Street analyst accurately predicted General Electric’s earnings per share for 20 consecutive years—an impressive technical skill many aspire to master. Captain Boat is happy to share this knowledge. One such forecasting model is the Foster Model, which uses a company’s historical earnings data to predict future performance. But here lies a critical underlying assumption we must examine: Can past performance reliably predict future results? If this assumption fails, all subsequent analysis becomes meaningless. What do you think? Past performance should indeed offer some predictive value—and the more historical data available, the better. Take JD.com, for example: during its first two pre-IPO years, it posted mounting losses—so extrapolating from that early data alone would never yield today’s profitable reality. However, analyzing JD.com’s more recent performance reveals a steady transition from losses to profitability, enabling us to reasonably project continued earnings improvement over the next few years. The same logic applies to Vipshop. Since historical earnings data can help forecast future performance, let’s now formally introduce the Foster Model.

Oliver’s Alpha Gallery–3: A Mathematical Modeling Approach to Better Measuring Earnings Surprises

Oliver the Cat Alpha Gallery Series–2: ‘How to Better Measure Earnings Surprises?’ — Mathematical Modeling Edition Review of the Previous Article The previous article introduced the ‘Earnings Surprise’ factor (since this article presents the mathematical derivation building upon the prior one, please ensure you’ve read the introductory section of the previous article). Let’s briefly recap the main points from last time: Current research measures the magnitude of earnings surprises using a metric defined on a probability space: SUE = \frac{E_t - \mathbb{E}[E_t]}{\sigma(E_t - \mathbb{E}[E_t])} \\ where the calligraphic ‘E’ denotes expectation, and the regular ‘E’ stands for earnings—i.e., reported EPS or similar figures. In the previous article, I neglected to mention that the denominator need not necessarily be the standard deviation; some studies instead normalize using the stock’s return on a specific day prior to the earnings announcement (see Professor Shi Chuan’s PEAD.txt on Zhihu for reference). In practice, we must estimate SUE. Traditional approaches use consensus analyst forecasts (i.e., the mean of sell-side analysts’ earnings predictions). However, Chiang et al., through empirical analysis—including regressions of CAR and POSTCAR on \hat{SUE}, regressions incorporating Chiang’s FOM metric, and multiple regressions using both metrics—demonstrated that estimation via the simple mean is suboptimal. We know that, under a normal population distribution, the sample mean constitutes the Uniformly Minimum Variance Unbiased Estimator (UMVUE) of the expectation. So why does using the mean prove inadequate here? Chiang et al. propose several reasons: 1. Analyst forecasts are subject to numerous external influences, causing systematic bias in consensus expectations (empirical evidence also confirms such bias exists). 2. Biased analyst forecasts do not follow a normal distribution (the authors confirmed non-normality via hypothesis testing and constructed a hierarchical model wherein each normal distribution’s mean parameter itself follows another normal distribution). Main Content of This Article Above, we reviewed the core findings of Chiang et al.’s study. Next, we introduce key technical details. Some readers may believe understanding only how FOM is constructed suffices—but I contend that Chiang et al.’s modeling and analytical approach is truly remarkable and represents the most brilliant aspect of their work. The following content is divided into two parts: 1. A parametric model of analyst forecasts; 2. A series of lemmas and theorems progressively demonstrating why FOM—as a nonparametric estimator—outperforms parametric alternatives. A. Setup 1. Overall Model Assume: A = e + \epsilon_{A} \\ where A denotes the true earnings value (i.e., actual reported earnings), e represents the market’s unobserved expectation (i.e., the quantity we aim to estimate—the ‘unobserved market expectation’; translation remains unsettled), and \epsilon_{A} is a random error term.

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Alto Ingredients Beats Earnings Forecasts, Analysts Update Models

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