Transformers (deep learning models) are better at predicting the tail distribution

This article is based on one of my working paper.


In a setting where we predict PEAD with earnings call transcripts, I found

  • deep learning models perform better than traditional regression and earnings surprise models

  • (more importantly) the performance lead is most significant on extreme data points (i.e., the tails of the distribution)!

    “For example, when we ask the four models to predict the full sample, the performance lead of Transformer against SUE is about 3.5% (3.94%-0.44%). However, if we only predict the top and bottom 10% of CAR(0,21) (i.e., the tails of the distribution), Transformer’s performance lead jumps to 8.19% (9.05%-0.86%).”

PEAD (post-earnings-announcement-drift) is the observation that stock prices drifted upward if there’re good surprises in the earnings announcement, and that it drifted downward on bad surprises. I use CAR(0,21), the cumulative abnormal return in the first 21 trading days (roughly one month), to operationalize PEAD. I use earnings call transcripts and several financial ratios to predict PEAD: $$ CAR(0,21) = f(transcript, X) $$ where $X$ is a collection of financial ratios, including but not limited to market cap, volatility, previous CAR (e.g., CAR(-21, -3)), earnings surprises, and number of analyst forecasts. $f$ is the prediction model. We’ll compare the performance of the following four models:

  • Hierarchical Transformer: Sentences are first encoded into an embedding with a Transformer (Vaswani et al., 2017), and then the sentence embeddings are encoded into a document-level embedding with another Transformer. The architecture is similar to (Yang et al., 2020)
  • Hierarchical LSTM: Similar to Hierarchical Transformer, but I replace the Transformer coders with an LSTM encoder. The architecture is similar to (Yang et al., 2023).
  • OLS. The good old linear regression model. Note that I didn’t include transcript text as the input since OLS struggles with text.
  • SUE. The famous “Standard Unexpected Earnings” model. In this model, the only predictors are earnings surprise, operationalized as the actual earnings minus the average analyst forecasts.
Summary of the four models
  • Hierarchical Transformer and LSTM are deep learning (deep neural network) models. LSTM is arguably the most popular NLP (natural language processing) neural network architecture before 2018. Transform is first proposed in 2017, and quickly overtook LSTM as the go-to architecture in today’s NLP models. It’s the building block of large language models like ChatGPT.
  • OLS and SUE are more traditional and they’re frequently seen on academic paper (especially finance).

I collect all earnings calls for S&P 500 stocks during 2008 and 2010. To minimize the impact of outlier years, each model is trained and evaluated in a rolling window (Meursault et al., 2021). Each window consists of two years’ of training data and one quarter’s test data. Specifically, in the first window, we use 2008Q1-2009Q4 for training and test on 2010Q1; in the second window, we train on 2008Q2-2010Q1 and test on 2010Q2, etc. There’re in total 48 testing periods, ranging from 2010Q1 to 2021Q4.

Given the four prediction models, we’re particularly interested in the model performance on different quantiles of CAR(0,21). This is very meaningful in practice. As can be seen from the following figure, most CAR(0,21) is centered around zero. (Half stocks have an positive drift and the other half has a negative drift. Make sense, right?) However, we’re often more interested in the tails because they represent large (positive or negative) price drift, and most trading strategies profit when there’s a big price movement.

In our test, we’ll train four CAR(0,21) prediction models on the full dataset. Then we look at model performance on different quantiles of CAR(0,21). For example, we can ask the model to predict the top 10% and bottom 10% of CAR(0,21) (that’s 20% of the full sample), and calculate the model performance. Then we extend the to the top 20% and bottom 20%, and calculate the model performance again.

The result is shown in the following figure.

The y-axis show the model performance (as measured in $R^2$, the higher the better). The x-axis shows the sample size on which the model is evaluated. “20” means we predict the top and bottom 10% CAR(0,21), which are the tails of the distribution. “100” means we predict the full sample (i.e., top and bottom 50%). As the x-axis moves from the left the right, the sample size become larger and less extreme. Two observations stand out:

  • First, deep learning models (LSTM and TSFM) significantly outperform OLS and SUE, and Transformer is better than LSTM. Both are not a surprise.
  • Second, and perhaps more interesting, Transformer is especially good at predicting extreme data points. For example, when we ask the four models to predict the full sample, the performance lead of Transformer against SUE is about 3.5% (3.94%-0.44%). However, if we only predict the top and bottom 10% of CAR(0,21), Transformer’s performance lead jumps to 8.19% (9.05%-0.86%).
Why Transformer is good at the extreme data points?

Without further investigation, this is my guess:

  • When companies have a large (either positive or negative) PEAD, it means something special is taking place. Compared with normal time (when company having a small PEAD), this special development ultimately results in some “marks” in the language. May it’s a particular set of vocabulary, maybe it’s a particular way of speaking (e.g., using more passive verbs, or using more third-person perspective). Anyhow, they’re captured by the Transformer architecture.
  • LSTM is also deep neural network based, but it’s non-contextual, meaning the definition of a word is fixed. This severely restrict its power.
  • Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you need. 5998–6008.
  • Yang, L., Ng, T. L. J., Smyth, B., & Dong, R. (2020). Html: Hierarchical transformer-based multi-task learning for volatility prediction. Proceedings of The Web Conference 2020, 441–451.
  • Yang, Y., Qin, Y., Fan, Y., & Zhang, Z. (2023). Unlocking the Power of Voice for Financial Risk Prediction: A Theory-Driven Deep Learning Design Approach. Management Information Systems Quarterly, 47(1), 63–96.
  • Meursault, V., Liang, P. J., Routledge, B. R., & Scanlon, M. M. (2021). PEAD.txt: Post-Earnings-Announcement Drift Using Text. Journal of Financial and Quantitative Analysis, 1–50.