Using Rolling Fama–MacBeth Slopes to Predict Stock Returns

Summary

The document clarifies how to use lagged firm characteristics, such as profitability and accruals, in a rolling return-prediction setup. Its answer says to estimate slopes by regressing past returns on those characteristics over a rolling historical window, then apply the resulting out-of-sample slopes to current characteristics to form predicted returns. This addresses the question of whether firm-specific betas are needed: the approach described uses characteristics directly as predictors, rather than first estimating a separate beta for each firm in the CAPM style.

The explanation is brief and offers no empirical results, equations, or detailed guidance on choosing window lengths, aligning predictors with returns, or evaluating forecasts. It distinguishes the intended out-of-sample use of rolling estimates but does not fully define in-sample versus out-of-sample Fama–MacBeth procedures. Those implementation details need to be settled before treating the description as a complete forecasting workflow.

Key ideas

• Lagged firm characteristics can serve directly as predictors in rolling return regressions.
• Estimate slopes using historical returns and characteristics within each rolling window.
• Apply the estimated slopes to current characteristics to calculate predicted returns.
• The answer gives a high-level procedure but does not specify window design or forecast evaluation.

Tags

# Fama-MacBeth regressions to predict stock returns; confusion on which steps to use


# Fama-MacBeth regressions to predict stock returns; confusion on which steps to use












When following Lewellen (2015) (open access here), I am confused as to whether I need to estimate any lambdas. As I already have values for lagged firm characteristics such as ROA and accruals etc. that I can multiply with their respective betas based on rolling return windows. Do I then need to still regress returns on these betas to get lambdas for each month? In other words, what are the in- and out-of-sample FM slopes? And how should I calculate the predicted returns?

References

- Lewellen, J. (2015). The cross-section of expected stock returns. Critical Finance Review, 4(1), 1–44. https://doi.org/10.1561/104.00000024

## Answer by Julien Maas (score 2, accepted)

https://quant.stackexchange.com/a/77667

Unlike for the CAPM, where we obtain the beta's by regressing a firm's returns against the market return over the same period, here we already have firm specific characteristics.

So we can simply regress the returns on the lagged firm characteristics in a past rolling window. This will give us the out of sample slopes that we can multiply with the firm characteristics to calculate predicted returns.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.