Estimating Fama–MacBeth Slopes Separately Within Size Groups

Summary

The document addresses how to estimate rolling cross-sectional return betas and out-of-sample slopes when studying expected stock returns across size groups using Fama–MacBeth regressions. It asks whether to estimate slopes within each size group or across the full stock universe, then sort predicted returns into groups afterward.

The answer recommends estimating the cross-sectional slopes separately for each group and date. It points to the graphs and tables in Lewellen’s study as evidence that out-of-sample slopes differ across size groups over time. The note is brief and does not lay out a full regression specification, discuss standard errors, or compare the alternative pooled approach empirically, so the recommendation is tied to the referenced size-group analysis.

Key ideas

• Estimate cross-sectional out-of-sample slopes separately within each size group when following the described approach.
• The slopes can vary by both date and size group.
• The answer bases its recommendation on patterns reported in a referenced study’s graphs and tables.
• The note does not provide a detailed specification or a direct empirical comparison with pooled estimation.

Tags

# FM regressions for size groups when examining a cross section of expected stock returns


# FM regressions for size groups when examining a cross section of expected stock returns












When doing FM regressions for size groups similar to Lewellen (2015) (open access here), should I obtain the cross sectional rolling return window betas using only the size group? (E.g only use large stocks to estimate the betas that will be used to calculate the expected returns for stocks within this group.) Or should I obtain the cross sectional rolling return window betas using the entire sample? (E.g use all stocks to estimate betas and then calculate the expected return for each stock and then look at the averages of each size group separately.)

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 1, accepted)

https://quant.stackexchange.com/a/77668

As can be seen in the graphs and tables in Lewellen's paper, the cross sectional out of sample slopes differ for each size group, for each date, and should thus be obtained using only the stocks in the respective size group.

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.