Applying Fama–MacBeth Regression with Rolling Windows

Summary

The document discusses how to combine rolling-window estimation with the two-stage Fama–MacBeth method. The questioner estimates portfolio factor exposures over rolling five-year samples, producing many sets of estimates, and asks which exposure estimates belong in the cross-sectional stage. The answer emphasizes that the cross-sectional regressions are run for each time period using the relevant period’s returns and estimated exposures, rather than applying one second-stage regression to a pooled collection of rolling estimates.

The resulting period-by-period coefficient estimates are then averaged over time to obtain the Fama–MacBeth estimates. The document provides a short procedural clarification rather than a worked example or statistical derivation. It does not spell out how to align rolling-window estimates with each cross-section, handle overlapping windows, or compute standard errors; those choices matter for implementation and inference.

Key ideas

• Fama–MacBeth estimation runs a cross-sectional regression for each time period.
• Each cross-section should use factor exposures aligned to that period’s returns.
• Rolling windows produce successive exposure estimates rather than one pooled set for a single second stage.
• Average the time-series of cross-sectional coefficient estimates to form the Fama–MacBeth estimate.
• The answer does not discuss standard errors or the effects of overlapping rolling windows.

Tags

# Fama Macbeth regression with rolling window


# Fama Macbeth regression with rolling window












I am confused about how to run fama macbeth regressions for portfolios with rolling window. For example if I have 25 portfolios and time period is 50 years(monthly), rolling window period is 5 years. In first step I regress my portfolio returns on factors in 5 year sub samples. This yields hundreds of betas. I don't get exactly how I need to carry a second stage regression if I have hundreds of betas. I take time 0 and am supposed to run cross sectional regression on returns, but which betas should I use? Do I take y0i=a+lambda?

## Answer by hao (score 1)

https://quant.stackexchange.com/a/49825

For applying Fama/MacBeth (1973) regression, it is necessary to always run the cross-sectional regressions and then averaging the betas across years. In this case, as you run Fama/MacBeth regression, the first step is to get the cross-section regression, after which you get the betas for each characteristics. Then you do a rolling window of 5 years, every time you would get the betas for the characteristics. Add them up and take the average.

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