Robust Standard Errors for Fama-French Fund Regressions

Summary

The document addresses inference in regressions using the Fama-French four-factor model to compare ESG and conventional mutual fund performance. Its focus is on heteroskedasticity and serial correlation, which can make conventional standard errors unreliable even when the regression specification is otherwise retained. It suggests checking for conditional heteroskedasticity and using White-corrected standard errors when present, as well as testing for serial correlation and adjusting standard errors with a method attributed to Hansen.

The central lesson is that robust standard errors are intended to improve uncertainty estimates, not change the estimated factor exposures or fund alpha. The answer offers example diagnostics and one econometrics textbook reference, but it provides no details about test assumptions, model implementation, or empirical findings. The appropriate correction depends on the error structure and data design, so the brief recommendations are a starting point rather than a complete inference procedure.

Key ideas

• Heteroskedasticity and serial correlation can undermine conventional regression standard errors.
• The answer recommends White-corrected standard errors for conditional heteroskedasticity.
• It recommends a Hansen adjustment when serial correlation is present.
• Robust standard errors address inference uncertainty rather than changing the regression estimates.
• The brief guidance does not discuss implementation details or the assumptions behind each correction.

Tags

# What about autocorrelation and heteroskedasticity in Fama French?


# What about autocorrelation and heteroskedasticity in Fama French?












I am analysing ESG and conventional mutual funds. I decided to measure the extra performance of each category using the Fama French 4 factor model, but it seems to me that in previous literature they do not investigate issues such as autocorrelation and heteroskedasticity. SOme paper just write down that they use Robust Standard Errors. Could you please explain me why and in case provide me some books, papers or links where I can investigate this topic? Thank you

## Answer by Felix (score 2)

https://quant.stackexchange.com/a/63938

If you face heteroskedasticity, you have to check if heteroskedasticity is conditional (e.g., with a Breush-Pagan Chi-square test). If so, you have to use White-corrected standard errors.

If you have serial correlation (e.g., you can test that with a Durbin-Watson test), you can use the Hansen method to adjust the standard errors.

Basically, what you do with both methods is to use "robust" standard errors. Otherwise, your standard errors are underestimated.

I recommend Wooldridge, J. M. (2015). Introductory econometrics: A modern approach. Cengage learning.

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