Estimating Daily Fama-French Abnormal Returns Without Look-Ahead Bias

Summary

The document explains how to derive daily stock returns relative to the Fama-French three-factor model. The question asks whether regression residuals represent daily outperformance, or whether one should subtract factor contributions, weighted by estimated betas, from the stock return. The answer says these approaches are equivalent when they use the same regression coefficients and inputs: subtracting the fitted factor component yields the regression residual.

It also warns that estimating factor loadings on the same period used to assess performance can introduce look-ahead bias in an event-study setting. As an example, it suggests estimating coefficients on an earlier window and applying them to a later period. The document provides a conceptual procedure but no regression output, statistical significance analysis, or guidance on changing betas over time. The interpretation of residuals as abnormal returns depends on the estimation window and model assumptions.

Key ideas

• Regression residuals equal observed excess returns minus the factor contributions implied by estimated betas.
• The factor contributions are calculated by multiplying each factor series by its fitted loading.
• Estimating betas using data from the evaluation period can introduce look-ahead bias.
• Estimate factor loadings on an earlier period and apply them to later returns to reduce that bias.

Tags

# Fama french model: Daily excess return calculation


# Fama french model: Daily excess return calculation












I have a decent knowledge of econometrics, but would like to have some help with the procedure of FF regression.Suppose I would like to know if a stock, say AAPL, has outperformed the Fama French 3 factor model.So,I download data from Kenneth French website and run the regression with (AAPL minus risk free rate) as dependant variable and SMB,HML and RMRF as indpt variable.

1) The alpha or intercept value is a "single value" or a number and not a time series.But,I want to know how each day the AAPL stock has outperformed the fame french model.So, if I take the residuals(which will be a time series data) from the above regression,is it the excess returns over FF model? Is the procedure right or wrong?

2) Or should I multiply the betas from the regression with SMB,HML,RMRFcoloumns , then AAPL-(bta1*SMB + beta2*HML + beta3*RMRF).

Thanks in advance.

## Answer by user28909 (score 1, accepted)

https://quant.stackexchange.com/a/35234

By doing (2) you are technically calculating the residuals which you are proposing in (1).

Be aware of look-ahead bias though, you could mitigate such bias by, say, estimating beta 1,2, and 3 according to time series regression from 2005 to 2010. Then use estimated coefficients to calculate the residuals over the years 2010 to 2015 similar to the methodology of event studies.

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.