Using Fama-French Factors to Explain Portfolio Returns
Summary
The discussion explains how to use Fama-French factor returns in regressions on a portfolio’s returns. It recommends aligning the time series and fitting a multiple regression with an intercept, then interpreting the factor loadings, intercept, goodness of fit, and statistical significance. SMB and HML loadings indicate exposure to size and value factors, while the intercept is commonly treated as alpha after accounting for included factors.
A high R-squared indicates that the included factors explain a larger share of return variation; t-statistics or p-values help assess whether estimated exposures are distinguishable from zero. The replies also distinguish factor regressions from regressions on the six portfolios: the latter can indicate resemblance to an existing portfolio, while factor regressions are more useful for exposure analysis or removing factor contributions from a return series. Interpretation depends on the research objective and the chosen data; statistical significance alone does not establish a causal explanation or investment merit.
Key ideas
- Align portfolio returns with factor returns before estimating a multiple regression with an intercept.
- Factor coefficients describe the portfolio’s estimated exposures to the included factors.
- The intercept is interpreted as return unexplained by the specified factors, while R-squared measures explained variation.
- Use t-statistics or p-values to assess the statistical significance of estimated exposures.
- Regressing on factor-mimicking portfolios and on the six portfolios answers different descriptive questions.
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# How exactly do I calculate and interpret factors in Fama-French model? # How exactly do I calculate and interpret factors in Fama-French model? Could anyone explain me how to interpret factors and what kind of regressions I should run? I have already calculated the factor returns as well as 6 Fama-French portfolio returns, the only problem is I do not know how to properly combine all the information and reach useful results. Do I run regressions on SMB and HML to find whether those factors explain market movements by looking at R squared and then run regressions on 6 portfolios to see how significant the portfolio returns are? ## Answer by vonjd (score 6) https://quant.stackexchange.com/a/31456 The clearest hands-on explanation I have seen so far is the following: Bernstein, W.: Rolling Your Own: Three-Factor Analysis Everything is explained very clearly and step-by-step with Excel. Concerning your question: The R-squared tells you how much percent are explained by the factors. The intercept is your alpha, the coefficients of the factors tell you in which direction the portfolio is tilted (e.g. HML for a value fund) and the t- and p-values tell you whether the factors are statistically significant. As @WillGu correctly mentions you should use the data from the FF website. Hope this helps to get you started. ## Answer by Will Gu (score 1) https://quant.stackexchange.com/a/31450 I believe you have every right to "calculate" the FF factor returns, but you might just use the factors returns on their website. As you mentioned, you can regress on these factors and $R^2$ should tell you how much of the variance in your return series can be explained by FF factors. I'm not quite sure what goal you are trying to achieve, but one use case would be something like "alpha research". If these factors are represented by available products in the market, you might just subtract their contributions from your returns series and focus on the residuals. On the other hand, running regression on the 6 portfolios (returns also available on their website among others) shows how much of your return variance can be explained by the 6-portfolio returns. The only usefulness of this kind of analysis IMHO is to see what existing portfolio does your return series mostly look like. ## Answer by Swagato Acharjee (score 1) https://quant.stackexchange.com/a/31491 The Fama French SMB and HML portfolios represent the Size premium and the Value premium respectively observed in the equity markets. Its not clear what your intention is but here's what I would suggest - Take the return series of your portfolio, align it with the factor returns of the SMB and HML portfolios which you can download from Kenneth French's website as pointed by @WillGu - Run a multiple regression of your portfolio returns vs HML and SMB with an intercept. - Observe the coefficients on SMB, HML and also the intercept as well as their t-stats (p-values) - Observe the R-squared - Here is one interpretation If you observe high R-squared and significant coefficients, this would mean a large percentage of your returns are explained by SMB and HML. In addition, if you observe a significant and nonzero intercept - it would mean your portfolio returns are also being explained by factors outside of SMB and HML.
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