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I regressed ten portfolios on the Fama French factors and get significant loadings on the SMB factor. However, if I look at the actual average market cap of these portfolios, the portfolios with the highest factor loading are not the one with the smallest market cap. What could be the reason for that?

My portfolios are equal-weighted, so they all load at least slightly positive on the SMB factor.

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    $\begingroup$ The highest SMB factor loading just mean the portfolio is highly sensitive to the SMB factor. $\endgroup$
    – Kian
    Apr 11, 2015 at 13:39

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Portfolio behaving like a small cap portfolio is not necessarily a small cap portfolio. Your regression shows the appearance, not the fundamentals.

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  • $\begingroup$ Hi @IgorPozdeev and welcome to quant.SE! Could you deepen your answer by explaining what do you mean for "appeareance"? $\endgroup$
    – Quantopik
    Jun 17, 2015 at 15:07
  • $\begingroup$ @Quantopic: I mean, regression coef's reveal how a stock behaves, not what a stock is. Imagine you wake up somewhere with a thermometer in your hand. Thermometer shows +40: the only thing you can now say is that you are in a place which looks like Egypt, but it can in fact be anything. $\endgroup$
    – Igor Pozdeev
    Jun 18, 2015 at 10:54
  • $\begingroup$ You're right, but I think @early_bird constructed (or should have been constructed) such portfolios as suggested by Fama & French paper, and, in such case, the portfolios factor loadings should be monotonically decreasing in the market cap, differently from his result. Although the loadings can change with respect to the market, on 10 portfolios you've to see the monotonic pattern found by the authors' paper. IMHO, it is more probably he has been wrong constructing the factor. $\endgroup$
    – Quantopik
    Jun 18, 2015 at 13:42
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By assuming the procedure you followed in replicate the model is correct and there are not errors in data mining or quality, your findings could be affected and influenced by several reasons.

I report as follows those that, according to me, could be the main ones:

  1. Data sample: the dataset you used to replicate the Fama-French model could be too little in terms of observations and time-period; keep in mind that in almost all their papers, Fama & French used a data sample that allows to analyze several years (about at least 20 years).

So, try to increase the time period and the number of observations of the dataset to get better results;

  1. Portfolio coarseness: some of your portfolios could be composed by too little stocks and the results could be biased; the factor loadings should be monotonically decreasing in the market capitalization.

Be sure that each portfolio is composed by the same number of stocks (more or less), constructing them by using the distribution percentiles.

  1. Populated class: each portfolio has to be populated enough with a minimum number of stocks that have more or less similar economic features and eliminate the others.

  2. Econometrics issues: check that all hypothesis about the linear regression model are fulfilled (Normality, Homoskedasticity, autocorrelation,...) in order that your results ac quire more reliability.

  3. Time period: may be that their results are influenced by the time period they used in their analysis and that the phenomenon disappeared during the last years; the SMB variable is based on the Small Size effect and, it is proven that this kind of phenomena disappear after someone makes them of public domain, e.g. publishing papers. Think about the January effect: there are a lot of papers that documented it disappeared!

Those are some of the main issues could influence your results.

Check them and after, if they are all satisfied, read the later Fama & French's papers to check if their way to analyze the sample is equal to the yours.

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There could be a number of reasons, let go over this.

First, your sample (the 10 portfolios) might differ from the sample FF used to compute the SMB factor. May be you're using a smaller market or sector? To check this look at the average beta's of your regressions or regress your full sample on the SMB factor. If your market consists of smaller stocks than used by FF it's likely that you have SMB exposure on all your portfolios

Second, equally weighting introduces a small cap bias as small companies have a similar influence on the portfolio as large firms. Of course you can download the equally weighted SMB factor from French's website but my experience is that doesn't work very well unless your sample is similar to theirs

Third, the presence of the SMB factor varies over time so plot the FF SMB factor and select a period in which the SMB factor performed well and then use that period as window for your regressions.

The solution would be to create your own SMB factor specific to your sample.

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