I am required to prepare a portfolio containing 10 companies and analyse their returns over 10 years utilising the Fama-French 3 factor and Carhart 4 factor models. I chose the largest market cap companies from the DJIA in 2022 and obtained the following results for my 10-year sample (2012 - 2021):

Variable Coefficient Std. Error t-Statistic Prob.
C -0.259163 0.176005 -1.472477 0.1436
RMRF 0.895686 0.046966 19.07095 0.0000
SMB -0.165007 0.070582 -2.337815 0.0211
HML -0.068021 0.063147 -1.077183 0.2837
UMD -0.109321 0.057791 -1.891660 0.0611

From alpha I can see that although the portfolio underperformed due to the negative constant, this is statistically insignificant so CAPM, FF and Carhart are relevant and significant risks are being captured within the models. I can also see that the market risk is statistically significant and the portfolio is sensitive to market changes as it follows market trends.

However I am having a challenging time trying to interpret the SMB, HML and UMD and would appreciate assistance with my interpretations:

Size: the portfolio is moving against the movement of small cap stocks. This shows that the portfolio is exposed to large cap stocks which aligns with how companies were selected.

Value: value stocks are not relevant here. This signals that the portfolio is behaving as a growth stock portfolio (?)

Momentum: momentum is not significant here, but the portfolio seems to go against momentum.

Thanks a lot. I have tried looking for similar queries but have not found detailed information.

  • 5
    $\begingroup$ I feel like OP's question is significantly detailed and well written to stay open. $\endgroup$ Jan 5, 2023 at 0:00

1 Answer 1


I'd say your assessment is mostly correct. Your portfolio is high beta (0.9), basically tracking the index, and tilted towards large cap companies. This makes sense since you chose the largest 10 companies in the DJIA.

I don't know what your exact portfolio construction method is (e.g. rebalanced periodically or held constant) but in terms of value your exposure is not significant. Perhaps not too surprising since (I assume) you're loading on companies such as UNH, HD, AMGN etc. which all have low book to market ratios compared to e.g. financials. I've picked those companies by looking at DJIA on 2022-12-31. In terms of momentum your 2022 large cap portfolio might have not done terribly over the last year. But it certainly wasn't great in the period prior to 2020 where growth (i.e. technology) stocks were outperforming.

Perhaps it helps to think of factors as portfolios of stocks and comparing your holdings (or sectors) vs those portfolios to get a feel.

  • $\begingroup$ Thanks for this. The portfolio is equal-weighted and constant and I have HD and AMGN. My alpha has been insignificant except in 2020 where it was significant and negative - I think this is related to covid? My model also shows insignificant market risk in 2017 under Carhart which I don't understand. Size is statistically significant and negative in 2016 and 2020 under both models. I understand that this means my portfolio is moving against value stocks i.e. behaving like growth stocks? Sourcing articles explaining statistically significant and negative factors is proving to be difficult $\endgroup$
    – YasG
    Jan 11, 2023 at 15:21

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