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Interpreting Fama-French and Carhart Factor Loadings

Article Quant Q&A · Author: YasG
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Summary

The document discusses how to interpret regression coefficients from Fama-French three-factor and Carhart four-factor models applied to a portfolio of large DJIA companies. The portfolio has a statistically significant market loading, a negative and statistically significant size loading, and negative value and momentum loadings that are not statistically significant at conventional levels. Its intercept is also negative but not statistically significant.

The response reads the market estimate as indicating high market sensitivity and the size estimate as consistent with a large-company tilt. It cautions against drawing a strong conclusion about value or momentum from insignificant coefficients. It suggests comparing the portfolio’s holdings or sectors with the factor portfolios to make the loadings more intuitive. The analysis is limited by missing details about portfolio construction and rebalancing, and it offers an interpretation rather than a broader test of the model or evidence that the factors capture all relevant risks.

Key ideas

  • Factor coefficients describe a portfolio’s sensitivity to the returns of the model’s factor portfolios.
  • A significant negative size loading is consistent with exposure tilted toward larger companies.
  • An insignificant value or momentum coefficient does not establish a reliable exposure in either direction.
  • Portfolio construction and rebalancing choices affect how factor loadings should be interpreted.
  • Comparing holdings or sectors with factor portfolios can help explain estimated loadings.

Tags

Factor investingEquitiesStatisticsPortfolio construction
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# How do I interpret my Fama-French and Carhart factor coefficients?


# How do I interpret my Fama-French and Carhart factor coefficients?












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.

## Answer by oronimbus (score 2)

https://quant.stackexchange.com/a/74269

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.

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.