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I am currently writing my thesis using the Carhart Four-Factor Model. I got my results but I am not sure how to word them.

Coefficient on my SMB is 0.22. Wording: if small companies returns are 1% over that of amall companies in a given month, my portfolio's return is expected to increase with 0.22%.

This feels like a really poor explanation because it's not just small-big but I don't know how to word it properly. The same for the HML and UMD factors. If someone could give insight that would be great.

Thanks in advance

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Intuitive way to look at it, in my opinion, is that returns similar to the ones generated by your strategy could be achieved by a passive exposure to the four factor model portfolios, and the value added by your strategy (alpha). It should be of interest to you whether your alpha is significantly positive, which of the factors have statistically significant coefficients, and why. This is what I suppose you aim to achieve by using FF4 as the basis of estimating your risk adjusted returns?

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Complementing Ana's answer: The goal with a multivariate regression is to control by known factors (such as FFs) and check if there is abnormal returns on top of the known ones.

In general, when reading a paper we will like to check if the signals of the factors are on the same direction and significance level of past literature (and look for explanation otherwise) and check if the "rest" read "Alpha" will be positive and significant.

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