Interpreting Carhart Factor Loadings and Their Significance

# How to interpret Carhart Four-Factor Model?


# How to interpret Carhart Four-Factor Model?












I am reading up on the `Carhart Four-Factor` model.

Let's say there a regression of stock returns on alpha, `RM-RF`, `SMB` (small minus big stocks returns), `HML` (high minus low value stock returns) and `UMD` (up minus down trend stocks).

Let's say my portfolio consists of mostly high value stocks (Apple, Google), yet my `HML` coefficient has a t-value of 5 and is therefore very significant. How would I interpret this and how is this possible? I am trying to do the regression but `RMRF`, `SMB`, `HML` and `UMD` all have very highly significant coefficients whereas alpha's coefficient is always the only one very far from significant at ~0.4 t value.

I have trouble how to interpret the other coefficients meaning and therefore help would be much appreciated.

## Answer by farnsy (score 1)

https://quant.stackexchange.com/a/31351

Factor models tell you how the returns of your portfolio are related to the returns of the models' factors. In this case, after controlling for the relation with the size, momentum, and market factors, your portfolio is positively related to the value factor. We often say it loads on the value factor (meaning it is exposed to the type of risk that is in the HML portfolio).

Why does that surprise you? Is it because you think ex ante that you know that your portfolio is made up of growth stocks? If so, bear in mind the following:

- There a many definitions of value/growth. You seem to have in mind that value means "cheap." This is one definition, but not the one Fama and French use to construct their HML factor.

- Just because a stock qualifies as value, even by the Fama-French definition, that doesn't mean it will necessarily have a positive loading on the HML factor. That's the fallacy of division. If you have a lot of stocks in your portfolio and they really are growth stocks, then maybe you made a mistake in your math somehow. Otherwise I think you are making wrong assumptions about the probability of the member of a population (or several members) having traits that differ from those of the population as a whole.

Generically, the interpretation of a positive coefficient is that your particular portfolio has a lot of whatever type of risk is in the value portfolio, not that is is necessarily a value portfolio. If yours really is a diversified portfolio of growth stocks (as defined by Fama and French), a negative HML coefficient would be likely, but I doubt that is really the case for your portfolio.

## Answer by Jeffrey Bloemen (score 0)

https://quant.stackexchange.com/a/27856

I have made a portfolio that invests more weight in higher market cap stocks.

The t-value on the `SMB` coefficient is now very small, which makes sense as my portfolio is now skewed to bigger companies. However, how do I interpret a significant negative `HML` and `UMD`?

My portfolio has a negative relationship with `HML` maybe because then I have many low value stocks? And `UMD` largely negative means my portfolio has negative momentum?

## Answer by Alexandre Ludolf (score 0)

https://quant.stackexchange.com/a/27956

your modeling was similar to the original paper? in this case a negative momentum coeficient is telling you that for this timeframe the winners of the last period are not the winners in this period.