# How to use financial ratios in a factor model?

I am trying to understand how factor loadings in a general factor model are computed. For simplicity sake, lets assume a simple model:

$$R = B \times F + \epsilon$$

$$R = N \times 1$$ $$B = N \times K$$ $$F = K \times 1$$

where $B$ are the factor loadings and $F$ is the factor return and $N$ is the number of securities.

The way this equation is setup, a factor that is common to all $N$ assets, like GDP, inflation, or market index, can easily be plugged in as a factor return ($F$) into the above equation. But how about financial ratios? Let's say for example the PE ratio. The PE ratio is different for each security, which would in turn give us a different factor loading for each security. But how can we plugin a factor return for PE ratio into $F$; its different for each security.

Or is my understanding of using fundamental ratios in a factor model totally off?

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Your looking at the dependent variable "price" against independent "factors". Its about finding statistical correlation in the factors to price.. – cdcaveman Feb 20 '13 at 8:48
You seem to be confusing alpha models and risk models. See this previous question. – chrisaycock Feb 20 '13 at 12:10