I have studied factor models in a very introductory manner, going through there Fama-French model and then APT. I understand the concept of decomposing returns into factors, but I don't understand how funds can trade on the basis of these factors. My question is then twofold:
1) How can you find factors? Say we are trading Equity or Commodities, from the time series of companies or of commodity prices, how do we proceed to quantitatively delineate factors to trade on?
2) Once we have these factors, how can we generate alpha from them?
I know successful models are in proprietary hands, but if anyone has an example that resembles as closely as possible what is usually done in practise, that would be very appreciated.