Hi Could somebody please help me with the following: An exam question asks explain the differences between APT and Factor models. I know APT is based on Factor models but can distinguish the difference even from reading the various text books.

not sure what they mean. In general , a factor structure in the covariance of returns imply APT, but you do not need a factor structure in the cov of returns for factor pricing. ICAPM would be an example.

i was thinking maybe along the lines of assumptions. I know for APT the number of assets most be large, i think infinite for perfect APT, and i know its based on no Arbitrage. This assumption is not needed for factor models ( i think) ,just the factors wheather Extracted, external or firm Characteristics. Does anybody else have any ideas regarding the latter.

I'm not sure about the exact answer to your question but here's my stab at it. APT was developed by Stephen Ross in the 1970s. APT uses multi-factors to determine the return on an asset. Single factor models, such as CAPM (1-factor model), have been around since the 60s. The other famous factor model is Fama and French's 3 factor model, which was published in 1992. Basically, when the CAPM was developed, the "factor" that they chose was excess market returns because during that time, if I remember correctly, there were studies done that 50% of the movement of stock prices are related by movements in the market. Fama and French performed a study that came out showing that their 3 factors (if I remember correctly, the factors are excess market return, small minus large capitalization, and high minus low book/price) are able to explain the movement in stock prices better. Basically, these factor models specify the "factors" that are used where as APT does not specify which factors to use. That is, if you tell someone to do CAPM and Fama and French, they know exactly which data to get. But, if you just say APT, then depending on the assumptions the person makes they may end up with a different actors.