Question

Explain why the Fama-French 3-factor model could be a specific instance of the APT.

Answer 1

Fama french 3 factor model:

Re = Rf + beta (Rm - Rf) + B size (small - big) + B value (high - low)

SMB = small market capitalisation minus big market capitalisation

HML =high book to market ratio minus low book to market ratio.

APT is also an extension of the CAPM like the Fama and French Model,

the APT includes the formula for the CAPM plus the various macro economic variables.

Re = Rf + beta * risk premium factor 1 + beta *risk premium factor 2 + beta*risk premium factor 3 +.....

Arbitrage Pricing Theory, return on an asset is dependent on various macroeconomic factors like inflation, exchange rates, market indices, production measures, market sentiments, changes in interest rates, movement of yield curves etc. Where beta is the sensitivity to the various factors.

SO, yes the Fama French is a specific instance of the APT.