CHAPTER 10: ARBITRAGE PRICING THEORY ANDMULTIFACTOR MODELS OF RISK AND RETURNPROBLEM SET18.a.The Fama-French (FF) three-factor model holds that one of the factorsdriving returns is firm size. An index with returns highly correlated withfirm size (i.e., market capitalization) that captures this factor is SMB(small minus big), the return for a portfolio of small stocks in excess of thereturn for a portfolio of large stocks. The returns for a small firm will bepositively correlated with SMB. Moreover, according to FF, the smallerthe firm, the greater its residual from the other two factors, the marketportfolio and the HML portfolio (i.e., the return for a portfolio of highbook-to-market stocks in excess of the return for a portfolio of low book-to-market stocks). So, the ratio of the variance of this residual to thevariance of the return on SMB will be larger and, together with the highercorrelation, results in a high beta on the SMB factor.
