unidentifiedstatisticalfactorswithspecificeconomicfactors
andtheresultantmodelshouldhaveaneconomicbasiswhile
stillretainingmuchofthestrengthof thearbitragepricing
model.Thatispreciselywhatmultifactormodelstryto do.
OncethenumberoffactorshasbeenidentifiedintheAPM,
theirbehaviorovertimecanbeextractedfromthedata.The
behavior of the unnamed factors over time can then be
comparedto thebehaviorofmacroeconomicvariablesover
that same period to see whether any of the variables is
correlated,overtime,withtheidentifiedfactors.Forinstance,
Chen, Roll, and Ross (1986)
3 suggest that the followingmacroeconomic variables are
highly correlated with the factors that come out of factor
analysis:industrialproduction,changesindefaultpremium,
shifts in the term structure, unanticipated inflation, and
changesintherealrateofreturn.Thesevariablescanthenbe
used to come up with a model of expected returns, with
firm-specific betas calculated relative to each variable.
where
βGNP= Beta relative to changes in industrial production
E(RGNP)=Expectedreturnonaportfoliowithabetaof 1 on
the industrial production factor and 0 on all other factors
βI= Beta relative to changes in inflation
E(RI)=Expectedreturnonaportfoliowithabetaof 1 onthe
inflation factor and 0 on all other factors