Investments, tenth edition

   Factor Models of Security Returns 

 We begin with a familiar single-factor model like the one introduced in Chapter 8. Uncer-

tainty in asset returns has two sources: a common or macroeconomic factor and firm-

specific events. The common factor is constructed to have zero expected value, because 

we use it to measure  new  information concerning the macroeconomy, which, by definition, 

has zero expected value. 

 If we call  F  the deviation of the common factor from its expected value,  b  

 i 

  the sensi-

tivity of firm  i  to that factor, and  e  

 i 

  the firm-specific disturbance, the factor model states 

that the actual excess return on firm  i  will equal its initially expected value plus a (zero 

expected value) random amount attributable to unanticipated economywide events, plus 

another (zero expected value) random amount attributable to firm-specific events. 

 Formally, the    single-factor  model    of excess returns is described by Equation 10.1:   

 

R

i

5 E(R

i

)

1 b

i

F

1 e

i

 

 (10.1)  

where  E ( R  

 i  

 ) is the expected excess return on stock  i.  Notice that if the macro factor has a 

value of 0 in any particular period (i.e., no macro surprises), the excess return on the secu-

rity will equal its previously expected value,  E ( R  

 i  

 ), plus the effect of firm-specific events 

only. The nonsystematic components of returns, the  e  

 i 

 s, are assumed to be uncorrelated 

across stocks and with the factor  F.    

     10.1 

Multifactor Models: An Overview 

 To make the factor model more concrete, consider an example. Suppose that the macro 

factor,  F,  is taken to be news about the state of the business cycle, measured by the 

unexpected percentage change in gross domestic product (GDP), and that the consen-

sus is that GDP will increase by 4% this year. Suppose also that a stock’s  b  value is 1.2.