Investments, tenth edition

  Using the APT to Find Cost of Capital 

 Elton, Gruber, and Mei *  use the APT to derive the cost of 

capital for electric utilities. They assume that the relevant 

risk factors are unanticipated developments in the term 

structure of interest rates, the level of interest rates, infla-

tion rates, the business cycle (measured by GDP), foreign 

exchange rates, and a summary measure they devise to 

measure other macro factors.

  Their first step is to estimate the risk premium associ-

ated with exposure to each risk source. They accomplish 

this in a two-step strategy (which we will describe in con-

siderable detail in Chapter 13):

    1.  

 Estimate “factor loadings” (i.e., betas) of a large sample 

of firms.  Regress returns of 100 randomly selected 

stocks against the systematic risk factors. They use a 

time-series regression for each stock (e.g., 60 months 

of data), therefore estimating 100 regressions, one for 

each stock.  

   2.  

 Estimate the reward earned per unit of exposure to 

each risk factor.  For each month, regress the return 

of each stock against the five betas estimated. The 

coefficient on each beta is the extra average return 

earned as beta increases, i.e., it is an estimate of the 

risk premium for that risk factor from that month’s 

data. These estimates are of course subject to sam-

pling error. Therefore, average the risk premium esti-

mates across the 12 months in each year. The  average  

response of return to risk is less subject to sampling 

error.   

The risk premiums are in the middle column of the table at 

the top of the next column. 

 Notice that some risk premiums are negative. The 

interpretation of this result is that risk premium should be 

positive for risk factors you don’t want exposure to, but 

 negative  for factors you  do  want exposure to. For example, 

you should desire securities that have higher returns when 

inflation increases and be willing to accept lower expected 

returns on such securities; this shows up as a negative risk 

premium.