Investments, tenth edition

  Estimating the SCL   

View Equation 13.1 as a security characteristic line (SCL), as 

in Chapter 8. For each stock,  i,  you estimate the beta coefficient as the slope of a    first-pass 

regression    equation. (The terminology  first-pass  regression is due to the fact that the esti-

mated coefficients will be used as input into a    second-pass  regression.     )   

r

it

2 r

ft

5 a

i

1 b

i

(r

Mt

2 r

ft

)

1 e

it

  

bod61671_ch13_414-444.indd   415

bod61671_ch13_414-444.indd   415

7/17/13   3:47 PM

7/17/13   3:47 PM

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416 

P A R T   I I I

  Equilibrium in Capital Markets

 You will use the following statistics in later analysis:

      r

i

2 r

f

  5  Sample averages (over the 60 observations) of the excess return on each of 

the 100 stocks.  

   b  

 i 

   5  Sample estimates of the beta coefficients of each of the 100 stocks.  

     r

M

2 r

f

  5 Sample average of the excess return of the market index.  

   s  

2

 ( e  

 i 

 )  5  Estimates of the variance of the residuals for each of the 100 stocks.    

 The sample average excess returns on each stock and the market portfolio are taken as 

estimates of expected excess returns, and the values of  b  

 i 

  are estimates of the true beta 

coefficients for the 100 stocks during the sample period.  s  

2

 ( e  

 i 

 ) estimates the nonsystem-

atic risk of each of the 100 stocks. It is understood that all these statistics include estima-

tion errors.   

     a.   How many regression estimates of the SCL do we have from the sample?  

    b.   How many observations are there in each of the regressions?  

    c.   According to the CAPM, what should be the intercept in each of these regressions?   

 CONCEPT CHECK