Investments, tenth edition

13.1 

  Estimating the SML   

Now view Equation 13.1 as a security market line (SML) with 

100 observations for the stocks in your sample. You can estimate  g  

0

  and  g  

1

  in the following 

second-pass regression equation with the estimates  b  

 i 

  from the first pass as the independent 

variable:   

 

r

i

2 r

f

5 g

0

1 g

1

b

i

     i

5 1, c,  100 

 (13.2)   

 Compare Equations 13.1 and 13.2; you should conclude that if the CAPM is valid, then  g  

0

  

and  g  

1

   should  satisfy   

g

0

5 0 and g

1

5 r

M

2 r

f

  

 In fact, however, you can go a step further and argue that the key property of the expected 

return–beta relationship described by the SML is that the expected excess return on securi-

ties is determined  only  by the systematic risk (as measured by beta) and should be inde-

pendent of the nonsystematic risk, as measured by the variance of the residuals,  s  

2

 ( e  

 i 

 ), 

which also were estimated from the first-pass regression. These estimates can be added as 

a variable in Equation 13.2 of an expanded SML that now looks like this:   

 

r

i

2 r

f

5 g

0

1 g

1

b

i

1 g

2

s

2

(e

i

) 

 (13.3)   

 This   second-pass  regression equation is estimated with the hypotheses   

g

0

5 0; g

1

5 r

M

2 r

f

; g

2

5 0  

 The hypothesis that  g  

2

   5  0 is consistent with the notion that nonsystematic risk should 

not be “priced,” that is, that there is no risk premium earned for bearing nonsystem-

atic risk. More generally, according to the CAPM, the risk premium depends only on 

beta. Therefore,  any  additional right-hand-side variable in Equation 13.3 beyond beta 

should have a coefficient that is insignificantly different from zero in the second-pass 

regression.   

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7/17/13   3:47 PM

7/17/13   3:47 PM

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  C H A P T E R  

1 3

  Empirical Evidence on Security Returns 

417