SML 60

ƒ

The curve generated by asset i and M ca

nnot cross the capital market line,

i.p. the curve at

α

=0

has to be tangent to the CML, i.e.

ƒ

To prove this we first

calculate the derivative:

ƒ

Now we are able to evaluate this derivative at

H

=0

and set it equal to the

slope of the CML

ƒ

Solving for

ri

yields the desired result!

M

f

M

r

r

d

r

d

σ

σ

α

α α

−

=

=^0

Single-period random cash flows: CAPM

()

α

α α

α α

σ

σ

α

σ

α

ασ

α

σ

α

σ

/

) 1

(

)

2

(^1) (
/ /
2
2
M
iM
i
M
i
r
r
d
d
d
r
d
d
r
d
−

• −


• 
  

  −

  
  

  =
  ()
  ()
  M
  f
  M
  M
  M
  iM
  M
  i
  M
  M
  M
  iM
  M
  i
  r
  r
  r
  r
  Note
  r
  r
  d
  rd
  σ
  σ
  σ
  σ
  σ σ σ σ σ σ
  α
  α
  α
  α α
  −

  
  

  −
  −

  
  

  −
  −

  
  

  =

  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  

  /
  /
  2
  0
  2
  0