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H
AAS
S
CHOOL
OF
B
USINESS
UGBA 103
U
NIVERSITY
OF
C
ALIFORNIA
AT
B
ERKELEY
A
VINASH
V
ERMA
B
RIEF
T
EACHING
N
OTE
Let us first note that squared correlation, commonly referred to as “Rsquared,” between
returns on S
ecurity i
and those on the market portfolio measures the percentage of the
total risk of the security that cannot be diversified away. To elaborate, we can decompose
the total risk of S
ecurity i,
denoted
2
i
σ
, into two components in the following equation:
βσ
ε
i
iM
M
i
2
2
2
2
=
+
.
The first term on the RHS is the systematic or the undiversifiable risk, and the second
term is the unsystematic or diversifiable risk. It follows that the percentage of the
undiversifiable risk to the total is:
2
2
2
i
M
iM
β
.
Now, by definition:
M
i
iM
im
M
i
iM
iM
ρ
*
*
*
=
⇒
≡
;
And, again by definition:
iM
iM
M
≡
2
.
Substituting for
iM
from the first expression in the numerator of the second, we get:
i
M
iM
iM
≡
Squaring both sides shows us that Rsquared is indeed the fraction of the total risk of a
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This note was uploaded on 09/11/2011 for the course UGBA 103 taught by Professor Berk during the Summer '07 term at University of California, Berkeley.
 Summer '07
 Berk

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