CHAPTER 10: INDEX MODELS
3.
a.
The two figures depict the stocks’ security characteristic lines (SCL).
Stock A
has a higher firmspecific risk because the deviations of the observations from
the SCL are larger for Stock A than for Stock B.
Deviations are measured by
the vertical distance of each observation from the SCL.
b.
Beta is the slope of the SCL, which is the measure of systematic risk.
The
SCL for Stock B is steeper; hence Stock B’s systematic risk is greater.
b.
The R
2
(or squared correlation coefficient) of the SCL is the ratio of the
explained variance of the stock’s return to total variance, and the total
variance is the sum of the explained variance plus the unexplained variance
(the stock’s residual variance).
)
i
2
2
M
2
i
2
M
2
i
2
e
(
R
σ
+
σ
β
σ
β
=
Since the explained variance for Stock B is greater than for Stock A (the
explained variance is
2
M
2
B
σ
β
, which is greater since its beta is higher),
and
its
residual variance
σ
2
(e
B
) is smaller, its R
2
is higher than Stock A’s.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '08
 STAFF
 Finance, Regression Analysis, Standard Deviation, systematic risk

Click to edit the document details