Chapter 10 Return and Risk: The CapitalAssetPricing Model (CAPM)
10.1 Individual Securities
Characteristics of securities
Expected return
 return that an individual expects a stock to earn over the next
period
Variance and Standard Deviation
Covariance and Correlation
Returns on individual securities are related to one
another
o
Covariance is a statistic measuring the interrelationship between two securities
→can be restated in terms of correlation
10.2 Expected Return, Variance, and Covariance
Expected Return and Variance
Variance
can be calculated in four steps:
Calculate the expected return of two securities:
Expected Return Security A = (R
At
+ R
At+1
+ R
At+2
+ R
At+3
)/ t
Expected Return Security B = (R
Bt
+ R
Bt+1
+ R
Bt+2
+ R
Bt+3
)/ t
Calculate the
deviation
of each possible return from each of the securities
expected return calculated previously
Calculate the
squared deviations
from the
deviations calculated
before
Calculate the
variance
, which is the average of all squared deviations for a
security
After having calculated the
variance
, we can calculate the
standard deviation
by
taking the
square root of the variance
→Because variance is still expressed in
squared terms, it is difficult to interpret → Standard deviation has a much simpler
interpretation
Covariance and Correlation
Variance and standard deviation
measure the variability of individual stocks →to
measure the
relationship
between the return on one stock and the return of
another, we make use of
covariance
and
correlation
Covariance and correlation measure
how two random variables are related
.
Using the standard deviations for the two securities that we calculated in the
section above and the deviation of each possible return from the expected return,
we can calculate
covariance
in two steps
o
First
calculate the deviations
from their
expected return
for both securities
and than
multiply
the outcomes:
(
R
At
– R
A
) * (R
Bt
– R
B
)
Calculate average
value of
product deviations
σ
AB
= Cov (R
A
, R
B
) = Cov (R
B,
R
A
)
=
(R
At
– R
A
) * (R
Bt
– R
B
)
N
Note that is the above expression will be
positive
in any state where
both
returns
are
above
their averages
, and will be
still
positive
in any state where
both terms are
below
their averages
1
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On the other hand, if
one return
is generally
above
its
average
when the other
one is
below
its average, or vice versa, this is indicative of a
negative
dependency
or negative relationship between the two returns
Further, if there is
no relation
between the two returns →the one return tells us
nothing about the other one
o
there will be no tendency for the deviations to be positive or
negative together → On average they will tend to offset each other
and cancel out, making the covariance close to zero
The covariance formula seems to capture what we are looking for
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 Spring '09
 HH
 Standard Deviation, Variance, Capital Asset Pricing Model, Modern portfolio theory, risky securities

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