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C
HAPTER
3
R
ISK AND
R
ETURN:
P
ART
II
OVERVIEW
In Chapter 2 we presented the key elements of
risk and return analysis.
There we saw that
much of the risk inherent in a stock can be
eliminated by diversification, so rational
investors should hold portfolios of stocks
rather than just one stock.
We also introduced
the Capital Asset Pricing Model (CAPM),
which links risk and required rates of return,
using a stock’s beta coefficient as the relevant
measure of risk.
In this chapter, we extend the Chapter 2
material by presenting an indepth treatment
of portfolio concepts and the CAPM.
We
continue the discussion of risk and return by
adding a riskfree asset to the set of
investment opportunities.
This leads all
investors to hold the same welldiversified
portfolio of risky assets, and then to account
for differing degrees of risk aversion by
combining the risky portfolio in different
proportions
with
the
riskfree
asset.
Additionally, we show how betas are
actually calculated, and we discuss two
alternative
views
of
the
risk/return
relationship, the Arbitrage Pricing Theory
(APT) and the FamaFrench 3Factor
Model.
The riskiness of a portfolio, because it is assumed to be a single asset held in isolation, is
measured by the standard deviation of its return distribution. This equation is exactly the
same as the one for the standard deviation of a single asset, except that here the asset is a
portfolio of assets (for example, a mutual fund).
(
29
.
P
rˆ
r
σ
deviation
standard
Portfolio
n
1
i
i
2
P
pi
p
∑
=

=
=
Two key concepts in portfolio analysis are covariance and the correlation coefficient.
Covariance
is a measure of the general movement relationship between two variables.
It
combines the variance or volatility of a stock’s returns with the tendency of those returns
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EXTENSIONS
5  2
to move up or down at the same time other stocks move up or down.
The following
equation defines the covariance (Cov) between Stocks A and B:
.
)P
rˆ

(r
)
rˆ

(r
=
(AB)
Cov
=
Covariance
n
1
=
i
i
B
Bi
A
Ai
∑
If the returns move together, the terms in parentheses will both be positive or both
be negative, hence the product of the two terms will be positive, while if the returns
move counter to one another, the products will tend to be negative.
Cov(AB) will be large and positive if two assets have large standard deviations
and tend to move together; it will be large and negative for two high
σ
assets which
move counter to one another; and it will be small if the two assets’ returns move
randomly, rather than up or down with one another, or if either of the assets has a
small standard deviation.
The
correlation coefficient
also measures the degree of comovement between two variables,
but its values are limited to the range from 1.0 (perfect negative correlation) to +1.0
(perfect positive correlation).
The relationship between covariance and the correlation
coefficient can be expressed as
.
Cov(AB)
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