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Chapter 11
Risk and Return
Goals
Understand the impact of diversification
Understand the systematic risk principle
Understand SML and CAPM
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3
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Expected Returns
•
Expected returns are based on the probabilities of possible outcomes
•
In this context, “expected” means “average” if the process is repeated
many times
Example: suppose you have predicted the following returns for stocks
C and T in three possible states of nature. What are the expected
returns?
State
Probability
C
T
Boom
0.3
0.15
0.25
Normal
0.5
0.10
0.20
Recession
0.2
0.02
0.01
∑
=
=
n
i
i
i
R
p
R
E
1
)
(
5
Variance and Standard Deviation
•
Variance and standard deviation measure the volatility of returns
•
Weighted average of squared deviations
Example: consider the previous example. What are the variance and
standard deviation for each stock?
Stock C:
Stock T:
∑
=

=
n
i
i
i
R
E
R
p
1
2
2
))
(
(
σ
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Portfolios
•
A portfolio is a collection of assets
•
The riskreturn tradeoff for a portfolio is measured by the portfolio
expected return and standard deviation, just as with individual assets
Example: suppose you have $15,000 to invest and you have purchased
securities in the following amounts. What are your portfolio weights in
each security?
$2,000 of DCLK
$3,000 of KO
$4,000 of INTC
$6,000 of KEI
7
Portfolio Expected Returns
•
The expected return of a portfolio is the weighted average of the
expected returns of the respective assets in the portfolio.
•
You can also find the expected return by finding the portfolio return in
each possible state and computing the expected value as we did with
individual securities.
Example: Consider the portfolio weights computed previously. If the
individual stocks have the following expected returns, what is the
expected return for the portfolio?
•
DCLK: 19.65%, KO: 8.96%, INTC: 9.67%, KEI: 8.13%
∑
=
=
m
j
j
j
P
R
E
w
R
E
1
)
(
)
(
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Portfolio Variance
•
Compute the portfolio return for each state:
R
P
= w
1
R
1
+ w
2
R
2
+ … + w
m
R
m
•
Compute the expected portfolio return using the same formula as for an
individual asset
•
Compute the portfolio variance and standard deviation using the same
formulas as for an individual asset
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This note was uploaded on 06/20/2010 for the course CB EF4441 taught by Professor Professorng during the Spring '10 term at 東京国際大学.
 Spring '10
 ProfessorNg

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