FM11 Ch 05 Risk and Return_ Portfolio Theory and Asset Pricing Models

5 - 1
CHAPTER 5
Risk and Return: Portfolio Theory and
Asset Pricing Models

Portfolio Theory

Capital Asset Pricing Model (CAPM)

Efficient frontier

Capital Market Line (CML)

Security Market Line (SML)

Beta calculation

Arbitrage pricing theory

Fama-French 3-factor model
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Portfolio Theory

Suppose Asset A has an expected return of 10 percent and a standard
deviation of 20 percent. Asset B has an expected return of 16 percent
and a standard deviation of 40 percent. If the correlation between A and
B is 0.6, what are the expected return and standard deviation for a
portfolio comprised of 30 percent Asset A and 70 percent Asset B?
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Portfolio Expected Return
%.2.14142.0

)16.0(7.0)1.0(3.0
r
ˆ
)w1(r
ˆ
wr
ˆ
BAAAP
==
+=
−+=
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Portfolio Standard Deviation
309.0
)4.0)(2.0)(4.0)(7.0)(3.0(2)4.0(7.0)2.0(3.0
)W1(W2)W1(W
2222
BAABAA
2
B
2
A
2
A
2
Ap
=
++=
−+−+=
σσρσσσ

5 - 5
Attainable Portfolios: ρ
AB
= 0.4
ρ
AB
= +0.4: Attainable Set of
Risk/Return Combinations
0%
5%
10%
15%
20%
0% 10% 20% 30% 40%
Risk,
σ
p
Expected return
5 - 6
Attainable Portfolios: ρ
AB
= +1
ρ
AB
= +1.0: Attainable Set of Risk/Return
Combinations
0%
5%
10%
15%

20%
0% 10% 20% 30% 40%
Risk,
σ
p
Expected return
5 - 7
Attainable Portfolios: ρ
AB
= -1
ρ
AB
= -1.0: Attainable Set of Risk/Return
Combinations
0%
5%
10%
15%
20%
0% 10% 20% 30% 40%
Risk,
σ
p
Expected return
5 - 8
Attainable Portfolios with Risk-Free
Asset (Expected risk-free return = 5%)
Attainable Set of Risk/Return
Combinations with Risk-Free Asset
0%

5%
10%
15%
0% 5% 10% 15% 20%
Risk,
σ
p
Expected return
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Expected
Portfolio
Return, r
p
Risk, σ
p
Efficient Set
Feasible Set
Feasible and Efficient Portfolios
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
The feasible set of portfolios represents all portfolios
that can be constructed from a given set of stocks.

An efficient portfolio is one that offers:

the most return for a given amount of risk,
or

the least risk for a give amount of return.


The collection of efficient portfolios is called the
efficient set or efficient frontier.
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I
B
2
I
B
1
I
A
2
I
A
1
Optimal Portfolio
Investor A
Optimal
Portfolio
Investor B
Risk σ
p
Expected
Return, r
p
Optimal Portfolios
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
Indifference curves reflect an
investor’s attitude toward risk as

reflected in his or her risk/return
tradeoff function. They differ
among investors because of
differences in risk aversion.

An investor’s optimal portfolio is
defined by the tangency point
between the efficient set and the
investor’s indifference curve.
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What is the CAPM?

The CAPM is an equilibrium model
that specifies the relationship
between risk and required rate of
return for assets held in well-
diversified portfolios.

It is based on the premise that only
one factor affects risk.

What is that factor?
5 - 14

Investors all think in terms of
a single holding period.

All investors have identical expectations.

Investors can borrow or lend unlimited amounts at the risk-free rate.

What are the assumptions
of the CAPM?
(More )
5 - 15

All assets are perfectly divisible.

There are no taxes and no transactions costs.

All investors are price takers, that is, investors’ buying and selling
won’t influence stock prices.

Quantities of all assets are given and fixed.
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
When a risk-free asset is added to the feasible set, investors can create
portfolios that combine this asset with a portfolio of risky assets.

The straight line connecting rRF with M, the tangency point between the
line and the old efficient set, becomes the new efficient frontier.
What impact does r
RF
have on
the efficient frontier?
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M
Z
.
A
r

RF
σ
M
Risk, σ
p
Efficient Set with a Risk-Free Asset
The Capital Market
Line (CML):
New Efficient Set
.
.
B
r
M
^
Expected
Return, r
p
5 - 18

The Capital Market Line (CML) is all linear
combinations of the risk-free asset and Portfolio M.

Portfolios below the CML are inferior.

The CML defines the new efficient set.

All investors will choose a portfolio on
the CML.
What is the Capital Market Line?

5 - 19
r
p
= r
RF
+
SlopeIntercept
^
σ
p
.
The CML Equation
r
M
- r
RF
^
σ
M
Risk
measure
5 - 20

The expected rate of return on any efficient
portfolio is equal to the risk-free rate plus a risk
premium.

The optimal portfolio for any investor is the
point of tangency between the CML and the
investor’s indifference curves.

What does the CML tell us?
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r
RF
σ
M
Risk, σ
p
I
1
I
2
CML
R = Optimal
Portfolio
.
R
.
M
r
R
r
M
σ
R
^
^
Expected
Return, r
p

5 - 22

The CML gives the risk/return relationship for
efficient portfolios.

The Security Market Line (SML), also part of the
CAPM, gives the risk/return relationship for
individual stocks.
What is the Security Market Line (SML)?
5 - 23

The measure of risk used in the SML is the beta
coefficient of company i, bi.

The SML equation:
ri = rRF + (RPM) bi
The SML Equation
5 - 24

Run a regression line of past returns on Stock i
versus returns on the market.

The regression line is called the characteristic
line.

The slope coefficient of the characteristic line is
defined as the beta coefficient.
How are betas calculated?
5 - 25
Illustration of beta calculation

Year r
M
r
i

1 15% 18%
2 -5 -10
3 12 16
r
i
_
r
M
_
-5 0 5 10 15 20
20
15
10
5
-5
-10
.
.
.
r
i
= -2.59 + 1.44 k
M
^ ^