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Chapter 6
Risk and Return: The CAPM
and Beyond
Professor XXX
Course Name / #
Efficient Risky Portfolios
Variance of return - a poor measure of
risk
Investors can only expect compensation
for systematic risk
Asset pricing models aim to define and
quantify systematic risk
Begin developing pricing model by asking:
Are some portfolios better than others?
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Expanding The Feasible Set On
The Efficient Frontier
E(RP)
EF including domestic
& foreign assets
EF including domestic
stocks, bonds, and
real estate
EF for portfolios of
domestic stocks
P
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Are Some Portfolios Better
Than Others?
Efficient portfolios achieve the highest possible return for any level of volatility
Two
N –– Asset
Asset Portfolios
Portfolios
E(RP)
efficient portfolios
efficient portfolios
•
MVP
•F
•E •
•
• • C• (50%A,
• 50%B)
•
•
•
•
• •
D
• 25%B)
• • MVP (75%A,
•
• Stock B
Stock A
inefficient portfolios
P
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What happens when we add a risk-free asset to the picture?
Expected Return (per month) and
Standard Deviation for Various Portfolios
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Riskless Borrowing And Lending
Risky asset X
Risk-free
asset Y
Three possible returns:
-10%; 10%; 30%
Return: 6%
Expected return =
10%
Standard
deviation =16.3%
Buying asset Y = Lending
money at 6% interest
How would a portfolio with $100 (50%) in asset X and $100
(50%) in asset Y perform?
$100 Asset X
$100 Asset Y
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Three possible returns:
-2%; 8%; 18%
Expected return =
8%
Standard
deviation =8.16%
Portfolio has lower return but also less volatility than 100% in X
Portfolio has higher return and higher volatility than 100% in risk-free
Riskless Borrowing And Lending
(Continued)
What if we sell short asset Y instead of buying it?
Borrow $100 at 6%
Must repay $106
Invest $300 in X
Original $200 investment plus $100 in borrowed funds
When X Pays –10%
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Net Return on $200 Investment 
$270 - $106 - $200
 18%
$200
When X Pays 10%
Net Return on $200 Investment 
$330 - $106 - $200
 12%
$200
When X Pays 30%
Net Return on $200 Investment 
$390 - $106 - $200
 42%
$200
Expected return on the portfolio is 12%. Higher expected return comes
at the expense of greater volatility
Riskless Borrowing And Lending
(Continued)
The more we invest in X, the higher the expected return
The expected return is higher, but so is the volatility
This relationship is linear
Portfolio
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Expected
Return
Standard
Deviation
50% risky, 50% risk-free
8%
8.16%
100% risky, 0% risk free
10%
16.33%
150% risky, -50% risk free
12%
24.49%
Portfolios Of Risky & Risk-Free
Assets
E(RP)
16.5%
•MF
12%
9%
RF=6%
•
0
9
9
•B
•A
15%
30%
52%
P
New Efficient Frontier
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The Market Portfolio
Only one risky portfolio is efficient
Suppose investors agree on which portfolio is
efficient
Equilibrium requires this to be the Market Portfolio
Market Portfolio: value weighted portfolio of all
available risky assets
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The line connecting Rf to the market portfolio called the Capital Market Line
Finding the Optimal Risky
Portfolio
If investors can borrow and lend at the riskfree rate, then from the entire feasible set of
risky portfolios, one portfolio will emerge that
maximizes the return investors can expect for
a given standard deviation.
To determine the composition of the optimal
portfolio, you need to know the expected
return and standard deviation for every risky
asset, as well as the covariance between
every pair of assets.
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Finding the Optimal Portfolio
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The Capital Market Line
 The line connecting Rf to the market portfolio
is called the Capital Market Line (CML)
 CML quantifies the relationship between the
expected return and standard deviation for
portfolios consisting of the risk-free asset and
the market portfolio, using
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Capital Asset Pricing Model
(CAPM)
Only beta changes from one security to the next.
For that reason, analysts
classify the CAPM as a single-factor model,
meaning that just one variable explains
differences in returns across securities.
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The Security Market Line
Plots the relationship between expected
return and betas
In equilibrium, all assets lie on this line
If stock lies above the line
Expected return is too high
Investors bid up price until expected return
falls
If stock lies below the line
Expected return is too low
Investors sell stock, driving down price until
expected return rises
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The Security Market Line
E(RP)
SML
A - Undervalued
•
•
RM
RF
•
B
•
•
• B - Overvalued
•
 =1.0
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A Slope = E(R ) - R = Market
m
F
Risk Premium (MRP)
i
Beta
 im
i  2
m
The numerator is the covariance of the
stock with the market
The denominator is the market’s variance
In the CAPM, a stock’s systematic risk is captured
by beta
The higher the beta, the higher the expected return on the stock
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Beta And Expected Return
Beta measures a stock’s exposure to market risk
The market risk premium is the reward for bearing
market risk:
• Rm - Rf
E(Ri) = Rf + ß [E(Rm) – Rf]
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• Return for
bearing no
market risk
• Stock’s
exposure to
market risk
• Reward for
bearing
market risk
Calculating Expected Returns
E(Ri) = Rf + ß [E(Rm) – Rf]
• Assume
• Risk–free rate = 2%
• Expected return on the market = 8%
If Stock’s Beta Is
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Then Expected Return Is
0
2%
0.5
5%
1
8%
2
14%
When Beta = 0, The Return Equals The Risk-Free Return
When Beta = 1, The Return Equals The Expected Market Return
Scatterplot for Returns on
Sharper Image and S&P500
Sharper Image Weekly Return
0.3
Slope = Beta = 1.44
0.2
0.1
0
-0.3
-0.2
-0.1
0
-0.1
0.1
R-square = 0.19
-0.2
-0.3
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0.2
S&P500 Weekly Return
0.3
Scatterplot for Returns on
ConAgra and S&P500
ConAgra Weekly Return
0.15
0.1
0.05
beta = 0.11
0
-0.15
-0.1
-0.05
0
0.05
-0.05
R-square = 0.003
-0.1
-0.15
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0.1
S&P500 Weekly Return
0.15
Scatterplot for Returns on
Citigroup and S&P500
0.2
Citigroup Weekly Return
0.15
beta = 1.20
0.1
0.05
0
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
-0.05
R-square = 0.50
-0.1
-0.15
-0.2
S&P500 Weekly Return
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0.15
0.2
Using The Security Market Line
The SML and where P&G and GE place on it
r%
SML
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12.4%
slope = E(Rm) – RF =
MRP = 10% - 2% = 8%
= Y ÷ X
•
10
6.8%
5
Rf = 2%
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P&G
1
GE
2

Shifts In The SML Due To A Shift In
Required Market Return
r%
SML1
15
SML2
11.1%
•
•
10
Shift due to change in
market risk premium
from 8% to 7%
6.2%
5
Rf = 2%
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P&G
1
GE
2

Shifts In The SML Due To A Shift In
The Risk-Free Rate
SML2
r%
SML1
15
14.4%
Shift due to change in
risk-free rate from 2% to
4%, with market risk
premium remaining at
8%. Note all returns
increase by 2%
•
10
8.8%
5
Rf = 4%
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P&G
1
GE
2

Alternatives To CAPM
Arbitrage Pricing Theory
Fama-French Model
Ri  R f     i1 Rm  R f    i 2 Rsmall  Rbig    i 3 Rhigh  Rlow 
Betas represent sensitivities to each source of risk
Terms in parentheses are the rewards for bearing
each type of risk.
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The Current State of APT
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Investors demand compensation for
taking risk because they are risk
averse.
There is widespread agreement that
systematic risk drives returns.
You can measure systematic risk in
several different ways depending on
the asset pricing model you choose.
The CAPM is still widely used in
practice in both corporate finance and
investment-oriented professions.